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http://dx.doi.org/10.7468/jksmec.2019.22.4.223

Analysis of Problem-Solving Protocol of Mathematical Gifted Children from Cognitive Linguistic and Meta-affect Viewpoint  

Do, Joowon (Seoul Banghyun Elementary School)
Paik, Suckyoon (Department of Mathematics Education, Seoul National University of Education)
Publication Information
Education of Primary School Mathematics / v.22, no.4, 2019 , pp. 223-237 More about this Journal
Abstract
There is a close interaction between the linguistic-syntactic representation system and the affective representation system that appear in the mathematical process. On the other hand, since the mathematical conceptual system is fundamentally metaphoric, the analysis of the mathematical concept structure through linguistic representation can help to identify the source of cognitive and affective obstacles that interfere with mathematics learning. In this study, we analyzed the problem-solving protocols of mathematical gifted children from the perspective of cognitive language and meta-affect to identify the relationship between the functional characteristics of the text and metaphor they use and the functional characteristics of meta-affect. As a result, the behavior of the cognitive and affective characteristics of mathematically gifted children differed according to the success of problem solving. In the case of unsuccessful problem-solving, the use of metaphor as an internal representation system was relatively more frequent than in the successful case. In addition, while the cognitive linguistic aspects of metaphors play an important role in problem-solving, meta-affective attributes are closely related to the external representation of metaphors.
Keywords
mathematical gifted children; problem-solving; cognitive linguistics; metaphor; meta-affect;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Goldin, G. A. & Steingold, N. (2001). System of mathematical representations and development of mathematical concepts. In F. R. Curcio (Ed.), The Roles of Representation in School Mathematics: 2001 Yearbook (pp. 1-23). Reston: National Council of teachers of Mathematics.
2 Knowles, M. & Moon, R. (2006). Introducing Metaphor. Routledge. 김주식.김동환(역) (2008). 은유 소개. 서울: 한국문화사.
3 Kosslyn, S. M. (1980). Image and Mind. Cambridge. MA: Harvard University Press.
4 Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. Chicago: The University of Chicago Press.
5 Lakoff, G. & Johnson, M. (1980, 2003). Metaphors We Live by, Chicago & London: University of Chicago Press. 노양진.나익주(역) (2006). 삶으로서의 은유. 서울: 박이정.
6 Lakoff, G. & Nunez, R. E. (2000). Where Mathematics Comes from? NY: Basic Books.
7 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.
8 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.
9 McLeod, D. B. & Adams, V. M. (1989). Affect and Mathematical Problem Solving: A New Perspective (pp. 245-258). New York: Springer-Verlag.
10 NCTM (2000). Principles and Standards for School Mathematics. 류희찬 외(역) (2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
11 Nunez, R. E. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. PME 1, 3-22.
12 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.
13 Schoenfeld, A. H. (1985). Mathematical Problem Solving. NY: Academic Press.
14 Yin, R. K. (2014). Case Study Research: Design and Methods(5th ed.). Thousand Oaks, CA: Sage.
15 Ministry of Education (2015). Mathematics curriculum, Ministry of Education Notice No. 2015-74 [Separate Book 8].
16 Kim, S. M. (2005). Metaphors on Mathematics Teaching. School Mathematics, 7(4), 445-467.
17 Kim, S. M., & Shin, I. S. (2007). On the Mathematical Metaphors in the mathematics classroom, J. Korea Soc. Math. Ed. Ser. C: Education of Primary School Mathematics, 10(1), 29-39.
18 Do. J. (2018). Aspects of Meta-affect in Collaborative Mathematical Problem-Solvong Processes. Dissertation, Seoul National University of Education.
19 Kim, J. D. (2003). Metaphorical world in cognitive linguistic perspective. Seoul: Korean Cultural History.
20 Kim, J. Y. (2011). A Study of Teaching Methods Using Metaphor in Mathematics. School Mathematics, 13(4), 563-580.
21 Do, J., & Paik, S. (2019). Aspects of Meta-affect in Problem-Solving Process of Mathematically Gifted Children, Mathematics Education in Korea, 23(1), 59-74.
22 Lee, S. Y., & Woo, J. H. (2002). Analogies and metaphors in school mathematics. The Journal of Educational Research in Mathematics, 12(4), 523-542.
23 Ju, M. K., & Kwon, O. N. (2003). Students' Conceptual Metaphor of Differential Equations: A Sociocultural Perspective on the Duality of the Students' Conceptual Model. School Mathematics, 5(1), 135-149.
24 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.   DOI
25 Bal, A. P. (2015). Skill of using and transform multiple representations of the prospective teachers. Journal of Mathematical Behavior, 197(25), 682-588.
26 Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts. In R. Lesh., & M. Landau (Eds.), Acquisition of Mathematics Concepts and Process (pp. 91-126). New York: Academic Press, Inc.
27 Brinker, K. (1992). Linguistische Textanalyse. Eine Einfuhrung in Grundbegriffe und Methoden. 3. Aufl. (Grundlagen der Germanistik 29). Berlin. 이성만(역) (1994). 텍스트언어학의 이해 - 언어학적 베스트분석의 기본 개념과 방법. 서울: 한국문화사.
28 Clark, B. (1988). Growing up gifted(3th ed.). Columbus, OH: Merrill.
29 DeBellis, V. A. (1996). Interactions between Affect and Cognition during Mathematical Problem Solving: A Two-year Case Study of Four Elementary School Children. Ann Arbor, MI: University Microfilms No. 96-30716.
30 Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137-165.   DOI
31 Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving, Mathematical Thinking and Learning, 2(3), 209-219.   DOI
32 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.   DOI
33 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.
34 Goldin, G. A. & Kaput, J. (1996). A joint perspective on the idea of representation in learningand doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning, Erlbaum (pp. 397-430). NJ: Hillsdale.