What Does it Mean to Learn Math?

This month I had the privilege of leading a presentation and discussion with the El Cerrito High School Mathematics Department on Creating Mathematics Learning Environments for Developing Mathematical Thinkers.  I began the presentation by posing a question to the math teachers: What does it mean to learn math?

I asked the teachers to consider their own professional and personal thoughts and beliefs, as well as how they might have answered the question when they themselves were students.  I also asked them to think about how their math students and their students' parents might answer the question.  Take a look at what the teachers had to say:

Our discussion highlighted an important distinctions in the ways that mathematics learning is viewed.  On the one hand (and the left side of the white board above) is the notion that learning mathematics is about memorizing and applying procedures and formulas to calculate and solve math problems.  From this perspective, students do math as a means to an ends.  Their goals are to get the correct answers and to get a good grade.  The math teachers associated this way of thinking about learning math with many negative emotions and feelings such as anxiety and torture.

On the other hand (and the right side of the white board above), the math teachers also described a view of mathematics learning that is expansive and meaningful.  Learning math can be about engaging in mathematical thinking, making connections, and using logic, symbols, and a mathematical language to solve nontrivial problems. Several teachers shared personal reasons why learning mathematics can be interesting, fun, and important.  One teacher shared her appreciation for the beauty in math that she wants all of her students to see and experience. Another teacher shared his love for engaging in complex problems with required him to struggle and think creatively over several days before triumphantly uncovering a solution.  The teachers shared many positive emotions and feelings associated with this view of mathematics learning such as excitement and appreciation.

As one of my graduate school mentors, Dr. Alan Schoenfeld, wrote,

"Learning to think mathematically means developing a mathematical point of view and competence with the 'tools of the trade,' using the tools for mathematical sense-making."

(Schoenfeld, 1992, p. 334)

For parents and educators, it is important to recognize our personal views about mathematics learning and what it means to learn math, as these guide the ways that we work with children.  Our own views and beliefs about math come out in the ways that we structure math lessons and activities, the ways that we model mathematical thinking and problem solving, the ways that we help with math homework, the ways that we respond when children are having difficulty with math.  I would encourage anyone who works with a child learning math to consider what it means to learn math and what that child needs to continue developing as a mathematical thinker. 

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Reference: Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning. New York: Macmillan.

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