How I Help All My Students to Be Good at Math

A math teacher explains how she emphasizes effort over achievement.
Manuel Balce Ceneta/AP Photo

As a mathematics educator for the last seven years, I can attest that most folks believe they either are or are not “math people.” And that idea of innate math ability is very harmful to both those who believe they possess it and to those who believe they don’t.  Furthermore, our new era of educational accountability perpetuates this fallacy and clouds the message we want our students to receive in math class.

Algebra is Not the Same as Geometry

There is most certainly no such ability that allows some students to pass algebra and others to fail. This argument is made forcefully and articulately in Noah Smith and Miles Kimball’s recent article, so I won’t rehash the point except to say that math draws on a huge range of cognitive processes. Those who are weak at arithmetic can be very good at abstract mathematics. Many students who hate algebra love geometry. Each student I have taught, including those designated as gifted and those diagnosed with severe learning difficulties, has had strengths that helped him or her learn some topics in mathematics easily, and has had weaknesses that made learning other topics in math incredibly difficult. 

I tell all students alike that math requires perseverance and a willingness to take risks and make mistakes. These qualities are much more predictive of mathematical success than innate ability (if such a thing exists). Students often place themselves in the “not math people” category before they even know that each math teacher teaches it differently, or that different topics in math draw on different skills. 

Overconfidence Is as Harmful as Underconfidence

How else is the belief harmful? For those who believe they are not “math people,” it makes them feel helpless. Math requires effort, patience and time. You have to believe that eventually, you will be able to understand. You have to sort through what you understand and what you don’t. You have to then formulate a good question and be courageous enough to ask the teacher to answer the question in front of a classroom, admitting that you don’t understand something in front of your peers—some of whom groan and say, “But it’s sooo easy.  How come you don’t get it!?” It’s so much easier just to say, “Hey, I wasn’t born with this mystical mathematics ability so it’s not my fault.” But you would be wrong.

Math can make even the smartest people feel dumb, and believing in an intrinsic mathematics ability isolates the stupidity. It’s not me who’s stupid, it’s just one part of my brain that’s stupid—and there’s nothing I can do about that part of my brain so I don’t need to humiliate myself in class tomorrow by asking the question I want to ask. People with this mindset keep getting further and further behind in math because if they don’t feel themselves capable of learning something, they’ve let themselves off the hook and invest their mental energy in other realms.
 
Further, those who think of themselves “math people” can suffer from overconfidence. Recently I’ve been seeing a lot students claiming they know and understand everything so they don’t need to practice or take notes. Their homework and test grades are still abysmal. I believe some of this overconfidence comes from the testing they’ve had to endure. These kids are bright and have learned test-taking skills easily so their standardized test scores are consistently high. But truly understanding math requires effort and perseverance and isn’t worth the time if they can still perform well on tests. I have four students in one of my classes who frequently cite their high test scores as an excuse for not doing homework, not taking notes, or performing poorly on free-response tests. They believe themselves “math people” because they’ve been successful on the one measure the state cares about and they see no need to put more effort in.

Do We Judge? Or Do We Educate?

Schools can be about sorting, or about educating. I think right now we want them to be about both, but this is impossible. Schools focused on sorting are obsessed with fairness. Only students who produce “A” work (as decided by the teacher or the state) get As. Honor roll highlights the best students, standardized tests rank schools and designate children as “below basic,” “basic,” “proficient,” or “advanced.” These rankings make it easier for colleges and employers to sort out the students they want from those they don’t.

In a world where schools are designed to sort out those who are going to college, those who are going into vocations, those who are going into unskilled labor and those who are going to prison, belief in innate math ability is appropriate. Those who have it are sorted into more difficult math classes, those who don’t stop taking math as soon as possible. We test, judge and sort. Theoretically, the fear that they will be sorted into an undesirable category is what keeps some students motivated.

Our educational goal should be to help all students learn as much and as deeply as they possibly can, and to instill in them a love of learning. In Diane Ravitch’s new book, Reign of Error, she cites a study conducted in the 1980s by Richard J. Murnane and David K. Cohen. Teachers given poor evaluations performed more poorly, while those given positive evaluations, even if undeserved, worked harder and were more willing to seek help for their problems. Though this study was about teachers, I don’t see why it can’t apply to students as well.  When I give students a lot of credit for persevering showing them that their efforts are valuable early in the term, I get higher quality work from them as the term progresses because they don’t give up when things get hard. Using grades to encourage perseverance rather than to sort or judge means that I don’t need to inflate their grades at the end because the accumulated effort they’ve put in has allowed them to truly master the material.  

There’s a lot of research (see Daniel Pink’s TED talk on the puzzle of motivation) that says people perform poorly on difficult cognitive tasks when there are extrinsic rewards for the successful accomplishment of those tasks.  Students tend to have more difficulty thinking in math when they’re under time constraints, extrinsic pressure or are fearful of being judged.  My goal is to remove these pressures to help students perform better.

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Elizabeth Cleland has taught in Indiana, Oregon, New York, and California in public, charter, and private high schools. 

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