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The Geometric Supposer by Beth Wilson, Michal Yerushalmy, Judah L. Schwartz

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6    Instructional Implications of Students’ Understandings of the Differences Between Empirical Verification and Mathematical Proof

Daniel Chazan

Michigan State University

Schwartz (1989) suggested that students using the Geometric Supposer1 computer microworld should investigate geometry in both scientific (empirical) and mathematical (deductive) ways and should use what Polya (1954) called plausible and demonstrative reasoning.2 In classrooms, teachers typically ask students to make a construction with the Supposer, create hypotheses and test them with the Supposer’s measurement capabilities, write conjectures, and then provide supporting arguments (formal or informal proofs) for their conjectures (Yerushalmy & Houde, 1986). High school ...

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