by Eden Costagliola
I have two pet peeves about the way people talk about math.
The first is when people say, “Do the math.” Arithmetic is a very small part of mathematics, and many brilliant mathematicians are slow or inaccurate at arithmetic. From the Civil Rights and Women’s Liberation movements we learned that we sometimes denigrate people in subtle ways through speech, and, for me, Do the math is a put down that discourages potential mathematicians.
My second pet peeve is the question, “When are we ever going to use this stuff?” Many students who struggle with math ask this question, which is often a veiled cry for help. Just as an eating disorder is not usually about eating, When are we ever going to use this stuff is not really about the application of math. I take the question as a sign that I need to analyze the situation and figure out how best to help the student, and, as the student begins to understand the math, he/she naturally begins to understand and apply it and therefore understand its value.
Truth is, most mathematicians work entirely without numbers, and pure mathematics is truly an art form. A mathmatician is motivated by a kind of daydreaming curiosity and the beauty of mathematics, rather than some concrete problem. Students may never need to write a lab report in “real life,” but we still want them to understand the process and habit of mind of the lab report, because it’s the logical thinking of the lab report that they learn to apply in their lives. Higher level math is similarly about habits of mind, and traditionally these habits of mind begin with Algebra 1.
With this in mind, I’d like to introduce you to The New School Math Department. While we teach traditional material in traditional sequence (i.e., Algebra 1 through AP Calculus), the methods by which we teach are examples of New School pedagogy in action. Our students give explanations and proofs both informally and formally; they teach and design projects that explore real world problems. Most importantly, we teach students how to think like mathematicians – to describe, visualize, represent symbolically, prove, check for plausibility, make conjectures, change or simplify problems, work backwards and closely re-examine problems.
The abstract concepts of mathematics are difficult for many students to grasp, but we teach our students to persevere. We find new ways to reach our students to build new and enhanced logical reasoning abilities. I often tell my students that the exercises they’re doing are stretching their brains to be capable of more complicated thought processes. This aspect of our classes cannot be undervalued, for that mental capacity is carried with them everywhere.
I like to believe we’re good at inspiring mathematical curiosity in our students. Our students continue thinking about mathematical ideas beyond class, and they sometimes come up with original ideas that they are curious enough to explore. Our math students also learn to appreciate the beauty of mathematical advancements, ideas, and logic in their historical context. Pure mathematics is an art form with a rich history and we share our love for that aspect with the students along with the practical applications.