This study followed the Exploration-Proof Spectrum, [EP-Spectrum], by observing the development of deductive reasoning to provide evidence of the spectrum from exploration to argumentation and then to proof production. The aim of this study was to evaluate students’ performance at making inferences during explorative and argumentative activities. The teaching experiment, employing the exploration approach, was conducted with a class of 35 ninth-graders in Taiwan. We compared the different types of inferences made during exploration, argumentation, and proof. Through a teaching experiment concerning one specific geometric property, the study discovered that the continuity and discontinuity of a logical structure exists in each stage prior to the proof stage, and some results demonstrated that exploration and argumentation are useful to students’ deductive reasoning.
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Construction and Transformation of Logical Structures in Ninth-graders´ Inferring Types
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