DOI QR코드

DOI QR Code

A Study on the Mathematical Problem Solving Teaching based on the Problem solving approach according to the Intuitive and the Formal Inquiry

직관적·형식적 탐구 기반의 문제해결식 접근법에 따른 수학 문제해결 지도 방안 탐색

  • Lee, Daehyun (Dept. of Math. Edu., Gwangju National Univ. of Edu.)
  • Received : 2019.10.17
  • Accepted : 2019.12.26
  • Published : 2019.12.31

Abstract

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

References

  1. S. AN, Z. WU, Teaching Elementary and Middle School Mathematics Using the MSA Approach: Model, Strategy, and Application, CA: Education for All, 2017.
  2. J. BOALER, Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching, CA: Jossey-Bass, 2016.
  3. J. DEWEY, How we think, D. C. Heath and Co, 1933.
  4. J. HADAMARD, An essay on the psychology of invention in the mathematical field, Priceton university press, Princeton, 1945.
  5. JEONG E. S., Reconsideration of teaching mathematics problem solving in elementary school, Journal of elementary mathematics education in Korea 19(2) (2015), 123-141.
  6. KANG O. K. et al, A Improving Study on the Teaching Method for Mathematics Problem Solving, Seoul: KEDI Research Report RR 85-9, 1985.
  7. KIM H. M., An analysis of the research trend in Korea regarding mathematical problem solving, Journal of Learner-Centered Curriculum and Instruction 16(8) (2016), 831-850. https://doi.org/10.22251/jlcci.2016.16.11.831
  8. KIM J. K., LIM M. G., An effect coming to the problem solving ability from the problem posing activity by presenting the problem situation, Journal of Elementary Mathematics Education in Korea, 5 (2001), 77-98.
  9. KIM S. J., A study on multi-cultural society in Korea: Focusing on multi-cultural policy, Social Capital and Corruption, Korean corruption studies review 23(1) (2018), 95-120.
  10. KOFAC, Developmental Research of 2015 Revised Mathematics Curriculum Draft II, KOFAC Research Report DB15120005, 2015.
  11. LEE I. H. et al, A Study on the Development of the 2014 National Assessment of Educational Achievement(NAEA), KICE RRE 2014-5-1, 2014.
  12. F. K. LESTER, Musings about mathematical problem-solving research: 1970-1994, Journal for Research in Mathematics Education 25(6) (1994), 660-675. https://doi.org/10.2307/749578
  13. Ministry of Culture and Education, Elementary Curriculum, Ministry of Culture and Education Notice 442, 1981.
  14. Ministry of Culture and Education, Elementary Curriculum, Ministry of Culture and Education Notice 87-9, 1987.
  15. Ministry of Education, Elementary Curriculum, Ministry of Education Notice 1992-16, 1992.
  16. Ministry of Education, Mathematics Curriculum, Ministry of Education Notice 1997-15, 1997.
  17. Ministry of Education and Human Resource, Mathematics Curriculum, Ministry of Education and Human Resource Notice 2007-79, 2007.
  18. Ministry of Education, Science and Technology, Mathematics Curriculum, Ministry of Education, Science and Technology Notice 2011-361, 2011.
  19. Ministry of Education, Mathematics Curriculum, Ministry of Education Notice 2015-74, 2015.
  20. Ministry of Education, Mathematics Teacher's Guide 1-1, Cheonjae Education, 2017.
  21. National Council of Teachers of Mathematics, An Agenda for Action: Recommendations for School Mathematics of the 1980s, Reston, VA: The National Council of Teachers of Mathematics, Inc., 1980.
  22. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics, Reston, VA: The National Council of Teachers of Mathematics, Inc., 1989.
  23. National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, Reston, VA: The National Council of Teachers of Mathematics, Inc., 2000.
  24. OECD, PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy, Paris: OECD, 2013.
  25. H. POINCARE, La Valeur de la Science, 1905. 김형보 역, 과학의 가치, 서울 : 단대출판부, 1983.
  26. G. POLTA, How to solve it, Vol. 2, New York: Doubleday, 1957.
  27. S. K. REED, Word Problems-Research and Curriculum Reform, NJ: Lawrence Erlbaum Associates, Publishers, 1999.
  28. T. L. SCHROEDER, F. K. JR. LESTER, Developing understanding in mathematics via problem solving, In P. R. Trafton, A. P. Shulte(Eds.), New Directions for Elementary School Mathematics(pp. 31-42), Reston, VA.: The National Council of Teachers of Mathematics, Inc., 1989.
  29. R. R. SKEMP, The Psychology of Learning Mathematics: Vol 2, Harmonsworth: Penguin, 1986.
  30. SONG M. Y. et al, OECD Programme for International Students Assessment: Analyzing PISA 2012 Results, KICE RRE 2013-6-1, 2013.
  31. The California Department of Education, Mathematics Framework for California Public Schools-Kindergarten through Grade Twelve-, The California Department of Education, 2015.
  32. G. WALLAS, The Art of Thought, Harcourt Brace, 1926.
  33. M. WERTHEIMER, Productive Thinking, New York: Harper & Brothers published, 1945.
  34. E. WITTMANN, The complementary roles of intuitive and reflective thinking in mathematics teaching, Educational Studies in Mathematics 12(3) (1981), 389-397. https://doi.org/10.1007/BF00311068
  35. C. WOLERAM, Teaching kids real mathematics with computers, Retrieved from https://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers, 2010.
  36. YANG E. K., WHANG W. H., Relationship between mathematical learning styles and the selection of mathematical problem solving strategies, The Mathematical Education 44(4) (2005), 565-586.
  37. YOU Y. J., PARK M. K., An analysis of the children's scaffolding processes in mathematical problem solving, Journal of elementary mathematics education in Korea 13(1) (2009), 75-95.