Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Observing Student Reasoning and Proof
 Introduction | Inscribed Triangles | Problem Reflection #1 | Inscribed Triangle Continued | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal

Think about the student work and reflect on the following questions. When you've formulated an answer to each question, select "Show Answer" to see our response.

 1. How does this problem bring up the need for proof? Show Answer
 Sample Answer: Although the problem begins with a lot of procedural work, drawing triangles, measuring angles, etc., it also leads well to a need for a conjecture, or what Sonia calls an "argument," that angle C is always 90 degrees. By asking the students to measure at least 5 triangles, the teacher has also provided a way to get enough data for students to observe patterns, see discrepancies and make conjectures about both. However, they can begin to see that individual observations, no matter how numerous, will not constitute proof that angle C must be a right angle.
 2. How do the students show their understanding of proof? Show Answer
 Sample Answer: Ms. Saleh's questions bring out that the students understand that something that is true must be true for "every single" case and they see that this is not feasible. It's unclear whether they understand that it could be proved without testing each case, but they are reasoning about the mathematical situation and will move on to testing conjectures.

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