Exploring the Nature of the Transition to Geometric Proof Through Design Experiments From the Holistic Perspective

Abstract

The gulf between empirical and deductive reasoning is a global problem that has produced many students who have extreme difficulties learning proofs. In this paper, we explore the conditions that aid students in entering into proof learning and how they can increase their ability before learning proofs through design experiments. First we discuss the theoretical backgrounds of the holistic perspective and didactical situation theory, and set our research framework as the transition from empirical to theoretical recognition consisting of the three aspects of inference, figure, and social influence. Next, we report our design experiments in plane geometry redesigned for the seventh grade, and examine how students may enter the world of proof by learning geometric transformation and construction as summarized in the three aspects of the framework. Finally, we suggest key ideas for designing lessons that promote transition.