By Jerry Brodkey, posted November 21, 2015 —

For many years, I taught AP Calculus to some of our school’s strongest students as well as Geometry and Algebra to eleventh- and twelfth-grade students who had struggled in math. I am not a big believer in memorization, so I had posters of math concepts all over the walls as reminders and references. These posters would go up and come down as needed.

One poster, the most important poster, was never removed from its central location over the front board that I always used. This poster was titled “Basic Philosophy.” It said:

1. Everyone can succeed in this class.

2. There is nothing wrong in making mistakes.

3. Do not listen to anyone who tells you are no good in math.

I referred to this poster frequently and discussed it with parents at Back-to-School Night and parent conferences. The poster’s philosophy played a critical role in my class. Mistakes were seen as learning opportunities; trying out an idea and finding that it didn’t work were to be praised. Every question by any student at any time was honored and valued. Every student could learn from his or her mistakes and ultimately succeed.

At the end of the year, students wrote reflection papers about their experiences in math. Student after student commented on the power of this poster. No one felt the need to be perfect; everyone could make mistakes.

Here are a few student comments:

• “Instead of fearing math like I used to, I truly enjoyed learning math.”
  
• “Whenever I made a mistake, I was not ashamed but eager to figure out how to fix my mistake.  Usually in classes where I get called on, I feel nervous, but in this class I was excited to get called on to see if I understood the topic.”
  
• “The most valuable part of the class was truly learning and understanding the material.”
  
• “It was a comfortable learning environment, and I never felt scared to ask for help if I was unclear on a topic.”
  
• “Even when I wasn’t doing well, I felt I was learning.”
  
• “I was able to bounce back and use my failure to motivate me to be successful.”
  
• “I am very proud of my work this year. Math has always been my hardest subject . . . however, this year I feel like my understanding has increased dramatically.
  
• “I feel better prepared for all college classes because of this course, not just math.
  
• “I learned how to really take responsibility for my own learning and to not be afraid to ask questions . . . I had set a goal to understand the material, ask for help when needed, and feel as though I was leaving this class with a true understanding of the course . . . The most valuable lesson I have taken away from this year is to ask questions constantly even if I think they sound silly.”
  
• “I don’t want to look back on Calculus as having been a class in which I didn’t perform as well as I probably could have but rather as a reminder, as I move on to college, that there will be difficult classes and difficult processes that are a part of life, that can be very rewarding, but that ultimately are what you make of them.”
  
• “I will continue to learn from the lessons I learned in this class—that I should be confident in my abilities and that I am capable of anything I set my mind to.”

In my next three posts in this blog series, I will amplify these ideas and talk specifically about how I tried to integrate this philosophy into my teaching.

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.