June 30th, 2014
Welcome back on this lovely Monday to our Summer Blogstitute! We have a lovely post from Kassia Omohundro Wedekind this morning, author of Math Exchanges and How Did You Solve That? Kassia talks about how her students’ attitudes change throughout the year when it comes to thinking about themselves as mathematicians. And while Kassia talks about math here, the question could be asked in all classrooms: “What is the legacy of our (math) classrooms?” Be sure to leave a comment or ask a question for a chance to win a package of eight Stenhouse books! Last week’s winner is Terri R. Keep commenting!
On Being a Mathematician
In the last days of the school year I always think about how far we are from the first days of school. So much change and growth happens in a classroom between September and June, and as a math coach I get to watch these changes happen in many classrooms and throughout many grades. I had been thinking specifically about how students’ mindset about mathematics can change throughout a single school year when fifth-grade teacher Mary Beth Dillane and I sat down for a coaching session to reflect on our work together this year.
The fifth graders in Mary Beth’s class began the year with a variety of different feelings about math. Some hated it. Some loved it. Some loved it as long as it came easily and quickly. One cried at Mary Beth’s table in the back of classroom, “I’m bad at math. I’m always going to be bad at math.” And most had just not thought much about themselves as mathematicians: people who construct meaning and contribute mathematical ideas.
And yet the first day I visited Mary Beth’s classroom, about midway through the school year, I could immediately tell how much she valued community. The students huddled together in groups working collaboratively on chart paper, lingering over a single problem. A class-constructed number line labeled with fractions, decimals, and whole numbers from zero to two hung in a prominent spot on the wall. Above it were the words and ideas of Mary Beth’s students. (“Connor and Khalil’s rule: Decimals and fractions are the same shown in different ways.”) At the front of a class was a hand-written quote from Mary Anne Radmacher, “Courage doesn’t always roar. Sometimes it is the voice at the end of the day that says I’ll try again tomorrow.” Already Mary Beth’s students’ ideas about learning and what it meant to do math were expanding and changing. We continued to work on this throughout the year, explicitly teaching behaviors and practices of mathematicians.
So it didn’t surprise me when our last coaching sessions turned to the topic of how the students have changed as mathematicians and how they view the learning of math in general. We discussed our own ideas about how each student had changed (“Did you see how they persevered on that problem? They spent the whole class working on it and didn’t want to stop!”), but we wanted to hear from the students themselves too. So, a couple of weeks before the end of the school year, I decided to interview some of Mary Beth’s students about how they viewed themselves as mathematicians and their general mindset about math. I asked them several questions (Who is a mathematician? How do you feel about math? What is math? Are there some people who are just good or bad at math?). I want to share just a few of their ideas and words with you.
Who is a mathematician? What kind of person is a mathematician?
“A person who looks at different perspectives to find their answer.”
“A mathematician is a thinker, a strategy person, shares ideas.”
“A mathematician is a person who, like, thinks, thinks about the problems . . . risk-takes about the problem. If they think it’s hard, they still do it.”
“A mathematician is a person who checks and checks if it makes sense.”
What is math?
“Numbers—decimals, fractions, everything.”
“Like, stuff. Like diameters, circumference.”
As we talked about the student interviews, Mary Beth and I realized that while the students had broadened their understanding of what kind of people they are as mathematicians, they still have very narrow definitions of math. We know that so much of math isn’t about calculating and numbers. It’s more than the “stuff”—it’s the thinking. We know we need to explore different ways of communicating that to our students.
I think asking these kinds of questions of our students is important. (Next year, Mary Beth and I plan to do a similar interview with students during the first week of school as well as at a couple of other points in the year so we can reflect on how we are helping them grow as mathematicians.) But perhaps it is even more important to ask these questions of ourselves as teachers. What is the lasting legacy of our math classrooms? We hope that it is deep understanding of mathematical content. But just as much, we hope that it is the sense that all people are mathematicians who are capable of the problem solving and persistence required of mathematics.
As Mary Beth’s class of fifth graders prepares to head off to middle school we both ask ourselves, “Are they ready? Are they independent enough? Do they know enough about fractions?” We think about our students who have struggled this year, who have made so much progress, but who still would be thought of by many as “behind.” Like overprotective parents we’ll have to fight the urge to drive over to the middle school in the first days of the next school year and peer through the windows of their classroom, shouting, “Brian, use the number line in your head!” “Giselle, think about what makes sense!” But we won’t. We’ll watch them go, those mathematicians, and take on the world. And we’ll keep working on helping kids be “thinkers,” “strategy people,” and sense makers.