What Is Math?

                            By Wendy Petti

What is math? It might seem obvious: We hope we know what we're teaching -- and that our students know what they're learning! But responses to that question can be surprisingly diverse.

Before you read on, please take a few minutes to reflect and record your own thoughts on "What is math?"

Illustration courtesy of Wendy Petti.

I'm a math educator -- I teach grade 4 math, I've created a math Web site, and I write about topics in math education. Yet I cannot easily express what math is. I'm in good company. Bertrand Russell has quipped, "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." Math teacher Sanderson M. Smith observes that "students can gain a tremendous appreciation for mathematics if they understand that the question 'What is mathematics?' has been analyzed and debated since the time of the Pythagoreans, around 550 B.C. "

It is worth pursuing a clear understanding of the meaning and scope of mathematics so that we might provide our students with a richer learning experience and help them more fully appreciate the beauty and power of mathematics.

STUDENTS AND TEACHERS REFLECT ON
"WHAT IS MATH?"

In my math classes, no matter how much attention we pay to the five content standards and five process standards, many of my students seem to focus on number and operation when they share their thoughts and feelings about math. One of my students had an "aha!" moment the morning after a student-led math night: "I look at math a different way now. I've usually thought of math as something we need to do, to know how much money we need to pay, things like that. But this morning I woke up and said, 'Wow! Math is everywhere!'"

A 2005 Math Cats writing contest on "What is math?" produced these reflections:

• From an elementary school volunteer: "Math is more than a subject we learn in school. Math is every breath we take and every second of the day. From the moment we wake up in the morning, math is the core of everything we do..."
• From a first-grade teacher:
  "Math is you.
  Math is me.
  Math is everything we see!
  Infinity and beyond our wildest dreams
  Math encompasses all extremes!"
• From a 13-year-old: "Math is the entire world simplified on a piece of paper... Math is ingeniousness morphed into a tiny simple formula so we can harness its fantastic powers."
• From a 12-year-old: "Math is the universal language of the world."
• From an 11-year-old: "No one can live without math; it means different things to different people. But to me it means love, liberty, learning. I could keep going but to sum it up, math is my life."