The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Pre-service teachers' conceptions about considering the realistic contexts in the word problems

실생활 문장제에서 현실맥락 고려에 관한 예비교사들의 인식 분석

  • Received : 2021.10.17
  • Accepted : 2021.11.09
  • Published : 2021.11.30
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Abstract

We investigated whether and how pre-service teachers took the realistic contexts seriously in the course of solving word problems; additionally, we investigated how pre-service teachers evaluated students' realistic and non-realistic answers to word problems. Many pre-service teachers, similar to students, solved some of the realistic problems unrealistically without taking the realistic contexts seriously. Besides, they evaluated students' non-realistic answers higher than the realistic answers. Whether the pre-service teachers could solve problems realistically or not, they did not appreciate students' realistic considerations for the reasons that those were not fitted to the intentions of the word problems, or those were evidence of the flaws of the problem. Furthermore, the analysis of premises implied in the pre-service teachers' evaluation comments showed the implicit didactic contracts about realistic word problem solving that they accepted and also anticipated students to follow. Our analysis of the pre-service teachers' conceptions of realistic word problems can help teacher educators design the teacher program to challenge and revise pre-service teachers' folk pedagogy.

이 연구는 예비교사들을 대상으로 1) 실생활 문장제의 해결 과정에서 현실맥락을 예민하게 고려하는지, 2) 교사 입장에서 문제의 현실맥락을 예민하게 고려한/고려하지 않은 학생 응답을 어떻게 평가하는지를 조사하였다. 예비교사들 역시 학생들과 마찬가지로 일부 실생활 문장제에 대하여 현실맥락을 예민하게 고려하지 않았으며, 현실맥락을 예민하게 생각하지 않은 채 전형적인 풀이를 적용한 학생 응답을 현실맥락에 예민하게 반응한 답보다 높이 평가하였다. 예비교사 자신이 문제 해결 과정에서 현실맥락을 예민하게 고려했던 경우와 아니었던 경우 모두 학생의 현실맥락 고려를 문제 의도에 부합하지 않는다는 점에서 혹은 문제 오류의 증거로 긍정적으로 수용하지 않았다. 예비교사들의 학생 응답에 대한 평가의견에 내포된 전제로부터 예비교사들이 수용했으며 실생활 문장제의 교수 학습 상황과 학생들에게 기대한 암묵적인 교수학적 계약을 구체적으로 관찰할 수 있었다. 실생활 문장제에 대한 예비교사들의 인식을 탐색한 본 연구의 결과는 예비교사들이 실생활 문장제에 대해 가지고 있는 통상 교수학에 도전하고 수정할 수 있는 교사 교육 프로그램의 개발에 기여할 수 있을 것이다.

Keywords

Acknowledgement

이 연구는 인천대학교 2021년도 자체연구비 지원에 의해 연구되었음.

References

  1. Boaler, J. (1993). The Role of contexts in the mathematics classroom: Do they make mathematics more "real"? For the learning of mathematics, 13(2), 12-17.
  2. Brousseau, G., & Warfield, V. M. (1999). The case of Gael. The Journal of Mathematical Behavior, 18(1), 7-52. https://doi.org/10.1016/S0732-3123(99)00020-6
  3. Bruner, J. (1986). Actual minds, possible worlds. Harvard university press.
  4. Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211-230. doi:10.1007/s10649-006-7834-1
  5. Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers' approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26(2), 152-160. doi:10.1016/j.tate.2009.03.016
  6. Depaepe, F., De Corte, E., & Verschaffel, L. (2015). Students' non-realistic mathematical modeling as a drawback of teachers' beliefs about and approaches to word problem solving. In From beliefs to dynamic affect systems in mathematics education (pp. 137-156). Cham: Springer.
  7. Duan, X., Depaepe, F., & Verschaffel, L. (2011). Chinese upper elementary school mathematics teachers' attitudes towards the place and value of problematic word problems in mathematics education. Frontiers of Education in China, 6(3), 449-469. doi:10.1007/s11516-011-0141-3
  8. Gravemeijer, K. (1997). Solving word problems: A case of modelling? Learning and Instruction, 7(4), 389-397. https://doi.org/10.1016/S0959-4752(97)00011-X
  9. Greer, B. (1993). The mathematical modeling perspective on wor(l)d problems. The Journal of Mathematical Behavior, 12, 239-250.
  10. Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307. https://doi.org/10.1016/S0959-4752(97)00006-6
  11. Heo, J. S. (2008). An analysis of seventh graders' cognition on realistic word problems. Master Thesis. Graduate School of Korea National University of Education.
  12. Hwang, S. et al. (2018). Middle school mathematics 1. Seoul: Mirae-n Company.
  13. Inoue, N. (2005). The realistic reasons behind unrealistic solutions: the role of interpretive activity in word problem solving. Learning and Instruction, 15(1), 69-83. doi:10.1016/j.learninstruc.2004.12.004
  14. Lee, J. Y. et al. (2018). Middle School Mathematics 1. Seoul: Chunjae.
  15. Kim, H. et al. (2018) Middle school mathematics 1. Seoul: Shinsago Company.
  16. Kim, M. K. (2004). Children's realistic response on realistic word problems. Journal of Korea Society of Educational Studies in Mathematics, 6(2), 135-151.
  17. Released PISA Items Maths (2006). Project Consortium: Australian Council for Educational Research, Retrieved May 9, 2021, from https://www.oecd.org
  18. Reusser, K., & Stebler, R. (1997). Every word problem has a solution-The social rationality of mathematical modeling in schools. Learning and Instruction, 7(4), 309-327. https://doi.org/10.1016/S0959-4752(97)00014-5
  19. Schoenfeld, A. H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311-343). Hillsdale: Lawrence Erlbaum Associates.
  20. Park, K.(2006). A Study on didactical contracts as hidden rules in managing mathematics class, Journal of Educational Research in Mathematics, 16(1), 43-58
  21. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers' conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339-359. https://doi.org/10.1016/S0959-4752(97)00008-X
  22. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273-294. https://doi.org/10.1016/0959-4752(94)90002-7
  23. Yoshida, H., Verschaffel, L., & De Cort, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties?. Learning and Instruction, 7(4), 329-338. https://doi.org/10.1016/S0959-4752(97)00007-8