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Unformatted text preview: G. González A. Poetzel Problems on Explaining Procedures Do one problem in algebra and one problem in geometry for homework. Read and think about all of the problems. 1. Susi Wan is teaching the procedure for bisecting a segment to her geometry class. She says: “If you have a segment AB, put the tip of the compass on A, fix the radius of the compass so that it has the length of segment AB, and then trace a circle with center on A. Don’t change the radius and trace a circle with center on B. When you join the intersection points of the two circles you have the perpendicular bisector.” a. Discuss whether Susi is promoting “flexibility” when performing a procedure. b. If you think that there are things that she should say differently, script a different explanation. If you think that her explanation is fine, identify her teaching actions according to the rubric of explaining procedures. c. Make a diagram that you might expect students to have as a result of this new explanation. d. One of Susi’s students raises her hand and says, “How do we know for sure if it really is the perpendicular bisector?”. Script a response to this question that can help students to know how to justify the procedure. 2. Ron Schwatz is teaching a lesson on solving linear equations to his algebra class and he says: “Make sure that you align all the equal signs as you solve the equation. Also, if you add something to the right side make sure that you add the same thing to the left side. The same applies when you subtract something to one side. You should do the same to the other side to keep the equation balanced. I want to see zeros in the next line when you get rid of a term. At the end, the x always goes in the left side because you are saying ‘my x equals whatever.’” a. What kind of work do you expect Ron’s students to do when they solve equations? b. What are plausible reasons for Ron’s emphasis in steps when performing the procedure? c. How could Ron promote “flexibility” when performing a procedure? d. How could Ron modify his explanation so that he would teach students the justification for the procedure? e. How could Ron teach students to have means of control? f. Script a few lines about what should Ron say to teach students about means of control. G. González A. Poetzel 3. Miguel Feliciano is teaching his algebra students how to make a table and a graph of a quadratic function. a. Select the first two examples that he can use. Explain your choice of examples (what criteria helped you to choose these examples?). b. Identify notation that Miguel should teach students to use. c. Script a few lines to describe what he should say to lead students to make decisions about what points would give them enough information to draw the graph. d. If Miguel wanted to hold his students accountable for performing and understanding this procedure, what might he do next in his lesson? Justify your choice of actions using the rubric for explaining a procedure. 4. Lisa Carr is teaching her geometry students how to calculate the area of a regular polygon given the length of one of its sides. a. Identify mathematical terms that she should include in her explanation. b. Choose two examples that she could present to students. Explain what the unique features are for each one of the examples and what elements the two examples have in common. c. Script a few lines that she could say to her students to summarize the procedure by comparing the two examples. d. Create a new problem on which students should be able to work on their own and that could be useful for Lisa to assess their understanding of the procedure for calculating areas of regular polygons. ...
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- Fall '11