Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Reasoning and ProofSession 04 Overviewtab atab bTab ctab dtab eReference
Part C

Defining Reasoning and Proof
  Introduction | Deductive Reasoning | Proof by Contradiction | Inductive Reasoning | Proof by Mathematical Induction | The Teachers' Role | Your Journal


Consider the standard, the material in this section and the examples you have worked through earlier in the course. Reflect on how you can support reasoning and proof in your own classroom. Choose one of the questions to answer in your journal.

Questions to write and reflect about:
  • Suppose one of your students thinks that demonstrating that a mathematical conjecture is true for 1,000 instances constitutes formal proof. How would you respond?
  • Put yourself in the position of a student who has always been very proficient at mathematical procedures, receiving consistently high marks and expecting to be one of the fastest students to figure something out or hand something in. Now consider that this student has encountered a formal proof of a geometry conjecture for the first time and is baffled by it. She challenges the teacher you by saying, "that's not math, I'm good at math. I don't know what that even is." How would you respond?
  • How can you get a sense of when and in what way to introduce formal definitions and rigorous proofs or procedures in the context of working with new content with your class?
  • If a colleague challenged you to say why the reasoning and proof standard was valuable and helpful in your work as a mathematics teacher, what would you say? Do you believe it is? Why or why not?
Three ways to write and reflect:
  • Use pen and paper.
  • Use a word processor.
  • Use the form below.
Be sure to save what you have written before you navigate out of the journal section.


Your work will be displayed in a printer-friendly format to enable you to print.

Thanks for writing in your journal. Please keep your entries in whatever format you choose -- you will find them useful for reference later.

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