What is Mathematics?

I struggled with how to begin my blog. How much of my background do I share? How much of my past journey do I include right now? The picture of the train tracks on my biography page is one of my favorite places (near the seal sanctuary in Carpinteria, CA) and inspires the idea of being on a journey. I stopped at cities and places before, and you’ll read about those throughout as they come back to me in my travels ahead. As teachers, students, and parents, we all hop on the train in different places. There is no final destination.

Last fall, I began a journey to explore ways to help my young students in Kindergarten develop and nurture a more full sense of what mathematics is. In my 7th year teaching this grade level, it always takes me aback in September when I hear students say things like, “we solve problems like 2 plus 3” in talking about what math is. They seem to think it means writing “answers” on blanks or after equal signs. At five years old, they already think math is about following rules and just getting answers the teacher wants. As their teacher, this saddens me. However, at this young age, I can definitely do something about this.

Last fall, as part of my graduate work in the Math Leadership Program at Mount Holyoke College, I embarked on action research tackling this problem. We know now that humans are born with mathematical minds, and from the very beginning of life, try to mathematize their world.1 The title of my blog comes from this very notion. Children, all children, have mathematizing minds. (I must also give credit to my former teaching partner, Lesley Sheldon, for coming up with this exact title.)

I engaged my students in short weekly activities I called “wondering workshops.” During which, I put in front of them an interesting mathematical image or open-ended task and invited them to engage in observing and wondering. I wanted them to engage in what mathematicians engage in, and feel the joy and creativity that mathematicians talk about.

One problem I encountered was the need for more explicit language development. My students weren’t able to easily or readily identify new or more things that mathematicians do. They could however say what they were doing if I asked. For example, they might say, “I am sorting,” or “I am counting.” They also engaged in actions like noticing and wondering but did not necessarily associate those things with doing mathematics.

I began building a web with my students around mathematics. They are accustomed to building webs in other areas of our curriculum so I knew this visual model was something that could come in handy here. This is what we have so far in mid February.

My plan is to regularly engage my students with this web at the end of each math workshop. I want my students to build language skills as well as make connections to all the pieces and aspects of mathematics. This endeavor also aims to build student agency and increase access to the discipline for all students, some of whom may not come to see themselves as “good” at math. I want to demolish the possibility that this will even occur with any of my students.

References:

1. Research and work on the idea of infants mathematizing:

   • Antell, S.E. & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695-701.

   • Starkey, P. & Cooper, R.G., Jr. (1980). Perception of numbers by human infants. Science, 210, 1033-1035.

   • Dehaene, Stanislas. (1997) The Number Sense: How the Mind Creates Mathematics. Oxford University Press.