Math instruction is changing — and for the better, says Nancy Pfaff, a Lake Washington School District teacher who has won a prestigious Presidential Award for Excellence in Mathematics and Science Instruction.
Pfaff learned last week that she is one of two teachers in Washington state to receive a Presidential Award this year, one of the highest honors for U.S. math and science teachers. (The other Washington winner is Pamela Nolan-Beasley, a science teacher from Waitsburg, north of Walla Walla.)
A lot has changed, Pfaff says, since she first started teaching elementary-school math 37 years ago, and much of that is based on a growing understanding of how children learn.
We talked with Pfaff (pronounced Paff) about the state of math instruction in the United States, our students’ performance on the PISA, and how she gets students to love math.
Q: What are you doing now?
A: I work at two different schools — Blackwell Elementary and Thoreau Elementary — and children come to me from seven or eight schools at each of those sites. It’s a once-a-week enrichment program for kids identified as gifted.
For the 2011-12 school year — the year the award is based on — I was at Horace Mann Elementary. We had a really unique situation, where there were three of us working with two classes of sixth-graders. I taught all the math to those two large classes, and I also helped students in grades 4-6 who were struggling in math.
When you were a student at Washington State University, you were one of only a few people to major in mathematics and elementary education. Why were there so few?
I think people who are passionate about math often want to teach their subject and go to the higher grades.
Why did you want to teach elementary math instead?
I love math. I’m good at math. I grew up in a family in which we played with math a lot. My dad and I used to play cribbage, play mastermind, do jigsaw puzzles. The kids in our family grew up playing with math ideas and patterns and relationships, and I think that led all of us to be fairly good with math.
I chose elementary because I love teaching, especially working with young children. I’d had many experiences working with young children, including babysitting, teaching Sunday school, and helping out in my mother’s first-grade classroom. Every time I was on vacation, my mother let me come in and help.
The stereotype is that many elementary teachers are afraid of math. Is that true in your experience?
I wouldn’t say they are fearful of math. But you have a lot of people, because reading is so important, you have a lot of people in elementary education who have subject majors in literacy.
That said, there are a lot of great math teachers in a lot of schools who do great things with kids.
We’re learning how to teach math better, as a field. The way we teach math has been changing and I think that’s great. It’s exciting and it’s positive.
How is math instruction changing?
Since I have learned more about how kids learn, I use discussions a lot more, where kids solve problems and then talk to other students about their solutions. They learn how to verify their solutions with evidence.
If you’ve ever noticed that when you try to teach somebody something, it deepens your own learning about it — I think that’s true with students, too.
It was amazing how strong kids got after a year of really using that discussion-based approach, that focus on problem solving.
There is a lot of concern about the math skills of American students. What do we need to do to improve students’ math knowledge?
That’s a big question. If had the exact answer to that, I’d be rich, right?
So let me ask it this way: When you see American students’ relatively low scores on the international PISA exam, what do you think?
I agree we should be doing more in mathematics. I’m not sure I agree with the ranking system.
But we need to help kids be more fluent in their mathematics. We need to help kids learn how to solve problems in context, not just computation — and I’m in no way saying that computation isn’t important. Computation is important but it can’t be done in isolation.
I don’t know how other countries educate their kids, but I think we’re on the right track with some of the things we’re doing here with our new Common Core standards, because we’re not only focusing on the content, we’re focusing on the thinking skills that go along with the content.
Do you have to fight the widespread believe that it’s OK not to be good at math?
I was driving to work one day and at three different times on the radio, someone made a joke about not being good at math. And I thought, wow, there’s a cultural message there. You never hear anybody tell a joke about not being good at reading.
If kids hear their parents say they weren’t good at math, it almost excuses the hard work it takes to get good at math.
When I work with older kids who struggle in math, they just tell me, “I’m not good in math.”
And what do you tell them?
You will be good in math. Everybody has things in math they are good at.
If you were in charge of improving math instruction in this country, what would you do?
I think we need to improve training for teachers. We’re pretty good at providing ongoing training in literacy, but quite often, when districts have to make choices about what kind of training to provide, the emphasis in elementary education is on literacy rather than mathematics.
I also would like to see math practice reflect what we know about how kids learn, and there are a couple of things — like always making sure teachers connect new ideas to the math students already understand. And having a nice balance between understanding concepts and procedures.
There’s also getting kids to think about their own thinking, helping them understand how to identify whether they understand a concept and, if not, how to ask the right questions about what to do next.
All these are things I’m trying to do in my own practice.
What does it mean to have a good balance between concepts and procedures?
A good example: When you are trying to teach little people how to add, you give them a lot of experience in putting groups together. That way, as they’re computing, it makes sense in their heads what they’re doing — that two plus three means putting two cats with three cats, to create a group of five cats.
You are being honored, in part, for helping kids learn to love math. How do you do that?
I always have loved math and a lot of my friends don’t. I think the difference is the playful way I learned math. Math to me was always a puzzle to solve, not a computation problem. I approach students who don’t love math by trying to show them all the fun things.
Kids don’t understand that math is way more than computation because in elementary school there is so much computation to learn. So it’s taking the time to build three-dimensional kites with straws and take them out and fly them. It’s playing with mathematical ideas in a way that engages them and doesn’t feel like work. Then they are more willing to do the hard stuff.
In your three decades as a math teacher, have you seen students’ math skills erode?
No. I think we’re expecting more. The world has drastically changed over the 30-some years that I’ve been teaching. Kids are doing more complex things with math at younger ages.
When I think back to the way I learned math, we all had a math book and did the math problems. Our kids still do that, but my kids do a lot more complex thinking about math now because we know they need to.
Why do they need to?
I think about some of my buddies who didn’t learn math as strongly as I did. We’ve seen that some of our ways of teaching math have worked for some kids, but not for all kids. In the American system, we have to find ways to reach all kids.