Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
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|
We'll now look at how two middle school students, Sara and Evan, solved two similar Building Rafts problems.
Just to be clear: At this level, we are not concerned with formal proof, but we are concerned with student reasoning. Students must be able to provide convincing mathematical arguments to justify their work. One series of steps in thinking about such arguments is based on the work of John Mason, to wit: First, can you convince yourself? Next, can you convince a friend? Finally, can you convince a skeptic? If students can make a convincing argument, we can then show them how to take the next step: making a formal proof. As you observe Sara and Evan's work, ask yourself: Have these students reasoned well? Have they provided convincing arguments?
Note: If you have Cuisenaire rods available, you may want to use them as you work through this section.
First, let's see how Sara approached the problem.
Sara had an unlimited supply of red Cuisenaire rods. The dimensions of one red rod are 2 cm by 1 cm by 1 cm:
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