• Title/Summary/Keyword: theory of mathematical education

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Two Approaches to Introducing Abstract Algebra to Undergraduate Students (추상대수학 강좌의 두 가지 접근 방법)

  • Park Hye Sook;Kim Suh-Ryung;Kim Wan Soon
    • Communications of Mathematical Education
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    • v.19 no.4 s.24
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    • pp.599-620
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    • 2005
  • There can be two different approaches to introducing Abstract Algebra to undergraduate students: One is to introduce group concept prior to ring concept, and the other is to do the other way around. Although the former is almost conventional, it is worth while to take the latter into consideration in the viewpoint that students are already familiar to rings of integers and polynomials. In this paper, we investigated 16 most commonly used Abstract Algebra undergraduate textbooks and found that 5 of them introduce ring theory prior to group theory while the rest do the other way around. In addition, we interviewed several undergraduate students who already have taken an Abstract Algebra course to look into which approach they prefer. Then we compare pros and cons of two approaches on the basis of the results of the interview and the historico-genetic principle of teaching and learning in Abstract Algebra and suggest that it certainly be one of alternatives to introduce ring theory before group theory in its standpoint.

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Piaget's Theory in the Development of Creative Thinking

  • Supratman, Ahman Maedi
    • Research in Mathematical Education
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    • v.17 no.4
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    • pp.291-307
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    • 2013
  • Piaget's revolutionary study on the cognitive development of children has focused on the development of logic. Logical operations and a variety of classifications based on the set of accepted rules involve convergent thinking. Children and adults have logical and creative thinking which deal with a reality of thinking. This study aims to examine a cognitive structure of students, which is closely related to the Piaget's cognitive development theories of students when creative thinking. Students were given an open mathematical problem and were expected to be able to take advantage of sensitivity, fluency, flexibility, originality, and elaboration which can be seen as clearly of their structure cognitive.

A Study on Group Theoretic Approximation Model for Gwaeyul of Geomungo (거문고 괘율에 관한 군론적 근사화 모형 개발 연구)

  • Shin, Hyunyong
    • Communications of Mathematical Education
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    • v.28 no.3
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    • pp.367-374
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    • 2014
  • Recently, interdisciplinary relation is emphasized on and various models are proposed. Since group theory is one of the important areas of modern mathematics, all the mathematics teachers for secondary school are familiar with it. Group theory, the theory of symmetries, are effectively applied to music or arts. In this paper, we understand the approximation model for gwaeyul of geomungo group theoretically to show the relation between mathematics and music(Korean music, in particular). This paper, in fact, proposes a group theoretic approximation model for gwaeyul of geomungo. The materials like this will be of help to teachers who try to integrate mathematics to other areas.

The Role of "Personal Knowledge" in Solid Geometry among Primary School Mathematics Teachers

  • Patkin, Dorit
    • Research in Mathematical Education
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    • v.14 no.3
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    • pp.263-279
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    • 2010
  • Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

Mathematics Education for Gifted Students in Korea

  • Shin, Hyunyong;Han, Inki
    • Research in Mathematical Education
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    • v.4 no.2
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    • pp.79-93
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    • 2000
  • The purpose of this article is to introduce the gifted education of mathematics in Korea. We first discuss what is going on in Korea for mathematics education for gifted students. The curriculums for the institutes for gifted education are mentioned. Some focus of this article is proposing some teaching materials that are actively utilizing many basic concents of cryptography and super-string theory, along with careful use of calculators and computers. Many of the materials haven been designed with problem-posing approach on through invoking the cognitive conflict.

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MIXED MULTIPLICITIES OF MAXIMAL DEGREES

  • Thanh, Truong Thi Hong;Viet, Duong Quoc
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.605-622
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    • 2018
  • The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.