Category Archives: home school

Online School: e-learning as a Product

When you work as a product manager, you start seeing product analysis opportunities everywhere. In our current economic system, everyone is buying and selling, even if it doesn’t seem that way, and you see similar patterns repeated. Successful products and services share patterns, as do mediocre ones with failures. Often the difference between success and failure are due to factors outside your control, such as market timing and a bit of luck. However, all successful products and services are really good at managing the things they can control. They know who they are, what they do, and what makes them unique and how they appeal to people who are interested in them. They focus on what makes them different from their competitors, and enhance that, rather than trying to copy others. They know what their customers look for, and what they find appealing, and they make sure they address those wants and needs. In other words, they really understand their product differentiator.

Today, I want to write about e-learning for K-12, or for both primary and secondary education. What can we learn when we analyze online learning for our kids from a product management perspective? Education may not seem like a product, but it is a service, and looking at it from this perspective is helpful. When you focus on e-learning as a product, interesting and important insights start to emerge. user needs that seem to be at odds with each other start to form patterns, and focusing on a product differentiator can help e-learning ventures be successful.

Here in North America, “K-12” tends to refer to publicly funded schools. There are also charter schools (a combination of private and public), private schools, alternative schools, and school from the home, such as homeschooling and unschooling. While it might not seem like a publicly funded service is a product, that a product manager might be interested in, education works within the same system everything else does. Within the political climate of the past few decades, public funding for education has changed, and isn’t as concentrated on traditional public schools anymore. This fragmentation of education funding highlights differences and creates more competition. Parents are looking at specialized schools and programming for their kids, and more people are looking at alternatives. Another wrinkle is that the customers are split across decision makers, who are adults, and students, who are children. The adults make the choices for the products and services, but the primary users are the children. Since adults make the decisions, their frame of reference is based on their own education experience from the past, the values they teach and reinforce at home, and in many cases, choices that revolve around conspicuous consumption and status. Thanks to technology, globalization, fragmenting social structures and a more individualistic view of society, there are a lot of competitors to traditional publicly funded in-person school. There are a lot of choices for education approaches for adults to pick for their children. Education solutions also face competition from activities that students themselves engage in. From social media to video games to television and movies, there are many technology and online tools that hold the attention of our children and are in direct competition with education pursuits. From different school funding models, different school focuses and approaches, alternative schools, home schooling, to the tools our children utilize and activities we engage in, makes the competition landscape for publicly funded schools complex. Their competition is coming from all directions, which puts pressure on policy makers, lawmakers, and especially parents and the children doing the actual work within the service provided to them.

More and more, school systems and discussions about how our children learn are topics of concern, controversy, and for parents in particular, sources of stress and anxiety. Thanks to charged political rhetoric and social media driven controversial headlines and stories, education issues are often over simplified and lack crucial nuance. Solutions are often pitched as overly simple, and as a binary choice of either one or the other approach, often with value judgments assigned to either side of the debate. “Our preferred approach is inherently good, and that other approach we are uncomfortable with is inherently bad.” For example, some education proponents feel that students should only learn math using rote memorization vs. those that advocate for experiential learning in math. Some education proponents feel that teaching reading should be done with a whole language approach, while others advocate for structured literacy. Some advocate for lots of testing, others utilize ongoing observation and coaching. Some teachers are more authoritarian, while others utilize completely child-led approaches to teaching. Some feel that computing technology is an asset for learning, others ban any electronic devices. Similarly, some proponents advocate for virtual or e-learning approaches, while others demand students only learn in-person.

I’m just scratching the surface here. Education is full of complicated issues, and requires careful thought and exploring not just the fragmentation of approaches from the general to the specific, but to move from simple polarities to detailed nuance. This isn’t easy, but we will explore what makes e-learning effective, what it can address, and why people want to utilize it.

e-learning Has a Perception Problem

Publicly funded e-learning is an interesting phenomenon to study because it doesn’t get the attention or resources that publicly funded in-person schools do. When it is mentioned publicly, it is often mentioned in passing, or within a narrow context. Furthermore, defining e-learning is quite broad, it just means you utilize technology in an educational setting. It can be as simple as using a learning game developed by a company, to an all encompassing virtual school that is publicly or privately funded. There is more to online learning than local school districts implementing e-learning temporarily due to exigent circumstances. This leads to one of the most interesting aspects of e-learning at the time of writing is it has a poor perception in the public sphere. Parents, politicians, periodical writers and news organizations often attach a negative value judgment to e-learning. That is because the majority of people who experienced e-learning experienced a particular approach to e-learning that was flawed during the covid-19 pandemic restrictions. The e-learning they experienced was an attempt to replicate in-person schooling online. It was poorly executed, it was poorly planned, it was done in a rush under extreme circumstances, and it was temporary, so there was little effort to improve the experience. e-learning, when done well, is not at all what most people think of when their children were home, staring at screens all day while harried teachers desperately tried to implement a completely different approach to learning. There is much more to online learning than local school districts implementing e-learning temporarily due to exigent circumstances. When done well, e-learning does not look like what you experienced in the past.

Overall, e-learning isn’t any better or worse than any other kind of learning. Similarly, in-person learning isn’t inherently superior to e-learning. They are different, with different strengths and weaknesses, and require different approaches and skills. Just like anything other product or service, e-learning can be poor, mediocre, good, or even fantastic, depending on the implementation. Successful e-learning programs depend heavily on the expertise and skills of the administrators and teachers in the program. It requires different professional development, different approaches to teaching, different use of technology, different classroom management approaches, and different levels of family and community support. In fact, in-person schools attempting to do online learning is a classic product differentiator problem. Their strength is the in-person, highly structured social learning experience. Trying to replicate an in-person school experience through an online solution loses the aspects that differentiate in-person school from others, and it is an unmitigated disaster. (Similarly, when e-learning solutions try to move towards in-person, they lose their differentiator and fail too.)

e-learning, when done well, is not one long online meeting with students trying to stay engaged while staring at a computer screen all day. There is a mix of activities that includes some in-camera meeting time in a virtual classroom with a teacher, virtual collaboration with other students, and activities students perform off camera on their own. There are instructional videos, virtual manipulatives, activities and games they can use to complete schoolwork and assignments when they choose. As adults, we often have to attend virtual meetings for work, and spend an entire day staring at virtual meeting screens, or even worse, sitting through professional training webinars where we feel bored and exhausted. It turns out that it doesn’t have to be that way, and there are a lot of technology solutions and teaching approaches that can create a fun, engaging and rewarding online learning environment.

The super power of e-learning can be found in its flexibility that is provided by technology. This enables flexibility of location, timing and schedules. These open spots during a learning day that are freed up for e-learners can be filled with specialized activities and additional learning opportunities depending on individual need. Conversely, a lack of flexibility in e-learning means it will fail.

In short, there is nothing inherently good or bad about e-learning, just as there is nothing inherently good or bad with in-person learning. Each approach can be done extremely well, each approach can be done extremely poorly. At the time of writing, they are very different approaches that serve completely different user needs. Understanding the differences on how to find out the best approach for you and your children requires being open to studying each of these offerings based on their strengths and weaknesses and how each one will fit your current needs. That requires understanding the product differentiator.

What’s Your Product Differentiator?

As a product manager, I am always asking questions to determine why people like to use our products and services. I always ask: “What is our product differentiator?” Or in other words, what is unique about our product and service that gets the attention of the people who will want to use it? Without a differentiator, we will have a small, limited market at best, or no one using what we are offering, at worst. This sounds simple, but the vast majority of organizations I work with struggle when they try to answer it clearly. After extensive research, interviewing parents, and some intense analysis, I will offer my answer to this question. The differentiator with e-learning is simple, but varied and rich.

The product differentiator for e-learning is flexibility in learning.

Flexibility in learning is a vague term, and there are different aspects of flexibility that are important to families and learners. Flexibility in learning includes flexibility in:

  • location: can learn anywhere
  • time: can complete much of their work at different times during the day
  • sources of information: online experts, community experts, libraries, learning management systems, family and friends
  • teaching approaches and expertise: professional school teachers specializing in e-learning, private teachers and tutors, family members, community members
  • online resources: how to videos, lectures, learning tools, applications, games, collaboration tools
  • learning environments: home, workspaces, when travelling, etc
  • extracurricular activities: free play, sports, dance, art, music, science, create spaces
  • technology for learning: supply your own or utilize what you can access that works best
  • approach: full time e-learning, or part time homeschool, hybrid, modular, etc

Flexibility in some of the areas listed above are what makes e-learning so powerful for certain families. In fact, could write entire blog posts about each bullet point above. A mix of these items is what makes it so attractive and useful for them. Not having to travel to a school building each day can be attractive for many, since students can learn from home, and they aren’t losing time each day to commuting. Families that like to travel can have productive learning time from literally anywhere in the world. e-learning takes local education expertise and knowledge and distributes it, thanks to technology. Furthermore, technology enhances sources of information for learning, as well as providing alternative approaches for learning. If I had to pick one though, it would be flexibility in a daily e-learning schedule. The more time students have to work on supplemental activities, the more the family can customize the learning experience to better suit the individual.

Here is an example. The Smith family have decided to travel in Europe for two months to visit family and sight see. They value experiences in education and feel their children’s education shouldn’t be bound to a classroom. Sightseeing and enjoying world class heritage sights, historical locations, art collections and museums can be important educational activities. However, they can only do this during the school year due to costs and work timing for the parents. Taking their kids out of school for two months would be very disruptive, so they sign up for an e-learning service for their children. While they have to cope a bit with time differences for mandatory sessions in-camera with their teachers and classmates, these are short, and do not take up the majority of their learning day. Once they finish their assignments for the day, they can enjoy exploring the Louvre with their family for the afternoon. However, one of the children is having trouble with multiplying fractions, and doesn’t understand what the teacher was showing them in class. They ask their parent for help, who quickly realizes explaining how to multiply fractions is actually really hard, and while they can do it, they can’t address the questions their child has. They decide to discover an alternative approach together, and search on Youtube for a good explanation. After two or three videos that don’t help, they stumble on a math teacher’s account, and they have just the right explanation that resonates with the child. They show manipulatives with colorful visualizations, and explain in such a way that it seems simple. The child returns to their required math work for the day, and tries again. An alternative explanation to what the teacher in school was providing supplemented the provided information, and a child went from feeling lost and frustrated to feeling like they understood the assignment. That flexibility in sources of information and access to experts is a huge win for them today.

The Smith family were also motivated to try e-learning because their other child had trouble with bullying at school. This child is neurodivergent, and found the classroom experience difficult. Administration did the best they could to deal with the bully, but the bullying shifted from the classroom to the cafeteria, to change rooms for PE, practice rooms for band, study areas and the library, to off school property and the bus ride home. While teachers and administrators at the school were concerned and did their best, the parents of the bully didn’t care, and there was only so much they could do. Due to their neurodivergence, the child also had trouble staying still in class, and some teachers found them disruptive. Some teachers would provide accommodation, or would use group work and have students move around, while others would kick the child out of class if they were having trouble staying still. Eventually, the in-person school experience became distressing, was a source of extreme stress. The “socialization” aspect of in-person schooling was a negative experience.

In short, a safe learning environment had become an unsafe learning environment. A student who loved school, got excellent grades started to suffer with failing grades, and feeling sick each morning on every school day, begging parents to stay home. e-learning provided an opportunity to create a safer environment where the child could learn without fear of bullying, or reprisals for not being able to stay still. The alternative learning space allowed for movement when learning, to avoid extremely negative in-person experiences, and they and the parents could control their social interactions in a more healthy way. The online teachers didn’t care if they needed to stand up and move while listening to a math lecture, or if they wanted to listen to their favorite music when doing their math homework. Instructors also allowed them to turn their camera off if they were having a difficult day, and if they were in a collaborative environment that was difficult, they could leave the virtual room and ask for help. Inclusivity of a student with unique needs is much more easily addressed with a product or service whose differentiator is flexibility in learning.

The flexibility in the learning environment that e-learning depends on, is all but impossible for in-person. That flexibility allowed a student to change their negative school experience into a positive experience before they were lost to anxiety, apathy, and losing faith in getting an education altogether. The flexibility of e-learning is in contrast to the rigidity of in-person schooling. The flexibility of e-learning is what makes it great, you can tailor the experience for the family and child’s needs. Alternatively, the planned, structured, inflexible approach that in-person schooling depends on is what makes it work so well. While each approach gets kids in and out of the process with an education, they come at it from completely different approaches. They are at opposite ends of a spectrum, with a lot of variety of combinations in between.

One major function of in-person school in addition to education is child care, housing the most kids in the most cost effective way as possible to free the parents up to work. In addition, students learn social skills by being around others, and working within structured environments helps prepare them for work and other activities required by adults. Publicly funded in-person school also allows for centralization of education control, to ensure that there is a minimal standard being met. The community and individual families outsource their children’s education to the school system, who determines curricula, hires people with expertise to teach and train, and manages the safety and logistics of the school experience. The rigidity of in-person school means they have a large degree of control over what children are exposed to, what students learn, and they provide a standardized approach that is predictable and measurable.

This is a one-sized fits most solution, which is focused on educating children to become the adults we need to work and contribute to our society. However, we are asking a lot of schools who are faced with increased budget pressure and are being asked to do more with less. Schools need to provide safe childcare, a well rounded education, socialization, physical activity, and a sense of what it means to follow the rules and norms of community. That is a tremendous amount to ask of one institution.

Increasingly, parents are frustrated with public in-person schools that are so poorly funded they are unable to meet all of those needs, so they augment school with activities they seek out and enrol their children in, or they pull them from public in-person school altogether. Often, these students move to private schools, to religious schools, or alternative schools like Montessori or Waldorf, homeschool, or unschooling approaches. Rather than entrench in the face of competition and demand everyone return to in-person, state run schools, there are options if you look at the competitive market. Public schools can increase their market share by providing the best in-person schools they can, and by creating, staffing and implementing fantastic e-learning solutions as well. They have different strengths and weaknesses and will appeal to different customers. Merely copying and pasting what you do in-person and trying to make that virtual won’t work, but you can still leverage a lot of what you already know and work with, and provide families and students with a solution to school that is more suited to their needs. Furthermore, since the current public school model was designed in a bygone era to help provide factory workers, e-learning can help to prepare knowledge workers that are more suited to the modern economy and current society. That said, both in-person schools and e-learning school solutions can both improve by focusing on their differentiators and working to do better. It just requires the will to solve the right problems, adequate funding, and not spreading the solutions too thin. Rigidity is easier to manage, but flexibility appeals to those that buck the system. Increasingly, families and members of society are searching for individualized solutions, and unique approaches to difficult problems.

How I Determined the Product Differentiator

Now let’s back up a bit and see how we got to this answer. Time to show my work.

As I mentioned before, clearly stating a product differentiator sounds obvious, but it isn’t an easy question to answer. When you ask the people who design, develop, build and sell the product, they often struggle. In many cases, the question is met with derision. “Of course we understand what we are building and providing!” But what feels right, intuitively to individuals who are thinking about it can quickly fall apart when you actually write it down and try to share with others. Suddenly, writer’s block kicks in, and once people have a statement written down, they are shocked to see their coworkers have different ideas of what the company is providing altogether. This happens because they are too close to it, and get focused on the details of what they see every day.

An obvious solution to this problem is to ask the people who use your product and service, and why. However, when you ask the people who use your products and services, they may not have the expertise to answer the question adequately. Similarly to the people who build and provide the product, they may have intuitive thoughts in their head that are difficult to explain to someone else. Often when you poll end users, they all seem to have different answers. Many of the people who use our things aren’t able to clearly articulate why, even though they may feel strongly about using them. Our products and services address a need they have, and they depend on it. Beyond that, without expertise in product placement, marketing, sales, and clear communication skills around those concepts, it is a difficult question to answer. Put another way, if we are having trouble answering that question ourselves, it can be too much to expect for people who don’t study and work in product to tell us what we need to hear.

There are a lot of tools we can use to help cope with this. When you talk to people who use your things, themes will appear. I have often printed out questionnaire or interview answers from customers, read them over and over, and watched for patterns. While there may be different language and examples provided, certain themes will appear as you summarize. I will write the themes out, then use different color highlighter in the printed answers to find each one. Answers that don’t seem to fit those themes can be set aside for the moment. At this point, seemingly differing thoughts and opinions start to converge around tangible ideas that we can then use to discern why people like our product or service, and why they use it. Sometimes though, this effort doesn’t provide any new insight. Sometimes, there is a key reason expressed by just one end user that encapsulates what we do. That is extremely difficult to find while going over all the different things people have said to you. And sometimes, you end up with some interesting ideas and opinions, but nothing at all that you can use to help identify your product differentiator.

Often, you have to identify a product differentiator by using analysis and good old fashioned problem solving. In other words, you have to figure it out yourself first, then test to see whether you understand it or not.

Systems thinking in product analysis is a powerful tool, because it allows you to expand your perceptions. Instead of looking at a system or a product in a familiar way, you use a thinking tool to change your perspective. Often, we get entrenched in a particular view of something because that is what we are familiar with. One of my consultant tricks is to question my own suggestions and solution ideas. One of my mentors used to say that if you couldn’t think of three ways your solution idea will fail, you don’t understand the problem space well enough. Entrenched positions on topics based on individual experience is what leads to polarization. Since all you are exposed to or permit yourself to be exposed to are ideas that reinforce your position, other ideas seem strange, or even threatening. Let’s use education as an example. Parents want the best education for their children, but as parents, our views of education are heavily influenced by what we experienced when we went through it. When a child brings home a problem to work on, and the student is being taught an unfamiliar problem solving approach, many parents feel surprised and threatened by it, because they aren’t familiar with alternative approaches. They learned a particular way, they don’t understand this new way, and that can bring up a lot of negative emotions.

Using a Tetrad

When you work with me on software products, you’ll likely see me use a systems thinking tool called a tetrad. I use thinking tools like this to help see a problem from different perspectives. Usually when we analyze something, we latch on to our best idea, and think about the positive outcomes of applying that idea. We rarely look at how that idea can fail, because it’s threatening and hard. However, looking at failure is a powerful observation tool. Canadian Philosopher Marshall McLuhan, thought about embracing failure to help solve problems, and his approach to analyzing media has repercussions that are felt today. McLuhan analyzed mass media using a tetrad model, using four main areas to analyze media. He would look to see where current media solutions were failing, and that helped him “predict the future” by generating ideas on how the current failure modes would lead to new solutions. It was a simple systems thinking exercise combined with some science fiction style brainstorming on what might be used to solve the current problems. McLuhan believed that the use of new technology to address the problems faced by current technology would show us the future. He was often right. I use a slightly modified McLuhan Tetrad for product analysis.

The tetrad us an analysis tool that prompts us to ask 4 different kinds of questions about the concept we are studying. In product analysis, we ask these questions and brainstorm about a product or service. Here are my modified tetrad questions regarding a product:

What does the product:

  • enhance or improve? What are the benefits of our product or service?
  • make obsolete? What products does this product or service replace or make irrelevant?
  • retrieve from the past? What products or features that have fallen out of use are brought back?
  • look like when it reverses or deteriorates? How does the product fail?

We can answer these questions for e-learning as a product.

e-learning Enhances

What are the benefits of e-learning?

  • can learn from anywhere
  • can learn from anyone
  • flexible schedule
  • control over the learning environment
  • can access many teachers and experts using technology
  • alternative lessons and explanations of concepts available online
  • various media of information: visualization, video, apps, games, demos, animations, manipulatives
  • apps and workspaces for safe exploration (can experiment virtually before committing answers)
  • safety in learning environment and social environments, safe places for learning exploration
  • easier to schedule alternative learning activities
  • greater visibility and insight into what is being taught and learned
  • more time for extracurricular activities

Example: A family who lacks transportation options enrols in e-learning because the school in their district is overcrowded. They are a single income family and can’t afford to drive their children to the school they have been assigned because they only have one vehicle, and don’t want their children on a school bus for an hour and a half each day. The parent who stays home is able to support the children’s e-learning while the other goes out to work. After a while, they see benefits of e-learning and are pleased with their children’s academic performance. Furthermore, since there is no commute for the children, they have more time for playing outside at the local park, and to explore hobbies.

e-learning Replaces/Obsolesces

What does e-learning replace?

  • in-person only education
  • single teacher or instructor per topic
  • fixed physical space for school
  • limited sources of information

Example: A student finds a particular science unit interesting, and finds they do well on assignments and want to learn more. They find videos by a NASA scientist that they devour in between in-camera class time and school assignments. They decide to learn more, and ask their parents and teachers for help finding activities. The parents purchase an app subscription to study the topic more deeply, and the teachers assign an extra research project they can leverage for extra points in school. Th eteacher has an industry contact who points the student to books and tools they can utilize further. The student uses expert videos online, applications, library access, as well as parent and teacher knowledge.

e-learning Retrieves

What features from past approaches to education does e-learning bring back?

  • community education
  • apprentice model

Prior to publicly-funded, government mandated and controlled education, communities educated their children in various ways. They learned from local people with expertise, starting with their family, then to others with different education such as religious leaders, expert workers in a guild, and people with specialized knowledge from jobs. While you can still utilize these sources of knowledge with in-person school after school and on weekends, it is much easier to do with e-learning since you can incorporate it in the student’s school day.

Example: A student is struggling with writing clearly. The parents have a friend who is a professional writer who used to work as a teaching assistant when they were in grad school. Several days a week, they provide 15 minute online coaching sessions with the student to help show them how to improve. They provide feedback on writing the student is working on for school, they show them examples, and point them to other people and resources they can use to learn more.

e-learning Reverses/Fails

How does e-learning fail?

  • long days spent entirely in meetings.
  • copying in-person experiences: virtualizing every social event in-person provides
  • not engaging enough, so students turn to other virtual tools such as social media, tv/movies, video games, etc.
  • distracting learning environments at home
  • not enough physical activity and in-person socialization opportunities
  • behaviour issues. Classroom management breaks down, or students find it difficult to learn virtually, etc.
  • lack of supervision. younger children with inadequate home supervision may not do assigned work, or may not participate during in-camera time
  • students not doing the work themselves: cheating, parents or other adults doing too much to “help”, etc.
  • lack of access to technology

Example: A family who travels a lot find themselves with an e-learning program that starts to increase online meetings, and has short, inflexible deadlines on assignments. Instead of being able to work remotely and learn from the travel experience, the children spend upwards of 6 hours a day in online meetings. They find it tiring, and they have to be up at odd hours to do their work, missing out on the cultural, historical learning experience of the place they are currently staying.

Another way that e-learning can fail is due to externalities such as funding. Even though we can analyze e-learning as a product, publicly funded schools often have little say in how they operate, and face pressure from school boards, governments, and other groups that decide curricula, funding, staffing, resources, etc. If these groups have a negative perception of e-learning, or they overstep and try to control it by making it more like what they were used to attending in-person school when they were kids, they can cause e-learning to fail in various ways. They can cut funding, they can make demands on how e-learning is presented, they can push tools and resources that aren’t engaging for students, or aren’t compatible with online learning, and more.

Example: A family whose child has special needs is thriving in an e-learning environment. After a psycho-educational assessment, they were unable to get funding at the school for assistance for their child. Once they moved to an e-learning solution, they were able to create a learning environment at home that fit their child’s needs better. In the time saved during the day from a commute, and the sheer amount of time students need to wait for others, or move from classroom to classroom, etc, they were able to schedule therapy and other aid sessions during the school day. However, the local school administration for that district decide that e-learning is not worth funding, and start to interfere and starve funding. They demand more in-person style activities, they demand more formal testing, and they set minimum classroom times for each day. The effects of this are children who have to be in-camera, in meetings at scheduled times for longer periods during the day. This neuro-divergent child who was able to manage a few short in-camera meetings a day, plus work to do on their own, but with a schedule that allowed for expert coaching and intervention, suddenly finds themselves regressing and unable to cope with school, once again.

Further Analysis

When I interviewed people about e-learning, a lot of the negativity came from experiencing or hearing about failed approaches. The thought of your own child sitting in videoconferencing all day long, and filling in virtual worksheets does not sound like an education solution anyone would want to experience. It’s boring, it’s demotivating, it’s exhausting, it’s downright unhealthy. These parents viewed school from a child-care perspective. Someone is looking after my child and teaching them all day, only it is virtual.

Conversely, a lot of the positivity came from parents who have experienced successful models, and supplement e-learning with things they want their child to experience that in-person school doesn’t address very well. These parents were in a position to provide child care (home or travel learning environment, supplement extracurricular activities, provide guidance and direction as needed, etc.) Those with teaching expertise are caring for my child and teaching them for part of the day, the rest of the day is up to us to fill with what our values and needs as a family require. In other words, they need a minimum of supervised time, and the rest of the day they need e-learning to stay out of the way, so they can capitalize on a dynamic schedule that they could fill with other activities.

Focusing on the negative is the secret sauce of finding a differentiator, and three categories of failure modes emerged. Those that are due to a lack of childcare and/or technology to enable e-learning, problems the school can work on themselves to provide a better product, and problems that are existential, or threaten the product itself. A lack of childcare options at home, or access to PC and internet technology means that a certain part of the population are excluded from e-learning. For these families and students, in-person is the only choice they have at this time. For other families and students, the implementation of the product on behalf of the school has an impact on their experience. Dealing with engagement, scheduling, classroom management, utilizing technology tools, training parents or other adults on how to be good learning coaches, dealing with cheating, etc are things under the school’s control to address and improve. For the schools themselves, the ways in which they approach e-learning has a huge impact on whether they will succeed or fail. One theme emerged over and over, when e-learning tried to mimic in-person learning, it failed in various and spectacular ways. Analyzing this is what led me to the product differentiator: flexibility.

Overall, families who choose e-learning have their own unique needs and goals. Indeed, when I interviewed families about why they choose e-learning, I got a whole range of answers that didn’t seem to align at first. Here is a sample of answers.

We utilize e-learning because of:

  • disabilities. Our child can’t get to and from a physical school easily.
  • neuro divergence support. Our child needs extra support for their learning disability that the in-person school can’t provide.
  • health concerns. Our family needs to isolate more while a family member is undergoing cancer treatments.
  • safety. The school building is so old and outdated that it is causing sick building syndrome.
  • convenience. Our family doesn’t want to worry about getting kids to and from a physical building every school day.
  • travel. Our family spends part of the year with family overseas.
  • no nearby school. We want a specialized education for our science obsessed child.
  • timing. Our child works best in the evenings, and is able to thrive in an environment that fits their own circadian rhythm better.
  • supplemental support due to learning challenges and disabilities. Our child has severe dyslexia and was slipping through the cracks in a large classroom.
  • student athletes who train and travel. Our child competes internationally, and has a training and travel schedule that doesn’t fit traditional school.
  • alternative approaches: homeschool, self directed, unschool, forest school. Our family values child-directed learning, but we lack the teaching expertise to support them thoroughly. Also, we want to make sure they meet local standards so they have all the options they need for post-secondary.
  • hybrid schooling approaches: modular, homeschool, blended in-person and e-learning. We need a mix of things to make things work in our family, and part time e-learning supplements that.
  • cultural and religious needs. We want our children to learn about their heritage, culture and religious background. We can fit family time with elders in e-learning schedule, in addition to language classes and religious studies.

All of these families have different goals and needs. All of these families will have different goals and outcomes for their children’s education. All of these families will have differing childcare needs during the day. Some will need more or less in-camera, supervised time. However, if you look at what they all have in common, it is flexibility. There are different aspects of flexibility, but the flexibility of e-learning allows the parents to fill in the learning schedule for the day with what their family needs, rather than expecting a school to do it all for them. Furthermore, all of these families could use the exact same e-learning solution to reach their goals. The e-learning solution provides a minimal framework to ensure children are learning the appropriate things at the appropriate time in their education experience, and that they are at a minimal standard.

The most important aspect of flexibility for these parents is flexibility in schedule. Providing a minimal amount of required in-camera/supervised time during thee day, allowing students and families to complete required work on their own time provides opportunities for flexibility everywhere else. The parents are then able to fill in the blanks around that with what each child needs, through their own resources, online resources, community resources, etc.

One of the challenges with e-learning is that it requires families to provide their own childcare during e-learning. The degree of childcare required for each e-learning family is also different. For younger children, an adult needs to be involved a lot more than older children who are literate and can work more on their own. In a family where the adult who is at home but doesn’t have time to be around as much as their child needs requires a different level of child care than a family with an adult who can dedicate themselves full time during a school day. For example, a parent might have a part-time job that has requirements to be met during the day, while acting as their child’s learning coach. In my own research, the amount and level of (virtual) childcare required was the largest source of conflicting needs between families. If you ask a family who are homeschoolers, or a travelling family, they need as little in-camera time as possible. A parent who needs to focus on their own tasks more during the day, such as domestic chores, part time work or volunteer time, etc will require much more (virtual) childcare. If the e-learning provider has more scheduled events during the day, one family will suffer because they will now have to cut out activities they are utilizing for their student. If the e-learning provider reduces in-camera events, the parent who has less time to supervise during the day will have a student who suffers.

The way to harmonize this problem is to provide optional activities for those who need them during the day. The family whose child spends some afternoons at forest school can utilize the minimum required in-camera time, and extend the day with something valuable for their child. The family whose child needs supervised time in the afternoons can attend optional office hours with teachers, optional virtual study halls to work on their homework with others, and optional fun or enrichment events. If you make the entire schedule mandatory, or start enforcing that students be in a particular place at a particular time to a greater and greater extent, the flexibility of the e-learning schedule erodes, which then takes away flexibility in other areas that e-learning students benefit from. Addressing the differing needs of childcare, requires not only expertise and funding, but flexibility with the e-learning product itself. While some might be in-camera, scheduled, supervised activities, others may be assignments or research projects for those who want or need to spend more time. Furthermore, these needs can be dynamic, based on temporary conditions families experience, such as periods of illness, travel, events, etc.

Make Your e-learning Product Better.

Focusing on your product/service differentiator is imperative to improving what you have. Products and services literally live and die based on how well they understand and execute on their differentiators. That said, differentiators are hard work to understand and it is hard to focus teams and organizations on the best features to fulfill the differentiator. Furthermore, many important stakeholders within your organization will have vastly different ideas on what you need to do. Often, the people who control the money have the least informed, but most powerful influence on the product or service. Getting it right can require going against the grain of what organizational leadership is pushing you towards. That said, improving a product or service is simple at its essence.

When I analyze a product or service, I look at three areas to improve:

  1. Enhance the good
  2. Reduce the bad
  3. Strengthen your advantages

In other words, are you:

  • reducing problems (user friction, unneeded costs, sources of complaints)
  • enhancing good things that you do well (engagement, productivity, utility or fun)
  • focusing on your differentiator(s) (providing people with an experience you do better than absolutely anyone else)

In simpler terms, a famous quote from the movie FUBAR is appropriate here: Turn up the good, turn down the suck.

It’s important to look at the problems first, to see what you can easily address to improve what you have. Then look at the positives and what you might add to the product or service as time goes on, to make it even better. For example, we can address:

e-learning problems: friction with schedules, behavior issues, technology problems
e-learning strengths: flexible schedules, rich and varied sources in learning, social collaboration, safety in exploration

However, focusing on the differentiator, especially with the nuanced differentiator of flexibility that e-learning has can be much more difficult at first. Not only do you have to constantly prove the worth of the approach just to get a minimal level of support and funding, the sheer effort involved in keeping the service running is a massive job. However, product analysis can help us here again.

One area McLuhan would focus on for insight was the reversal or failure aspects of a concept. How do they fail? How do they currently fail? What causes them to become ineffective? McLuhan was so good at this analysis, he could describe technology solutions that hadn’t been invented yet, such as a vivid description of what became the world wide web. In our tetrad exercise above, we can see that e-learning loses effectiveness when it becomes less flexible. However, we also see people leaving public school because it doesn’t meet their needs. Future school solutions will likely become more fragmented and individualized, as technology opens up massive sources of expertise and knowledge that is accessible from anywhere. One interesting model of education is https://manisharoses.medium.com/not-school-or-homeschooling-but-modular-learning-5233927f8fc9 A popular current approach to modular learning is to have educational instruction provided virtually by teachers and other learning experts, while socialization, physical activity and other pursuits are managed by the family and students.

Make it Better, Don’t Make it Worse!

You can get feedback from customers on what works, and what doesn’t work for them individually. However, when it comes to product or service features and needs, they tend to express their ideas based on what they know. In education, parents tend to prefer approaches that they know and experienced themselves. Often times this is at odds with what the education system provides today, and what the kids actually want or need. The trick is to look at the gap that isn’t being addressed in the market, and how your product or service addresses it, even when it doesn’t seem to fit what people ask for. Once you have analyzed and focused correctly, the seemingly disparate needs will suddenly sync up. “Oh course! That is exactly what we need! I didn’t know how to say that before!”

There are also powerful stories you can tell about e-learning success that helps center and focus on improving it. There are lots of stories on the variation of learning tools available online that help students overcome difficulties, or specialize in interest areas. There are huge bodies of knowledge online. Since in-person schools were set up in a time when training factory workers was central to society, they are a bit outdated. e-learning on the other hand is more suited to technology centered or knowledge based jobs. Learning how to learn as an adult sets students up for lifelong learning. After all e-learning is how we adults learn on-the-job, etc. Students can get any expert from anywhere to provide insight and learning provided they are publicly available online. Finally, vitual learning environments are absolute havens of safe exploration: solve problems virtually and explore before committing an answer to submit for a grade.

Simple ways to improve your product is to:

  • Reduce friction
  • Increase engagement
  • Understand how competitors fail and how you can address those market gaps

Reducing friction in a product or service can be all encompassing, but worth the effort. If people can work better in an organization, they will be more productive. If students can learn without getting stuck waiting all the time, they will have a better learning experience. If content is more interesting and relevant to the present day needs of students, and in formats they already use and prefer, they will be more likely to utilize it. Finally, finding out how your competitors fail provides opportunities for you to address things they simply cannot.

One area to improve is in how you staff teams. e-learning requires a different approach to teaching, and it requires teachers who not only enjoy teaching virtually, but have utilized professional development to learn how to do it well. One area of research can be found on social media, where popular teachers are talking about how they left in-person teaching and transitioned to e-learning. There are also companies and independent practitioners who train teachers how to transition from in-person to virtual. Learning why these teachers make the transition, what they do to be effective to learn how to teach virtually, and even more importantly, learning how to attract that talent to your organization can go a long way into both reducing friction and increasing engagement in your e-learning offering. They aren’t difficult to find if you search on social media.

Another area to improve is in the use of technology. Using virtual manipulatives, how to videos, games, and other activities that utilize technology effectively can really help reduce friction and increase engagement. Using the machine to enhance student activities, rather than creating virtual copies of worksheets and exams is crucial to providing a better product offering. Visualize problems and solutions, start over and redo, speed of processing power aids exploration.

Virtual tools are great because you can change your answer easily. There is no eraser on paper required, no rcrumpling up an exam, or squishing a clay and starting over. Students can experiment and have richer learning experiences because they can show and tell safely online. They don’t have to commit until they are ready, even within an examination or group assignment context.

Variation of approaches with a huge amount of knowledge and training opportunities. If you want to learn something, you can read, you can watch videos, you can try activities, you can play games, etc. If one method doesn’t work, you can find another until the right combination f or you appears. Looking for tools that create better virtual meetings, group projects, recording and sharing videos of public speaking, creating and sharing projects, as well as artistic and other endeavours are great sources of increasing engagement.

This is an amazing aspect of e-learning. You have a potentially unlimited amount of approaches, teachers and methods of understanding. In traditional school, you were limited by your teachers, your assignments, your textbooks your library, your friends and family. Online learning expands this so you can find something that helps you get unstuck, or meet a challenge, or really master a topic that no one around you has any ability to help you with.

One area to explore to improve e-learning experiences is to look at competitors. An obvious competitor to e-learning is in-person learning. It is extremely tempting to try to copy what works well for in-person and replicate that virtually. However, it is impossible from a logistics and user experience perspective, and it is a fools errand from a product perspective. Instead of focusing on your differentiator and enhancing and improving what you do well, you will try to copy someone else’s differentiator, and you will always, always fail. Rather than trying to replicate what in-person schools are doing, think of them as products and services that address a completely different market. You don’t want those customers because they don’t need what you have to offer. Instead, you need to attract the customers who need your offering, and they will get value from it.

Bottom line: Embrace your e-learning market, and reject your competitor’s in-person market.

A simple way to analyze your competition to help grow your own market share is to find areas where they fail. Why are parents pulling their children from in-person public schools? What do you offer that might appeal to them or meet their needs? This information isn’t difficult to find, there are articles and posts all over social media where parents complain about public school, and sing the praises of alternatives they are using. Rather than trying to draw away people who use in-person school, focus on those who are leaving or have already left.

For those families who are outside of the public school system, look for opportunities to enhance what they are doing. Part time e-learning can have a huge impact on homeschool families for example, or families looking for a blend of approaches. One of the biggest weaknesses of homeschooling is a skill gap. Parents who aren’t professional teachers can only do so much to help their children get an education. Furthermore, part time e-learning from your local school district ensures your child isn’t behind for their grade level, or they meet standardized requirements for post secondary or other programs upon graduating.

To learn more about expanding your market and improving your differentiator, find people who are leaving in-person learning and learn from them. Are they administrators and teachers? What motived them? How did they learn to excel as e-learning professionals. Are they parents and families? What specific aspects were lacking in in-person school? Finally, see how you can easily address both of these groups because they compose a completely different, and growing market for you to focus your e-learning solution.

Competition for Students

For adults, the obvious competition is alternative education programs that focus on us, the adult decision makers. But who are the competitors to e-learning when you focus on the people who are using the product day in and day out, the children? Students use technology all the time for social interactions (social media, communications apps), gaming (video game apps), and watching movies and tv (streaming). In fact, lately, a lot of media time is spent decrying the problems that smartphones are causing in school. While banning them outright during class time is one potential solution, historically, prohibition doesn’t work that well. Another approach is to find out why we are losing our customers to online activities our children engage in, and see if we can address those with our product offering.

All students whether they are in-person or virtual learners face competition from online activities such as streaming, social media and video games. Video games are interesting because they are well studied from a product perspective, and I have personal experience working in that space. As for the use of video games capturing our students attention, in-person schools have absolutely no hope or redeeming qualities to compete. E-learning solutions can at least provide virtual alternatives that may not be as exciting or compelling as video games, but they can utilize the underlying mechanisms of video games to improve their learning experiences.

There is a trap here though that our adult brains think is the ideal solution: the gamification of school. Unfortunately, trying to make school into a game isn’t going to work very well. For one, we have no hope of competing directly with game shops who have huge budgets and teams of experts. Also, our kids are smart. They will see through this quickly and realize it isn’t what the adults are trying to sell them.Furthermore, the simple, popular approaches to gamification such as points, badges, leaderboards (PBL) have limited long term effectiveness. Instead of trying to make school into a game, we can instead analyze the mechanics of games and see what makes them so effective, then bring those aspects into our e-learning solution. This is a game inspired design approach. Instead of trying to make all learning into a game, we look at elements of games, study them, and apply similar approaches to our non-game solution. Game-inspired solutions rarely contain video game technology directly, but are heavily influenced by game design.

In fact, one of my secret tools as a product manager is to use game inspired analysis and design in most of the applications I work with. Most people never know that I am using game mechanics, beause I don’t try to make it look like a game. Instead, I try to get the end results that games are so effective at, even if it is an accounting application or for recording time sheets. When I am working on a game, or game-like solution, then the visualization is different, but the process and underpinnings are the same.

Here are some underpinning mechanics of what make games compelling:

  • entertaining content
  • social connections and collaboration
  • challenges, meaningful struggle
  • achievements and recognition
  • visible progress and feedback
  • normalize making mistakes (mistakes are fun, not sources of anxiety)
  • safe places to explore, fail, try again, repeat, succeed
  • clear, figure-outable tasks
  • visual progress and feedback

All of these items can be easily addressed with e-learning solutions. It just takes a bit of professional development, research, and applying tools to get the results you are looking for. Even socialization needs can be addressed virtually, the social bonds that children facilitate and experience online are powerful and compelling. While they never replace in-person social interactions, they can be implemented in effective ways. Social collaboration in games can be fascinating to study. MMOs (massively multiplayer online games) can have dozens, hundreds, or even thousands of people working together to reach a goal. The project management, social co-ordination and people skills required are immense and under studied.

One important aspect of games is that everyone can learn without feeling judgment or shame, so you can explore and learn from your mistakes. Rather than only rewarding getting things right all the time, players iterate towards the correct answer rather than feel pressure to be correct all the time. Mistakes help you learn, and help you make progress to reach goals within the game. Mistakes are incorporated in game play in various ways. They are learning opportunities, but can also provide a sense of randomness to make things more interesting, or silliness to reduce a stressful situation, or to make things fun.

Digital mediums provide perfect opportunities for learning without real world consequences. If games can exploit this, why can’t digital learning experiences also take the stress out of making mistakes?

Another vital aspect of games is that game designers understand the various user types of their customers, and design accordingly. Gamification consultant Andrzej Marczewski created a breakdown of game player types that I have adapted and use in my product analysis and design work:

  • Achiever: driven by completion and gratification. They like leaderboards, visible status, and progression to understand what to do next, and what they
    have left to complete.
  • Gatherer: collects items in a game such as utilities, points, health, objects, status items and wealth.
  • Explorer: enjoys finding the limits of a game and experimenting with the boundaries. They want to experience different things from a sensory perspective,
    and find out alternate workflows that others may not use or know about. They often find shortcuts, bugs or cheats. Map based games appeal to explorers, but so do learning
    based games.
  • Socializer: craves social connections, and interaction. They like to communicate and interact with others when they play.
  • Philanthropist: loves to help and share. They will coach newbies, team up with others to guide and share knowledge, and they will send in-game gifts to
    others, even people they have never met or interacted with before.
  • Disruptor: is motivated by change. They can be unpredictable in game, and will force changes that could be positive of negative. Some disruptors are
    griefers who get pleasure from seeing others lose in the game, and will actively work to sabotage others, and even themselves if they are bored enough. (Griefing is a huge
    part of a lot of games, and the disruption can be a fun outlet, or it can be destructive, if it isn’t incorporated in designs.)

It doesn’t require much creativity to see how these relate to students. In fact, with a bit of thought, a teacher could probably identify each of these player types as students who are motivated exactly the same way in learning environments. In fact, I have had success using game mechanics and applying gamer user types when working with learning and educational apps. The crossover is compelling and useful.

Once again, I am barely scratching the surface here, but it should be obvious that analyzing why games are popular, figuring out motivations for playing games, and what features children find engaging is helpful to improve our e-learning offering. We have a fighting chance to meet children where they are, to create compelling alternatives to playing games, or socializing or watching TV, because we are starting with the same technology platform these activities depend on. When we pivot towards exploiting the technology to its fullest, rather than copying two dimensional worksheets and long “I do, you do, we do” lectures, we can do something unique and effective. We can do things in-person just can’t do, just like they can do things we will never match.

Conclusion

The super power of e-learning can be found in its flexibility that is provided by technology. This enables flexibility of location, timing and schedules. These open spots during a learning day that are freed up for e-learners can be filled with specialized activities and additional learning opportunities depending on individual need. Conversely, a lack of flexibility in e-learning means it will fail.

While the differentiator for e-learning is nuanced, it is simply based on flexibility, and exploiting technology to provide the best possible solution to families and learners. The customers of e-learning are split between parents and children, and is overseen by government and other regulatory agencies. To get students enrolled in e-learning requires parental decision and buy-in based on how e-learning meets needs in-person is not currently addressing. Students are the recipients and users of the product and they need to find it compelling and useful. All of this must be done within a political, legal and regulatory framework regarding safety, privacy, and following an approved curriculum with measurable standards. While this is an unusual situation from a product perspective, it requires two interrelated approaches. Parents need to understand the product differentiator and lose the negative perception of e-learning. This means messaging around how e-learning is not just virtualized in-person school, and with examples to show how it is different and how it relates. For e-learning to succeed for the students, it needs a degree of flexibility, and focused expertise, and to make it a venerable competitor to the online activities that capture the majority of our children’s attention. These are easily achievable with some creative problem solving, good marketing and PR, and old fashioned hard work.

It’s important to note that if your differentiator becomes muddled and your e-learning solution fails, many families will not return to your district’s in-person solutions. Instead, they will find a different e-learning provider in another location. After all, with powerful videoconferencing solutions, learning management solutions, videos, reading materials and hands-on experiments, people can get great educational experiences and outcomes from anywhere in the world. We are no longer limited by what we can provide in a physical location. The sooner we realize this, the sooner we can offer fantastic alternatives. If we aren’t, someone else most certainly is.

Hey Educational App Designers, Stop Creating Glorified Worksheets!

Educational app designs need a rethink.

I am a product manager and UX designer in the software industry, and I’m also a parent of an elementary school aged child. Learning applications are a big part of our educational experience, and I find I am constantly frustrated by them. While they often have great promise and claims, and they use modern graphics and game engines, they rarely use the technology to help facilitate learning. In fact, they often put fantastic game engines around worksheets. They have spectacular characters, a wonderful environment and storyline, then for the actual math or literacy, they just display a virtual worksheet to complete. Even worse, if the user gets a question wrong, instead of showing them how to fix the problem and learn from it using the technology, they just lose points, need to find the correct answer somehow, and at worst, are unable to progress. The fun part of the app is often the parts around the actual learning, rather than making the learning part the fun part and main focus. No matter how cool and amazing the application is, if you are just wrapping that around the same old printed worksheets students have used for decades, you a really aren’t making good use of the technology.

Educational apps that don’t use game engines or a game format still tend to use game mechanics in their design to help students understand progress, facts they have mastered, concepts and activities they have tried, etc. When you know what to look for, you see the mechanics in virtually every educational app, but no matter how cool, new, flashy or exciting, they tend to devolve into learning as worksheets.

Here are three examples of math apps we have tried in the past.

We downloaded a math app, and it was a sandbox style game with customizable avatars, a rich environment to explore, and lots of clever use of music and animation. When it was time to do math work to earn points to buy things to add to your game environment, the user had to answer a series of questions, in a certain period of time. While the graphics were nice, and there was animation to help make it more engaging, it was still just look at a math equation, enter in the answer, and move on. If you didn’t reach a certain number of points in a certain amount of time, your progress was stuck. You couldn’t do anything more in the game other than wander around until you passed that level. This isn’t much fun, particularly if it is a skill you need to work on. Not only do you need more practice, but the game isn’t fun anymore.

Another math app we tried had an immersive RPG play style. You choose and customize an avatar, and your character does quests, engages with other players, and had boss battles, and other fun activities. This looks fun! However, when it was time to do math questions, you are literally taken out of your immersive environment and shown a virtual math worksheet, like the kind you print out and fill in by hand. At least with this app you aren’t punished for getting answers wrong, you just get a certain number of points to continue. However, there isn’t a lot of actual math learning going on, you have to practice those skills off screen, then come back to it. My son was so impressed with this game and loved it so much, he dedicated daily homework to develop skills to advance further. We spent three weeks of doing daily math practice and worksheets so he could master the level. While we were impressed with how motivated he was, we were baffled on why the game didn’t provide that practice. There was a little bit of support to show what the correct answers were, but beyond that, it was just doing worksheets.

The worst example of a math app with poor mechanics was one that used no graphics at all. It just had math equations, a timer, and a score. There were no visual indications of how many questions to answer, and many of the questions required off screen work, since there was nothing to do other than fill in the answer and hope for the best. To do the work to solve the problems required several minutes of whiteboard or work on paper off screen, then enter in your answer. If you had a typo, or an off by one error, you not only get a message that your answer is wrong, but your score reduces. If your score doesn’t reach a certain level, you just continue, over and over, until it reaches a certain point. You have no sense of progress, and while the app would show the correct answer, it didn’t do anything to teach the student how to do better. You get points for the correct answer, so you better come to the app with a lot of facts memorized. If you make some mistakes, not only do you not get much feedback, but you get punished. Furthermore, if you are too slow, that also affects your score, dragging the effort out even longer.

There are lots of apps that at least provide visuals and let students change their minds, but they are still mostly virtual worksheets that are trying to get students to enter the correct answer. While there is a place for that, such as dragging letters around to make words, dragging words around to figure out parts of speech, or moving objects into groups to divide or multiply, they are still not utilizing technology to help learn very much.

In math, it is so simple to design a visual calculator, and let people play around with numbers and see how that affects outcomes, and how patterns start to emerge. Once math stops being abstract, and people can play with manipulatives and see what happens, things can really click in a learner’s brain. Math manipulatives such as number blocks, Montessori boards, cuisinaire rods and more are extremely helpful learning tools, but virtualizing them, adding in animation and allowing safe exploration would be incredibly powerful. Instead of catering to learners who do well with worksheets and flash cards, learners who are struggling to understand a concept should be able to visualize the concept in various ways, play around with inputs and outputs, and see how the concept manifests itself. Not everyone can translate abstract math concepts into visualizations or numbers in their minds. Providing ways to see not just how objects and patterns interact with math, but how those concepts can be applied with virtual tools holds a lot of power. While all the technology is available to us, educational apps tend to fall back on some sort of worksheet, which only appeals to a certain kind of learner. On the other hand, virtual objects you can interact with and learn from are more engaging to every learner, and they can help people actually learn something new.

Use Technology as a Safe Place For Learning from Mistakes

What drives me up the wall with educational apps is they tend to only focus on getting correct answers. Instead, they should provide a space for experimentation. What happens if I play with addends or minuends? What happens if I multiply negative numbers together? What happens if I play with the variables and use huge and small numbers in a multiplication problem? What happens if the divisor is larger than the dividend? What if the divisor is an emoji or a letter? What does it look like if I make a word problem come alive? What happens to a graph if we loop through a huge number of values for x and y in a linear equation? What happens if I watch an animation of a huge range of possible inputs? What if the inputs are at extremes or nonsensical? Imagine how that can be quickly visualized, and different types of inputs can change the outputs, and what patterns arise from different kinds of mathematical concepts.

The beauty of virtual tools is they are SAFE places to make mistakes. You get to put in some inputs, and then watch what happens. In real life, when you make a mistake on a worksheet, you have to erase it and fix it. Virtually, there are no eraser smudges, you just change it. Furthermore, a printed worksheet can’t come alive and show you what happens when a train leaves Philadelphia at 6:00pm and another leaves New York at 7:00pm, or how many ball bearings can fit in the back of a pickup truck. Game engines with virtual tools can. Furthermore, making mistakes should be fun learning experiences, rather than being punitive. Sure, there is a point in learning where it is important to have precision and to be able to do things by hand is vital. However, playing around with technology and seeing what might happen will help students form a picture in their mind of how a concept works, not just memorizing how to get the right answer.

Actually using game engines, game design and having and understanding of different styles of game play will help people with different needs be able to learn the concepts in the app itself. Different players will have different needs, and while some people like timed tests and fact based answer seeking, others are vastly different. Andrzej Marczewski makes it easy for us to learn and incorporate Gamer User Types in our designs. For example, a socializer might want to help others learn something they struggled with, and provide a tutorial of something cool they discovered. A griefer might giggle away putting in extreme values. An explorer might try lots of different combinations of things to see how that is visualized or what virtual outcomes might be. An achiever might be motivated more by virtual rewards and determining how many and what kinds of activities to complete. There are a lot of differing user goals and scenarios, and there is a tremendous amount of knowledge and experience in the games industry we can learn from.

A number of years ago, I was asked to do a UX audit of an anatomy app. It had beautiful graphics, and a ton of fantastic information. However, it was really just a digitized version of something like Gray’s Anatomy, the famous anatomy text book. Sure, you could search, you could look at amazing graphics and click around to help you memorize, but was not using the technology to help teach. I saw two problems immediately: it was a digitized book or worksheet, and it was static. Anatomy in living organisms is not static. A living organism has different states in their body at all times. For example, there was no use of technology to show oxygenated vs deoxygenated blood in a circulatory system, or to simulate illness, pathologies, or other things a med student needs to do to apply their anatomy knowledge. Furthermore, testing was fact based. You needed to memorize facts using the app, and then state those facts in an exam. The learning was about reading and looking and memorizing, not experiencing. When you are a medical professional, one of the most important sources of learning is from mistakes, or from failures. A patient doesn’t respond well either due to a lack of knowledge or the wrong treatment, and you learn what not to do.

My design concept was to digitize that virtual patient experience, as sort of a medical study Tamagotchi. Instead of memorizing a virtual anatomy text book, why not have a virtual patient to keep alive for a semester? Sure, you have the required anatomy to understand and commit to memory, but you have a simulated patient who can have certain illnesses, pathologies or states to manage. It sounds crass, but if your virtual patient dies a lot of times, you are going to learn a tremendous amount from that experience that you can use in the real world. It is much safer to learn and fail and see what happens to your virtual patient, rather than memorize and get a poor score if you get things wrong. If you can fail virtually and learn from it, that has a lot of value. I would prefer to play and experiment and be rewarded for learning from mistakes, rather than memorizing text books facts and being afraid to fail an exam. Exam scores have real world consequences, but playing around in an app and having fun, piquing curiosity to explore “what if” scenarios, or having instructors throw you challenges to keep your virtual patient alive is something we can absolutely do with computers that we just can’t do with dead tree text books.

Another area to learn from video games is how they treat failure. To make a game engaging, failure is part of the game, not a punishment. In popular games, their designs never make you feel lost or dumb. You feel like a super hero, and when things go wrong, you can recover and try again. In fact, many games make the failure part incredibly fun and rewarding. Who doesn’t want their avatar to scream in a ridiculous way and burst into flames if they fall off a balance rope in an obstacle course? Some failure modes are so fun and hilarious that people spend more time crashing their characters than completing tasks. Even games that are extremely challenging and are designed to be frustrating are engaging and use that frustration and failure to encourage people to try again. You aren’t left feeling stuck and dumb, you feel like you need to try again, just one more time. Furthermore, if your character crashes and burns, you just respawn and try again. You aren’t stuck unable to play without doing a lot of work outside of the game to continue. The game helps you succeed, and if you are really stuck, game communities are fabulous places of sharing knowledge and helping each other.

The more I experience educational apps with my kid, the more I see that educational app designers completely miss the power of virtual technology and learning. They should design the apps around experimentation and reward failure as a part of learning, but they end up digitizing worksheets. They expect people to know facts, they don’t help people pique their curiosity in a safe way. They have an extremely narrow view of learning and teaching. Why don’t they support inquiry and experience? Why do they just duplicate books and worksheets, even when they have a fancy MMO or RPG engine around the learning? Virtual learning environments themselves are fantastic places to do whatever you want to learn. Where else can you safely find out what happens if you feed something poison, or if you fly the rocket into the ground, or you play around with your math question variables, or if you rearrange your words in a nonsensical way. These are pretty bad ideas in the real world, but great learning experiences in a virtual one. Plus, mistakes can help you learn, and they can be fun and silly. Laughing at a ridiculous mistake on a math concept and visualizing the carnage is a much more effective learning technique than getting a long division problem wrong, after you spent ten minutes solving it off screen.

Using the technology to just digitize the printed worksheets completely misses out on this important approach to learning. Sure, at the end of the experimentation, you want the student to have knowledge and skills and to have learned, but we have game engines, and graphics and powerful machines that can be used to learn what we need them to learn, and we instead just give them worksheets. And in many cases, the worksheets are even worse than a printed one.

Bottom Line: Let students play with the concepts you are trying to teach and let them succeed and fail in a safe way, using everything technology affords us. Stop punishing learners for making mistakes, let them make mistakes and explore the outcomes virtually. Stop taking dead tree technology, digitizing it, and rewarding people for getting the correct answers and calling that an educational experience. Use the technology to show, tell, demonstrate, play with and really get a solid grounding in the concepts without real world consequences. That is the differentiator with learning with technology: you have limitless access to information, and tons of rich tools to virtualize problem solving and learning in stunning ways. Provide structure and opportunities to learn, don’t just expect people to write an answer on a worksheet. Give them more.

UPDATE:

April 24, 2024

I was reading this article about educational apps: The 5 Percent Problem: Online mathematics programs may benefit most the kids who need it least, and there are some thought provoking points. This quote in particular stood out: “…the programs may have been unintentionally designed to fit high achievers better, says Stacy Marple, a researcher at WestEd who has studied several online programs.”

Put another way, if you design apps that expect learners to already have mastery, they will tolerate your virtual worksheets because they can easily enter in the answers. They have the knowledge, skills, and confidence to grind away to get back to the fun part after the get the math or literacy “worksheet” completed. For learners who don’t already have mastery, they will be frustrated and stuck, because there aren’t mechanisms in place to help them safely learn, to build their understanding and confidence, and to actually help.

Adventures in Homeschool: Our Math Additions (and Divisions)

When I was a kid, I was a star memorizer. At an early age I could memorize sections of prose, poetry, and all kinds of facts. When I started working in mathematics, we did more memorizing. I was good at that part, memorizing math facts. Trouble was, I didn’t really understand them as deeply as I needed.

Now that I found myself in charge of my son’s math education, I started to branch out from the lesson plans and exercises I had purchased and tried out. Since we were working together, and he was curious, I decided to experiment a bit. First of all, I wanted to help him with a different approach to math than I had experienced. I had struggled a lot with math, up until university. Next, I wanted to be sure our approach to math was appropriate for his learning. Instead of being guided by my own experiences, I would let them inform us, but try to get my direction from kiddo and his interests.

Looking at my own struggles with mathematics required a bit of self reflection. Over the years I had thought a lot about why I had struggled, and for me, it was often because critical information was withheld. Someone, somewhere, had decided that parts of the topics I was learning weren’t age appropriate, so I would learn a certain set of facts at a certain grade level. Later on, more information would be added, and the facts and approaches I had learned were challenged or upended completely. Those transitions were hard for me. I also had trouble because I needed to understand the topic more deeply. When I would ask questions about math topics, particularly with regards to their application in real life, I didn’t get satisfying answers.

Most of the time, the explanations from the teachers didn’t leave me feeling like I fully understood the topic. In fact, I wasn’t able to delve deeply enough in math concepts to truly own them until I took math classes in university. I memorized and applied, but I didn’t fully understand. It wasn’t until I had a math tutor in Grade 12 that I found someone who could fill in those blanks for me. When I went to university, that changed. Whenever I asked math professors “why” questions, they usually appreciated it and explained further, or pointed me to publications with alternative explanations, or trips to the library. I was also inspired by how some of my math and computer science professors taught math to their own kids. They focused on simple, intuitive application that was relevant to kiddos, and they didn’t gatekeep and withhold information. Once things began to click for my math brain in university, I vowed that my kids would get help on the “why” questions. If it was from me, then so be it.

To brainstorm, I talked to programmer friends and asked about their math learning experiences. Many of them just understood math naturally, and didn’t struggle with any of it. Many had mixed experiences, and some had experiences that sounded like mine. They didn’t like how rules changed and wished they had been given a fuller picture earlier. Furthermore, when any of us were curious about topics beyond our grade level or outside of the curriculum, that was usually discouraged. “You’ll learn that later.”

All of us found that programming helped out math skills since it was a real world application. The math facts come alive, and you understand a lot of the “whys”. For example, an abstract concept like a variable in algebra (a letter symbol in an equation) is part of what you always do when you program: you create variables and do things with them. High volume automation of math provides visualization and patterns that you can’t replicate with paper and pencil, and that provides more insight. Even better, small errors can have huge implications in a program, so your attention to detail changes.

My question for my programmer friends was: “What did you miss out on in your early math education that you think I should provide kiddo exposure to?” Their answers provided this list:

  • Zero-based counting
  • Negative numbers
  • Working with fractions earlier
  • Multiplication basics alongside arithmetic
  • Understanding decimals
  • Using variables
  • Thinking about functions
  • Sequencing and loops
  • Abstract data types: lists, arrays
  • Data operations: stacks (LIFO and FIFO, evaluation, etc.)

Some of these are quite simple and actionable. For example, starting to count with 0 instead of 1 is trivial, and should always be done, in my not so humble opinion. When you start looking at place values, or even counting beyond 10, it is extremely helpful to have started at 0. Negative numbers aren’t that easy to grasp, but you can work with them, especially with number lines. Fractions, multiplication, decimals and variables can be worked into early math exercises, but it takes a bit of thought.

About half the list relate to computer programming, so I wasn’t sure how to handle those. Kiddo wants to learn how to code, but I would really need to gauge his interest and follow his energy there. However, they can easily be broken down into concepts he can understand at 5-6 years old.

That led me to thinking I needed to help him understand math concepts at a simple, intuitive level first. If he could relate a math concept to everyday life, and to things that mean something to him, we could build on that. From there, he would need to learn and apply the concepts, and through repeated exposure, he would memorize rules and facts by doing something with them.

I went in two directions with this: utilizing informal math concepts on every day life at home, and a formal math learning structure.

First of all, I found Betty Choi’s blog, and she provided a lot of ideas on how to incorporate math into everyday activities with our kiddos. I got a lot of direction from her post: How to Teach Basic Math for Free Anytime and Everywhere and printed out the PDF and taped it to our fridge. (If you’re teaching math to young kids, download this PDF on teaching math.)

She has wonderful ideas about counting actions (claps, steps, etc.), adding and subtracting toys, multiplying with groups of objects, dividing up food (this is great for fractions too) and applying fractions from recipes. These were great, and we were able to do a lot with them to help make these concepts intuitive. For example, a kiddo who understands how to divide up chocolate chips equally will have an easier time learning division formally later on.

Food division is a lot of fun because you can really focus on the basics of division, with a payoff of a tasty treat. To start, I gathered 10 chocolate chips and asked kiddo to divide them equally so we could share. Kiddos often have an innate sense of fairness, so he carefully arranged them in two rows. At first he made a pattern and tried to make a symmetrical pattern with the other group. That was fine, but he was worried that one person might have more than the other. We played with the patterns by re-arranging them into shapes that were easier to subitize. Five is a wonderful number for this because you can create unique patterns. Next, I asked him to count each group, just to be sure. Once he was satisfied we had divided the chocolate chips equally, we ate them. Nice!

After we had worked on dividing up food objects into equal parts, either for two or three of us, I decided to see how he would manage a remainder. Instead of 10 grapes, I gave him 11 grapes, and asked him to divide them into five equal parts. He started in by making pairs, but then he ended up with an extra. I left him to twist in the wind a bit, to see how he would manage it. He tried adding it to one group, but one group had three grapes while the others had two. He kept rearranging, trying, going back to his original pairs, and puzzling over the extra. Finally, he set it to the side and asked me for help. “I can get 5 pairs, but there is an extra that doesn’t fit, so I just put it to the side.” I praised his thinking because he had just discovered remainders. “This is exactly what you do when you divide numbers and end up with some numbers left over. In division, this is called a remainder!”

Kiddo wondered what use a remainder might be. Using food as a guide, I suggested that if he was the one divvying up the chocolate chips, he could secretly eat the remainder. This is one of the perks when you cook food for others. You can surreptitiously snack as you prepare. This appealed to him greatly. It turns out, stolen edible division remainders are an effective math learning tool.

I also discovered a helpful homeschooler blog from the Natural Math community, Duct Tape Rocket. I got some helpful ideas on games to get kiddos thinking and working on simple programming concepts. After reading some of the posts on the blog, kiddo and I started playing around in the Scratch Jr. program.

We also discovered CodeSpark Academy, a fun app where kids learn programming basics in a simple game format. CodeSpark not only helps kiddos learn about sequencing, but all kinds of concepts including loops and working with stacks. Kiddo would get rewarded for his algorithms, but he got more points when he used constructs like loops. When he was disappointed he wasn’t getting full stars for a task, we had a chat and worked through the concept. He was motivated to achieve more in the game, so he started to use loops in his own work and was rewarded for it. We also spent a lot of time together figuring out how to do LIFO and FIFO tasks in the game.

Next, I formalized what we should cover based on this list from Natural Math:

  • Subitizing: The ability to instantly recognize quantities without counting
  • Counting: Addition and subtraction are based on sequences, dealing with objects one-by-one
  • Unitizing: Multiplication and division are based on equal groups or units
  • Exponentiating: Self-similar structures, such as fractals

Patterns are a clear underpinning shared with all of these concepts, so getting kiddo to work more formally with identifying and creating patterns was a natural place for us to work on. Identifying patterns and groups and performing operations on them can be done with just about anything, anywhere, especially if you are out in nature. Subitizing is also a patterns activity. Thankfully, I had a lot of helpful exercises from my kindergarten no-prep lesson plans, so we were able to move forward with pattern and subitizing exercises for a while.

Exponentiating work involved watching videos and looking for repeating patterns in nature, such as in the veins of a leaf, or in the crystal formations of ice. Unitizing was more difficult. I needed to figure out activities that were appropriate for a 5 year old, so I started to research further.

Adventures in Homeschooling: Fun With Arrays

As we transitioned to math activities that were more engaging for my kiddo, I started to notice similarities and patterns. At this point, I was using the book Moebius Noodles as our primary inspiration for math activities. For example, we would have a lot of fun playing around with body symmetry exercises, where one person mirrored the other. We would estimate height by guessing and then building a tower with Duplo blocks. The tower would inevitably collapse, leading to lessons about structure and making a solid base. We played a “program Dad” game where he would direct me around the house by telling me exactly what to do. We found that using a checkerboard tile exercise mat helped a lot. For example, kiddo would tell me to move forward three squares, then turn one square to the right. We played around with grids, working with numbers or drawing items within the shape.

I am a programmer, so playing with grids make me think of arrays. Arrays are used a lot in programming languages as handy data structures. You can use them to store and access objects that you want to interact with in a computer program. When I was learning about arrays in programming, I found simple examples made sense, but when you added more dimensions or started thinking about performance, I struggled. I had trouble with thinking in abstractions. It took a long time to overcome that. The actual concepts, code and mathematics were simple, but my brain struggled to think about something virtual with different dimensions. Similarly, when I started a linear algebra course, I spent too much brain power getting my head wrapped around how arrays were formed, and keeping track of what number was in what row or column. The actual math was often elementary level, but the abstractions were difficult to grok. I felt that adding in thinking about more than one dimension, and thinking about abstractions in math would help my kiddo develop better math skills. If he could get used to thinking about abstractions I wasn’t exposed to until I was in my late teens, what would that do to his problem solving brain?

We would also look for array patterns around the house. We would examine Duplo and Lego bricks, muffin tins, egg cartons, game boards, crayon organizers, drink holders, watercolor paint trays… the list goes on. There are array shapes everywhere, and we would find them and discuss them. What pattern do they make? What could we call this in math or programming? Soon, kiddo was spotting array patterns himself and pointing them out. Next, I wanted to add a bit of structure to his thinking about arrays. To make things more interesting, I would ask him to identify the rows (horizontal) and the columns (vertical). We would play around with that concept. For example with an egg tray, it is natural to set it down so that it has more columns than rows, because that is how it is labeled. But what happens if we turn it so it has more rows than columns? We would identify an egg and its location: 3rd row, 2nd column, and then move the egg tray. Now it is 2nd row, 3rd column. Did the egg change, or did the “address” of the egg change? Turns out the egg is the same, but the way we describe to find that exact egg can change, depending on our perspective.

Games and Arrays

Since kiddo could easily count to 30, he could easily keep track of rows and columns in a 10×10 array. I printed out a 10×10 checkerboard and we started to play with it. I would ask him to help me determine where the rows and columns were. This took some practice, and I told him that when I was taking linear algebra in university, and then later when I worked with tables in HTML, I would remember that columns were vertical, like columns holding up a roof. Rows I remembered as horizontal, like rows on the ground in a vegetable garden. Columns hold up, rows are planted on the side. Next, we would count, making sure we kept track of the row number and the column number, which is the “address” or location in the array. Once kiddo could identify rows and columns on his own, and find a location when prompted, we started to add complexity.

I would set the checkerboard down, and ask him to locate row 2, column 3. He would take his finger, and count down to row 2, and then he would move his finger 3 spots over. While my brain was thinking of patterns in applied math, his brain was spotting a familiar pattern: games. We transitioned from counting and pointing to making simple games together. Every morning, we would take out the checkerboard, and we added in dice and game play pieces. Using dice meant I needed to expand the size of our array to 12×12. Next, for playing pieces we found Lego bricks, bingo chips, and other objects worked, but we settled on mini ring fidgets. These worked best because they weren’t associated with anything else that distracted us. From there, we would take turns rolling a single die. We both started at top left, just off of the grid, and after a roll, you would count forward to match the number on the die and move your playing piece to that position. We would move row by row from beginning to end. The first person to get to the end won.

Next, we added a die so we had a pair, and rolled both dice at once. The number on the left most die represented the row, while the next number represented the column. Instead of moving through the game board from the first column and moving through from row to row, you had to keep track of the row/column pair. This added a lot of randomization, and could cause someone who was “winning” to get knocked back. Now we were thinking and playing and having more fun. To add more randomization and surprise, kiddo would add in extra objects. If you landed on a Lego brick, you had to count the rows/columns of the brick and move to that spot on the board. If you landed on a different colored fidget ring, you had to start over. If you landed on a smiley face sticker, you could skip to the end. Now we were having a lot more fun, but it was hard to “win” because of all the randomization. To move beyond this, I added in two variations. The first was to get him to create the activities from scratch, and the second was to add in zero-based counting.

We were playing with the emerging array game every weekday morning. We would set up on the floor, and we would play around and have fun. When it started to get stale, I asked him to run the sessions. At first, I just had him tell me the rules of the game, and explain how everything worked. It was often muddled, the rules would change to favor kiddo and disadvantage dad, and the lessons about arrays were completely lost. However, I was pushing for engagement rather than mastery, so I didn’t care. On days when I ran the game, we did it according to rows and columns and reviewed what we knew about arrays. On days he led the array games, whatever happened was what was supposed to happen that day.

At first I was concerned he wasn’t taking anything away from the lessons, but when we played the game the way I had set up, he seemed to grasp the concepts more firmly. The random play was reinforcing what I was hoping he would learn. Even though he wasn’t playing by “the rules”, he was exploring the boundaries and being creative. Math lessons aside, creativity with designing your own game with dad has tremendous value on its own. It was actually reinforcing the lessons, even though it didn’t seem like it at first. He was truly owning the concept and chasing down ideas he had as things in the lesson reminded him of games we played, video games, following recipes in the kitchen, etc. There were also disagreements and lessons about playing fair, being a good sport, and other important issues. It was hard at first to not correct and bring him back to the topic at hand, but I found his brain was working on it, even if I didn’t see it at first. If I could just shut up and be a 5 year old with him in the moment, good things came out of it. I realized he was doing what I was hoping for anyway, he was applying the math. He was taking the theory and making it real.

The next variation was to make it more difficult, and to keep track of rows and columns using zero-based counting. One of my frustrations when I was programming was having to switch my brain from starting at “1” to starting at “0”. Many programming languages use zero as the first number, and I found it hard to adapt at first. When I taught adults to program later on, many also struggled with this. Instead of using your programming brain, you were expending energy trying to count to 10 starting at 0. With kiddo, I am a stickler for starting counts at zero, not one. It makes everything easier for him to have that solid grasp of zero. It helped him with place values, with counting, and it helps him with simple arithmetic. Understanding zero also helps with abstract concepts as well. Since he was familiar with starting to count with zero, and using place values to increase or decrease, transitioning from 1 to 0 based counting for arrays wasn’t that much of a stretch.

Arrays and Muffin Tins

To make this come alive, I looked for kid friendly array activities to explain this better than I could. Unfortunately, I couldn’t find anything online other than identifying arrays and looking at rows and columns. Good activities, but not what I wanted. I wanted kiddo to start thinking about arrays as an abstraction, but add the realism by keeping track of rows and columns to access something stored at each address. I wondered about a cardboard fold out activity, like a mailbox. I talked to a programmer friend, and she said her daughter had worked on a “muffin tin” math activity. Each indentation in the pan was covered with cardboard, and the kiddos would take the top off to discover items in each section of the tin. This is easy enough to do, why couldn’t I do that with arrays?

A muffin tin with paper addresses for each element in an array. It starts with 0,0 at the top left and ends with 4,3 at the bottom right.
A muffin tin set up like an array with numbers representing rows and columns.

With a bit of thought, I came up with a simple activity. I printed out slips of paper with a pair of numbers to represent the row and column, which would cover the indentations of a muffin tin. Under each address, within the muffin tin indentations, I put in a small toy. I started with Lego pieces and one Lego character. Next, I asked kiddo to find the Lego character. He needed to lift up the paper that had the row/column location, look underneath, then put it back and move on. Finally, he found the Lego character. I asked him what row and column he found the character at. Unfortunately, the location papers were scattered, so we repeated the activity, but with more care this time. To add interest, I changed the location of the character, and asked him to write down the row and column on the paper, once he had found the character again. This time, it worked. He was starting to engage. To increase engagement, I turned my back, and asked him to put the character in a new location, and then I would have to find it. He started to have fun.

Kiddo hid the Lego character at a location, and put the paper locations back on top of each indentation. Trouble was, they were out of order. Instead of pointing this out, I pointed along with my finger by moving by address, rather than physical location. Instead of starting at the top corner where 0,0 should be, I started where 0,0 actually was placed, which was somewhere else on the tin. Next I found 0,1, then 0,2 and so on. Some where in the correct location, but some were not. I feigned surprise and said I was confused. Kiddo patiently explained I should start at the top and work my way down. I suggested that if that was the case, he needed to make sure the addresses of each tin indentation was in order. He quickly shuffled the papers around so that the muffin tin rows/columns matched correctly. I then started and worked my way through until I found the Lego character.

We took turns with this activity several times, and he had lots of fun. He would try to surprise me with the location of the Lego character by putting it in the last position so I had to count all the way to the end, or at the beginning so I found it right away. He would put it back in the same location, or he would try to distract me by saying something funny while I was moving through each item. There was a lot of giggling, and when the papers with the row/column addresses got mixed up, he was quick to help sort them again.

The next day, I asked him to set up the muffin tin activity. His job was to put items in each indentation, and then put the correct address slip of paper over top, in order. We had a couple of oopses with 0,0 and 3,4, but with some clarification he remembered how it worked. This time however, we got Mom to hide the Lego character, and then we took turns trying to find it. To begin, we both started at the top left and worked our way through. The next time though, I surprised him with an algorithm. When it was my turn, I didn’t start at the beginning, I started at the end. Then I switched back to the beginning, then back again and so on. I found the Lego character first, since I was using a consistent approach. Next, I checked at the end, then the middle, and then moved back and forth from middle to end, and once again, I found the Lego character first. Kiddo was disappointed and feeling a bit frustrated that I was winning. He accused me of cheating.

This turned into a wonderful teachable moment where I could explain algorithms.

How do you explain algorithms to a 5 year old? The simplest way to describe it for him was that it was a set of steps to solve a problem. We looked at recipes for food we had prepared together, we looked at Lego instructions, and we looked at simple school assignments. Next, I explained what I was doing, that I was using a strategy called Binary search to find the Lego character faster. Since the array is small, it doesn’t give me much of an advantage, but I had lucked out by winning twice in a row. That had piqued his interest. I then explained that he had intuitively used a good algorithm, linear search, and that had worked well. He had started losing the game when he got excited and stopped concentrating. Instead of using a linear search, he was using a random search which is the least efficient. He might choose the same wrong address several times using a random search. That’s not efficient, or as effective. It is more effective and efficient (ie. find the Lego character faster) by using a consistent strategy.

A consistent strategy to solve a problem is another way to think about an algorithm. When you start to lose discipline due to emotions or getting distracted, your problem solving suffers. It’s harder to keep track, it’s easy to forget, and an opponent with a consistent approach will play better.

To reinforce the algorithm idea, we worked together on using each search algorithm. Since it is a small set of data, both linear and binary search were effective. He wanted to try binary search, so we worked together on finding logical places to divide up the data, and then work within those divisions. For example, he might look at the last address first, then look at the middle address. Next, he would move between those two addresses with each turn. He might then change tactics and try a linear search from the first address to the middle. This is a bit tricky for a young mind, because kiddo has to keep track of rows and columns, as well as the artificial divisions we were making in the grid of the array. To help keep track, we used pencils or longer Lego pieces as placeholders.

After a few days, kiddo was doing really well with the muffin tin array game. He was using a strategy to choose an algorithm, and he was comfortable with zero based counting. One day I sat back and watched him. I felt amazement and joy watching him. Not only was he demonstrating a basic understanding of arrays, but he was thinking about computer programming on his own terms. This applied math, or the “why” is absolutely crucial in learning. It was within his skill level, it was relevant to his interests, and it was fun for him.

We do programming work because kiddo has an interest in it. The TedEd Think Like a Coder series was particularly interesting to him. He had discovered this series on his own, and he looked forward to new episodes when they were released. Each episode prompted a lot of discussions about coding and me trying to replicate what they were doing in the story for him on my own PC. Sometimes I would struggle, and remembering to show him my mistakes, we would talk about how my code wasn’t working, or when I needed to look something up or ask for help from a colleague with better coding skills.

Programming is also an easy place for me to answer applied math questions, and to talk about day in the life applications of math. Sometimes the only way I can start to answer a “why do we do this” question is by working it out in code to show him an example. No, we don’t learn math for no reason at all. Yes, some people work with math every day.

Making it Real With Code

Looking at array addresses of rows and columns as zeroes felt arbitrary to kiddo. While he understood it and got it right most of the time, it really felt like one of those “grown up” things that didn’t make a lot of sense. Isn’t zero just another way to describe “nothing”? To help with this, we worked together on our home address vs. that number represented as a quantity. Next, we looked at my phone number, and then represented it as a quantity. Then we added some numbers together, which made a sum. What was different? Kiddo explained that the number in our home address and in my phone number stood for something unique, so people could find it or phone me. But a quantity was an amount of objects. A sum was calculating the total of groups of objects. We played around with this concept for a while, and stuck to the idea that an address for your house is a sort of unique label. Our neighborhood has free standing mailboxes that are labelled with a unique number that is assigned for each house address, and the contents are accessed by a key. To get the mail from another part of the world to an individual here, depends on various unique number labels.

Next, we looked at array addresses. We aren’t counting items, we are using the location in an array as a unique label. When we use zero-based counting, “0,0” is the first box in a grid. If we use one-based, “1,1” is the label. But what if we used names? How about emojis? Could we use sounds? Absolutely! We could use anything at all, really. However, number labels that follow a logical pattern work well. They are efficient and effective since they are easily understood.

To take this further, we opened up a language interpreter on my PC called irb, for the programming language Ruby. Kiddo had visited a local fish hatchery, so I typed in the following:

fish_array = ["trout", "pike", "perch"]

I explained that this was a simple array of words for fish. We read through them together I asked if he could help add in more. He suggested “walleye”, “goldeye” and “sturgeon”, so I added them to the array. We now had this array of strings, or words for fish:

fish_array = ["trout", "pike", "perch", "walleye","goldeye", "sturgeon"]

Next, I told him that I was going to use a bit of code to access the first fish in the array. I typed in:

puts fish_array[1]

and the interpreter printed this to the screen:
"pike"

“Aha! Dad! That’s not the first one!”

What do I need to do to fix it?

“You need to type ZERO, NOT ONE!”

I changed the code and tried again.

puts fish_array[0]

the interpreter printed this to the screen:
"trout"

That worked! You fixed the bug!

Kiddo really enjoyed this. We were controlling the computer, and it was important to keep track of what you were doing, because one simple error could give you the wrong answer. I explained that in computer programming, we often call this an off by one error.

We played around with this for a while, adding in array indexes that didn’t exist, to see what error would be produced. Then, I created a larger array, and used an iterator to print through each item, rather than typing in an address. Kiddo liked the idea of looping, we could do things quickly and efficiently, and you didn’t necessarily have to figure it out yourself, you could get the computer to determine what was correct for you.

We had fun. He wasn’t learning these concepts, but I was exposing him to some simple programming basics and explaining what we were doing. He had opinions and ideas about the content of arrays, and what to print out, and I would follow his lead by adding in conditionals, branching, etc. He then asked an interesting question. Essentially, he wanted to know if we could have an array that was made up of arrays. “Of course!”

I muddled around in the code to generate an array made up of arrays, and showed him how we accessed elements in an array of arrays. This started to look to him like our muffin tin game, since we needed to keep track of more than one index or address number. After a while, we had the code looping through each array within the array and printing things out, but that was getting complex and he was getting tired.

I sat back and I felt a bit shocked. Here we were, playing around with concepts I had struggled to learn when I was nineteen or twenty, and my 5 year old kiddo had grokked the basics. He could follow the form, he could play and have fun, and he understood that things could be stored in arrays, whether they were in muffin tins or mailboxes (physical), or in computer memory (virtual).

Adventures in Homeschooling: Eliminating Fear From Learning

In my first year of university, I had a professor in a business class who was a big fan of W. Edwards Deming. Deming is credited as the founder of the quality movement, particularly in manufacturing. Deming published a list of principals called the 14 Points, a list of approaches to management to help create a quality-focused working culture.

They are incredibly useful, even today. However, Point 8, “Drive out fear” puzzled me and my classmates. This is a workplace, what could people be afraid of? They are professionals, they are doing work they have expertise in, and helping the company succeed. What could possibly make people afraid? I have to admit we snickered a bit every time it came up. “BOO!”

Our patient prof explained that there was an authoritarian management style where bosses and managers rule by fear, and use it as a motivator. He agreed with Deming, and felt this was counterproductive, since fear causes people to avoid talking about problems, and motivates them to game systems. You will have a hard time finding out the truth from people who are afraid. They will try to spin narratives towards something that reflects positively on them, rather than talking about problems customers face, for example. Under a fear based system, eventually, the system will be broken and customers will suffer, and decision makers will likely find out when it is too late. (This is often referred to as a theory x management style.)

However, there is a lot more to fear in the workplace. One of the most common underlying issues I dealt with as a consultant was fear. People have a lot of fears in the workplace, even in consensus-driven, people-focused workplaces. People are afraid of losing their jobs, or of not moving up in an organization. They are afraid of losing money or status, and what that means in their professional and personal lives. They are afraid of making a mistake. They are afraid of certain kinds of changes, and they are afraid of upheaval. They are afraid of certain tasks, and certain aspects of their jobs. They are afraid of certain people, sometimes for subtle reasons. They are afraid of looking stupid, or not knowing an answer. They are afraid of asking certain kinds of questions, and they are afraid of providing blunt, honest feedback. They are afraid of disruption, or of disrupting something themselves.

Imagine what all that fear is doing to their well being and ability to think clearly and carefully about problems, let alone what it is doing to overall team productivity.

In my experience, the less fear, the more effective a team is. In fact, one of the most effective things a team can do to build up workers and be more productive is to reduce sources of fear. Fear steals so much energy and obscures good problem solving communication. You can’t deal with all the fears we have in the workplace, and those change due to environmental conditions and events. However, when you create a culture that drives out fear, really good things happen. People are happier and more productive, and everyone benefits from that. If all I do is help a team reduce their fear, and that is all I am able to do, that team will be more productive when I move on to another project. Drive out fear is a powerful philosophy.

…one of the most effective things a team can do to build up workers and be more productive is to reduce sources of fear. Fear steals so much energy and obscures good problem solving communication.

When kiddo and I started doing homeschooling together, I observed similar patterns in him that I had seen in people in professional settings. There was a lot of fear there at times. He had similar fears. He was afraid of getting the wrong answer or just making a mistake. He was afraid of answering a question in case he got it wrong and felt foolish. He was afraid to ask me questions that might reveal he knew less than he was letting on. He was worried about my reactions, and how we dealt with conflict.

Instead of being an outside observer seeing patterns in a team, I had to face up to the fact that I was the source of a lot of his fear. That hard fact requires a lot of self reflection and working on my own behavior. It’s hard, but it’s a reality.

Observe the Child

The first thing I started to do was watch kiddo carefully. When did he stop engaging, and when did that start? When did his behavior shift from having fun to going silent? What was the source? Did he need a break? Did he need to go to the washroom? Was he just having a bad day? Or was there something in our approach together that was making him uncomfortable? When did things shift? Was it a direct question? Was it something he wanted to hide from me? Did we shift from fun to something decidedly unfun?

It was a lot of work, and I had to try to filter out typical child behaviors from those that were issues we could address. Kids get bored, or distracted, or just might not feel like doing schooly things today. To observe him while working with him was hard. I also watched him when he worked on learning apps. Learning apps tend to be based on teaching approaches, and are heavily influenced by the educational experiences of the app developers. As a result, the same patterns will appear when they are working on apps as they are in person.

I started to note the patterns where he felt pressure:

  • Direct questions about his knowledge on a topic
  • Closed ended questions
  • Worksheets
  • Starting a new topic
  • Trying an exercise on a new topic
  • Reviewing his work

I also noticed patterns in our approach where his behavior would shift from engaged to disengaged.

  • Dad talking too much
  • Spending too much time on an exercise
  • Closed ended worksheet questions
  • Time pressure

A lot of these had underlying fear issues. Many of these were a direct result of my leadership/teaching style. Gulp.

Observe Yourself!

Next I had to take a hard look at myself. Kids are kids, and we can’t expect them to manage their emotions or be as self aware as adults. I couldn’t expect him to change his behavior that much, I had to look at what I could change to support him.

One thing I noticed was my body language, my tone of voice, and how those could be sources of fear or discomfort for him. I’m bigger than him, so I would inadvertently tower over him when he felt on the spot, asking a question. Or, I might raise my voice while repeating a concept that wasn’t clicking for him. I worked on my body positioning and trying not to raise my voice, or spend too long with “teacher voice” explanations.

In my software design work, I found that body language can be subtle and influential. In my design book, I talk about how during user tests of new software designs we can unintentionally encourage test subjects with subtle body movements. We might tilt our head towards the answer we want, or shift our body slightly. We might frown when someone does something when we hope they do something else, and smile when they do what we were hoping they might do. We might tap a pointer or pen towards the answer we want.

This was a lot more difficult, but I started to work on being more bland and flat when I asked questions, and I resisted any movement that might hint at what the answer might be. I knew it was working when he would stop and observe me more carefully before committing to an activity or answer. He was looking for the cues that weren’t apparent anymore. In fact, we even had a conversation or two about it, and he admitted to gaming the system by watching my tells. Thankfully, we were able to turn this into a humorous activity and have some fun with it, which contributed to him feeling safer and more secure in his learning with me.

Make Sure Kids See You Make Mistakes!

I knew we were making progress, but I still felt like kiddo was feeling pressure from my behavior. Fortunately, I have skilled professionals I can talk to. My friend Dr. Katie Crossman is an education expert. Katie has elementary school aged kids as well, and we would share experiences as our respective kiddos were learning at home. When I talked about trying to drive out fear from our learning experiences, she suggested I point out when I make mistakes. Katie talked about her knitting hobby, where you rip out sections you have already knitted, and start over if you have made a mistake. (This is known as “frogging.”) It can look frustrating to an outsider, but it is just part of the process. Katie told me that when she discovers she needs to “rip it”, she calls over her kids to show them and talk it through. There are lots of mistakes we silently make around the home, and if we stop and show our kiddos, it is a good learning experience.

There are a couple reasons this is important. When kids are homeschooling, they are learning things that we as adults learned many years ago, and the knowledge is second nature to us. If we ask them a question, it might be a challenge and they have to think, but to us, we have the answer instantly. Since they aren’t around a group of their peers, it can make them feel like they are always wrong, and we are always right. For example, think of teaching a simple math concept like 1 + 1 to a smaller child. They pause and work through, while we answer instantly. Or, they may ask us out of context of learning, and we just know the answer, without realizing they might be testing us. We’re adding pressure, even though we don’t mean to, or are unaware of it.

The other opportunity we have with showing our mistakes is to model our behavior for them. What do we do when we make a mistake? How do we solve the problem and move on? Do we get frustrated and give up? Do we research and try again? Do we call in an expert if it is a problem we can’t fix? These are extremely important lessons that take a lot of thought and self discipline to master. (Note, surprise home repairs are not always a good learning experience unless you want to model frustrated noises, angry tool selection and swear words.)

My kiddo and I started this together, and he was shocked at first. Dad can make mistakes? Wow! Once we got over the initial surprise, I would tell him stories about mistakes I made at work, or presenting to a crowd, or working on hobbies. I shared one story of when I made a mistake woodworking with a friend. We were making a workbench for my garage, and I was supposed to drill out holes to counter sink bolts. I drilled out the holes to countersink in the wrong spot, and it looked awful. My master cabinet maker friend sent me out of the shop to get coffee. While I was gone, he ran the boards through a planer to sand away my mistake, then had me do it again. I was surprised he could figure out how to fix it, and he laughed and said: “That’s the difference between an amateur and a professional. A professional knows how to fix their mistakes.” That story resonated with him, and this phrase became a bit of a mantra in our home.

I also told of embarrassing mistakes (I once presented to a group with a line of whiteboard marker drawn across my forehead), stupid mistakes (I misspelled an item in an inventory system as a joke, which muddled up the counts), and expensive mistakes. (Early in my career I made a mistake that cost the company thousands of dollars. I was sure I was going to get fired, but my manager said, why would he fire me after spending thousands of dollars training me not to make that mistake again?)

Thanks to Katie’s advice, we started to create our own fearless culture about working with mistakes. Talking about mistakes, regaling stories of mistakes of the past, reading stories about mistakes, pointing out my mistakes and walking through how to solve them, and most importantly not punishing in any way for kiddo’s learning mistakes.

Create a Safe Learning Space

Environments are crucial to feeling secure and productive. Since we were at home, we started out by dedicating a learning space that provided consistency. I worked with kiddo to put up posters he found helpful, and to have our materials nearby. He added his own personal touches and felt like he owned the space. Previously, we had been much more ad hoc, and task switching from play to learning could be tricky. Beyond that though, I wanted to make sure we had a learning relationship where he could feel comfortable asking any question he wanted without judgment, and mistakes weren’t viewed as a negative thing.

I talked to a teacher friend, and she suggested that I create “judgment free” activities. Turn kiddo loose on an activity, and don’t evaluate it in any way. Reward for doing something, anything, even if it doesn’t resemble the goals of the activity. One of her favorites is daily journal writing. Get kiddo to write down whatever they would like, and reward them for doing the thing, not on the actual contents of their writing. This worked well for the most part. Sometimes he would scribble and doodle, other times he would draw a picture and write a few sentences. Or he might write down birthday gift ideas. On bad days, I encouraged him to write down his negative feelings about me, which he didn’t need to share. He could keep his thoughts private, or, if he was more comfortable letting me know how he really felt, he could write it down. No matter what he wrote, I didn’t judge it, and only read it if he wanted me to.

One important aspect of a safe learning space is to create safety net that encourages mistakes that don’t have overly negative consequences. I discussed this with an earlier post: Fail Fast and FAFO. It can be as simple as putting down plastic to protect surfaces from messy experiments, or as complex as a discussion about a mistake with a hard consequence.

Feeling Psychologically Safe

I described approaches to feeling psychologically safe in learning in this post: Adventures in Homeschooling: Fail Fast and FAFO. There are a couple of areas related to fear that I wanted to expand on. First of all, with the fears themselves, it is important to help kiddos identify their sources of fear. Sometimes those sources might be surprising, and sometimes they might feel a bit trivial to an adult. However, it is absolutely vital to not diminish or invalidate their fears. Imagine fears you had as a child. No matter how irrational they might seem now, they feel real, and they are stealing energy away from being happy and productive in things kids need to be happy and productive in. Whether that is play, daydreaming, solving a problem or learning with you. Identify, validate and discuss fears. Don’t dismiss them or undermine them.

The second area I want to talk about today is in creating a psychologically safe home environment. This brings us to philosophical or values-driven approaches to parenting and home life. My partner and I like the positive parenting approach. It seemed to match our values and the kind of environment we wanted for kiddo. In short, we approach with a warm, kind, yet firm approach. There is structure, but we don’t enforcement it through fear or demanding compliance. There are consequences for actions, but we want to make sure that they are understood and developmentally appropriate. There is respect, but it is earned rather than demanded. Most of all, we look at filling up self-esteem at home. The analogy of a “self esteem bucket” is a popular one. The way we interpret it is that when you are out in life, there are lots of things that can get you down. Your home is a refuge where you can always go to recharge, and part of our job as parents is to help kiddo fill his self-esteem bucket when he is with us.

While all this sounds great on paper, and we read books and attended workshops and worked on this approach, we had to adjust and make it our own. First off, as Xer parents, this is the opposite of how we were raised. Secondly, your kiddos really determine your path. What seems good on paper needs adjusting due to the needs of your own kiddo. However, even when we get it wrong, we work on creating a safe environment. We want kiddo to know that we are his biggest fans, we are always in his corner, no matter what. There is nothing he can do or get wrong that will make us stop loving him or feel supported. We want him to be fearless about solving problems and being responsible for figuring out his own life. That means he will get things wrong, he will do things we don’t like, and he will fail at things. All of these things are important to grow through, and our job is to help support him through that.

A psychologically safe learning environment means that the consequences from learning actions don’t come with moralizing or judgment. They are learning opportunities, and he is always accepted, always supported, always safe, and always loved. We try to handle conflict in supportive ways. When voices get raised, tempers flare, and we don’t respect our own approach to working together, we own up to it, apologize and work to do better. In fact, these homeschool conflicts led to a family motto:

We are a problem-solving family.

We use science, knowledge, skill, respect and empathy to work together to try to solve any problem that may come up. We often get it wrong, but we really try to work together to focus on the fact that mistakes help us learn!

Reducing Math Anxiety

I watched my kiddo when we were doing math, and I started to notice patterns where he would show signs of anxiety. He’d stop smiling, he’d stiffen up, he might go quiet, or he might start to distract to get out of doing something. At first I found this frustrating, but eventually I realized that these were important cues. At first, this would happen every time I tried to pose a math question. “How many fingers am I holding…” or “How many do I have if I add these together…” or if I put a worksheet in front of him. He might enjoy it at first, and then I would see him tense up as he answered the questions. I realized that these questions and activities are high risk for a kid. You are either correct or not. When we worked with other subjects like literacy, there were key differences. We:

  1. don’t expect perfection and exact precision.
  2. reward for engagement and effort.
  3. make room for individual ideas and creativity.
  4. are patient when a concept isn’t mastered right away.

When you compare how we teach math and how we teach kids how to read, the difference is stark. Imagine if we were working on letter sounds, and we told them they were wrong if they pronounced the “short a” sound slightly incorrectly? What do we do instead? We reward effort, we gently correct, and we give them lots of time and room to improve with practice. On the other hand, what do we do with math? We present them with a question, and if they don’t get it 100% correct, it is wrong. That’s it. While it’s important to have precision in math, we put demands on kiddos that they don’t need before they are ready.

Here is an example from an online school experience we had. Over the course of a week, kiddo was given two assignments that he could work on every day. A writing assignment, and a math assignment. His writing assignment ended up being a short “five finger” style with a topic sentence, three descriptive sentences, and one that explained his feelings on the topic. It had a run on sentence or two, some missed punctuation, and a couple of words were spelled phonetically, but incorrectly. What was his grade? Top marks. He met the rubric for the assignment, and got a big thumbs up. While he had some small mistakes, those were fine for his level, and would get dealt with as he learned more over the next couple of years. His math assignment though, was a different story. There were 25 simple arithmetic questions to complete each day, with a total of 100. He got 1 of them incorrect, and the assignment was returned to him, and he was asked to correct that one question. How do you think that made him feel? Was it necessary to demand perfect precision in a math assignment when no other subjects in first grade are marked that way?

I described some approaches of how we overcame math anxiety in this post Adventures in Homeschooling: Embracing Math Mistakes. While the topic is mathematics, these approaches help with any kind of topic where there is learning anxiety.

Reducing Writing Anxiety: Drafts vs. Final Versions

Math anxiety was the first hurdle to overcome, but similar fears cropped up in literacy and especially in handwriting. We are proponents of learning good handwriting skills, both printing and cursive. More importantly, kiddo is extremely motivated to write. He loves the Story Pirates podcast and takes part in their workshops and works on his own original stories. Handwriting helps this process, but it is challenging to learn, and it can take years to get complete mastery. Beyond handwriting, writing itself is hard, and you almost never get it right on the first try. When kiddo would get frustrated with his letter writing practice, or that something he was trying to write wasn’t clear, his Mom and I both talked about “drafts vs. final versions” in writing. Both of us are pro writers, and neither of us have submitted something to an editor and had them publish it verbatim. We’ve always had to revise a draft, often several times, before it was ready to print.

When kiddo struggles because he needs to redo writing work, we remind him that he is working on drafts, and the final version will emerge. He shouldn’t be overly focused on trying to get it right the first time, he should focus on getting his ideas and creativity out. Then you start editing, and working on your draft. Once you are happy with it, you submit it. Creating and enhancing “drafts” of writing feels safer, there is less pressure to get it right the first time, and it models real world writing. You almost never get it right the first time, and pushing to at least one draft after your first attempt always results in a better final product. This has created another family motto:

Is it a draft or a final version?

It turns out that thinking about checking and revising your work isn’t just related to writing. We can apply this to all sorts of work, and it takes the risk out of it.

Iterate towards a solution.

Drafts in a non-writing discipline can be thought of as iterative or incremental solutions. If you need to, you work through a few versions until you finalize your work. This isn’t a sign of a problem, it’s a sign that you are human and you don’t need to be perfect.

When you work in software development, you almost never get anything right the first time. In fact, because working over time towards a solution is so inherent in STEM, there are entire software development processes related to iterative design and development. Rather than feeling pressure to come up with the correct solution in a hurry, like a timed math test, you are far more productive, not to mention a lot faster and efficient, if you iterate towards a solution. You get the right answer, but you take the time to use the right problem solving approach, and you get it wrong a few times before you get it right. Over time, the simpler patterns that you use over and over become second nature, and you focus your energy on the really hard problems.

This mindset works extremely well for kiddos who are learning. We want the right answer, but going slow to go fast and working through and learning from mistakes takes a lot of pressure off of them. If they don’t feel like they have to get all the answers correct the first time, they can actually slow down and learn from their mistakes, rather than memorizing answers out of fear of failure. Iterating towards a solution rather than passing or failing takes a lot of the fear out of learning. It is also much more realistic in the workplace. I almost never have to urge a new grad to work more quickly. In fact, they usually come out of school feeling like they have to get the correct answer as quickly as possible, and that is counter productive. They rush, they are full of fear about getting the wrong answer, and that gets in the way of learning and productivity. It also slows everything down. When people rush and try to get the correct answer quickly, it creates extra work and rework, and it is incredibly disruptive. Iterating and learning as you iterate is a vital skill to learn, and it helps people feel like they can be human and make mistakes safely. Furthermore, many mistakes lead to innovative solutions, so they are a vital part of the process both in learning and in product development.

Curiosity and Research

Another area we try to foster is for self-directed learning. What do you find interesting? What do you want to learn about? What aspect or thread of what you have been working on do you want to explore? What topic has cropped up that you want to look into further? We then look for resources on the shelf or online. Sometimes these end up as multi-day projects if kiddo has a learning itch that he really needs to scratch. Sometimes a single video or article is enough to satisfy his curiousity.

The trick here is to encourage learning on whatever the topic might be, even if it seems unrelated. That can be a bit jarring when you are teaching a particular topic and that causes an unrelated learning urge. It’s hard to be flexible and let go of that lesson and instead follow the energy of the kiddo. The benefits are amazing though, learning becomes more interesting, and they start to take responsibility for their own education. They also get their own way, which is important to them. Interest in a topic is one of the most powerful learning motivations. As a home school parent, I feel a responsibility to encourage that behavior, since it will serve kiddo well throughout their school career, and as a lifelong learner.

Thankfully, there are a ton of resources available thanks to technology. You can watch world renowned experts on videos, you can take part in online workshops and classes, you can play related games, you can download materials, or order manipulatives and books online, delivered to your doorstep. You can watch reels on social media, you can follow hashtags, and watch livestreams of nature events or animals. It is mind boggling how much technology can be used for research and learning. Tech is your learning friend, if you use it that way.

Engagement over Mastery

I have become a big fan of modular learning, and that has influenced our homeschool approach. Kiddo has unique needs, and he thrives when there is a balance of structured and unstructured learning. Modular learning also fits how we learn as adults with on-the-job training, attending conferences and workshops, getting certifications, etc. Both of his parents have changed careers, and undertaken training online and in-person to facilitate that. We’ve taught him to treat technology as a learning tool in addition to an entertainment tool, and it fits his personality. We discovered Modulo App, and that has been a huge help for us as we plan out a course together with learning, and look for hands-on tools and ideas we can actually apply to learning.

While we really like Modulo App and have utilized it to help, there is one thing they highlight that I disagree with. They talk about a mastery approach to learning:

“In a mastery-based approach, learning is personalized, students learn at their own pace, sequentially, take as much time as they need to fully master one concept before moving on to the next concept in the sequence, and the educator takes responsibility for the outcomes. In 1-1 mastery-based learning, one tutor supports one student through this approach, customizing the learning process to fit their pace and unique learning modalities.”

This is an area that my experience has caused me to disagree with. In fact, I prefer repeated exposure rather than pushing to mastery. This is especially true in early elementary when developing literacy skills and math number sense can take years to master.

To be completely honest, I find Bloom overrated in general. We are also not a family who respects hierarchy or authority that much, and none of us like being told we can’t do something. My responsibility as kiddo’s learning coach looks like this: if he wants to learn differential equations at 8 years old, then it is my job to figure out how to explore the topic in terms that he understands. I make the differential equations relevant to him, explain at his current level, and then create activities that are within his current math skill, with just enough challenge to help learn. If it’s too much, we set it aside and try again. We despise gatekeeping around learning. We value trying and failing, trying again, trying a different approach, leaving it and coming back to it, etc.

In our experience, pushing to mastery too soon is another source of fear and anxiety, at least in our household. Instead of pushing for mastery, we push for engagement. A lot of learning theory overlooks the interest levels of the kiddo who is sitting there trying to do the work. It’s all well and good to use modern approaches with scientific underpinning, with relevant, fun, hands-on activities that are rich and in safe, supportive environments. If the kiddo isn’t interested in learning though, you aren’t going to get very far. However, we may start a lesson with a completely disinterested kiddo. In fact, this can happen more often than we might care to admit.

If kiddo isn’t interested in a topic at first, it is my job to help him. I do this by trying to make activities and lessons fun and relevant. I draw from his interests such as Minecraft, Pokemon, Bayblades and video games. I also try to get him moving and use manipulatives, or explore with software. I try to use humour and make things interesting. If I get it right, he transitions from disinterest or downright shutting down on me to some form of engagement. If he gets the gist of the lesson, and then makes it his own, then we are on the road to mastery. If I push for him to memorize facts or to repeat until he can show mastery, kiddo will shut down and we won’t make much progress. Or, he will memorize facts that help in the short term, but are quickly forgotten because he hasn’t understood the underlying reasons for what the lesson was. For example, memorizing words in a book make it appear that he is reading fluently, but moving to a new book he now struggles with, shows he hasn’t developed mastery yet. Or in math, he may move around a number line and get the correct arithmetic answers, but a few weeks later, he has forgotten how to do it because he wasn’t trying to solve a math problem, he was gaming a manipulative.

Instead of pushing for mastery, we push for engagement. A lot of learning theory overlooks the interest levels of the kiddo who is sitting there trying to do the work.

An exploration-based approach to learning, coupled with aspects of self-directed learning or unschooling means that kiddos are going to come up against learning lessons that are beyond their current capabilities. That’s fine, and that can be managed in various ways. If they are really interested and committed, often they will surprise you and grasp concepts that curriculum systems gatekeep for later years of school. Other times, they get exposure, they try, they realize they aren’t ready, and you file it away to try again later. Mastery appears in time, and that is something you watch for and encourage. After a while, mastery is the consistent observed behavior in a topic, but it also has all this extra richness around it that experimentation, fun and time passing can add to it.

Any kind of pressure, no matter how well meaning, is important to identify and push out. Instead of correct behavior and mastery, watching kids make things their own and grasp the underpinning theory is much more important to our learning. Even in cases where educators encourage children to “find their own way” or figure out their own way to solve problems can be a source of stress. Instead, it is something I watch for and encourage when I see it. When it doesn’t happen naturally, I provide a variety of approaches to solving a problem, and they develop preferences, and eventual mastery in several approaches. This takes time, and requires breaking up the materials, rather than focusing solely on a topic and not moving on until they have shown mastery. Furthermore, sometimes a topic doesn’t click at the time, and falls into place weeks, months, or even years later. That’s how we all learn, and how we all keep learning and find it interesting. “You learn something new every day” is often related to something that you didn’t understand in the past, but repeated exposure in different ways leads to eventual understanding.

Bottom line: when mastery appears, encourage it, but don’t enforce it. Engaged kiddos will learn a lot, even if it isn’t directly related to the task at hand. Kiddos who display mastery quickly may have memorized patterns and not grasp the underlying material. I prefer to follow the energy of the kiddo and see what happens over time.

Context and Comprehension

One other thing I use to change the game for him is context.

In math, “2 + 2 = 4” is only valid within the correct context. It isn’t immutable, no matter what the hardcore education people like to chirp on about. Things are only valid or invalid in their context. To break the anxiety and pressure cycle, sometimes we brainstorm around meaning of math facts. What if “+” meant something else? How would I explain this to an alien? Then I show kiddo when ” 2 + 2 = 4″ is false. If they are integers, it is correct, but if they are strings, “2 + 2 = 22”, and if they are floats, “2 + 2 = 4.0”. I have spent a lot of time on the symbology of math, and how we can challenge those ideas in fun or interesting ways. “Right” is only correct in the right context, and being able to turn that context switch on and off is extremely important. In the real world, understanding context is vital, because if you leap to a solution by just looking at the symbols, you usually get it wrong. Slowing down and getting context, asking clarifying questions, reading everything, etc is important. Once again though, to flip the script, I will ask for wrong answers only first, and see if we can devolve into silliness to get the brain going. It might take hours, days or weeks for this transition, if my experience has anything to show for it.

Understanding context is important, because correctness is completely context dependent. With math symbols in particular, computer programming is a domain where the symbols change. Since my kiddo wants to learn to code, we show him the differences. For example, “x” is the traditional symbol for multiplication, but in many programming languages, it is a “*”. The equals sign “=” is often an assignment operator, and is frequently changed to double equals “==” when programming. As a result, “1 x 1 = 1” isn’t going to work in many computer languages. Instead, it would look like “1 * 1 == 1”. While the meaning is the same, the symbology is different.

Context discussions are important for solving word problems in school, for developing critical thinking skills, and understanding the difference between facts and opinions. There is also a nice side effect: they take the sting out of being wrong. One fun exercise when kiddo is disappointed in getting the wrong answers, and after we review work and he figures out solutions to what he missed, we have philosophical discussions about what it means to be right and wrong. Under what context would his answers be correct? What if the symbols meant something different? What if we were on a backwards planet? What if we had a disability or a challenge that made things appear different to us than our teachers? What if it was a planet run by kids?

Instead of getting caught in a morass of moral relativism or confusing absurdly harmful opinions as valid as scientific fact, we explore the context around meaning. Ok, so you got most of your math questions wrong, and you learned what you missed, but now, can you think of how your approach might be correct? Under what circumstances would this not be wrong? Or, maybe you misinterpreted directions and wrote a position paper on the wrong topic. Your arguments were cogent, your writing was clear, but you missed an important detail. How do you learn from that? How can you re-use your existing work for something else?

Another side effect of these discussions is that it really pushes you as a teacher to understand the theory behind the learning. That also means that kiddo is trying to make sense of concepts as well. For example, you may understand how to multiply fractions, but do you know why it works? Can you explain what is happening in real terms? Context shifts force you as a learning coach and kiddo as a learning machine to start from first principles. Understanding context and meaning leads to much deeper comprehension, which leads to a better set of knowledge as a lifelong learner and problem solver.

Real World Examples

A lot of times in school we are encouraged to memorize facts and formulas and produce correct answers in a short period of time. This looks good on exams and on metrics regulatory bodies use to evaluate learning, but it doesn’t encourage comprehension or experimentation. “But Why???” is an extremely powerful learning tool. “Why do I have to learn this? When will I ever use this as an adult?” are great opportunities for us to explain why it’s important to have these skills. Many times we don’t know ourselves, so it’s a great chance to say: “I don’t really know. Let’s research and learn together!”

Thankfully with technology, we can get these answers, either through using our mobile devices or a PC. We can find real world experts, we can find lots of explanations, and we can find real world stories where people have used that one thing to do amazing things in their jobs, for research, and sometimes for all of humankind. Real world examples also help put context around learning, but more importantly, they can inspire us. We can find people who we can relate to, whether it is someone of a similar gender, ethnocultural background, or just someone who we like, their stories can inspire interest and a desire to learn more. These stories that connect us to people that connect us to our curricula and to our daily learning are perhaps some of the most powerful motivators of all. When you hear about their doubts and fears and what they did to overcome them, and how they make a topic come alive, it’s exciting for kiddo and adult learning coaches alike.

It’s not so scary when a cool person you found online overcame their fears and challenges and applied something you are trying to learn in interesting ways.

Adventures in Homeschooling: Fail Fast and FAFO

Fail Fast

In software development, there is a programming philosophy called “fail fast”. The idea is that you start by generating an immediate and visible failure, and then you add just enough code to fix that failure. This is a paradigm shift, since normally in software development you write code first, then test to see if it works. Both approaches work, but failing fast has the advantage of helping you be more proactive in developing reliable software, but it also has a side effect: confidence.

Here is an example, from a fail fast software development approach called Test-Driven Development. You want to write some code for a mobile gaming app, and you have your IDE (Interactive Development Environment) ready to go. You’ve sketched out some screen designs, and you want to work on initial game play by placing an object on the screen that can be interacted with. Instead of writing the code that starts drawing things on the screen, you write a test for that code. Then you run the test, and of course it fails, so now you start to write the program code to get that test to pass. It might take several quick attempts of writing program code for that test to pass. Next, you add some variation and elaborate on that simple test by adding more.

Once you are satisfied with your combination of program code and tests, you proceed with your program development. Again, write a new test first with no corresponding program code, run the test, watch it fail, then add code until it passes. After a while, you have a suite of tests that you can run when you change your code, to verify that you haven’t broken existing functionality. That suite of tests provides confidence that allow you to make simple changes, but it also makes you think more about writing code that is more reliable as you are writing it. In short, the computer provides you a level of safety before you commit a program to a build and deliver it for people to look at. It feels really weird at first, but your brain makes the paradigm shift after a while.

FAFO

FAFO, or fucking around and finding out, is a popular term in online culture, but it also applies to learning. In fact, much of learning is about fucking around and finding out. Kids constantly do this. They try something, they observe the effects, and they learn and move on. Adults do this too, and not just when they engage in crappy online discourse. The scientific method, or hypotethico-deductive model is a formal, powerful, peer reviewed version of FAFO. FAFO, when it is safe, is a fantastic learning tool, and it comes completely naturally. As kiddos, we touch things, we taste things, we poke them with a stick, and we squeal and run away when things go awry. Trying, observing and adapting is crucial to learning. When you start adding knowledge and facts, FAFO gets squeezed out.

In childhood learning, we put a lot of pressure on kids to get things right. Instead of putting a worksheet in front of them, encouraging them to write out answers, then grading them on an answer key, how do we get them to fail fast and build their confidence? For me and my kiddo, using play and technology helps us fail fast, so we build confidence and explore in our learning, before committing to a correct answer. FAFO is a great learning tool, but it’s high risk when you use worksheets. You have to commit rather than explore and find out. That ability to explore wrong, right and indescribable answers before committing them to get graded is key.

…using play and technology helps us fail fast, so we build confidence and explore in our learning, before committing to a correct answer.FAFO is a great learning tool, but it’s high risk when you use worksheets. You have to commit rather than explore and find out.

Feeling Safe is Crucial

Failing fast in software development is possible when you have a safety net. FAFO is fun and a great learning approach when it is safe to do so. It turns out that other things like productivity, quality problem solving and providing feedback also require safety to be effective.

In the corporate world, there is a lot of talk and training about creating psychological safety in the workplace. In essence this means you create a culture and environment where people aren’t afraid to ask questions, make mistakes, or speak up when something is wrong. A psychologically safe workplace isn’t about enforced or toxic positivity, in fact, it is a place where problems can be confronted without punishment. Criticisms about product can be raised without also feeling forced to offer solutions. Outrageous ideas are welcomed and brainstormed together. Tough feedback, especially to leaders is welcomed. The people who need to hear the hard truths welcome hearing those hard things because it makes the product and the workplace better. The article What Is Psychological Safety at Work? How Leaders Can Build Psychologically Safe Workplaces articulates this well:

“Psychological safety at work doesn’t mean that everybody is nice to each other all the time. It means that people feel free to ‘brainstorm out loud,’ voice half-finished thoughts, openly challenge the status quo, share feedback, and work through disagreements together — knowing that leaders value honesty, candor, and truth-telling, and that team members will have one another’s backs.”

In my consulting work, I found that high performing teams had a high degree of psychological safety. They could try and fail without judgment, they could provide brutal, but important feedback without fear of reprisal, and they handled conflict well. I also noticed this in training sessions, especially with corporate clients. When I would set up in an office and participants in the company would start to trickle in, I could sense the fear almost right away. They were also afraid to take part in any of the group learning activities, because they were afraid of failing, and then being judged or punished for it.

In many companies, if management was around in the training room, people were extremely tentative. They didn’t want to answer questions or participate in the vital learning activities. If management left the room, they started to participate. I put a lot of work into my courses to make people feel safe to do whatever they needed to do to learn, as long as it was respectful of those around them. I didn’t always get it right, but I worked at it. Two instances stand out in particular.

In one instance, I had a room of about 60 employees with their managers sitting at the back. The development manager left early on along with several other senior managers. The QA manager though wanted to stay to learn for himself. At the first break of the morning he came up to me and said he felt his presence was interfering with participation levels, so he was going to leave. Sure enough, once the bosses were gone, people started to speak up, and they brought up problems they were having with their software development and asked how to apply coursework to their current situation. We had an extremely productive two days. My third day on-site was partially spent going through a highlight reel of the course with the manager. This was early in my training career and was extremely eye opening.

In another instance, I had a smaller team of about 15 people in a training session. When the development manager would come into the room, everyone went silent and would look at the floor. When they left, everyone would look over their shoulders to see if she was gone, and then they would participate again. She walked in again during a complicated systems problem solving activity and no one noticed. Instead of working as a group, they had asked to work on it individually to make it more challenging, and then they would compare their work as a group. This is a fantastic learning opportunity because you get a lot of perspectives. The right or correct answer with many systems thinking exercises is to generate different, yet valid perspectives. One of the shyest participants spoke up first, and mentioned that one of the prompt categories had been hard for her. It turned out she had misinterpreted the prompt, and wasn’t able to think of anything relevant. Usually when this happens, it leads to rich discussions about mental models, shared language and how different people or groups can interpret things differently. In fact, they may have completely different definitions for words that you use in a different context. The participant wasn’t “wrong”, and in fact, she had inadvertently brought us to our next discussion point, all through doing the work and feeling safe about it. Unfortunately, this didn’t happen. The manager who was standing at the back of the room suddenly spoke up, joking around and mocking the person for getting it wrong. She was instantly deflated and upset, and the tension ratcheted up with the entire group. The afternoon learning was completely ruined, no matter what I did to try to get them back on track.

When kiddos learn, we can put enormous levels of pressure on them, even by accident. When you are a parent homeschooling, this pressure increases. You want them to get the “right” answer, they want to please you, and you can give away a lot with your body language, your tone of voice, your approach, etc. Imagine this scenario. You work through some simple addition facts with small numbers. You carefully review the addition and equals symbols. You help them translate an equation into spoken language, “one plus one equals two”. You help them visualize it with some of their toys. You then have them review it with a fun online video. You then take out a math facts worksheet with 10 questions that have simple equations for them to solve. You read the directions on the worksheet, ask if they understand, and then you work through the first question together. You review, and they seem to get it. They know what is expected, they have the required background information, and they understand the concepts and have the skills to work through the problem. You turn them loose, and what happens? Are they feeling energetic and having fun with a challenge to show what they know? Or, are they freezing up and serious? As a parent learning coach, I’ve had both experiences. At first, we had a lot more of the freezing up and pressure than challenge and fun.

To help make this activity feel safer, I did away with the worksheet. I would take toys or math manipulatives, a plus sign and an equal sign and put them into an equation. I would take 2 Hotwheels cars, set them down on the table, then next add a plus sign. Then I would add 1 Hotwheel car. I had two Hotwheels representing the first addend, and then one car representing the next addend. I would add the printed out equals sign, and leave the sum empty. I asked kiddo to get Hotwheels to fill in the sum. After a bit of trepidation, he grabbed three Hotwheels to represent the sum. Next, I asked him to use his mini whiteboard to write out the equation in numbers. “2 + 1 = 3”. It took a few attempts, but in a day or two we had finished off the worksheet material, but in a way that allowed him to experiment before committing an answer. he could manipulate the Hotwheels or other manipulatives until they felt right, then write it on the whiteboard. Also, the whiteboard was easier to fix mistakes than writing down in pencil and then erasing. Also, I worked with him on how to check his work, so he could feel more confident before asking me to check his answers.

Experimenting with toys and math manipulatives are all well and good, but technology makes experimentation, failing fast and FAFO even more psychologically safe. I have long used virtual simulators, emulators and high volume test automation to experiment and learn about software systems. They are extremely powerful technology tools that allow you to explore and find out what happens to systems when they start to fail. You can then design and enhance your system to be much more robust, reliable and performant under real world use.

One of the first things I worked on to reduce risk in math work was to use technology to help, and make the activity virtual. I opened a slide deck, added in a plus and equal sign, and a bunch of small images at the top. I then asked him to create equations. I made text boxes where he could type in each addend and the sum, and he could add them up above the equation to experiment or check his work. He had a lot of fun with it, and would often ask to be alone to play around. Once he had written down some math facts, he would proudly show me his work on each slide he had created. When he made a mistake, I was very careful to ask him to review his work with me, and we would try to find a learning lesson if there was something to work on, or I would brush it off as a typo. After all, we all make typos!

Next, I used high volume automation using the programming language Ruby. Together, we wrote a function to add two numbers together. He came up with variable and function names, and the function would add the numbers and return the sum. Next, I added in a function that would loop from 0 to a number of his choosing and demonstrate the sum. Each addend would increase by 1, and with a bit of a delay added, he could watch the sums increase as the addends increased. We then repeated this with a subtraction example that would iterate down from a large number to 0.

Experimenting with toys and math manipulatives are all well and good, but technology makes experimentation, failing fast and FAFO even more psychologically safe. I have long used virtual simulators, emulators and high volume test automation to experiment and learn about software systems. They are extremely powerful technology tools that allow you to explore and find out what happens to systems when they start to fail. You can then design and enhance your system to be much more robust, reliable and performant under real world use.

If it works for adults who are solving incredible problems, then it is surely going to work for kiddos who need a safety net to fail fast, to FAFO and feel safe in making lots of mistakes and learning from them.

I found that our virtual work provided a lot of opportunity to fail fast, adjust quickly, and reduce the perceived risk of school work. Beyond that, we could use the tech to FAFO. What happens if you add in a character instead of a number? Well you get a type error. Ok, so what does that mean? We have to be explicit with the computer when programming and give it what it expects. But can a letter be a number? Well, sure.Then we talked about algebra and ended up working on one step algebra. We moved seamlessly from having trouble with simple arithmetic to basic algebra, all because kiddo felt safe to experiment and once his brain wasn’t processing anxiety and fear, we could move in whatever direction his curiousity took him. Technology is a wonderful place to safely play with exploration, but sadly, we seem to mostly try to replicate classroom experiments with virtual worksheets rather than tap into its power to enable and provide safety for judgment free failures and productive FAFO.

Adventures in Homeschool: Embracing Math Mistakes

One issue we were struggling with in home school was overcoming the fear of getting answers wrong in mathematics. Even at five years old, kiddo’s exposure to counting heavy math activities had provoked some anxiety. He could count to 30, he could identify numbers and do simple calculations while playing games, or around the house, but in a math learning context, he would get anxious and stop engaging.

At this point in homeschooling, I was using Natural Math activities from the book Moebius Noodles by Yelena McManaman and Maria Droujkova. There were fun activities such as symmetry and mirroring, creating functions, having fun making and playing with grids, and much more. The activities were fun, math time wasn’t prone to anxiety and conflict anymore, and we were progressing. We were still at the kindergarten level so I wasn’t overly concerned that we weren’t doing math fact work or determining calculations. However, I wanted to move beyond the form and function and start helping kiddo develop number sense.

Trouble was, whenever I tried to bring in math he had been doing in preschool, he got anxious. He felt pressure to get the right answer and it stopped being fun. We had conquered the “fun” aspect of math activities, but we needed to look more explicitly at numbers and their relationships to each other. We could go through the process of solving math facts, but now we needed to talk about the facts in a non-threatening way. In short, how can we banish the anxiety kiddo feels on always needing to provide the correct answer? I looked to web discussion forums for inspiration.

Cunningham’s law describes an online phenomenon about asking for help. In essence if you want to get help online, you don’t ask the question you want answered, instead, you make an obviously false statement and wait for refutations. If you ask: “How do I do…” you won’t get much engagement. People don’t seem to want to answer direct questions, especially if they have appeared on the forum before. However, if you confidently post a wrong answer, you will get many people pointing out that you are wrong, and providing examples to show you just how wrong you are. Soon you will get the answer to your “How do you do X”, you just had to ask it in a way that people would react to and feel compelled to engage with. The xkcd comic series has a cartoon describing this obligation.

Don’t Ask a Question. State an Incorrect Answer Instead.

When I was starting out as a public speaker at software development conferences, I had a lot of anxiety. Part of it was because it was new and public speaking is hard, but part of it is because the audiences in software development can be ruthless if you get something wrong. Heckling and heated arguments can occur when you get it right, let alone if you mess something up or if you have an incorrect interpretation. At the time, software consultant Brian Marick was very kind to me and offered encouragement and advice. One tip he had was to start off with a mistake in a talk, and get it out of the way. That way you could just focus on your content and not worry about making a mistake. You’d already made the mistake, and it wasn’t so bad after all, so now focus that nervous energy in a positive way.

I found this helpful, and with experience I learned to improvise and incorporate my mistakes into the talk. If I got a fact wrong and I was corrected, I thanked the person for taking the time to help me, and corrected my materials as best I could. Mistakes weren’t so bad, and in fact, they added a richness to my corporate training. Sometimes, this was due to me getting an important detail wrong. At the time I traveled so much I would forget what city I was in, or what company I was currently at.

I also used to use incorrect answers to warm up a shy group. If I had a group that was reluctant to engage with the activities in the training, I had a secret weapon. I’d deliberately pose and then answer a question with the wrong answer, and usually someone in the audience would blurt out that it was wrong. Or at least you could see them move from surprise to chuckles, once they figured out I was doing it on purpose. People would warm up and start adding in ideas about a better solution. It also helped with groups who didn’t know each other. If they were a bit reluctant or shy to collaborate, I would break the ice by suggesting incorrect solutions, then transition to correct examples.

There seems to be an innate need for many people to correct something that is wrong. If it worked with adult learners why not try this with kids?

In the book Moebius Noodles, they discussed teaching subitizing. This is something adults have developed through working through math over a number of years, but many of us weren’t explicitly taught. I liked the idea, but I had never heard of trying to teach it before. I started reading and watching videos about how to teach my kiddo how to subitize. Trouble was, if I held up fingers or a dice or pointed to a small group of toys and asked “How many?”, the old math anxiety would flare up. The fun would stop, and kiddo would be disappointed. I felt that we could easily work from 0-6, especially since we used dice in games and he was familiar with that number range. However, instead of doing it right, I was going to do it wrong and see what happened.

I started with body mirroring activities. We stood facing each other, and I bent one arm at the elbow and held my palm facing up. Kiddo mirrored me, watching intently. Next, I adjusted my hand so I was holding up three fingers. Kiddo mirrored me, watching quietly and intently. Then I blurted out: “I am holding up FIVE fingers!” He stared at me in shock. He didn’t say anything, so I said it again. “I am holding up FIVE fingers!” He gave me a puzzled look, so I repeated myself. “I am holding up FIVE fingers!” He responded this time: “No Daddy, you’re wrong.”

I repeated myself: “I am holding up FIVE fingers!” “No Dad, that isn’t right.” I asked him what was wrong with what I was saying. “It’s wrong, you are not holding up five fingers.” He looked concerned and wasn’t sure how to proceed. This time, I started using silly voices, making faces and hamming it up. “I am holding up FIVE fingers!” Once he realized I was being silly, he started to laugh, but kept telling me it was wrong. Finally, I asked him why it was wrong. “You’re holding up three fingers.” “Pardon?” “You’re holding up three fingers.” “Pardon?” “You’re holding up THREE fingers.” He was starting to giggle now. “What? How many?” “DAD! YOU ARE BEING SILLY. YOU’RE HOLDING UP THREE FINGERS!”

Aha! Finally! Math without fear!

I then asked him to do it. He started hamming it up and holding up random numbers of fingers and deliberately stating the wrong amount. He would ham it up until I guessed and corrected him, and then we would switch. After about 5 minutes, we were doing a basic subitizing exercise that was incorporated into our mirroring activity.

This was a huge breakthrough. We hadn’t had an experience like this in weeks/months. Now we could build on this.

Wrong Answers Only

In our daily work, I started to incorporate subitizing, simple arithmetic and counting. We would use manipulatives like mathlink cubes, Lego bricks, rocks, basically anything we could use to visualize. However, we had a rule. wrong answers only! I wanted to try to get the anxiety out, and model how math should feel. It should be challenging, but it should also be fun. It should be about discovery and exploration, and the mental math and memorization will come with doing, not by being judged on your accuracy.

I deliberately chose math problems that were below his current level, and then had him come up with the wrong answers only. I could tell that he really wanted to provide the right answer, but I would delay that and remind him that we were going for wrong answers only. In fact, the reward here was for the silliest answer. After a while, he would be practically vibrating to try to correct it, and then and only then would I ask him for the correct answer.

Here were some variations:

  • Try to make me laugh, or make yourself laugh with your answers.
  • Make them sillier and sillier.
  • If they want precision, then I have a rule that there needs to be 3 silly answers first, before doing the correct one.
  • If they are tired of doing wrong answers and want to do right answers, follow their energy and switch it up.

My goal here is reframing the learning. Instead of a winner takes all, high stakes math fact question, we explore and see what happens. Instead of getting a question wrong and fixing the answer, we embrace mistakes, and to try to banish fear. Part of this approach is to get kiddo used to the format of solving problems. Part of it is to overcome anxiety and panic when posed with a math question and being expected to get the right answer, every single time. If you can get the wrong answer and the wrong answer is the correct answer, then you have the capabilities to get the correct answer when you need to provide the right answer.

Switch the Context, Gently

I wanted to tap into the knowledge he had, and to get him to demonstrate it to us, but without any anxiety or fear. I worked hard to be matter of fact and not point something out and wreck the energy of the activity.

Once we were having fun answering with only incorrect or silly answers, it was obvious that he had the capabilities to answer correctly. Once he was tiring of silliness, or if he was starting to answer with the correct answer, I would silently shift. I might verbalize this if it felt confusing, or I might just go with his energy and watch him answer correctly. I didn’t praise him for the wrong answer, or the right answer, I reacted the same way no matter what he did. I was rewarding the approach and the effort, not the answer itself.

After a while, we could do subitizing without fear. I would hold up fingers, he would answer correctly. Then I would get him to do it with me. We would take turns with fingers, dice, toys, cereal pieces, or anything else that was a small number to count. To add some variation, I started holding up 1 finger on my right hand, and 2 on my left, slowly easing in to some basic arithmetic.

If he started to freeze up or show signs of anxiety, I would ask for “wrong answers only”. If he was really starting to get wound up, we would move and work out his emotions together, and return to mathy stuff later on, or the next day. After a while, he would ask to not do silly or wrong answers, and preferred to work at providing correct answers. To keep the positive energy going, I didn’t tell him if his answers were correct until he asked me because he was curious. I was careful not to reward him for being correct only, but to reward his efforts and the process we were doing. If he got one wrong, I built up his self esteem and let him know it was ok.

Finally, we were moving out of math anxiety, and were developing a solid base we could work from. Subitizing, counting activities and simple arithmetic could be completed without anxiety, fear or conflict. This was a major step forward.

Adventures in Homeschool: Revamping Preschool Math with Symmetry

In my previous posts, I wrote about issues we had with a traditional, North American approach to teaching and learning math basics. Utilizing popular approaches and activities weren’t working, so we had to try something new.

Natural Math was a lifeline for us to explore learning math with our kid. I liked the philosophy of opening up math, not putting in artificial age-based gatekeeping, that it de-emphasized counting based activities. I loved the focus on exploration, personalization of math and fun. This article, 5 Year-Olds Can Learn Calculus was an inspiration to us.

Reflection and Symmetry

One of the first activities we tried from Natural Math was body mirroring. I would stand and my son would stand opposite. I would move my right arm to a position, he would move his left arm to match me. I would extend my left leg, and he would match with his right leg. Then it was his turn. He would waggle fingers, kick a foot, or pull a funny face for me to match. Reflecting each other could easily devolve into silly giggling and fun, if someone got it wrong or did something funny

To add more variation, I also had him stand in front of a mirror and move himself, and watch carefully what happened. We would add more variation in with movement, such as moving to the side so only part of his body, or half his body was reflected. I would ask him to think like a scientist and carefully explain what he was observing. I was cautious with feedback, and I praised whatever he came up with. I also started modelling behaviour by doing it myself, and describing what I saw using different approaches. Then he would try and add more to his observations based on what he had seen me do.

My Gen Xer brain didn’t feel like this was really math, but at least he was enjoying it. I started to research reflection in mathematics to assuage my parent guilt, since I didn’t feel like I was doing a very good job in math learning.

After a few days of reflecting fun, I started to hold up a number of fingers for him to reflect as well. He would reflect different combinations of fingers on both hands with ease. I had to be careful though, if I called attention to it with: “How many fingers am I holding up”, he would get suspicious and stop having fun. I also ordered a small foldable mirror for him to play with, and once that arrived, I would put in a Lego character or a small toy, and show him the initial reflection, then fold one side in to increase the number of reflections.

Kiddo would play with that for extended periods of time, looking at things in the mirror, shifting the angle of the reflection to increase or decrease the numbers, and adding and subtracting items to add variation. It was also interesting to see what happened to an object placed in the centre, and how the object itself would get partially reflected. Reflecting half a Lego character would lead to us exploring symmetry. If you don’t get your Lego person exactly in the centre of the foldable mirror, it can reflect in unexpected ways.

Mom is an artist, and she suggested using small colorful and geometric objects to make patterns. Tangrams are fantastic items to use with a foldable mirror. He could make mandala-like reflections using tangram shapes and folding in the mirror. This led to conversations about infinite numbers, and to a topic that piqued his interest: fractals. We found videos on youtube discussing fractals, and we started to look for repeating patterns in nature. He would spot patterns in leaves, in rocks, in certain plants growing in the neighborhood or the river valley and shout out FRACTAL!

Since this was appealing to kiddo, I decided to try to tie fractals back to our reflection work, and found instructions on making a Sierpinski triangle. You draw out a large triangle on a piece of paper, find mid-points in each side of the triangle, and then draw a new triangle within the larger one. You repeat this process as many times as you can.

The Sierpinski triangle was a bit advanced for his learning at this point, and I realized we needed to look at symmetry more. Determining the line of symmetry in an object was intuitive from mirror play, but now we needed to be more explicit. I downloaded drawing and coloring worksheets to help learn more. I started with symmetry drawing exercises where a simple object would be drawn on half the paper, but at the line of symmetry, the rest of the paper would be blank and the child would need to draw it in. They would reflect the drawing in the other axes on the blank half. He found this a bit hard, so I started looking for exercises that were on a grid. The grid helped provide a guide, but the grid also had some hidden benefits. We were sneaking more math thinking we could build on later.

Counting away from the line of symmetry and then drawing a smaller part of the overall shape within that box requires more math thinking. There is counting, but now you are thinking in two dimensions. You need to keep track of rows and columns in a grid. There is counting involved, but the underpinning mathematics brings us to a matrix. Matrices lead us to arrays, and arrays lead us to different powerful abstractions for mathematics and programming. Cool!

Kiddo enjoyed working through the symmetry worksheets. We also found that the side that the drawing was on could have an effect. It was easier if the drawing was on the right side, with the left side blank, while a drawing on the left side with the blank right side left to fill in was a bit more difficult. The further away from the line of symmetry, the harder it was to get right. To get precision he was happy with counting, and keeping track of rows and columns. If he forgot, I coached him to write down the co-ordinates on his white board.

To add variation, especially when little hands get tired of drawing and coloring, we found worksheets that used the grid to make pixel-style art. He declared them to look like retro videogames or that they looked like Minecraft, and he would color in a block, rather than drawing with precision all the time. We also used bingo daubers to color in objects, as well as manipulatives like Mathlink cubes and color counting chips. These required less fine motor effort, but provided more time for variation and play.

After a few weeks, I noticed that our math time during the days was turning into a lot of fun. Instead of dreading it, or checking out when I put the math sign up to help with transitioning, he was starting to look forward to it. There was positive energy, questions, frustration with execution rather than with concepts, and he was becoming comfortable and fearless. Discussions would lead to math in real life, and he would spot symmetry in nature, or point out things around the house. Helping out with cooking and baking in the kitchen would lead to more topics for us to research and explore together.

Things were falling into place, now we needed to build on it.

Adventures in Homeschool: Revamping Preschool Math

While we were finding our way with homeschooling, our current approach to math wasn’t working. Kiddo was 5, going 6, and he had already learned a lot in preschool. He could count to 30, he could do simple arithmetic, and he could group items according to patterns. Trouble was, when I followed a lesson plan or printed off math materials, we had inconsistent results. Things started out ok, but kiddo would show signs of discomfort. He might avoid the activity by distracting, he might start the activity, then scribble all over the worksheet, or he might get upset and refuse to work on it. When we shifted to focusing on emotions and exercising to clear out the negativity, as soon as he returned to the worksheet, his mood would deteriorate. Obviously, there was something fundamentally wrong with the approach.

I came in to teaching my son predisposed with approaches that worked when I did corporate training. Some of the tools I used when teaching adults seemed appropriate for kiddos too:

  • Reward a problem solving approach rather than always getting the correct answer
  • Incorporate movement and collaboration in exercises and activities
  • Encourage productive struggle: let people figure out solutions on their own
  • Model behavior to demonstrate, then have students practice
  • Exploration, incorporating surprises or accidents, and having fun

When I started training, I was focused on knowledge and covering material, but people would get tired and bored with dense presentations, so over time I started to utilize exercises. I also got a sense of what worked well with groups and what didn’t work so well through trial and error. These were so ingrained, I found myself improvising and moving off of our daily lesson plan, when I followed the energy of my son.

I also had some unconscious biases from how I learned math as a kid:

  • Focus on correct answers rather than problem solving approaches
  • Memorizing “math facts”
  • Timed tests
  • Drills to review facts
  • Using worksheets

While I hated most of my math learning growing up, the repeated approach over twelve or thirteen years stuck with me more than I cared to admit. Furthermore, much of the math curricula and activities that I was following reinforced how I had been taught math. There were changes, such as topics such as subitizing and symmetry that were explicitly taught, rather than just picking them up as we did, but the format seemed very familiar to how I was taught. I found myself inadvertently putting pressure on my son to get the right answer on a worksheet in subtle ways. He would pick up on changes in body language, my breathing, etc. and would start to tighten up.

I decided to revamp our approach to math, and that would require some research, some hard work and retooling.

We decided to take a couple of weeks off from our homeschool kindergarten, while I researched and tried to retool. We downloaded some apps to try to help with literacy and math, and I watched to see what he liked and disliked. In the meantime I read books and searched the web for alternative approaches to teaching math to preschoolers. I didn’t come into this cold, I always knew I would need to support and enhance what he was learning in school, but I never expected to be leading the learning effort. I have taught a lot of adults how to program from my consulting and corporate training days, and there were some common problems that I had to help them overcome. Some of it was as simple as 0-based counting, and getting people to think more abstractly, rather than memorizing formulas or algorithms.

I had struggled in math and didn’t really come into my own until university, so I had a lot of thoughts about what I had missed out on in my education journey myself. I felt that my son needed to learn things I had struggled with later on, mostly because of exposure and memorizing previous “rules”. Once I was learning math in university, the approaches to learning were completely different, and I found approaches that worked well for me, but it was extremely difficult to keep up. I decided I wanted my son to have some advantages when it came to understanding:

  • zero-based counting
  • negative numbers
  • multiple dimensions (ie. arrays, grids, etc.)
  • variables (yes, letters can be numbers)
  • math can be fun.

When I was a kid, I felt this pattern when learning math. I would be taught something as a rule, only to have it change later on.

I always felt like it would have been better to teach me more of the picture, and that things were flexible, rather than absolute. For example, starting to count from 0 when looking at an array index or doing pointer math in programming was a lot of overhead at first. If I had been taught to look at 0 more often when I was younger, my brain could have spent more time on the hard parts. When I was younger, I hated how the transition to negative numbers, I felt betrayed. I was told that “2 – 3” wasn’t correct, and then all of a sudden, the rules changed. “2 – 3 == -1”. Now I had to start my math model all over. Another “rule” was that letters aren’t numbers, but then algebra came along, and that rule was cast aside. I would get extra help, go to the library and read, and find something that clicked for me, only to be told that what I actually wanted to learn was too advanced for this grade, or there wasn’t time in class. “You’ll learn that stuff later.”

This pattern repeated throughout my school career, gate keeping by age, and learning steeped in rote memorization and solving based on math facts. I suffered through timed drills, and I felt distant from the actual work. How would this apply to regular life?

It wasn’t until I was in university that math started to click for me and became fun. I even ended up in a career using applied math.

I also had a memory, from university. One of my favorite math professors was teaching his elementary aged children how to do basic linear algebra, calculus and other so-called advanced math topics. He railed against the gatekeeping we often do in elementary school curriculum. He also felt that most students weren’t taught how to think about math before they started post secondary education, and that he had to spend too much time expanding brains and getting people to move beyond memorization. The math that his kids were doing wasn’t difficult, it was just shown in a different context. His 7 year old was adding together two arrays, and the arithmetic was well within their skill level. The application of the arithmetic and keeping track of rows and columns was the challenge. However, kids love board games and can thrive with 2D arrays during play, so why not use that when learning math? You can teach abstractions and provide different contexts with basic math skills. Sadly, the book he had recommended for kids to learn more advanced topics was out of print, so I had to try to find other sources for us.

As a corporate trainer, I taught adults how to program, they were often struggling with off-by-one errors, or getting caught up in simple arithmetic because they weren’t used to starting with zero. For example, very basic programming errors could be caused by people looking at an array index, or loop counters and forgetting that they start with zero, rather than one, in many programming languages. The actual math thinking was kindergarten and first grade level, but there was often a mental block. Beyond that, looking at multi-dimensional arrays and simple algorithms or programming patterns could be extremely challenging.

It felt like a lot of people had to unlearn their approach to math first, then start learning how to actually apply the math to something in the real world. Since I had those same struggles, I could empathize and tailor my training work to help people who were having trouble learning how to program. I often thought of my old prof’s approach and wondered if there was something a bit off with how we teach math. Memorized facts don’t translate well when you are problem solving in the real world, other than to help provide a base to work from. Now, it was my responsibility to solve this problem for my son.

Finally, I found what I was looking for. Natural Math was an approach that made much more sense to me. In fact, it expanded on my thoughts of introducing him more math earlier, and emphasized fun, exploration and creativity. Unfortunately, there wasn’t a zero-prep lesson plan or worksheets I could buy and print out. There were books, lots of ideas, and different approaches and contexts I could use to create our own material.

After a couple of weeks of cramming, it was time to restart our homeschool kindergarten. We kept most of the lessons, but instead of a math worksheet or an activity with manipulatives like toys or duplo bricks, I would have him watch a video on a kindergarten math topic. I stopped using worksheets other than for topics he enjoyed to complete, such as filling in 2D graphs. He loved a particular worksheet style where he was asked to count objects, then fill in and color a bar graph based on the number of each object.

I watched him carefully, but I also had to watch myself. I could quickly ruin an otherwise positive learning experience. For example, if he made a small mistake in his graphing exercise, I would gently point out the mistake, and he would feel crushed. It would be something minor, such as him counting 5 red Duplo bricks, and then accidentally coloring in a bar graph for 6. I’d gently correct him, and the wind would go out of his sails, and a happy, smiling kiddo would look sad and start to withdraw.

The other part of my behavior I needed to adjust was to get over myself when it came to my reaction to his need to move and express himself. When he would make a connection in learning and was happy and proud of himself, he would jump up and down, flap his arms and spin. I felt that part of our homeschool work was to prepare him for learning in a classroom, so I would discourage the jumping and spinning. Once again, he would go from a happy kid who had just mastered a tricky learning problem and was full of joy to feeling shame and he would withdraw. I worked on my behavior, since what did I want him to learn? Did I want him to learn that he needed to be perfect in his math, or that he needed to master concepts and it was ok to get the wrong answer sometimes? Did I want him to sit still and stifle his emotions, or did I want him to experience joy and fun at a topic that can be challenging and many find intimidating? I decided I wanted to encourage the learning and the joy.

I decided to throw out the math resources we were using, or at least set them aside for a while and start something new. On the recommendation of the people behind Natural Math, I bought and read the book Moebius Noodles: Adventurous Math for the Playground Crowd. The hard part with Natural Math is that there are topics with examples, but there aren’t pre-free math resources you can download and start using. Instead, I read through the first chapter on symmetry, and tried the example they described in the live mirror section. To be honest, it didn’t really feel like math to me, but I was willing to try it out and see. One of the live mirror activities was to have the student stand facing you, and then you move your body, and they move to mirror it. For example, you stand with your arms at your sides, and lift your left arm and point it out from your body. They do the same thing, pretending to be your image in the mirror. For kiddo to get the hang of it, we also had him practice using a mirror first, then trying again with me.

While I didn’t feel like we were really doing math per se, the important outcome was my kiddo’s reaction. He LOVED it.

Over the next few days, we added complexity to the activity, using stuffies, toys, and other props. We tried things outside, and did more complicated movements. We even added in sequencing, where one person needed to follow 1-3 moves that the other did. We also watched videos of people dancing and doing other forms of copycat movements. The body movement and the focus on exploration, without any chance of failing to get the correct answer was a winning formula. Now we were on to something, but I needed to learn a lot more about this approach.

(to be continued…)

Introducing Adventures in Homeschooling

Today I’m going to introduce a new topic to this blog: homeschooling.

I’m a dad, and my son is elementary-aged. Together, we’ve had a bit of an unusual educational path, and people keep asking me to write and share what we’ve been up to. In addition to my software work, I am also my son’s learning coach. We use a blend of structured and unstructured learning, with some adult direction, some formal school interactions, and a lot of time and opportunity for self-directed learning.

To keep up with a kid who is an active learning machine requires that I keep learning too. I need to feed his learning appetite, to encourage and cheer him on, help set goals and milestones,remove impediments and protect him from politics. In short, it sounds a lot like what I do as a product manager working with software development teams, even if the implementation is different.

In March 2020, we–like everyone else–were suddenly pulled out of our routine and needed to find a way to help a four year-old (almost five year-old) learn at home. He had been in daycare and preschool, and was well prepared for kindergarten in the fall. While we weren’t worried about him falling behind, we needed him to keep learning and stay occupied while one of us worked from home. Since my health prevents me from full-time work, I took on the learning coach role, while my wife transitioned to full-time work from home and needed space and time to focus on her work.

We are fortunate because our kid has an insatiable desire to learn and is extremely driven. Since both his parents are techies, he sees devices as learning aids, as well as entertainment. He has a lot of patience when he wants to learn, and can focus on pouring his energy into a task when he puts his mind to it. At the time, he was frustrated because he couldn’t read, and he wanted to improve his music skills by working with me. We felt we would build on what he had been learning already, and branch out as he needed.

To start our home school, I researched and bought prep-free lesson plans for a month of kindergarten level activities. I read about how to get buy-in from your child by having them take an active role in homeschooling. We worked together on naming our school, we made a logo for it and I printed a poster for him. We talked about what he liked and didn’t like in school. We talked about learning goals, and setting up stations for learning in the house. I worked through the weekly overview of the lesson plans, and shared them with him. The first day we started by playing a learning song he chose to help us start the day. Then, we looked at the calendar and talked about today’s date, and shared our feelings.

At first, things went reasonably well. I found that 30 minutes of time in a lesson plan designed for a kindergarten class could take about five minutes for the two of us. Other times, if he was really into a topic, we might run long, throwing off our whole schedule. I didn’t want to fall behind, but I also felt that since we were essentially starting kindergarten materials early in the year (March instead of September), we could spread out the work. The hope was that in the fall he would return to in-person learning, and that anything we did at home would be preparation for that. However, I like plans and schedules, and it bothered me that we weren’t able to follow the plan. When a lesson ran short, kiddo suggested that we just take a break for the remainder of the time, then move to the next topic at the time in the plan. I decided to try, but quickly realized transitioning back to learning mode from break mode was tricky. It could be fraught with conflict.

On the other hand, if we stayed in learning mode for most of the morning, we were happier and felt more productive. Instead of breaks, I decided to revamp the lessons. We settled on a 15 minute format for lessons, rather than the 30-60 minutes in the lesson plan. It looked something like this:

  • Introduce the topic
  • Explain and teach the topic with a working example
  • Turn the topic over to the student
  • Once they are comfortable with the exercise and are finished with it, summarize and move on

One-on-one, this could take anywhere from five to fifteen minutes. It also seemed to work extremely well. Instead of free breaks in between topics, I could adjust the schedule, front-loading it for the morning, which matches kiddo’s energy. In the afternoons, I would catch up on software work, and, due to my health, I would also need to rest. Instead of leaving him to his own devices (which would often be non-stop YouTube kids, or working on a play project), I downloaded some educational apps for him to use. As his energy levels for learning waned, usually mid-afternoon, I left him completely unsupervised to do what he wanted. Surprisingly, he would obsess over YouTube kids for days on end, watching what parents would call “junk,” but then he would come up with learning goals and projects and all kinds of creative things to do on his own.

He would find an interest, ask to learn about it, and we would search out resources for him to consume, or help him set up art projects or experiments. Nice! We dialed it in, and figured out what worked for us. I used a modified schedule with a no-prep lesson plan that covered all the major topics, and we spent time bringing toys and books into his math and literacy work. When it seemed like he was just going to wile away the hours on something unproductive, he would get an idea and work to learn something new on his own.

Then one day, he literally flipped the table.

When it was time for learning, he refuses. We would argue, we would lash out at each other, and one day while working on some math exercises he had previously enjoyed, he tipped his craft table over. After that, each morning, and at every subject change in the schedule, instead of participating, he refused. He would sit and refuse to talk, participate or do anything.

After a few days of trying everything I could possibly think of, and consulting parenting books, online resources and chatting with other parents, I left him to his own devices for two weeks. In the meantime, I started to retool.

Feelings Matter for Learning

I knew I needed to approach things differently and get him to feel safe and comfortable learning again. The trouble is, a five year-old can rarely tell you what’s wrong with your approach or why they have big feelings. Furthermore, I am Gen X, and our learning approach was about being left to our own devices, lots of memorization in school, strict discipline and tough love. School was school, it wasn’t necessarily fun, but you did it to get where you needed to go. We rarely talked about feelings, and when we did, we often treated it as a big joke.

To figure out what would work for my son required a radical departure from what I thought learning should look like, and I didn’t have the option of buying and implementing zero-prep lesson plans anymore. I also had to spend a lot of time working on emotional regulation. First of all, I had to examine myself and my emotions, and I read a lot of Big Life Journal and Growth Mindset materials. I bought some packages with activities for kiddos, and instead of starting our typical schedule, I started with dealing with our emotions.

The first thing I changed was to start the day differently. We focused on emotional regulation first and got ourselves in the right mindset for learning. I found a couple of simple picture books about emotions, and we would start by reading them, then pointing to the color or the picture that best described the emotion we were feeling. If the emotion was negative, we would go outside and be active for 15 minutes. He’d blow off some steam, and nine times out of ten, start to feel positive. Linking his movement to his positive thoughts was an important observation that I return to, over and over.

When his emotions were positive, I would introduce some of the exercises from our lesson plan. But instead of trying to cover materials and make sure we got all the work done, I started to watch my son very closely. At what point would a positive emotion change, and what were we doing that caused that change? The first thing I noticed that could flip him from feeling good to starting to withdraw or feeling frustrated and angry was Math. He could go from smiling and chatting to quiet and withdrawn in an instant. If I could get him out of the situation and get him moving, we got back on track.

What was the trigger to go from positive to negative? At first, I thought it was just resistance to any sort of formal learning with a parent, which is normal. However, the negative reactions didn’t fit a pattern. They could come out of nowhere, and I realized that the feelings might have been brewing for minutes or hours before they would emerge. I needed to be much more aware and observe, and do “feelings temperature checks” often.

I noticed that once we went from theory to working through an example, any of the “school math” activities we worked on were affecting him negatively. For example, we were working on counting Hot Wheels cars, and then doing very simple arithmetic on a worksheet. He would start out happy, but while doing the math on the worksheet, his entire body would tense up. He’d go quiet and would be full of tension. Conversely, when he watched Jack Carson YouTube videos with math songs, he would move and dance and have fun. Clearly, I needed more of the latter, and less of the former in his learning. He would watch Numberblocks on TV and binge watch for hours, loving every minute of it. Then, when I tried to apply what he was learning from watching to a traditional math exercise, I wrecked it.

He was learning and really enjoying math, but not the way I was trying to teach it. I was taught math with memorization and figuring out equations and formulas, so I wasn’t sure how to approach it with my son.

Learning how to teach mathematics in a way that fit his energy and emotions was my next challenge.

(to be continued…)