Category Archives: Attitudes and Beliefs

Hooking non-math people on math

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A strange thing has been happening in my workshops. People are getting really excited about solving problems. Now this isn’t really a surprise when I’m talking about workshops with math teachers. I would hope they would be excited to do some math.

No, I’m talking about the non-math teachers—those that teach something boring like social studies (I kid…kind of) or PE or even the guidance counselors that somehow wind up in my meetings.

It turns out that even those people that claim to hate math are tinkering away at puzzles, shooing people away until they find the answer, and then lighting up when they think they found a solution. Sometimes people who don’t have to be in my meetings are asking to sit in or for copies of the problem so they can work on them in the other room.

It’s very strange. Especially when the adults I see working hard on the problems tell me over and over how much they hate math or how they have never been good at it. But there they are trying to solve problems, writing equations, constructing arguments and critiquing the arguments of their peers.

It seems that when I present the task as a puzzle and not a math task, it draws them in. Yes, some get frustrated for a bit. But quickly it becomes a mission and they keep going back to it. They persevere. They use multiple strategies. They engage in mathematical reasoning despite the fact that they claim to hate math and are bad at it.

One of the things we wind up talking about after doing these activities is how we translate this to our classrooms. How do we create this same excitement with our kids in our classroom?

The push-back is there—that teachers can’t do “fun” problems all the time, they don’t have enough time or that their kids don’t even know their multiplication facts. But when we dig deeper, it turns out that math teachers aren’t necessarily good marketers.

We don’t always know how to hook kids. We don’t highlight the sexy parts of math. We don’t draw them in with an intriguing puzzle and then make them beg for the tools to solve the problem with. Dan has talked about this a lot, but I think it bears repeating. We need to be better at selling our subject.

In an attempt to do that, here are some of the tasks that have created the most energy in my sessions:

The puzzles from the transition to algebra program 

Fawn’s Noah’s Ark problem

Writing equations for geometric patterns:

A mathematician’s lament

My favorite thing about Jo Boaler’s course “How to Learn Math” so far has been the assigned reading.  She assigned Paul Lockhart’s “A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.”  

I think this should be required reading for anyone who teaches math, supervises the teaching of math, or is a parent of a child learning math.

It’s a powerful piece.

He starts by describing a terrible nightmare a musician had.  In it, music is taught as math is in many of our schools:  as a collection of rules that must be memorized.  Students do not play or listen to music until after they have learned music notation and theory.

He then goes on to critique the current state of math education and claim that it is destroying the creative aspect of math by discouraging exploration and discovery.

Some of his suggestions are a bit unrealistic (just play games in math class) and some I completely disagree with (schools of education are a complete crock).

But I appreciate his ability to imagine what mathematics education could be.  I love his passion for mathematics.  And I love that he states so succinctly what we know from research about what many kids think about math: “They say,  ‘math class is stupid and boring’ and they are right.”

Years of research have show us that students have a great deal of anxiety about math and recent research shows this may begin at an even earlier age than we once believed.  Maybe Lockhart’s solutions are too radical.  Maybe they aren’t.  But it seems to me that doing the same thing that we have been doing won’t produce different results.

What do you think?

Want to read the book?  Click here.

Check out the some of research on math anxiety:

Vukovic, R. K., Kieffer, M. J., Bailey, S. P., & Harari, R. R. (2012). Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance. Contemporary Educational Psychology.

The worst thing you can say to a student struggling in math

“It’s easy.  Let me help you.”

Ok.  Maybe that’s not the worst thing you can say to a student, but it’s up there. Yet, well-intentioned teachers and parents say it all the time. Why?

For starters, the problem is easy to us. We don’t understand why a student is struggling with something that seems so obvious to us. Second, we are often uncomfortable watching students struggle and sometimes, the quickest way to alleviate the discomfort is to show a student how to solve the problem.

So why should we avoid saying this to students?

It’s likely that a student could interpret it as: “If it’s easy and I can’t do it, I must not be very smart.”   This is the last thing a struggling student needs to hear.

In addition, offering help creates the misconception that math is not something students can make sense of on their own. Furthermore, the help you give may not address the real reason the student is struggling.

So what can you do instead of offering to show a student how to solve a problem? The research offers one solution– find out why the student is struggling by interviewing them.

“Tell me what you are thinking,” can be a good place to start. Maybe the student doesn’t understand the vocabulary or language in a problem. Or maybe the student is missing the prior knowledge that is needed in order to solve this new task.

Finding out why the student is struggling is a good first step. We’ll explore next steps in future posts.

Want to know more?

Take a look at chapter 3 in Van de Walle’s book: Elementary and middle school mathematics: Teaching developmentally.

Read Children’s Mathematics: Cognitively Guided Instruction

Check out this article about how one teachers tried this in his classroom:  Buschman, L. (2001). Using Student Interviews To Guide Classroom Instruction: An Action Research Project. Teaching Children Mathematics, 8(4), 222-27.

What Predicts Success? A Look at Grit.

When Angela Duckworth was a NYC math teacher she noticed something that I think will sound familiar to most teachers: it wasn’t always her most talented students that performed best in her class.

She had a hunch that there was some quality that made those students successful and that doing well in school and life was about more than learning quickly and easily. She left the classroom and set out to research this hunch. After studying what made kids and adults successful in a variety of settings, she found a quality that was a significant predictor of success. She called this grit— a passion and perseverance for long-term goals

Grit was a predictor of which cadets would be successful at West Point, which salespeople would earn the most money, which students would graduate high school, which kids would succeed at the National Spelling Bee and which new teachers in tough neighborhoods would succeed.

I think grit is particularly important in succeeding in math class. I recently worked with a group of fourth graders. When I first began working with them, many students quickly gave up when presented with novel problems that didn’t allow them to follow step-by-step procedures they previously learned. It wasn’t because they didn’t have the ability to solve the problems. It was because they expected to be able to solve math tasks quickly and easily and when they couldn’t, they gave up.

Over time, I tried to create a culture where doing mathematics was not about who completed the most problems in the shortest amount of time. I encouraged them to use their resources to solve the problems and talked to them about how mathematicians often spend a long time solving one problem. After several months, students slowly became more comfortable when presented with challenging problems and the classroom culture began to shift.

The jury is still out on how to best foster grit. What we do know is that Duckworth has found that talent doesn’t make you gritty. In fact, grit is unrelated or inversely related to measures of talent. So how do we best foster grit in our students? I’d love to hear your ideas.

Want to know more?
Find your Grit score and other resources