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
"Teachers of mathematics in high school should strive to create a climate of discussing, questioning, and listening in their classes. Teachers should expect students to seek, formulate, and critique explanations so that classes become communities of inquiry. Teachers should also help students discuss the logical structure of their own arguments. Critiquing arguments and discussing conjectures are delicate matters: plausible guesses should be discussed even if they turn out to be wrong. Teachers should make clear that the ideas are at stake, not the students who suggest them. With guidance, students should develop high standards for accepting explanations, and they should understand that they have both the right and the responsibility to develop such arguments."

(NCTM, 2000, p. 346)


By the time students are in high school, they have had considerable experiences with mathematical reasoning and have at least some familiarity with concepts of proof. In grades 9-12, students must build on this experience to make sense of increasingly abstract aspects of mathematics, for example in terminology and representation. Greater demands on mathematical reasoning occur. In particular, high school work carries an expectation that students generate, evaluate and revise mathematical arguments themselves. By the of the high school years, students must have a clear understanding of the role of proof in mathematics, and should also have a repertoire of reasoning and proof approaches that they can use in mathematical work.

These elements form the core of the reasoning and proof standard. Let's examine several points in more detail, to expand working our knowledge and definition of the concept.

Next  Elements of the Standard

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