Assessing high school students’ understanding of geometric proof

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Abstract
Although proof and reasoning are seen as fundamental components of learning mathematics, research shows that students continue to struggle with understanding geometric proofs. In an exploratory study, we investigated two components of students’ understanding—their agreement with principles of proof understanding and their ability to construct proofs. This study focused on the development of two instruments for gathering information regarding these two components. Outcomes of the study include a ‘Proof Principles Questionnaire’ and a ‘Proof Construction Assessment.’ Data generated by these instruments indicate that students may not be well aware of the internal logic requirements of formal proofs. Although students agree that proofs must be general, they are easily swayed by arguments based on a finite number of examples. Some students claim that a prototypical example is sufficient for satisfying generality requirements. In terms of proof‐construction ability, students performed best on fill‐in type proofs and poorly on proofs that had to be fully constructed.

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