Finding The Joy in Math
If you peek into my seventh grade Pre-Algebra classroom, you may see some unusual things happening. The class may be examining bottles, cans and boxes to estimate their capacity. Students may be admiring a classmate’s drawing of a collapsed monarch. (“King Henry Died Drinking Chocolate Milk” is a mnemonic for the Metric prefixes.) Or we may be dancing—or at least singing—the Can-Can.
As instructors, our job is to help students experience “virtue, wisdom and joy” in their studies. For math students, this third aspect is often the most difficult to find; mathematics seems to consist entirely of exercises and problems. To win students over to the joy, math teachers must “become all things to all people” (1 Cor. 9:22), or as they say in teacher certification courses: appeal to all types of learners.
One math topic which especially calls for creativity is integer rules. These rules are key to moving forward in math, yet are a stumbling block for many young people. During my student teaching in public school, most of the eighth graders could not calculate 2 – 9 or -3 x 8. The topic had been taught in seventh grade, but it had not sunk in. The eighth grade teachers, seeing 110 kids per day for 47 minutes each, had no time to review. Instead the students were advised, “If you’re not sure, use your calculator.” I almost cried watching intelligent children type “-1 x 4” into the calculator.
So preparing to teach Pre-Algebra at The Saint Constantine School, I was forewarned that integer rules could be a tricky topic. But I was determined to find the joy. After all, the class is only 9 students, and has an entire 75 minutes! Since it has been many years since I learned the rules myself, I tried to get into the mind of a seventh grader. . .
We kicked off the topic in the parking lot, where each student drew a number line with chalk. We walked forward for positive numbers and backward for negatives, to show how they add up. Next we came inside and drew number lines on the board and on paper. We talked about how in the movie Up you can cut off a balloon (subtracting a positive) or put on a sandbag (adding a negative) and the house goes down in either case. Students were still hesitant, so we modeled the math with M&Ms (positives) and Cheerios (negatives). That was a popular lesson that students offered to repeat whenever necessary. We added integer operations to the regular fact quizzes timed with a two-minute hourglass. Integer coloring worksheets were offered as extra credit. (It is heartwarming to see that our students are so enthusiastic about extra credit, even those who don’t need it.)
In parallel we started doing actual algebra: -3x +2 = x – 6. The students caught on well to the algebraic manipulations, but many were still making mistakes with the integer rules. What now? I refused to give up and say “Use your calculator.” So we learned a song to the tune of London Bridges (“When the signs are alike…”) and the Can-Can (“But if the signs are different…”). Ask any Pre-Algebra student to sing it for you. Each student was given practice flash cards, and invited to Integer Bingo at lunch once a week. As one student exclaimed, “I would learn anything if I get to play Bingo!” Another added, “Especially if the prize is candy.”
The last approach tried was one observed from my mentor during student teaching: having students copy down the steps onto paper by hand. Originally I had written this off as a waste of time: the steps were written in the textbook! They were shown in slides (that school was less traditional than ours) and displayed on posters on the walls! Why spend class time writing them down?
Now I see the wisdom of my mentor’s approach. We learn by writing. And difficult tasks are easier if we can follow clear steps. So we wrote the steps on cards that students could refer to during problem-solving. This was my last effort, but the most effective for some students. One even offered to take the test a day early, because she felt more confident.
All the various approaches have added joy to the classroom, and the latest test showed students making good progress on integer rules. I complimented one young woman on her improvement, and she said, “I feel better about it now, I can do it.” I asked what made the difference for her. Was it the chalk? The Cheerios? The Bingo? It turns out it was the flash cards, the oldest trick in the book. So our ancestors knew something about multiple intelligences, long before the term was invented.
It’s a relief that the class has mastered the integer rules, because I was running out of ideas. The only thing left was to write a play called “The Mystery of the Missing Minus….”