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Secondary Teachers’ Views about Proof and Judgements on Mathematical Arguments

김한길
한국수학교육학회|2022.03|Mathematics Education Research and Practice|제25권 제1호|pp. 65-89|DOI https://doi.org/10.7468/jksmed.2022.25.1.65

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참고문헌

키워드

ProofReasoningSecondary TeacherTeacher Knowledge.

초록

Despite its recognition in the field of mathematics education and mathematics, students’ understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers’ judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

Abstract

Despite its recognition in the field of mathematics education and mathematics, students’ understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers’ judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

참고문헌 (69)

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관련 논문AI추천

High school students’ evaluation of mathematical arguments as proof: Exploring relationships between understanding, convincingness, and evaluationHangil Kim한국수학교육학회 · Mathematics Education Research and Practice2024 · 제27권 제2호Investigating the substance and acceptability of empirical arguments: The case of maximum-minimum theorem and intermediate value theorem in Korean textbooks김한길한국수학교육학회 · Mathematics Education Research and Practice2024 · 제27권 제1호수학 교사와 예비교사의 추론 및 증명구성 역량 및 특성 탐색김구연, 유은수한국수학교육학회 · 수학교육2019 · 제58권 제2호Guidance offered to teachers in curriculum materials for engaging students in proof tasks: The case of Korean grade 8 geometry김한길한국수학교육학회 · Mathematics Education Research and Practice2024 · 제27권 제2호Middle School Mathematics Teachers’ Responses to a Student’s Mistaken Mathematical Conjecture and Justification김영옥영남수학회 · East Asian Mathematical Journal2013 · 제29권 제2호Problem Posing in the Instruction of Proof: Bridging Everyday Lesson and Proof김한길한국수학교육학회 · Mathematics Education Research and Practice2021 · 제24권 제3호

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