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http://dx.doi.org/10.7468/jksmec.2020.23.3.117

Analysis of Elementary Mathematics Textbooks Contents and 3rd Graders' Understanding on Unit and Whole of Fractions  

Lim, Miin (Seoul Kaemyong Elementary School)
Publication Information
Education of Primary School Mathematics / v.23, no.3, 2020 , pp. 117-134 More about this Journal
Abstract
Based on the current curriculum, students learn the concept of fraction in the 3rd grade for the first time. At that time, fraction is introduced as whole-part relationship. But as the idea of fraction expands to improper fraction and so on, fraction as measurement would be naturally appeared. In that situation where fraction as whole-part relationship and fraction as measurement are dealt together, it is necessary for students to get experiences of understanding and exploring unit and whole adequately in order to fully understand the concept of fractions. Therefore, the purpose of this study is to analyze how to deal with unit fractions, how to implement activities to find the standard of reference from the part, and what visual representations were used to help students to understand the concept of fractions in elementary mathematics textbooks from the 7th to the 2015 revised curriculum. And we analyzed 60 3rd graders' understanding of finding and drawing the whole by looking at the part. Several didactical implications for teaching the concept of fractions were derived from the discussion according to the analysis results.
Keywords
fraction; unit; whole; elementary mathematics textbook; unit fraction; the standard of reference; visual representation;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Ministry of Education and Science Technology (2011a). Elementary school mathematics textbook 2-2. Seoul: Doosan Dong-A.
2 Ministry of Education and Science Technology (2011b). Elementary school mathematics textbook 3-2. Seoul: Doosan Dong-A.
3 Ministry of Education and Science Technology (2012a). Elementary school mathematics textbook 3-1. Seoul: Doosan Dong-A.
4 Ministry of Education and Science Technology (2012b). Elementary school mathematics textbook 4-1. Seoul: Doosan Dong-A.
5 Ministry of Education (2017a). Elementary school mathematics textbook 3-1. Seoul: Chunjae.
6 Ministry of Education (2017.b). Elementary school mathematics textbook 3-2. Seoul: Chunjae.
7 Ministry of Education (2018). Elementary school mathematics textbook 3-2. Seoul: Chunjae.
8 Ministry of Education (2019a). Elementary school mathematics textbook 3-1. Seoul: Chunjae.
9 Ministry of Education (2019b). Elementary school mathematics textbook 3-1 teacher's guide book. Seoul: Chunjae.
10 Ministry of Education (2019c). Elementary school mathematics activity book 3-1. Seoul: Chunjae.
11 Ministry of Education & Human Resource Development (2007a). Elementary school mathematics textbook 3-Ga. Seoul: Chunjae.
12 Ministry of Education & Human Resource Development (2007b). Elementary school mathematics textbook 3-Na. Seoul: Chunjae.
13 Ministry of Education & Human Resource Development (2007c). Elementary school mathematics textbook 4-Ga. Seoul: Chunjae.
14 Kim, M. K. (2009). A study of the sixth graders' knowledge of concepts and operations about fraction. Journal of the Korean School Mathematics Society, 12(2), 151-170.
15 Seo, D. Y. (2005). The historico-genetic instruction on fractions. The Journal of Educational Research in Mathematics, 15(3), 233-249.
16 Woo, J. H. (2011). The principles and methods of learning-teaching on mathematics. Seoul: Seoul National University Press.
17 Lim, M. I. (2018). An analysis of students' understanding on unit fraction : focusing on teaching context and visual representation. The Mathematical Education, 57(1), 37-54.   DOI
18 Yoo, H. J. (1995). A study on teaching-phenomenological analysis and direction of learning-teaching on rational number concept. Seoul National University doctoral thesis.
19 Jeong, E. S. (2006). An educational analysis on fraction concept. School Mathematics, 8(2), 123-138.
20 Choi, K. B. (2015). A comparative study of elementary school mathematics textbooks of Korea(2007 curriculums) and America(Harcourt Math) -focused on the introductions and operations of fractions and decimals-. Journal of Elementary Mathematics Education in Korea, 19(1), 17-37.
21 Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational numbers for teaching mathematics in grades 3-5. VA: NCTM. 방정숙, 송상헌, 김동원, 이지영, 정유경, 김정원 공역(2017). 유리수의 필수 이해. 서울: (주)교우.
22 Bassarear, T. (2008). Mathematics for elementary school teachers. Boston: Houghton Mifflin.
23 Chval, K., Lannin, J., & Jones, D. (2013). Putting essential understanding of fractions into practice in grades 3-5. VA: NCTM.
24 Steffe, L. P. (2001). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20, 267-307.   DOI
25 Dougherty, B. J., Flores, A., Louis, E., & Sophian, C. (2010). Developing essential understanding of number and numeration for teaching mathematics in prekindergarten-grade 2. VA: NCTM. 박만구, 김성옥, 송상헌 공역(2017). 수와 기수법의 필수 이해. 서울: (주)교우.
26 McLellan, J. A., & Dewey, J. (1896). The psychology of number and its applications to methods of teaching arithmetic. NY: D. Appleton & Company.
27 Smith, J. P. (2002). The development of students' knowledge of fractions and ratios. In Litwiller, B., & Bright, G. (Eds.), Making sense of fractions, ratios, and proportions. VA: NCTM.