The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Examining Pre- and In-service Mathematics Teachers' Proficiencies in Reasoning and Proof-Production

수학 교사와 예비교사의 추론 및 증명구성 역량 및 특성 탐색

  • Received : 2019.01.18
  • Accepted : 2019.03.26
  • Published : 2019.05.31
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Abstract

This study aims to examine pre- and in-service mathematics teachers' reasoning and how they justify their reasoning. For this purpose, we developed a set of mathematical tasks that are based on mathematical contents for middle grade students and conducted the survey to pre- and in-service teachers in Korea. Twenty-five pre-service teachers and 8 in-service teachers participated in the survey. The findings from the data analysis suggested as follows: a) the pre- and in-service mathematics teachers seemed to be very dependent of the manipulation of algebraic expressions so that they attempt to justify only by means of procedures such as known algorithms, rules, facts, etc., rather than trying to find out a mathematical structure in the first instance, b) the proof that teachers produced did not satisfy the generality when they attempted to justify using by other ways than the algebraic manipulation, c) the teachers appeared to rely on using formulas for finding patters and justifying their reasoning, d) a considerable number of the teachers seemed to stay at level 2 in terms of the proof production level, and e) more than 3/4 of the participating teachers appeared to have difficulty in mathematical reasoning and proof production particularly when faced completely new mathematical tasks.

이 연구에서는 중등 수학 교사와 예비교사들이 추론과 증명을 어떻게 이해하여 구성하는지를 탐색하였다. 연구 참여자들은 대부분 대수적인 증명을 시도하는데 이미 알고 있는 공식이나 식을 적용한 대수적 조작으로 답을 구하는 것에 그치며 주어진 문제에 내재된 수학적 구조를 통해 증명을 구성하지는 못하였다. 또한 참여자의 상당수가 대수적 식을 통한 증명만을 완전한 증명으로 판단하였으며 대부분은 기존에 접하지 못했던 새로운 문제유형에서 추론 및 증명구성을 완성하지 못하는 것으로 나타났다.

Keywords

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[Fig. 1] Survey Question

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[Fig. 2] Survey Question

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[Fig. 3] Survey Question

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[Fig. 4] Survey Question

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[Fig. 5] Survey Question

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[Fig. 6] Survey Question

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[Fig. 7] A Scoring Guide

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[Fig. 8] no context code

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[Fig. 9] Proof Production by Providing Examples

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[Fig. 10] Verbal Description

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[Fig. 11] Proof-Production by presenting Grid

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[Fig. 12] Proof Production by using a formula

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[Fig. 13] Proof Production by using a formula

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[Fig. 14] Proof Production by Using Formulas

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[Fig. 15] Proof Production by Empirical Argument

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[Fig. 16] Proof Production by Empirical Argument

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[Fig.17] Division of Fractions: Proof Production Level 2

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[Fig. 19] Triangles with Integer Dimensions: Proof Production Level 3

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[Fig. 20] Triangle with Integer Dimensions: Proof Production Level 1

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[Fig. 21] Proof Production Level 0

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[Fig. 22] Pentagon Train: Incorrect Proof Production

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[Fig. 23] Mismatch between Level 0 and 1

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[Fig. 18] Proof Production Level 1

[Table 1] Teaching·Learning Strategies for Promoting Reasoning (Ministry of Education, 2015, p. 55)

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[Table 2] Proof Production Level (Knuth, Choppin & Bieda, 2009, pp. 154-155)

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[Table 3] Proof Production Levels

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[Table 5] Participants Information: Inservice Teachers

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[Table 6] Instrument: Open-Ended Survey Questions

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[Table 7] Open-Ended Survey Questions

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[Table 8] Code Book

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[Table 9] The Even Number Sum Proof-Production

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[Table 10] Proof Production Levels 2

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[Table 11] Proof Production by Empirical Argument

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[Table 12] Division of Fractions Proof Production Levels

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[Table 13] Triangle with Integer Dimensions Proof Production Levels

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[Table 4] Participants Information: Preservice Teachers

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