My multiplicative, nonlinear kid
My daughter Katherine is now 12, but she still behaves in ways I trace to her experimental babyhood. Her behavior is opposite to what is described in many articles on mathematical concept developments. When she was little, we did not count, but worked with multiplicative structures such as fractals, iconic units (4=dog feet), splitting and stretching. Some of the materials we used are described in the “SubQuan and Friends” draft.
Here are two recent examples. I asked Katherine, in the style of the visualization game we call “Magic Math Lantern” – imagine y=x and now imagine y=x+3. However, she imagined y=3x. This is not random, but a constant in her behavior: if she forgets to pay attention to the operation, the default is multiplication or exponentiation, not addition. Multiplication is just easier for her to imagine.
Working further on families of functions, to my chagrin, it turned out Katya does not remember how they are called. Poking fun and chatting and laughing about our private “baby names” for entities brought up something that consistently prevents her from remembering, however: “How do you call those non-curvey thingies?”
The traditional names are:
- linear functions (default)
- nonlinear functions (anything else)
What Katherine wants:
- curvey functions (default)
- non-curvey functions (this one rare and special case of straight lines)
The linear/nonlinear terms do not match Katherine’s nonlinear default and is hard for her to remember. In the world, linear functions are very rare, but in secondary math, linear is king. There are a lot of articles about “linear misconceptions” – that is, students thinking that every operation or function is linear. Well, we have the opposite problem on our hands. Which shows that misconceptions as such are not inherent properties of the human brain development, but social constructs, and can be addressed by different practices in early childhood. My “Math-rich baby” course at P2PU is all about it.