In my last blog I talked about how the research I have been studying focuses on the “mathematics of children” and I claimed that research that articulates “mathematics of children” can provide powerful tools for a teacher.
Many of us experienced elementary school a long time ago and this creates a challenge for our teaching. We probably don’t remember how we came to know concepts like addition and subtraction. We may remember doing math, but we likely do not remember the task that allowed us to say, “Oh that is why you do this!”
Another potential challenge may be our limited procedural experience with mathematics. As a teacher, I worked diligently to proceed slowly and to show all steps as I taught procedures. I hoped that this would help my students understand new procedures and how they worked. I now recognize that I had a narrow view of math as procedures and I lacked tools to draw from, as I tried to provide students with experiences that would cause them to reflect and construct math concepts.
I have a deep respect for the amount of work it takes to construct meaning around math concepts. Our charge as teachers is to relate to what a child is going through and to know how to support them. I would like to attempt to draw an analogy to a construction I have recently experienced: cooking.
I love food and thoroughly enjoy tasting new combinations of flavors. My cooking experience began using a recipe, but I found myself (as a wife and working mother of 3 children) struggling to have all the ingredients on hand for a given recipe. I had to take risks and veer away from the recipe. It began with some substitution of ingredients… Rather than look at a recipe as locked rules, my recipe became a stepping off point. I began to look at ingredients such as chicken, onion, and garlic salt as fitting into categories. Did you know you can use butter, coconut oil, olive oil, and many other ingredients to saute onion and garlic for flavor? If you add meat and some sauce, presto!, you have something yummy to put over rice or pasta!
My friend and I often talk about healthy cooking for our families. Before she met me, she only cooked with a recipe. Now, with a little moral support, she has ventured into exploring adaptations and, like me, is creating meals without recipes.
I think that many of our students are only “recipe cooks”. They struggle to make sense of the mathematics and to understand math problems because the only tool in their tool belt is procedures. Understanding the “mathematics of students” has given me a tool to change that.
In following blogs I will tell some stories focused around the mathematics of students. I’ll discuss some of the following questions: How does the student see the problem? How does she solve it? What does the research tell me about her behavior? How can that inform a teacher move that I should make with the student?