Here’s an example demonstrating that rewarding students based on effort encourages them to continue to work hard. I taught a student for three years, through pre-algebra, algebra and geometry. She struggled in pre-algebra and algebra 1, almost always failing tests the first time and only passing thanks to credit for consistently doing homework, coming in for tutoring, and doing test corrections. She slowly increased in confidence and became a very capable math student in geometry (the best in the class at proofs). Here’s an e-mail she wrote me after I left:
I wanted to thank you. Even though you are not my teacher anymore, you still help me all the time. You wrote in my yearbook to remember that I am good at math, and I always go back to that and it actually helps me when I am stressed about algebra 2. Whenever I think about it, I feel as though I can push through and actually do it. I am doing pretty well in it so far and I owe part of that to you.
In math especially it’s easier to judge rather than to coax and reassure. Because there are always right and wrong answers, it’s so easy for standardized tests to sort students into those who can get the right answers and those who can’t. Standardized testing disregards the effort students have exerted and they deemphasize the processes of math. Students are left feeling helpless if they can’t achieve. These tests judge students based on an arbitrary benchmark set by state politicians who have little understanding of what developmentally appropriate skills truly are. Like novice chess players, students learn the rules of math and combine and manipulate them to learn how to play the game. Like a novice chess player, a math student will learn just as much if not more from her failures as from her successes. Focusing on the process of math helps both low achieving and high achieving students learn true mathematical logic and not get discouraged because they can’t reach a right answer, or bored because reaching the right answer is too easy. Many students know how to get the right answers on standardized tests but don’t know how to think about math.
How Parents Can Help
What can we do about helping students focus more on the process of math and on persistence, less on labeling themselves as “math people” or “non math people?” First of all, we adults need to model different behavior than I’ve seen demonstrated in my years as a teacher. The myth of innate math ability is perpetuated from generation to generation. When I tell adults I’m a math teacher, 90 percent of the time I get the comment, “I’m not a math person,” accompanied by a look of sheer terror and either tentative stories of math humiliation or an abrupt change of subject.
Once, a visiting school guidance counselor told my students, to my horror, that he hated math and not to listen to me when I told them math was important. They would never need it in the “real world.” I’ve been writing this article in coffee shops, occasionally making comments to my husband. On three successive visits strangers have overheard my comments to him, asked me what I’m doing, then told me that there definitely are “non math people” and that I’m looking at one. Upon elaborating my position though, all three changed their minds and have admitted the importance of math in their own lives. (One was an industrial architect.)
My students’ parents also believe in this fallacy and sometimes, perpetuate an anti-math attitude. They don’t use math at work, can’t help their students with their math homework, and are convinced themselves that they’re “not math people.” Furthermore, because these adults have survived without math, they tell their children that math isn’t necessary in the workplace. These adults have made their choices. They chose or were forced into careers where math wasn’t required and so they convince their children that only the “math people” will ever get anything out of a comprehensive mathematics education. Our job as role models is to give our students the freedom to make their own choices, including lucrative choices in fields that require math. In my education courses, we were always told that modeling is more powerful than teaching. Adults are modeling this self-defeatist attitude.
If at First You Try, You Will Succeed
In the classroom, we as teachers need to remove some of the stress we place on students and give them the freedom to fail. So many crossword puzzle enthusiasts (my whole family) look forward to checking their solutions against the key printed in tomorrow’s newspaper while so many students dread seeing their returned math test. Why? Because the crossword puzzle enthusiast knows he will learn more about doing crossword puzzles if he checks the key carefully, whereas the math student sees the returned test as a judgment about his intelligence. Students need to see that the attempt is just as valuable as the result.
In my classroom, I award students credit for all problems they attempt, regardless if they got the correct answer. I refuse to let students turn in tests until every question is answered and double checked. I penalize late work, but I always accept it because who cares when they learn, just that they learn. I admit my own mistakes and award students when they catch me in a mistake. Finally, I find it productive to simply acknowledge that learning math can be challenging; telling a struggling student that a problem is easy is one of the most dispiriting things you can say to them. Education needs to be about personal growth and teaching students to enjoy and revel in their knowledge, not on grooming students and sorting them for a job market that may be entirely different in 10 years. If students learn confidence, flexibility and that they’re good at learning, they’ll be ready for anything.