**Guest blogger Jerry Brodkey (see his earlier posts on 1/21/10, 1/24/10, and 3/20/10) ****teaches at Menlo-Atherton High School in Menlo Park, California. He has been a public secondary school teacher since 1975, and has taught most of the subjects in Social Studies and Mathematics. This year he is currently teaching ninth grade Algebra and Advanced Placement Calculus. He continues to find teaching to be challenging, enjoyable, and always intense. His undergraduate degree was from Rice University (BA 1974), and with graduate work at Stanford (MA 1976, Ph.D. 1987).**

For some reason this morning, I woke up thinking about what occurred in

my algebra class on Thursday. At one point in the lesson I put four

multi-step problems on the white boards and had all the students try

them at their desks. I then asked for volunteers who would show their

work on the board. Four students stepped forward and volunteered. When

they finished, the silent class and I looked at their work.

After a few minutes, I said; ” These are wonderful problems. Every

student showed their steps, I can follow their thinking. I really

appreciate students being willing to do so. Three of the four problems

are wrong. That is not at all a problem for me. Would anyone like to

come up and try these again below where the original work is?”

Four students volunteered. The work was beautiful. One of the problems

was done wrong a second time, and the one originally correct problem

was done wrong. A third student came up to work on the twice-wrong

problem. At that point we collectively discussed the problems, with the

people who did the problem wrong often being the person who identified

the incorrect path they had taken.

I again re-emphasized how valuable it was to see problems done

incorrectly, and how much I appreciated students being willing to show

their mistaken work.

I then put another four problems on the board. Two of the students who

did the problems incorrectly the first time again volunteered and this

time got them right.

We discussed all the problems once again. What I had planned on taking

five minutes took twenty minutes.

It was an unplanned, unscripted slice of an ordinary class, but maybe

one of the more important parts of the semester.

I don’t think the STAR (California standardized test) measures students’ ability to be able to make mistakes and learn from them. I don’t think this is in the Algebra California Standards.

I do know that as a parent/teacher/husband I am constantly making

mistakes and if I can take a deep breath and slow down, maybe, just

maybe, I can learn something from what went wrong.

*COMMENT FROM LARRY:*

*When I read about math teaching in actual classrooms or see it occur before my eyes, I find it rare that teachers focus on student thought processes, particularly when errors are made. Readers who have ever sat in math classes remember well what happened if they made mistakes on the chalkboard or in answering a teacher’s question. Those memories of wincing and occasional humiliation in the teacher’s responses still chill the bone marrow. Math education researcher Deborah Ball and others point out the importance of plumbing students conceptual errors because they represent fine teachable moments. Brodkey’s vignette from his class is one of those moments. Thank you, Jerry.*

sounds like you have developed quite a relationship with your students that has enabled them to feel safe when they make mistakes and therefore learn from them…good for you!!

I am curious – teaching social studies and then algebra and AP calculus are on opposite ends of the challenge index. What was your college major?

Thanks!

Jerry wrote the following reply:

My undergraduate major at Rice University was psychology. I did my student teaching in both social studies and in mathematics, and was fortunate to be credentialed in both subject areas. For many years I was able to teach a split assignment of both math and economics (or other social studies as needed). It was great to be able to teach in both fields as they seem to promote different types of interactions with students and different teaching styles and opportunities. Over the last several years, I’ve been teaching almost exclusively math since that is my school’s current need. I enjoy both very much.