“I’m not a math person.”
Think back. Just how and when did you come to believe that? Twelve years of being taught procedures, exercises and worksheets wouldn’t have proven that you were not a math person. Along the way, you may have learned to dislike or even fear math, after being given hundreds or thousands of opportunities to manipulate those symbols for no apparent reason.
Perhaps you were good at those operations, or maybe memorizing the procedures did the trick for you. Just how long did those memories last? Could you solve a fourth grade word problem now?
There is a popular notion that math is not really supposed to be joyful or interesting, that it is just something you are good at or not but nevertheless must do to balance your checking account. Math education need not be this way. Math education ought to be about learning to reason and creatively solve problems using the powerful tools math provides.
We at MathAmigos (mathamigos.org) are helping more than 100 teachers in Santa Fe Public Schools to change attitudes and approaches to math education, especially in the crucial elementary grades. We are using math circles, “Exploding Dots” and much more to address the math proficiency deficit in Santa Fe schools.
Three years ago, I began a middle school math circle (math
circles.org) by posing a simple problem: Given nine dots evenly arranged in a square grid, how many different triangles can you draw using only those original nine dots as the vertices (corners) of the triangles? After some guessing, followed by classifying and counting the number triangles of different shapes and sizes, these students discovered many more triangles than they expected.
Eventually, I asked if we were done. A girl off to the side said no and ran to the whiteboard and a new (and difficult to spot) triangle type. I asked her how many of these could be drawn using the nine dots, by rotating, reflecting or shifting that triangle. She instantly and with assurance said “eight.” This requires impressive insight and visualization. At the end of the day, I chatted with her math teacher, who was present at that session. He was stunned by her feat. He told me that while she was a normally quiet and able student, she was not especially engaged in math class. Then he said, “She loves art.”
In conventional math curriculum, would that student have ever been captivated by a tough math problem — so much so that she could not contain herself? In MathAmigos’ experiences in our public schools, teachers often remark that their least engaged math students have awakened to the joys of a good puzzle. Once engaged, students become better problem-solvers who learn how to cope with confusion and frustration.
Math circle sessions introduce students or teachers to solving unfamiliar mathematical mysteries and in the process learn problem-solving techniques. We like to say, “Be less helpful.” Minimal guidance is given, and the problems are accessible yet filled with surprising depth. New mathematical tools are introduced when they are needed.
In the process, students begin to take control of their own education. In early September, I watched a local middle school class analyze a two-person mathematical game to deduce the winning strategy. One student asked, “What if there are three players?” Soon, the entire class formed groups of three and was at the board analyzing that game. And inventing their own tools to solve it.
Is this the best and only way mathematics should be taught? Of course not. Such an approach must be complemented by teaching skills and principles. If we only teach skills, mathematics seems pointless, soulless. If math instruction is only the inquiry, one lacks the tools of the trade. Imagine removing literature from the English classes, and only teaching year after year of grammar and spelling. MathAmigos has found learning to problem-solve and reason mathematically benefits almost all students, including those with disabilities and students gifted with high mathematical ability.
SFPS teachers give our workshops excellent reviews for improving them as math teachers and on providing them with powerful new tools to use in the classroom.
Math is all around us, permeating the worlds of work, school and citizenship. It is a key to our everyday world, a key of discovery, logical thinking and even recreation that turns us into lifelong problem solvers ready for the 21st century. Our kids must be given the opportunity to learn that they are “math people.”
MathAmigos is a volunteer community organization of mathematicians, educators and teachers, and we are always looking for enthusiastic new partners to support our programs for teachers, students and schools. We have been fortunate to receive financial support (for participating teacher stipends and workshop expenses) and more from the Santa Fe Community Foundation, the city of Santa Fe, private donors and others.
Please consider contacting us at mathamigos.org if you’d like to join our math-loving team of workshop leaders, classroom coaches, event staff and more.