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Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

  • Michael OehrtmanEmail author
  • Anton E. Lawson
Article

Abstract

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.

Key words

axiom axiomatic method disproof hypothesis nature of mathematics nature of science proof theorem theory 

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Copyright information

© National Science Council, Taiwan 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsArizona State UniversityTempeUSA
  2. 2.School of Life SciencesArizona State UniversityTempeUSA

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