A Study on the Application of Perry's Epistemological Development Scheme in Mathematics Education

Perry의 인식론적 신념 발달도식의 수학교육 적용 방안 연구

  • Received : 2016.10.09
  • Accepted : 2016.11.12
  • Published : 2016.11.30

Abstract

The traditional teaching-learning in mathematics, which pursue only one correct answer, should be reexamined to cope with an age of uncertainty. In this research, Perry's epistemological development scheme was noticed as a theoretical approach to diagnose problems of dualistic mathematics lessons and to search solutions of the problems. And Design-Based Research method was adopted, We developed the epistemological development scheme through considering Perry's theory and related studies, scaffoldings and teaching-learning to enhance students' epistemological positions in mathematics. Based on these discussions we designed teaching experiment about operations with negative numbers, and analyzed its didactic implications.

본 연구는 인식론적 신념 발달을 위한 수학 교수학습 방안의 설계를 목표로 하였다. 인식론적 신념은 지식 및 앎의 본성에 관한 신념으로, 수학에 대한 인식론적 신념은 수학 교수학습 과정에서 중요한 요소이지만, 많은 학생들이 수학 수업에 대하여 교사로부터 문제풀이 방법을 전달받는 수동적 과정이라는 이원론적 신념을 가지고 있다. 이에 본 연구에서는 Perry의 발달도식을 재해석하여 수학교육에서의 인식론적 신념 발달도식을 제시하고, 인식론적 신념의 발달을 유도하기 위한 교수학습 방안으로 비평형 상황과 스캐폴딩을 제안하였다. 설계 기반 연구 방법을 활용하여, 설계한 교수학습 방안을 미시적으로 평가하기 위해 수학영재 중학생들을 대상으로 수행한 교수실험을 분석하여 논의하였다.

Keywords

References

  1. 김동엽. (2001). 문제중심 수업과 지시적 수업이 학습자의 인식론적 신념에 따라 수업의 유의미성 지각 및 학업성취에 미치는 효과. 한국교원대학교 대학원 박사학위논문.
  2. 김선희. (2014). 디지털 매체를 활용한 포럼연극 수업설계 모형 개발. 서울대학교 대학원 박사학위논문.
  3. 김홍진. (2008). 대학생의 인지발달과 예술교육에 대한 연구-Perry의 이론을 중심으로, 기초조형학연구, 9(2), 265-272.
  4. 류희찬 외. (2012). 중학교 수학 1, 서울: 천재교육
  5. 우정호, 최병철(2007). 음수 개념의 이해에 대한 교수학적 분석, 수학교육학연구, 17(1), 1-31.
  6. 유윤재(2007). 중등수학교재연구, 서울: 경문사.
  7. 이민형. (2016). 가치 논제 토론 수업을 위한 설계 기반 연구. 서울대학교 대학원 박사학위논문.
  8. 이상수, 강정찬, & 황주연. (2006). 효과적인 비계설정을 위한 수업설계모형. 교육정보미디어연구, 12(3), 149-175.
  9. 장선영, & 이명규. (2012). 웹기반 프로젝트중심 학습 환경에서 과제해결능력을 촉진시키는 스캐폴딩 설계모형 개발 연구. 교육공학연구, 28(2), 371-408.
  10. Alvermann, Gaoyin Qian, & Donna E. (2000). Relationship between epistemological beliefs and conceptual change learning, Reading & Writing Quarterly, 16(1), 59-74. https://doi.org/10.1080/105735600278060
  11. Berk, L. E., & Winsler, A. (1995). Scaffolding Children's Learning: Vygotsky and Early Childhood Education. NAEYC Research into Practice Series. Volume 7. National Association for the Education of Young Children, 1509 16th Street, NW, Washington, DC 20036-1426(NAEYC catalog# 146).
  12. Buehl, M. M. (2003). At the crossroads of epistemology and motivation: Modeling the relations between students' domain-specific epistemological beliefs, achievement motivation, and task performance.
  13. Copes, L. (1982). The Perry development scheme: A metaphor for learning and teaching mathematics, For the Learning of Mathematics 3(1), 38-44.
  14. Ernest, P. (1985). The philosophy of mathematics and mathematics education, Mathematics Education Science Technology, 16(5), 603-612.
  15. Finster, D. C. (1991). Developmental instruction: Part II. Application of the Perry model to general chemistry, J. Chem. Educ, 68(9), 752. https://doi.org/10.1021/ed068p752
  16. Frank, M. L. (1988). Problem solving and mathematical beliefs, Arithmetic Teacher, 35, 32-34.
  17. Gallagher, S. A. (1998). The road to critical thinking: The Perry scheme and meaningful differentiation. NASSP Bulletin, 82(595), 12-20. https://doi.org/10.1177/019263659808259504
  18. Garofalo, J. (1989). Beliefs and their influence on mathematical performance, Mathematics Teacher, 82, 502-505.
  19. Gelfand, I. M., Shen, A.(1995). Algebra, Birkhauser Boston (1995, Second Printing): Cambridge, Mass.
  20. Hallett, D., Chandler, M. J., & Krettenauer, T. (2002). Disentangling the course of epistemic development: Parsing knowledge by epistemic content. New Ideas in Psychology, 20(2), 285-307. https://doi.org/10.1016/S0732-118X(02)00011-9
  21. Hofer, B. K., & Pintrich, P. R. (1997). The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning, Review of Educational Research, 67, 88-140. https://doi.org/10.3102/00346543067001088
  22. Hofer, B. K. (2001). Personal epistemology research: Implications for learning and teaching, Educational Psychology Review, 13(4), 353-383. https://doi.org/10.1023/A:1011965830686
  23. Kardash, C. M., & Howell, K. L. (2000). Effects of epistemological beliefs and topic-specific beliefs on undergraduates' cognitive and strategic processing of dual-positional text, Journal of Educational Psychology, 92(3), 524. https://doi.org/10.1037/0022-0663.92.3.524
  24. King, P. M. (1977). The development of reflective judgment and formal operational thinking in adolescents and young adults, Dissertation Abstracts International, 38, 7233A.
  25. Kloss, R. J. (1994). A nudge is best: Helping students through the Perry scheme of intellectual development. College Teaching, 42(4), 151-158. https://doi.org/10.1080/87567555.1994.9926847
  26. Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of research, Review of educational research, 74(3), 317-377. https://doi.org/10.3102/00346543074003317
  27. Myers, S. A. (2010). Using the Perry Scheme to explore college student classroom participation, Communication Research Reports, 27(2), 123-130. https://doi.org/10.1080/08824091003738016
  28. Nieveen, N. (1999). Prototyping to reach product quality. Design approaches and tools in education and training, pp. 125-135.
  29. Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of educational research, 62(3), 307-332. https://doi.org/10.3102/00346543062003307
  30. Perry, W. G., Jr. (1968). Patterns of development in thought and values of students in a liberal arts college: A validation of a scheme. Cambridge, MA: Bureau of Study Counsel, Harvard University. (ERIC Document Reproduction Service No. ED 024315)
  31. Perry, W. G., Jr. (1970). Forms of intellectual and ethical development in the college years: A scheme. New York: Holt, Rinehart & Winston.
  32. Perry, W. G. (1985). Different worlds in the same classroom: Students' evolution in their vision of knowledge and their expectations of teachers, On teaching and learning, 1(1), 1-17.
  33. Perry, W., & Chickering, A. (1997). Cognitive and ethical growth: The making of meaning. College student development and academic life, 4, 48-116.
  34. Piaget, J. (1980). Experiments in contradiction. University of Chicago Press.
  35. Plomp, T., & Nieveen, N. (2007, November). An introduction to educational design research. In Proceedings of the Seminar Conducted at the East China Normal University [Z]. Shanghai: SLO-Netherlands Institute for Curriculum Development.
  36. Reinking, D., & Bradley, B. A. (2008). On formative and design experiments: Approaches to language and literacy research (Vol. 3). Teachers College Pr.
  37. Richey, R. C., & Klein, J. D. (2012). 교육공학연구를 위한 설계.개발 연구. (정현미, 김광수 역). 서울: 학지사. (원저 2007년 출판)
  38. Roberts, D. R., & Langer, J. A. (1991). Supporting the process of literary understanding: Analysis of a classroom discussion. Center for the Learning and Teaching of Literature, University at Albany, State University of New York.
  39. Schoenfeld, A. H. (1985). Mathematical problem solving, Orlando, FL: Academic Press.
  40. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of 'well-taught' mathematics courses, Educational psychologist 23(2), 145-166. https://doi.org/10.1207/s15326985ep2302_5
  41. Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior, Journal for research in mathematics education, 338-355.
  42. Schommer, M. (1990). Effects of beliefs about the nature of knowledge on comprehension, Journal of Educational Psychology, 82, 498-504. https://doi.org/10.1037/0022-0663.82.3.498
  43. Schommer, M. (1994). An emerging conceptualization of epistemological beliefs and their role in learning. In R. Garner & P. A. Alexander (Eds.), Beliefs about text and instruction with text (25-40). Hillsdale, NJ: Erlbaum.
  44. Schommer, M. (1998). The influence of age and education on epistemological beliefs, British Journal of Educational Psychology, 68(4), 551-562. https://doi.org/10.1111/j.2044-8279.1998.tb01311.x
  45. Schommer-Aikins, M. (2004). Explaining the epistemological belief system: Introducing the embedded systemic model and coordinated research approach, Educational psychologist, 39(1), 19-29. https://doi.org/10.1207/s15326985ep3901_3
  46. Stodolsky, S. S. (1985). Telling math: Origins of math aversion and anxiety, Educational Psychologist, 20, 125-133. https://doi.org/10.1207/s15326985ep2003_2
  47. Thoma, G. A. (1993). The Perry framework and tactics for teaching critical thinking in economics, The Journal of Economic Education, 24(2), 128-136. https://doi.org/10.1080/00220485.1993.10844786
  48. Thomas, J. A. (2008). Reviving Perry: An analysis of epistemological change by gender and ethnicity among gifted high school students, Gifted Child Quarterly, 52(1), 87-98. https://doi.org/10.1177/0016986207311422
  49. Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Eds.). (2006). Educational design research. Routledge.
  50. Vygotsky, L. S. (2009). 마인드 인 소사이어티. (정회욱 역), 서울: 학이시습. (원저 1978년 출판).
  51. Wadsworth, B. J. (1996). Piaget's theory of cognitive and affective development: Foundations of constructivism. Longman Publishing.
  52. Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of child psychology and psychiatry, 17(2), 89-100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x
  53. White, O. L. (2007). An investigation into the utilization of a constructivist teaching strategy to improve preservice elementary teachers geological content knowledge: Is there a relationship between intellectual level and content understanding?. ProQuest.