By Jerry Brodkey, posted January 4, 2016 —

Since I began teaching (nearly forty years ago), I have seen unmistakable changes in my students. More students have IEPs and 504 plans, many documenting student anxiety and stress. There is more pressure to get good grades, more pressure to be perfect. Even many strong students in my AP Calculus classes are fearful. What has happened, and what can be done?

In 1983 my school offered just one or two sections of AB Calculus; we had no BC Calculus. Last year my school offered eight sections of courses following precalculus, including BC Calculus and Differential Equations. There is more and more pressure to accelerate and race ahead.

Of the sixty-four students in my Calculus sections last year, perhaps fifteen to twenty were misaccelerated. Their math confidence was low, and they had weaknesses in algebra and basic math skills. They had been pushed forward because of parental pressure or the desire to keep up with their peers. Many came to my classes worried and anxious.

One of my primary goals was to make the material accessible and meaningful for every student. I tried to make the classroom tone relaxed but serious, with questions honored and praised. The classroom had to be a “safe” one, where every student could see mistakes as learning opportunities. How could such an environment be promoted?

When a student would ask me a question, I often would turn the question back to him or her. We would work together, in front of the entire class, on how to approach the problem. If a student said, “I don’t know,” I would typically reply, “That’s fine. What might you be considering?” If a student had done the problem incorrectly, I might ask him or her to come to the board and show the work to the class. We would try to determine what wrong path the student had taken.

Often I would give a problem for the entire class and then, after a period of time, if there were four or five students who missed the problem, ask them to please put their work on the board. We would analyze each student’s work, often with the student whose work we were dissecting leading the discussion. When we found the mistake, it was a chance to learn together. This process took a lot of trust.

After each test, students reworked the problems they had missed and wrote a reflection paper about that particular exam. How do they account for their performance? How did they study? How did they approach this unit? What might they do differently in the future? Many students told me they had never written a reflection paper for any other class.

Three times a year the students wrote major reflection papers. At the beginning of the year, students wrote about their math background and discussed their class goals. At the end of the first semester, I gave these papers back and asked students to write a second reflection. Were they on a path to meet their original goals? Had their goals changed? What was working for them in this class, and what wasn’t? What changes would they make the rest of the year? What changes would they like me to make in my teaching?

After the AP exam, with their two original papers in hand, students wrote a final reflection. Did they meet their goals? If yes, how do they account for their success? If not, why not? What did they learn about how they learn? What suggestions would they have for future students? What suggestions would they have for me? I read all their papers and wrote my own year’s reflection; then I shared mine with the class. I loved this process.

For students learning math, the classroom can be a place filled with anxiety, stress, and fear. I as the teacher can do my best to instead help make it a rewarding, confidence-building learning experience. Building a kinder classroom is one of my primary teaching goals.

JERRY BRODKEY, jbrodpmiler@yahoo.com, retired last June after nearly forty years of public school teaching, the last thirty-two at Menlo-Atherton High School in Atherton, California. The hardest part of retirement, he has found, is missing his students and colleagues, so he hopes to continue teaching in the future. Jerry enjoys hiking, traveling, reading, and sports and is looking forward to spending more time with his family in the San Francisco Bay Area.