Browse > Article

A Study on the Structural Conception Formation of the Center of Mass Concept  

Choi, Byung Chul (Kyungdong High School)
Publication Information
Journal of Educational Research in Mathematics / v.26, no.1, 2016 , pp. 23-45 More about this Journal
Abstract
We are able to analyze a social or a natural phenomenon by using the conception. if we understand a concept of an object. However it is not easy to understand a concept of an object. The process of comprehending the concept is a long rigorous mental journey. Hence, understanding concepts has been emphasized in studies in education. Previous studies demonstrate that conception has a dual nature, which has both an operational and a structural nature. We are able to acknowledge that structural conception develops from an operating conception. Nevertheless, discovering a dual nature of conception and knowing whether students acquired the dual nature, especially the structural nature are difficult to achieve. In this research, I examine the operational and the structural nature of a center of mass conception and analyze whether students acquire structural nature of the center of mass conception, and find implications which we would do to build the structural conception on a concept.
Keywords
center of mass; centroid; conception; operational nature; structural nature;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Gallardo, A.(2001). "Historical-Epistemological Analysis in Mathematics education : Two Works in Didactics of Algebra" In Sutherland et al.(eds), Perspectives on School Algebra. Kluwer Academic Publishers: Dordrecht. pp. 121-139.
2 Linchevski, L. & Williams, J.(1999). "Using Intuition From Everyday Life In 'Filling' The Gap In Children's Extension Of Their Number Concept To Include The Negative Number". Educational Studies in Mathematics, 39. pp. 131-47.   DOI
3 Sfard, A. & Linchevski, L.(1994). "The Gains And The Pitfalls Of Reification- The case Of Algebra". Educational Studies in Mathematics 26. pp. 191-228.   DOI
4 Sfard, A.(1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics 22. pp. 1-36.
5 Skemp, R.(1987). The Psychology of Learning Mathematics. Routledge; Expanded American Edition.
6 Thomas, G. B.,Weir, M.D. & Hass, J. R(2010). Thomas' Calculus: Early Transcendentals. Twelfth Edition. PEARSON: International Edition.
7 박규홍 외.(2010). 수학 2. 동화사.
8 우정호(2000). 수학학습-지도원리와 방법. 서울대학교출판부.
9 정상권 외.(2004). 함수와 추론. 서울대학교 과학교육연구소.
10 최병철(2006). 음수 개념의 이해에 관한 교수학적 분석. 서울대학교 대학원 박사학위논문.
11 홍갑주(2005). 도형의 무게중심과 관련된 오개념 및 논리적 문제. 학교수학 7(4). pp. 391-402.
12 Case, R, & Sandieson. R.(1988). A developmental Approach to the Identification and Teaching of Central Conceptual Structures in Mathematics and Science in the Middle Grades. In J. Hiebert. & M. Behr.(Eds.) Research Agenda for Mathematics Education: Number Concepts and Operations in the middle Grades.(pp. 236-259). Lawrence Erlbaum Associates.
13 Cobb, P.(1988): "The tension between theories of learning and instruction in mathematics education", Educational Psychologist 23, 87-104.   DOI
14 Davis, R. B. & Maher, C. A.(1997). How students think: The role of representation. In English, L. D.(Eds.), Mathematical reasoning: Analogies, metaphors, and images. pp. 93-115.