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

Schwartz (1989) suggested that students using the Geometric Supposer ¹ 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 teachers using the Geometric Supposer to teach Euclidean geometry noticed that some students did not seem to appreciate the teachers’ insistence on mathematical proofs when they had measurement evidence to support their conjectures. They did not distinguish between evidence and a deductive proof as ways of knowing that a geometrical statement is true.