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…)