초등학교 가분성(divisibility) 단원에서 개념적 사고의 알고리즘 효율성 분석 연구
An analysis of the algorithm efficiency of conceptual thinking in the divisibility unit of elementary school
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초록
이 논문에서는 초등학교 교과서에서의 가분성(divisibility) 개념을 중심으로, 개념적 사고의 과정을 그대로 Python 언어로 코딩하고 Computational Thinking (이하, CT) 중 하나인 자동화에 따른 계산의 효율성을 고찰하였다. 이로부터얻을 수 있는 교육적 시사점은 다음과 같다. 수학적인 개념적 사고를 CT의 관점에서 생각해 보고, 또한 역으로 컴퓨터 과학에서 중시하고 있는 CT에서 수학적 개념을 추출해 볼 수 있는 쌍방향의 활동이 수학 중심의 코딩교육에서 필요하다.
Abstract
In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.
참고문헌 (30)
- Ackermann, E., "Piaget's constructivism, Papert's constructionism: What's the difference?", Conference Proceedings (2001), Research Center In Education
- Aho, A. V., "Computation and computational thinking", The Computer Journal, 55(7), pp.832~835 (2012)
- Angeli, C., "A K-6Computational thinking curriculum framework : implications for teacher knowledge", Educational Technology & Society, 19(3), pp.47~57 (2016)
- Barr, D., "Computational thinking : a digital age skill for everyone", Learning &Leading with Technology, 38(6), pp.20~23 (2011)
- Barr, V., "Bringing computational thinking to K-12: what is involved and what is the role of the computer science education community?", Acm Inroads, 2(1), pp.48~54 (2011)
- "Bitesize. Introduction to computational thinking" (2017)[URL]
- Burton, D. M., "Elementary Number Theory" (1980), Allyn and Bacon, Inc
- 장경윤, "수학 교과에서 계산적 사고(Computational Thinking)교육", 학교수학, 19(3), pp.553~570 (2017), 대한수학교육학회
- Cuny, J., "Demystifying computational thinking for non-computer scientists", work in progress, ~ (2010)
- Gallian, J. A., "Contemporary Abstract Algebra" (1998), Houghton Mifflin Company
- "Google" (2015)[URL]
- Grover, S., "Computational thinking in K-12 a review of the state of the field", Educational Researcher, 42(1), pp.38~43 (2013)
- Guzdial, M., "Education: paving the way for computational thinking", Communications of the ACM, 51(8), pp.25~27 (2008)
- Ireland, K, "A Classical Introduction to Number Theory" (1982), Springer-Verlag
- Kang, W., "Didactic transposition of mathematical knowledges", Journal of the Korea Society of Mathematical Education, 30(3), pp.71~89 (1991)
- Kim, H. K., "A study on learning and teaching environments for computers and mathematics education", Doctoral, pp.2006
- National Research Council, "Report of a workshop on the pedagogical aspects of computational thinking" (2011), National Academics Press
- Papert, S., "Mindstorms : Children, Computers, and Powerful Ideals" (1980), Basic Books, Inc
- Papert, S, "An exploration in the space of mathematics educations", International Journal of Computers for Mathematical Learning, 1, pp.95~123 (1996)
- Repenning, A., "Proceedings of the 41st ACM technical symposium on Computer science education (SIGCSE’10)", pp.265~269 (2010), ACM Press
- So, H. S., "A Study on Computational Thinking-Based Free Semester Program: Focusing on Polyhedron and Figurate Number", Master’s, pp.2015
- Tedre, M., "The long quest for computational thinking", Proceedings of the 16th Koli Calling Conference on Computing Education Research, pp.120~129 (2016)
- Wing, J. M., "Computational thinking", Communications of the ACM, 49(3), pp.33~35 (2006)
- Wing, J. M., "Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society A : Mathematical", Physical and Engineering Sciences, 366(1881), pp.3717~3725 (2008)
- Wing, J. M., "Computational Thinking", Microsoft Asia Faculty Summit 2012, Tianjin, China (2012)
- Wing, J. M., "Wing, Computational thinking’s influence on research and education for all", Italian Journal of Educational Technology, 25(2), pp.7~14 (2017)
- Woo, J. H., "Learning Mathematics-Instruction Principles and Methods" (2006), Seoul National University Press
- Yadav, A., "Computational thinking for all : Pedagogical approaches to embedding 21st century problem solving in K-12classrooms", TechTrends, 60(6), pp.565~568 (2016)