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학제간연구 과학기술학 뇌인지과학 기술정책 기타 복합학

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논문 기본 정보

자료유형
학술저널
저자정보
저널정보
한국수학교육학회 수학교육 수학교육 제48권 제3호
발행연도
2009.1
수록면
303 - 328 (26page)

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In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations ―especially verval, visual and symbolic representations― and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the 0～2 vervalism level, but in the third class, about 65% of students are in the 6～7 level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in 11 items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.
#교구 #수학적 표현 #수학적 행동 특성 #정다면체 #manipulative materials #mathematical representation #mathematical behavioral characteristics #regular polytopes

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참고문헌 (51)

참고문헌 신청
Dienes,Z.P / 1960 / Building up mathematics / Hutchinson Educational google schola Fennema,E / 1973 / Manipulatives in the classroom / Arithematic Teacher 20 : 350 ~ 352 google schola Harel, G / 1994 / The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical concepts in Adavanced mathematical Thinking / Kluwer Academic Publishers : 82 ~ 94 google schola Lesh, R / 1987 / Experts from the conference in Problems of representation in Teaching and Learning of Mathematics / Lawrence Erlbaum Associates google schola Nakahara,T / 1994 / Study of the Representational system in Mathematics Eduction / Hiroshima journal of Mathematics Education 2 : 59 ~ 67 google schola

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