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http://dx.doi.org/10.7468/jksmec.2016.19.3.223

An Analysis of Algebraic Thinking by Third Graders  

Pang, JeongSuk (Korea National University of Education)
Choi, InYoung (Graduate School of Korea National University of Education)
Publication Information
Education of Primary School Mathematics / v.19, no.3, 2016 , pp. 223-247 More about this Journal
Abstract
Given the importance of developing algebraic thinking from early grades, this study investigated an overall performance and main characteristics of algebraic thinking from a total of 197 third grade students. The national elementary mathematics curriculum in Korea does not emphasize directly essential elements of algebraic thinking but indicates indirectly some of them. This study compared our students' performance related to algebraic thinking with results of Blanton et al. (2015) which reported considerable progress of algebraic thinking by emphasizing it through a regular curriculum. The results of this study showed that Korean students solved many items correctly as compatible to Blanton et al. (2015). However, our students tended to use 'computational' strategies rather than 'structural' ones in the process of solving items related to equation. When it comes to making algebraic expressions, they tended to assign a particular value to the unknown quantity followed by the equal sign. This paper is expected to explore the algebraic thinking by elementary school students and to provide implications of how to promote students' algebraic thinking.
Keywords
elementary school students' algebraic thinking; an analysis of algebraic thinking; characteristics of algebraic thinking;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 교육부 (2015a). 수학과 교육과정. 교육부 고시 제2015-74호 [별책 8].(Ministry of Education (2015a). Mathematics curriculum. Ministry of Education Notice 2015-74 [supplement 8].)
2 교육부 (2015b). 수학 1-1. 서울: 천재교육.(Ministry of Education (2015b). Elementary Mathematics 1-1. Seoul: Chunjae Education.)
3 기정순.정영옥 (2008). 등호 문맥에 따른 초등학생의 등호 개념 이해와 지도 방법 연구. 학교수학, 10(4), 537-555.(Ki, J. S. & Chong, Y. O. (2008). The analysis of elementary school students' understanding of the concept of equality sign in contexts and the effects of its teaching methods. School Mathematics, 10(4), 537-555.)
4 김정원 (2014). 초등학교 학생들의 함수적 사고의 특징 및 지도 방향 탐색. 박사학위논문, 한국교원대학교.(Kim, J. W. (2014). An investigation of the characteristics and instructional implications of functional thinking for elementary school students. Doctoral dissertation, KNUE.)
5 김정원.최지영.방정숙 (2016). 초등학생들은 '='를 어떻게 이해하는가?-문항유형별 실태조사. 수학교육학연구, 26(1), 79-101.(Kim, J. W., Choi, J, Y., & Pang, J. S. (2016). How do elementary school students understanding '='? - performance in various item types. Journal of Educational Research in Mathematics, 26(1), 79-101.)
6 우정호.김성준 (2007). 대수의 사고 요소 분석 및 학습-지도 방안의 탐색. 수학교육학연구, 17(4), 453-475.(Woo, J. H. & Kim, S. J. (2007). Analysis of the algebraic thinking factors and search for the direction of its learning and teaching. Journal of Educational Research in Mathematics, 17(4), 453-475.)
7 이경림.강정기.노은환 (2014). 중학교 1학년 학생의 대수적 표상 전환 및 정교화 연구. 한국학교수학회논문집, 17(4), 507-539.(Lee, K. R., Kang, J. G., & Roh, E. H. (2014). A study on the transformation of algebraic representation and the elaboration for grade 7. Journal of the Korean School Mathematics Society, 17(4), 507-539.)
8 최지영.방정숙 (2011). 초등학생들의 범자연수 연산의 성질에 대한 이해 분석. 수학교육학연구, 21(3), 239-259.(Choi, J. Y. & Pang, J. S. (2011). An analysis of the elementary school students; understanding of the properties of whole number operation. Journal of Educational Research in Mathematics, 21(3), 239-259.)
9 최지영.방정숙(2012). 초등학교 2, 4, 6학년 학생들의 함수적 관계 이해 실태 조사. 학교수학, 14(3), 275-296.(Choi, J. Y. & Pang, J. S. (2012). An analysis of the elementary school students; understanding of functional relationships. School Mathematics, 14(3), 275-296.)
10 최지영.방정숙 (2014). 초등학교 6학년 학생들의 함수적 관계 인식 및 사고 과정 분석-기하 패턴 탐구 상황에서의 사례연구-. 수학교육학연구, 24(2), 205-225.(Choi, J. Y. & Pang, J. S. (2014). An analysis on sixth graders' recognition and thinking of functional relationships-a case study with geometric growing patterns. Journal of Educational Research in Mathematics, 24(2), 205-225.)
11 하수현.이광호 (2011). 초등학교 6학년 학생들의 변수 개념 이해에 관한 사례 연구. 한국수학교육학회지 시리즈 A <수학교육>, 50(2), 213-231.(Ha, S. H. & Lee, G. H. (2011). Case study on the 6th graders' understanding of concepts of variable. The Mathematical Education, 50(2), 213-231.)
12 Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247.   DOI
13 Brizuela, B. M., Blanton, M., Sawrey, K., Newman-Owens, A., & Murphy Gardiner, A. (2015). Children's use of variables and variable notation to represent their algebraic ideas. Mathematical Thinking and Learning, 17(1), 34-63.   DOI
14 Blanton, M., & Kaput, J. (2004). Elementary grades students' capacity for functional thinking. In Proceedings of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 135-142). Bergen: Bergen University College.
15 Blanton, M., Levi, L., Crites, T., & Dougherty, B. (2011). Developing essential understanding of algebraic thinking in grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
16 Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J. S. (2015). The development of children's algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39-87.   DOI
17 Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children's learning of early algebra. Learning and Individual Differences, 38, 61-67.   DOI
18 Carpenter, T. P., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
19 Carraher, D. W., Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669-705). Reston, VA: National Council of Teachers of Mathematics.
20 Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 56-60.
21 Moss, J., & McNab, S, L. (2011). An approach to geometric and numeric patterning that fosters second grade students' reasoning and generalizing about functions and co-variation. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 277-302). Heidelberg: Springer.
22 Kaput, J. J. (2008). What is algebra? what is algebraic reasoning? In J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5-17). New York: Lawrence Erlbaum.
23 Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.
24 Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316-350.   DOI
25 Russell, S. J., Schifter, D., & Bastable, V. (2011). Developing algebraic thinking in the context of arithmetic. In J. Cai, & E. Knuth (Eds.), Early Algebraization: A Global Dialogue from Multiple Perspectives (pp. 43-69). New York: Springer.
26 Schifter, D., Monk, S., Russell, S. J., & Bastable, V. (2008). Early algebra: What does understanding the laws of arithmetic mean in the elementary grades? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 413-447). New York: Lawrence Erlbaum.
27 Warren, E. A., & Cooper, T. J. (2005). Introducing functional thinking in year 2: A case study of early algebra teaching. Comtemporary Issues in Early Childhood, 6(2), 150-162.   DOI