Observing Student Reasoning and Proof
 Introduction | Problem: Building Rafts with Rods | Solution: Building Rafts with Rods | Student Work #1 | Questions and Answers #1 | Student Work Reflection #1 | Student Work #2 | Questions and Answers #2 | Student Work Reflection #2 | Observe Classroom | Classroom Practice | Your Journal
 Now watch an extended video excerpt (duration 3:44) at left of the class you have just seen as they work on the Building Rafts with Rods problem. This problem encourages students to find a pattern or structure for the surface area of the raft as they add additional rods. The goal is for students to move from the more obvious recursive pattern -- a pattern in which succeeding results are based on the prior result -- to a general pattern for any given number of rods. Students use concrete materials as a representation to help them see how the pattern is growing. They communicate their ideas to one another to help test conjectures, refine ideas, and develop formulas. The teacher's role -- that is, phrasing questions to guide students, rather than telling them what to do -- is a critical part of developing reasoning skills. After you have completed the activity and watched the video segment, reflect on the following questions: How does the structure of the lesson encourage reasoning among the students? What is the evidence of student reasoning? Do students justify their answers? How? What parts of the reasoning process are the students struggling with? Is there evidence of proof for the general formula? How does the teacher guide the students without telling them what to do?
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