<p>This study explores high school mathematics teachers’ perceptions of visual proofs, or Proofs Without Words (PWWs). Using a mixed-methods design combining semi-structured interviews (<i>n</i> = 8) and questionnaires (<i>n</i> = 122), we examined (1) teachers’ acceptance of visual proofs as valid, (2) their perceptions of colleagues’ likely evaluations, and (3) their preferences regarding classroom use. Interviews first revealed two distinct levels of acceptance: Unconditional Acceptance, in which the student-produced visual proof was judged sufficient as presented, and Explanation-required Acceptance, in which teachers accepted the proof but preferred it to be accompanied by a verbal explanation. In questionnaire responses, 40% of respondents unconditionally accepted their assigned visual proof, and an additional 29% expressed explanation-required acceptance. However, many participants anticipated that their peers would assign lower grades to the visual proof than they would (58%). Notably, 93% indicated willingness to incorporate visual proofs into their teaching, citing pedagogical, aesthetic, and epistemological benefits. These findings indicate broad pedagogical endorsement of visual proofs, alongside tensions regarding proof standards that warrant further discussion in mathematics teacher education.</p>

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Teachers’ Perspectives on Visual Proofs: Assessing Validity, Anticipating Peer Views, and Considering Classroom use

  • Raz Harel,
  • Nadav Marco

摘要

This study explores high school mathematics teachers’ perceptions of visual proofs, or Proofs Without Words (PWWs). Using a mixed-methods design combining semi-structured interviews (n = 8) and questionnaires (n = 122), we examined (1) teachers’ acceptance of visual proofs as valid, (2) their perceptions of colleagues’ likely evaluations, and (3) their preferences regarding classroom use. Interviews first revealed two distinct levels of acceptance: Unconditional Acceptance, in which the student-produced visual proof was judged sufficient as presented, and Explanation-required Acceptance, in which teachers accepted the proof but preferred it to be accompanied by a verbal explanation. In questionnaire responses, 40% of respondents unconditionally accepted their assigned visual proof, and an additional 29% expressed explanation-required acceptance. However, many participants anticipated that their peers would assign lower grades to the visual proof than they would (58%). Notably, 93% indicated willingness to incorporate visual proofs into their teaching, citing pedagogical, aesthetic, and epistemological benefits. These findings indicate broad pedagogical endorsement of visual proofs, alongside tensions regarding proof standards that warrant further discussion in mathematics teacher education.