Browse > Article
http://dx.doi.org/10.9722/JGTE.2016.26.1.211

Characteristics of Algebraic Thinking and its Errors by Mathematically Gifted Students  

Kim, Kyung Eun (Pusan National University)
Seo, Hae Ae (Pusan National University)
Kim, Dong Hwa (Pusan National University)
Publication Information
Journal of Gifted/Talented Education / v.26, no.1, 2016 , pp. 211-230 More about this Journal
Abstract
The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.
Keywords
Mathematically gifted students; Algebraic thinking; Mathematical errors; Variables;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 교육부 (2013). 제3차 영재교육종합진흥계획(2013-2017). 서울: 교육부.
2 김남희, 나귀수, 박경미, 이경화, 정영옥, 홍진곤 (2011). 수학교육과정과 교재연구. 서울: 경문사.
3 김래영, 이민희 (2013). 중학교 2학년 서술형 평가 문항 반응에서 나타난 오류 분석: 대수 영역을 중심으로. 수학교육학연구, 23(3), 389-406.
4 김민정, 이경화, 송상헌 (2008). 초등 수학영재의 대수적 사고 특성에 관한 분석. 학교수학, 10(1), 23-42.
5 김성준 (2002a). 대수적 사고와 대수 기호에 관한 고찰. 수학교육학연구, 12(2), 229-245.
6 김성준 (2002b). 대수적 사고의 기원에 관한 고찰. 한국수학사학회지, 15(2), 49-68.
7 김성준 (2002c). 수학 학습에서 이행에 관한 고찰: 산술과 대수를 중심으로. 수학교육학연구, 12(1), 29-48.
8 김성준 (2004). 대수의 사고 요소 분석 및 학습-지도 방안의 탐색. 박사학위논문. 서울대학교 대학원.
9 김홍원 (1998). 수학 영재 판별 도구 개발-수학 창의적 문제 해결력 검사를 중심으로-. 영재교육연구, 8(2), 69-89.
10 남승인 (2011). 수학영재교육 대상자의 수학용어에 대한 오개념 실태 조사. 한국초등수학교육학회지, 15(1), 179-198.
11 류희찬, 김미정 (2004). 산술적 지식과 대수적 지식 사이의 이행 과정에서 나타난 연결과 단절 현상에 관한 연구. 수학교육학논총, 25, 269-295.
12 박미진, 서혜애, 김동화, 김지나, 남정희, 이상원, 김수진 (2013). 과학.수학 영재의 다중지능, 자기조절학습능력 및 개인성향의 차이. 영재교육연구, 23(5), 697-713.   DOI
13 송상헌, 임재훈, 정영옥, 권석일, 김지원 (2007). 초등수학영재들이 페그퍼즐 과제에서 보여주는 대수적 일반화 과정 분석. 수학교육학연구, 17(2), 163-177.
14 우정호, 김남희 (1996). 변수 개념의 교수학적 분석 및 학습-지도 방향 탐색. 수학교육학연구, 6(2), 197-210.
15 우정호, 김성준 (2007). 대수의 사고 요소 분석 및 학습-지도 방안의 탐색. 수학교육학연구, 17(4), 453-475.
16 유미경, 류성림 (2013). 초등수학영재와 일반학생의 패턴의 유형에 따른 일반화 방법 비교. 학교수학, 15(2), 459-479.
17 정현도, 강신포, 김성준 (2010). 초등학교 서술형 평가에서 나타나는 오류 유형 분석. 한국초등수학교육학회지, 14(3), 885-905.
18 최영기, 도종훈 (2004). 수학 영재학생들의 인지적, 정의적, 창의적 특성 분석. 학교수학, 6(4), 361-372.
19 Bell, A. (1996). Algebraic thought and the role of a manipulable symbolic language. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching. (pp.151-154). Netherlands: Kluwer Academic Publishers.
20 Blanton, M., Levi, L., Crites, T., & Dougherty, B. J. (2011). Developing essential understanding of algebraic thinking in grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
21 Clements, M. A. (1980). Analyzing children's errors on written mathematical tasks. Educational Studies in Mathematics, 2, 121
22 Newman, M. A. (1977). An analysis of sixth-grade pupils'errors on written mathematical tasks. In M. A. Clements & J. Foyster (Eds.), Research in Mathematics Education in Australia (pp.269-287). Melbourne: Swinburne College Press.
23 Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. New York, NY: Kluwer Academic Publishers.
24 Movshovitz-Hadar, N., Zaslavsky, O., & Inbar, S. (1987). An empirical classification model for errors in high school mathematics. Journal for Research in Mathematics Education, 18(1), 3-14.   DOI
25 Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago, IL: The University of Chicago Press.
26 Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180-184.
27 Smith, J. P., & Thompson, P. W. (2008). Quantitative reasoning and the development of algebraic reasoning. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp.95-132). New York, NY: Lawrence Erlbaum Associates.
28 Slavit, D. (1999). The role of operation sense in transitions from arithmetic to algebraic thought. Educational Studies in Mathematics, 37, 251-274.
29 Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. Coxford & A. Shulte (Eds.), The Ideas of algebra, K-12 (pp. 8-19). Reston, VA: NCTM.