DOI QR코드

DOI QR Code

An Analysis on secondary school students' problem-solving ability and problem-solving process through algebraic reasoning

중고등학생의 대수적 추론 문제해결능력과 문제해결과정 분석

  • Received : 2014.09.16
  • Accepted : 2015.01.21
  • Published : 2015.02.28

Abstract

The purpose of this study is to suggest how to go about teaching and learning secondary school algebra by analyzing problem-solving ability and problem-solving process through algebraic reasoning. In doing this, 393 students' data were thoroughly analyzed after setting up the exam questions and analytic standards. As with the test conducted with technical school students, the students scored low achievement in the algebraic reasoning test and even worse the majority tried to answer the questions by substituting arbitrary numbers. The students with high problem-solving abilities tended to utilize conceptual strategies as well as procedural strategies, whereas those with low problem-solving abilities were more keen on utilizing procedural strategies. All the subject groups mentioned above frequently utilized equations in solving the questions, and when that utilization failed they were left with the unanswered questions. When solving algebraic reasoning questions, students need to be guided to utilize both strategies based on the questions.

Keywords

References

  1. 우정호, 김성준(2007). 대수의 사고 요소 분석 및 학습-지도 방안의 탐색. 수학교육학연구, 17(4), 453-475.
  2. 차현화, 홍혜경(2005). 유아의 대수적 사고능력의 발달에 대한 분석. 유아교육연구, 25(5), 31-54.
  3. 최지영(2011). 초등학교에서의 대수적 추론 능력 향상을 위한 교수-학습 방향 탐색. 한국교원대학교 대학원 박사학위 논문.
  4. 최지영, 방정숙(2008). 초등학교 4학년 학생들의 대수적 사고 분석. 수학교육논문집, 22(2), 137-164.
  5. Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115-131.
  6. Beatty, R. & Bruce, C. D. (2012). From patterns to algebra: Lessons for exploring linear relationships. Nelson Education.
  7. Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  8. Chrysostomou, M., Pitta-Pantazi, D., Tsingi, C., Cleanthous, E., & Christou, C. (2013). Examining number sense and algebraic reasoning through cognitive styles. Educational Studies in Mathematics, 83(2), 205-223. https://doi.org/10.1007/s10649-012-9448-0
  9. Dobrynina, G. & Tsankova, J. (2005). Algebraic reasoning of young students and preservice elementary teachers. Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
  10. Gelman, R. & Meck, E. (1983). Preschoolers' counting: Principles before skill. Cognition, 13(3), 343-359. https://doi.org/10.1016/0010-0277(83)90014-8
  11. Kaput, J. J. & Blanton, M. L. (2005). A teacher-centered approach to algebrafying elementary mathematics. Understanding Mathematics and Science Matters, 99-125. Mahwah, NJ: Lawrence Erlbaum.
  12. Kim, A. (2012). The impact of unbalanced development between conceptual knowledge and procedural knowledge to knowledge development of students' in rational number domain. 수학교육학연구, 22(4), 517-534.
  13. Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts: Equivalence & Variable. Zentralblatt fur Didaktik der Mathematik, 37(1), 68-76. https://doi.org/10.1007/BF02655899
  14. Lannin, J. K. (2003). Developing algebraic reasoning through generalization. Mathematics Teaching in the Middle School, 8(7), 342-348.
  15. Lins, R. L. (1990). A framework of understanding what algebraic thinking is. In G. Booker, P. Cobb and T. N. Mendicuti(eds.), Proceedings of the 14th international conference of the international Group for the Psychology of Mathematics Education, 14(2), 93-100.
  16. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  17. Ontario Ministry of Education. (2013). Paying attention to algebraic reasoning K-12. Queen's Printer for Ontario.
  18. Piaget, J. (1965). The child's conception of number. New York: Norton.
  19. Putnam, R. T., deBettencourt, L. U., & Leinhardt, G. (1990). Understanding of derived fact strategies in addition and subtraction. Cognition and Instruction, 7(3), 245-285. https://doi.org/10.1207/s1532690xci0703_3
  20. Star, J. R. (2005). Research commentary: Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411.
  21. Thomas, M. & Tall, D. (2001). The long-term cognitive development of symbolic algebra. In International congress of mathematical instruction(ICMI) working group proceedings - The future of the teaching and learning of algebra, Melbourne, 2, 590-597.
  22. Watson, A. (2009). Paper(6): Algebraic reasoning. Key understandings in mathematics learning. A review commissioned by the Nuffield Foundation.