It’s a fun game. Using only horizontal and vertical checkers-style jumps and starting with any configuration of checkers below the line, how far above the line can a checker reach? Dr. Zvezdelina Stankova gives a thorough explanation and analysis of the problem in this video. Don’t worry, she gives time in the video to pause if you want to try the problem yourself.
As a mathematician, Dr. Stankova works to understand how to approach a problem. As a math teacher she works to understand how her students perceive a problem. In both roles, she has to be open to new information — either an unexpected solution to a problem or an unexpected way that a student perceives a problem.
In the video, after she explains the problem, but before she works out its solution, Dr. Stankova gauges Brady’s (the cameraman) sense of the problem, “Well what do you think [is the answer to the problem]?” [2:01] Brady initially gives the response that the answer to the question will be “disappointingly low.” This is, in fact, the correct answer to the question. However, Brady is only giving his hypothesis about the problem. Dr. Stankova’s final solution loses some of it punch if Brady is able to answer correctly with minimal effort.
Dr. Stankova reasserts the interesting-ness of the solution she is about to give when, dissatisfied with his response, she asks Brady to try again. Amazingly, Brady changes his answer to the incorrect response, which pleases Dr. Stankova. At his incorrect response, she coos, “That’s right. That’s what my gut feeling said about the problem.” [2:25] She is judging his response, not against nature, but against her own feelings. She may have succeeded in her role as mathematician, but this is a failure in her role as math teacher.
Why is it easier to ask a student to give an incorrect answer than to accept that a math problem has an easily-guessed solution? I do not have an answer, but this question does shine light on the challenge and art of teaching. Teaching necessarily requires us to let go of ideas we had held close. That is what makes it so challenging and so rewarding.
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