Math Geek Mom: Learning to Learn

I attended a Montessori kindergarten, and so it was with great interest that I picked up a book recently outlining Montessori Today (1996, by Paula Lillard Polk). As I read it, I was swept back to the days when I was six years old and just learning to read and write. I remembered writing words, reading simple books, and bringing “show and tell” items to share with my classmates. But most of all, I remembered learning things that led to an understanding of mathematics.

The cover of the book contains a picture of a cube made up of several blocks. When looking down at the cube from the top, the squares and rectangles making it up represent the squaring of the sum of three numbers. When looked at as a cube, with smaller cubes and blocks as its parts, they represent the cubing of the sum of those three numbers. Children are given this set of blocks to play with and mull over as little children in kindergarten, and later, as “big kids” in grade school, they learn the formulas that describe the blocks that they are so familiar with. Formulas that describe the squaring and cubing of the sums of two and more numbers are not just abstract ideas written in terms of “a”s and “b”s, but solid, real concepts that the child has played with since they were very young.

As I marveled at the idea of this, I remembered my own experience in high school of running a small “company” from ground up with groups of other students. When it came time for me to take an economics course in college, the concepts of marginal productivity and marginal cost were not abstract, mathematical ideas (although they are also that), but very real concepts that I had been exposed to for years. It is not surprising that I went on to earn a Ph.D. in economics, where such concepts are studied in detail. Like the Montessori students with their blocks, I had first “played with “ the concepts, only later to learn the abstract ideas that could be used to represent them.

As I read the book, I began to think of my own college courses, and how this unique method might be applied to teaching in college. And better yet, how could this approach be used in parenting? How can we expose our children and students to very tangible ideas first, only later to apply the abstract frameworks that describe the concepts?

The inquiry method that is used often in teaching math and science comes to mind immediately. In this approach, which our education students study in detail as part of their program, concepts are not just taught directly. Instead, a problem is given to the students, and to solve the problem they must uncover a mathematical concept on their own. For example, we might ask how many calories are burned by walking a mile. To figure this out, students must find a way to convert what they know about how many calories are burned while walking for five minutes at a certain pace with their knowledge of how long it will take them to walk a mile at that pace. As they solve the problem they use conversion factors without once sitting through a lecture in which they are told that is what they are.

The use of labs to accompany most science classes is yet another way to teach by having the students discover, rather than just repeat lectures. And the teaching of art and literature takes this same approach. A student must experience the beauty in art and literature before the knowledge of the history surrounding a work of art makes any sense. Indeed, the same holds true for our class in the history of math; it is only after our math majors know enough about math to be able to appreciate its beauty that the history of how it was developed takes on any meaning.

As a parent, I think of this approach when I struggle to teach the ideas and ideals that matter to me most. For things like truth, faith and justice cannot be taught by mere words. Instead, a child needs to absorb such concepts as they grow in their everyday lives. While such an approach to parenting or teaching is difficult, just when I am ready to give up on this approach, I recall the one thing that I think of as most significant in my own development. It was not the many years I spent in Catholic School as a child, or the four years I spent in college among some of the smartest people I will ever meet, or even the years I spent in graduate school learning my subject deeply. Rather, it was the one year I spent in a Montessori school as a kindergartener. That one year made all the difference in my life and the scholar I became. When it comes to learning how to learn, as it has been said, “All I need to know I learned in Kindergarten.”