Browse > Article
http://dx.doi.org/10.7468/mathedu.2014.53.3.383

Exploring students' thinking in proof production in geometry  

An, SunYoung (Sogang University)
Kim, Gooyeon (Sogang University)
Publication Information
The Mathematical Education / v.53, no.3, 2014 , pp. 383-397 More about this Journal
Abstract
This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.
Keywords
Students' thinking processes; middle school students; proof production; geometry;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 한인기 (2005). 한국과 러시아의 7-8학년 수학교과서 도형영역에 나타난 직관적 정당화와 엄밀한 증명, 수학교육 44(4), 535-546. (Han, I. (2005). A study on intuitive verification and rigor proof in geometry of Korean and Russian 7-8 grade's mathematics textbooks, Mathematical Education 44(4), 535-546.)   과학기술학회마을
2 이지현 (2011). 일상적 정의에서 수학적 정의로의 이행, 수학교육 50(4), 429-440. (Lee, J. H. (2011). The transition from everyday definitions to mathematical definitions: Gifted middle school students' conceptions of point and line definitions, Mathematical Education, 50(4), 429-440.)   과학기술학회마을   DOI
3 권지현, 김구연 (2013). 중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석, 수학교육 52(1), 111-128. (Kwon, J., & Kim, G. (2013). An analysis of mathematics tasks in the middle school geometry, Mathematical Education, 52(1), 111-128.)   과학기술학회마을   DOI
4 나귀수 (1997). 기하 개념의 이해와 적용에 관한 소고, 수학교육학연구 7(2), 349-358. (Na, G. S. (1997). An analysis of proof-lesson on the second grade in the middle school. Journal of the Korea Society of Educational Studies in Mathematics 7(2), 349-358.)
5 Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. Mathematics, Teachers and Children 216, 235-240.
6 Chazan, D. (1993). High school geometry students' justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics 24(4), 359-387.   DOI   ScienceOn
7 Dimakos, G., Nikoloudakis, E., Ferentinos, S., & Choustoulakis, E. (2007). Developing a proof-writing tool for novice lyceum geometry students. Teaching of Mathematics 10(2), 87-106.
8 Heinze, A., & Reiss, K. (2009). Developing argumentation and proof competences in the mathematics classroom. In D. A. Stylianou, M. L. Blanton & E. J. Knuth. (Eds.), Teaching and learning proof across the grades (pp. 191-203). New York: Routledge.
9 Harel, G. (1999). Students' understanding of proofs: A historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and its Applications 302(303), 601-613.
10 Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. Research in Collegiate Mathematics Education III 7, 234-282.
11 Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education 31, 396-428.   DOI
12 Herbst, P. G. (2006). Teaching geometry with problems: Negotiating instructional situations and mathematical tasks. Journal for Research in Mathematics Education 37(4), 313.
13 Mammana, C., & Villiani, V. (1998). Perspectives on the teaching of geometry for the 21st century. Kluwer: London.
14 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
15 Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist 23, 145-166.   DOI   ScienceOn
16 Usiskin, Z. (1982). Van hiele levels and achievement in secondary school geometry. CDASSG project report.
17 Waring, S. (2000). Can you prove it? Developing concepts of proof in primary and secondary schools. Leicester: Mathematical Association.