The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Analysis of characteristics from meta-affect viewpoint on problem-solving activities of mathematically gifted children

수학 영재아의 문제해결 활동에 대한 메타정의적 관점에서의 특성 분석

  • Received : 2019.09.10
  • Accepted : 2019.11.10
  • Published : 2019.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

According to previous studies, meta-affect based on the interaction between cognitive and affective elements in mathematics learning activities maintains a close mechanical relationship with the learner's mathematical ability in a similar way to meta-cognition. In this study, in order to grasp these characteristics phenomenologically, small group problem-solving cases of 5th grade elementary mathematically gifted children were analyzed from a meta-affective perspective. As a result, the two types of problem-solving cases of mathematically gifted children were relatively frequent in the types of meta-affect in which cognitive element related to the cognitive characteristics of mathematically gifted children appeared first. Meta-affects were actively acted as the meta-function of evaluation and attitude types. In the case of successful problem-solving, it was largely biased by the meta-function of evaluation type. In the case of unsuccessful problem-solving, it was largely biased by the meta-function of the monitoring type. It could be seen that the cognitive and affective characteristics of mathematically gifted children appear in problem solving activities through meta-affective activities. In particular, it was found that the affective competence of the problem solver acted on problem-solving activities by meta-affect in the form of emotion or attitude. The meta-affecive characteristics of mathematically gifted children and their working principles will provide implications in terms of emotions and attitudes related to mathematics learning.

선행연구에 의하면 수학 학습활동에서 인지적, 정의적 요소들 사이의 상호작용에 기반하는 메타정의는 메타인지와 유사한 방식으로 학습자의 수학적 능력과 긴밀한 역학적 관련성을 유지한다. 본 연구에서는 이러한 특성을 현상학적으로 파악하기 위하여 초등학교 5학년 수학 영재아의 소집단 문제해결 사례를 메타정의적 관점에서 분석하였다. 그 결과 수학 영재아의 인지적, 정의적 특성이 메타정의적 활동을 통해 문제해결 활동에 나타나고 있음을 알 수 있으며, 특히 문제해결자의 정의적 역량은 정서나 태도 형태의 메타정의로 문제해결 활동에 작용함을 알 수 있었다.

Keywords

References

  1. Clark, B. (1988). Growing up gifted(3th ed.). Columbus, OH: Merrill.
  2. DeBellis, V. A. & Goldin, G. A. (1997). The affective domain in mathematical problem- solving. In E. Pekhonen (Ed.) Proceedings of the PME 21, 2, 209-216.
  3. DeBellis, V. A. & Goldin, G. A. (2006). Affect and Meta-affect in Mathematical Problem Solving: A Representational Perspective. Educational Studies in Mathematics, 63(2), 131-147. https://doi.org/10.1007/s10649-006-9026-4
  4. Do, J. W. (2018). Aspects of meta-affect in collaborative mathematical problem-solving processes. Unpublished doctoral dissertation, Seoul National University of Education.
  5. Do, J. W. & Paik, S. Y. (2016). The function of meta-affect in mathematical problem solving. Journal of Elementary Mathematics Education in Korea 20(4) 563-581.
  6. Do, J. W. & Paik, S. Y. (2017). The sociodynamical function of meta-affect in mathematical problem-solving procedure J. Korea Soc. Math. Ed. Ser. C: Education of Primary School Mathematics 20(1), 85-99. https://doi.org/10.7468/jksmec.2017.20.1.85
  7. Do, J. W. & Paik, S. Y. (2018). Aspects of meta-affect according to mathematics learning achievement level in problem-solving processes. Journal of Elementary Mathematics Education in Korea 22(2) 143-159.
  8. Do, J. W. & Paik, S. Y. (2019). Aspects of meta-affect in problem-solving process of mathematically gifted children. Journal of Elementary Mathematics Education in Korea 23(1) 59-74.
  9. Fraiser, M. M. & Passow, A. H. (1994). Towards a new paradigm for identifying talent potential. Storrs, CT: University of Commecticut, The National Research Center on the Gifted and Talented.
  10. Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht: Kluwer.
  11. Goldin, G. A. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275-286). Reston, VA: NCTM.
  12. Goldin, G. A. (2004). Characteristics of affect as a system of representation. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the PME 28, 1 (pp. 109-114). Bergen: Bergen University College.
  13. Goldin, G. A. (2006). Commentary on "The articulation of symbol and mediation in mathematics education" by Moreno-Armella and Sriraman. ZDM: The International Journal on Mathematics Education, 38, 70-72. https://doi.org/10.1007/BF02655908
  14. Goldin, G. A. (2007). Aspects of affect and mathematical modeling processes. In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 281-296). NJ: Erlbaum.
  15. Goldin, G. A. (2009). The affective domain and students' mathematical inventiveness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 181-194). Rotterdam: Sense Publishers.
  16. Goldin, G. A. (2010). Commentary on symbols and mediation in mathematics education. In B. Sriraman & L. English (Eds.), Theories of mathematics education? (pp. 233-237). New York: Springer-Verlag.
  17. Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391-414). New York: Routledge.
  18. Malmivuori, M. L. (2001). Malmivuori, M. L. (2001). The dynamics of affect, cognition, and social environment in the regulation of personal learning processes: The case of mathematics. Research Report, 172, Helsinki: Helsinki University Press.
  19. Malmivuori, M. L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149-164. https://doi.org/10.1007/s10649-006-9022-8
  20. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.
  21. Moscucci, M. (2010). Why is there not enough fuss about affect and meta-affect among mathematics teacher? In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds), Proceedings of the CERME-6 (pp. 1811-1820). INRP, Lyon.
  22. Renzulli, J. S. & Reis, S. M. (1997). The schoolwide enrichment model: A how-to guide foe educational excellence (2nd ed.). Mansfield Center, CT: Creative Learning Press.
  23. Schloglmann, W. (2005). Meta-affect and strategies in mathematics learning. In M. Bosch (Ed), Proceeding of CERME-4 (pp. 275-284). Barcelona: FundEmi IQS.
  24. Yin, R. K. (2014). Case study research: Design and methods (5th ed.). Thousand Oaks, CA: Sage.