Math: Not a spectator sport

An excerpt from the solutions-based book “Why We Failed: 40 Years of Education Reform.” click here

I had the same experience as Anthony when I was a math teacher in the 1970s. After a long day of teaching at the blackboard and overhead projector, I turned around and realized my math students were just sitting back and watching and listening while I did all the work in the front of the classroom.

Their test scores on unit after unit showed that my hard work was not resulting in their understanding and being able to apply what I had taught. It was discouraging to say the least. I remember one day in frustration blurting out to one of my classes: “Math is not a spectator sport. You can’t just sit there and watch me do it.”

I assigned and collected homework to be graded, but the students who needed the practice the most didn’t usually do the homework or did it in a rush, all wrong but “completed.” Going through the motions with their homework was no help to their learning. So I made a huge shift in my teaching approach that paid big dividends in student learning.

I limited myself to two to four days of traditional lecture at the overhead or the blackboard. Then I had the students working on a “practice test” in groups in the classroom with me circulating to offer hints and suggestions. I gave no answers just hints and suggestions.

The practice test was challenging and took the best students in the class two hours or more in the classroom and at home to complete. It had the hardest questions I could find on the topic being taught and I graded these tests (one composite test from each group) and gave bonus points to the groups in the classroom with the best overall practice test score.

These bonus points were used by all the group members as an add-on to their scores on the actual unit test (40 minutes in length or one full class period and including questions of moderate difficulty, similar to the questions students would encounter on the Regents exam at the end of the year).

Frequently, the practice test took one whole week of instructional time and when the week was done as a way to prepare for the actual unit test I gave each student a copy of the practice test’s answer key so they could make their own corrections.

Initially, students worked on the practice test only in my classroom. Then one student who wanted to improve his grades convinced me he could learn more if I let him work on the practice test at home. Turns out he received help from his older sister who was a math whiz.

My first reaction on finding this out from another student who felt disadvantaged was horror that I was letting him cheat with help from another student. Then I realized that if he was able to learn the math this way, why not encourage it. So the “practice test” rules changed. It was “anything goes.” I didn’t care if your sister helped you, your older brother at college, if students worked in groups at home or if parents contributed. All I cared about was whether they could demonstrate on the actual test they had learned the math and could apply it themselves.

All of a sudden my students were arguing over the correct solutions to math problems in the cafeteria, on the bus and in the hallway before school. They were also much more engaged in their math study and more successful on the unit tests.

On day 21 of instruction for the unit on ratios and unit rates, Anthony said he handed out a copy of a preparation test. The prep test included the most challenging problems his students would possibly face on the end-of-unit ratios and unit rates test.

Groups worked together for the next five class periods completing the preparation test. Each student had a copy of the prep test and the group as a whole produced a handwritten copy with answers written by all members of the group on a rotating basis.

Anthony circulated as students worked, offering hints and questions but no answers. They were allowed to use textbooks, notebooks, parents and older siblings, evening phone calls to each other and to older siblings away at college, and even use the Internet to help them complete the prep test.

At the end of class on day five of prep test week (day 25 of the unit), Anthony collected each group’s prep test. He graded it that night (learning requires immediate feedback) and returned it to the group with corrected copies for each group member and an answer key for the preparation test. The group grade on the preparation test would correspond to a set of bonus points on the actual individual end-of-unit test.

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About Lonnie Palmer
In 1970, Lonnie Palmer graduated from Union College in Schenectady, NY, with a Bachelor’s Degree in Physics and planned to continue on to a Ph.D. program but was interrupted by a notice from the U.S. Government – a draft notice. Knowing his low number would preempt plans to continue his education, Palmer took a temporary position teaching high school science — and a reluctant education reformer was born. read more