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.