• Title/Summary/Keyword: Quasi-empirical mathematical philosophy

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Development and Application of Teaching and Learning Materials for Gifted Students in Elementary School (초등수학영재를 위한 교수학습 자료 개발 및 적용)

  • Kim, Sung Joon
    • East Asian mathematical journal
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    • v.37 no.4
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    • pp.443-460
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    • 2021
  • This study analyzes the characteristics of elementary math gifted classes through the development and application of teaching and learning materials. We used the guided reinvention methods including quasi-experiential perspectives. To this end, the applicability of Lakatos' quasi-empirical mathematical philosophy in elementary mathematics was examined, and the criteria for the development of teaching and learning materials for gifted students were presented, and then this study was conducted in this theoretical background. The subjects of the study were 21 elementary students at P University's Institute of Science and Gifted Education, and non-face-to-face real-time classes were conducted. Classes were divided into introduction, deployment1, deployment2, organization stages, and in each stage, small group cooperative learning was conducted based on group activities, and in this process, the characteristics of elementary mathematics gifted were analyzed. As a result of the study, elementary mathematics gifted students did not clearly present the essence of justification in the addition algorithm of fractions, but presented various interpretations of 'wrong' mathematics. They also showed their ingenuity in the process of spontaneously developing 'wrong' mathematics. On the other hand, by taking interest in new mathematics starting from 'wrong' mathematics, negative perceptions about it could be improved positively. It is expected that the development of teaching and learning materials dealing with various and original topics for the gifted students in elementary school will proceed through follow-up research.

A Study on the Application of Lakatos's Methodology to Teaching Elementary Mathematics (Lakatos 방법론을 초등수학에 적용하기 위한 연구)

  • 강문봉
    • Journal of Educational Research in Mathematics
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    • v.14 no.2
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    • pp.143-156
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    • 2004
  • Lakatos's mathematical philosophy implies that the mathematical knowledge is quasi-empirical and provides the context where mathematics grows and develops. So, it is educationally significant. But, it is not easy to apply Lakatos's methodology to teaching elementary mathematics, because Lakatos's logic of the mathematical discovery is based on the proofs and refutations but elementary mathematics does not contain any proof. This study is to develop the schemes that apply Lakatos's methodology to teaching elementary mathematics and to provide the teaching examples. I devised the teaching process and the curriculum development method. And I developed the teaching examples.

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A Study on Discrete Mathematics Subjects Focused on the Network Problem for the Mathematically Gifted Students in the Elementary School (초등 영재교육에 적용 가능한 이산수학 주제의 내용 구성에 관한 소고 -네트워크 문제를 중심으로-)

  • Choi, Keun-Bae
    • School Mathematics
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    • v.7 no.4
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    • pp.353-373
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    • 2005
  • The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

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