*THE
GREAT MISTAKE!*

THE GREAT MISTAKE! A Teaching StoryAuthor:Kari Augustine TEACHER'S NOTE: This story is from the internet newsletter THE ALGEBRA TIMES. I think it is a good focus point for the beginning of the school year. CREATIVE APPROACH TO MISTAKES When I was about eight years old, my father had a 'creative' way of handling the mistakes I made in math. Once he got home from work, he would ask me how I did on that day's quiz. I would sheepishly tell him that I got a 'D' (something about fractions didn't agree with my young mind). He would become enraged and start parading around the family room, wondering aloud how a child of his could make so many 'dumbbell' mistakes. He even sent me to my room a few times, evidently believing that would cure me of my confusion. As I said, this was 'creative.' He was creating anxiety in me and futile rage in himself. I think that being branded the child who makes 'dumbbell' mistakes also created in me a fear of math and a sense that I would never excel at it. Somehow in college, I regained my interest in math and even ended up majoring in it. But I never stopped thinking about my dad's way of handling mistakes. Not only that, but as a teacher and a tutor, I have seen how students freeze up when they find they are making mistakes. Surely, I thought, there must be a better way to deal with students' mistakes. Here are some thoughts on how I try to treat mistakes in a more positive way, a way that helps students actually learn to appreciate their mistakes. Procedure: When I'm working with a student on some problem and he/she makes a mistake, I congratulate him/her. "Hey, way to go! You just made an excellent mistake." The student usually shoots me a sidelong glance as if to check whether or not I just dropped down from Neptune. In this example, let's say the student just told me that: - 3 - 5 equals + 8 "No, I'm serious," I continue. "You just made a mistake that will help you understand what's really going on in this problem." Now, grudging seriousness from my young student. "What I want you to do," I say, "is tell me why you think the answer should be positive 8." "Well, doesn't a negative and a negative make a positive?" "Good question," I say. "When does a negative and a negative make a positive?" "When you're multiplying, right?" the student replies. "True," I say. "A negative number times another negative number gives you a positive number." "So don't two negatives always make a positive?" the student asks. At this point, I would break out of the Socratic mode and simply point out that addition is different than multiplication. I would use a quick analogy to explain why: - 3 - 5 = - 8 [ - 3 means you owe $3. - 5 means you owe $5. If you owe $3, and you also owe $5, altogether you owe $8, so the answer is - 8 ] When it appears that the student understands, I ask him three key questions: 1) What was your mistake? 2) What made you think this was true? 3) But what is in fact true? Once the student can answer these three questions clearly and completely, I do a little role-playing activity to reinforce the concept. The student and I switch roles. I pretend I am a student making this mistake, and the student is now the tutor. I make the mistake, and s/he must catch it and then lead me through the same process to clarify my thinking. Once a student can not only catch a mistake but can teach it, s/he really has nailed it down. Here, in a nutshell, are the five steps I go through to help students work through their mistakes in a constructive way. P - Point out the mistake and congratulate the student. E - Explore the mistake. Help the student do some detective work to figure out how or why s/he came to make this particular mistake. T - Teach the concept. A - Ask the student the three key questions. R - Role-reverse to reinforce the concept. You can recall the process with this acronym: P.E.T.A.R. Why go to all this trouble? Two main reasons: 1) First of all, this approach is gentle. It avoids creating scars that lead to math anxiety, and it keeps the learning process fun and light. 2) But just as important, this approach helps students become learners for life. We as adults are always learning. How? From our mistakes. Does anyone beat up on us when we learn in this way? Hopefully not! So if we teach children to learn from their mistakes, we help them develop the mature habit that will allow them to be lifelong learners. If you want to remember the gist of this whole discussion, just memorize this one little phrase: "WAY TO GO! THAT'S AN EXCELLENT MISTAKE!"