The Geometric Supposer

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 ...