An Analysis on Teaching Methods of Patterns in Elementary Mathematics Textbooks

- Journal title : Education of Primary School Mathematics
- Volume 19, Issue 1, 2016, pp.1-18
- Publisher : Korea Society of Mathematical Education
- DOI : 10.7468/jksmec.2016.19.1.1

Title & Authors

An Analysis on Teaching Methods of Patterns in Elementary Mathematics Textbooks

Pang, JeongSuk; Sunwoo, Jin;

Pang, JeongSuk; Sunwoo, Jin;

Abstract

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

Keywords

pattern;teaching methods of patterns;elementary mathematics textbooks;early algebraic thinking;

Language

Korean

References

1.

교육과학기술부 (2011). 2009 개정 수학과 교육과정. 서울: 교육과학기술부.(The Ministry of Education, Science, and Technology (2011). 2009 Reformed mathematics curriculum. Seoul: Author.)

2.

교육부 (2014a). 수학 3-1. 서울: 천재교육.(Ministry of Education (2014a). Elementary mathematics 3-1. Seoul: Chunjae Education.)

3.

교육부 (2014b). 수학 3-2. 서울: 천재교육.(Ministry of Education (2014b). Elementary mathematics 3-2. Seoul: Chunjae Education.)

4.

교육부 (2014c). 수학 4-1. 서울: 천재교육.(Ministry of Education (2014c). Elementary mathematics 4-1. Seoul: Chunjae Education.)

5.

교육부 (2014d). 수학 4-2. 서울: 천재교육.(Ministry of Education (2014d). Elementary mathematics 4-2. Seoul: Chunjae Education.)

6.

교육부 (2015a). 수학 1-2. 서울: 천재교육.(Ministry of Education (2015a). Elementary mathematics 1-2. Seoul: Chunjae Education.)

7.

교육부 (2015b). 수학 2-1. 서울: 천재교육.(Ministry of Education (2015b). Elementary mathematics 2-1. Seoul: Chunjae Education.)

8.

교육부 (2015c). 수학 2-2. 서울: 천재교육.(Ministry of Education (2015c). Elementary mathematics 2-2. Seoul: Chunjae Education.)

9.

교육부 (2015d). 수학 5-2. 서울: 천재교육.(Ministry of Education (2015d). Elementary mathematics 5-2. Seoul: Chunjae Education.)

10.

교육부 (2015e). 수학 6-1. 서울: 천재교육.(Ministry of Education (2015e). Elementary mathematics 6-1. Seoul: Chunjae Education.)

11.

교육부 (2015f). 수학 6-2. 서울: 천재교육.(Ministry of Education (2015f). Elementary mathematics 6-2. Seoul: Chunjae Education.)

12.

김남균.김은숙 (2009). 초등학교 6학년의 패턴의 일반화를 통한 대수 학습에 관한 연구. 한국수학교육학회지 시리즈 E <수학교육 논문집> 23(2), 399-428.(Kim, N. G., & Kim, E. S. (2009). A study on the 6th graders' Learning algebra through generalization of mathematical patterns. Communications of mathematical education 23(2), 399-428.)

13.

김성준 (2003). 패턴과 일반화를 강조한 대수 접근법 고찰. 학교수학 5(3), 343-360.(Kim, S. J. (2003). A study on approaches to algebra focusing on patterns and generalization. School Mathematics 5(3), 343-360.)

14.

김성희 (2013). 한국과 미국 초등학교 2학년 학생들의 패턴에 대한 이해 비교. 학습자중심교과교육연구 13(5), 637-660.(Kim, S. H. (2013). Comparison of second graders' patterning understandings between South Korea and the US. Journal of Learner-Centered Curriculum and Instruction 13(5), 637-660.)

15.

송상헌.임재훈.정영옥.권석일.김지원 (2007). 초등수학영재들이 페그퍼즐 과제에서 보여주는 대수적 일반화 과정 분석. 수학교육학연구 17(2), 163-177.(Song, S. H., Yim, J. H., Chong, Y. O., Kwon, S. I., & Kim, J. W. (2007). Analysis of the algebraic generalization on the mathematically gifted elementary school students' process of solving a Line Peg Puzzle. The Journal of Educational Research in Mathematics 17(2), 163-177.)

16.

송상헌.허지연.임재훈 (2006). 도형의 최대 분할 과제에서 초등학교 수학 영재들이 보여주는 정당화의 유형 분석. 수학교육학연구 16(1), 79-94.(Song, S. H., Heo, J. Y., & Yim, J. H. (2006). Analysis on the types of mathematically gifted students' justification on the tasks of figure division. The Journal of Educational Research in Mathematics 16(1), 79-94.)

17.

유미경.류성림 (2013). 초등수학영재와 일반학생의 패턴의 유형에 따른 일반화 방법 비교. 학교수학 15(2), 459-479.(Yu, M. G., & Ryu, S. R. (2013). A comparison between methods of generalization according to the types of pattern of mathematically gifted students and non-gifted students in elementary school. School Mathematics 15(2), 459-479.)

18.

최병훈.방정숙 (2011). 초등학교 1학년 학생들의 수학적 패턴 인식과 사고 과정 분석. 수학교육학연구 21(1), 67-86.(Choi, B. H., & Pang, J. S. (2011). Analysis on the first graders' recognition and thinking about mathematical patterns. The Journal of Educational Research in Mathematics 21(1), 67-86.)

19.

최병훈.방정숙 (2012). 초등학교 4,5,6학년 영재학급 학생의 패턴 일반화를 위한 해결 전략 비교. 수학교육학연구 22(4), 619-636.(Choi, B. H., & Pang, J. S. (2012). A comparison of mathematically gifted students' solution strategies of generalizing geometric patterns. The Journal of Educational Research in Mathematics 22(4), 619-636.)

20.

최지영.방정숙 (2014). 초등학교 6학년 학생들의 함수적 관계 인식 및 사고 과정 분석: 기하 패턴 탐구 상황에서의 사례연구. 수학교육학연구 24(2), 205-225.(Choi, J. Y., & Pang, J. S. (2014). An analysis on sixth graders' recognition and thinking of functional relationships: A case study with geometric growing patterns. The Journal of Educational Research in Mathematics 24(2), 205-225.)

21.

Australian Curriculum, Assessment and Reporting Authority (2015). Australian curriculum F-10 curriculum mathematics (version 8). Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1.

22.

Beatty, R. (2010). Supporting algebraic thinking: Prioritizing visual representations. Ontario Association for Mathematics Education Gazette, 49(2), 28-34.

23.

Billings, E. (2008). Exploring generalization through pictorial growth patterns. In C. E. Greenes, & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (70th yearbook of the National Council of Teachers of Mathematics, pp. 279-293). Reston, VA: NCTM.

24.

Blanton, M. L., & Kaput, J. J. (2011). Functional thinking as route into algebra in the elementary grades. In J. Cai, & E. Knuth (Eds.), Early algebraization (pp. 5-23). New York: Springer.

25.

Common Core State Standards Initiative (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/Math/

26.

Cooper, T., & Warren, E. (2011). Years 2 to 6 students' ability to generalize: Models, representations and theory for teaching and learning. In J. Cai., & E. Knuth.(Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 187-214). Berlin: Springer.

27.

Lee, C. H., & Lee, S. Y. (2013) Analysis of pattern generalization problems of Korean mathematics textbook. 교과교육학연구 17(4), 1365-1384.

28.

Moss, J., & McNab, S. L. (2011). An approach to geometric and numeric patterning that fosters second grade students' reasoning and generalizing about functions and co-variation. In J. Cai, & E. Knuth (Eds.), Early algebraization (pp. 277-301). New York: Springer.

29.

Moss, J., Beatty, R., Barkin, S., & Shillolo, G. (2008). "What is your theory? What is your rule?" Fourth graders build an understanding of functions through patterns and generalizing problems. In C. E. Greenes, & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (70th yearbook of the National Council of Teachers of Mathematics, pp. 155-168). Reston, VA: NCTM.

30.

Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal 21(2), 33-49.

31.

Ontario Ministry of Education (2005). The Ontario curriculum grades 1-8 mathematics (revised). Retrived from https://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf.

32.

Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical thin king and learning 5(1), 37-70.

33.

Radford, L. (2010). Layers of generality and types of generalization in pattern activities. Pentose Nucleic Acid (PNA) 4(2), 37-62.

34.

Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4. pp. 17-24). Ankara, Turkey: PME.

35.

Radford, L., & Peirce, C. S. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter (Vol. 1, pp. 2-21).

36.

Tabach, M., & Friedlander, A. (2008) The role of context in learning beginning algebra. In C. E. Greenes, & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (70th yearbook of the National Council of Teachers of Mathematics, pp. 233-246). Reston, VA: NCTM.

37.

Warren, E., & Cooper, T. (2007). Repeating patterns and multiplicative thinking: Analysis of classroom interactions with 9-year-old students that support the transition from the known to the novel. The Journal of Classroom Interaction, 7-17.

38.

Warren, E., & Cooper, T. (2008). Patterns that support early algebraic thinking in the elementary school. In C. E. Greenes, & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (70th yea book of the National Council of Teachers of Mathematics, pp. 113-126). Reston, VA: NCTM.