High school students’ evaluation of mathematical arguments as proof: Exploring relationships between understanding, convincingness, and evaluation
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Researchers continue to emphasize the centrality of proof in the context of school mathematics and the importance of proof to student learning of mathematics is well articulated in nationwide curricula. However, researchers reported that students’ performance in proving tasks is not promising and students are not likely to see the need to prove a proposition even if they learned mathematical proof previously. Research attributes this issue to students’ tendencies to accept an empirical argument as proof for a mathematical proposition, thus not being able to recognize the limitation of an empirical argument as proof for a mathematical proposition. In Korea, there is little research that investigated high school students’ views about the need for proof in mathematics and their understanding of the limitation of an empirical argument as proof for a mathematical generalization. Sixty-two 11th graders were invited to participate in an online survey and the responses were recorded in writing and on either a four- or five-point Likert scale. The students were asked to express their agreement with the need of proof in school mathematics and to evaluate a set of mathematical arguments as to whether the given arguments were proofs. Results indicate that a slight majority of students were able to identify a proof amongst the given arguments with the vast majority of students acknowledging the need for proof in mathematics.
Abstract
Researchers continue to emphasize the centrality of proof in the context of school mathematics and the importance of proof to student learning of mathematics is well articulated in nationwide curricula. However, researchers reported that students’ performance in proving tasks is not promising and students are not likely to see the need to prove a proposition even if they learned mathematical proof previously. Research attributes this issue to students’ tendencies to accept an empirical argument as proof for a mathematical proposition, thus not being able to recognize the limitation of an empirical argument as proof for a mathematical proposition. In Korea, there is little research that investigated high school students’ views about the need for proof in mathematics and their understanding of the limitation of an empirical argument as proof for a mathematical generalization. Sixty-two 11th graders were invited to participate in an online survey and the responses were recorded in writing and on either a four- or five-point Likert scale. The students were asked to express their agreement with the need of proof in school mathematics and to evaluate a set of mathematical arguments as to whether the given arguments were proofs. Results indicate that a slight majority of students were able to identify a proof amongst the given arguments with the vast majority of students acknowledging the need for proof in mathematics.
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