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http://dx.doi.org/10.7858/eamj.2018.015

Making Sense of Drawn Models for Operations of Fractions Involving Mixed Numbers  

Noh, Jihwa (Department of Mathematics Education Pusan National University)
Publication Information
East Asian mathematical journal / v.34, no.2, 2018 , pp. 203-217 More about this Journal
Abstract
This study examined preservice elementary teachers' patterns and tendencies in thinking of drawn models of multiplication with fractions. In particular, it investigated preservice elementary teachers' work in a context where they were asked to select among drawn models for symbolic expressions illustrating multiplication with non-whole number fractions including a mixed number. Preservice teachers' interpretations of fraction multiplication used in interpreting different types of drawn models were analysed-both quantitatively and qualitatively. Findings and implications are discussed and further research is suggested.
Keywords
Drawn model; Fraction; Fraction division; Fraction multiplication;
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1 Common Core State Standards Initiative. (2010). The common core state standards for mathematics . Washington DC: National Governors Association Center for Best Practices and Council of Chief State School Officers.
2 Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in pre-service teachers' practices. Educational Studies in Mathematics, 52(3), 243-270.   DOI
3 Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology , 24(5), 645-657.   DOI
4 Goldin, G. (2002). Representation in mathematical learning and problem solving. In L. English (Ed.), Handbook of international research in mathematics education (pp. 197-218). Mahwah, NJ: Lawrence Erlbaum.
5 Izsak, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143.   DOI
6 Luo, F., Lo, J., & Leu, Y. (2011). Fundamental fraction knowledge of pre-service elementary teachers: A cross-national study in the United States and Taiwan. School Science and Mathematics, 111(4), 164-177.   DOI
7 McAllister, C., & Beaver, C. (2012). Identification of error types in preservice teachers' attempts to create fraction story problems for specified operations. School Science & Mathematics, 112(2), 88-98.   DOI
8 Mack, N. K. (2008). Building a Foundation for Understanding the Multiplication of Fractions. Teaching Children Mathematics , 5(1), 34-38.
9 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
10 Charalambous, C. Y., Hill, H. C., & Mitchell, R. B. (2012). Two negative don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality. Journal of Curriculum Studies, 44(4). 489-513.   DOI
11 Newton, K. J. (2008). An extensive analysis of pre-service elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.   DOI
12 Post, T. R., Wachsmuth, I., Lesh, R., & Behr, M. J. (1985). Order and equivalence of rational number: A cognitive analysis. Journal for Research in Mathematics Education , 16(1), 18-36.   DOI
13 Siebert, D. (2002). Connecting Informal Thinking and Algorithms: The Case of Division of Fractions. In Litwiller, B. & Bright, G. (eds.), Making Sense of Fractions, Ratios, and Proportions (pp. 247-256). Reston, VA: NCTM.
14 Siebert, D., & Gaskin, N. (2006). Creating, naming and justifying fractions. Teaching Children Mathematics, 12, 394-400.
15 Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of Fraction Division. In Litwiller, B. & Bright, G. (eds.), Making Sense of Fractions, Ratios, and Proportions (pp. 153-161). Reston, VA: NCTM.
16 Smith, J. P. III. (2002). The Development of Students' Knowledge of Fractions and Ratios. In Litwiller, B. & Bright, G. (eds.), Making Sense of Fractions, Ratios, and Proportions (pp. 3-17). Reston, VA: NCTM.
17 Toluk-Ucar, Z. (2009). Developing preservice teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.   DOI
18 Whitin, D. J. (2004). Building a mathematical community through problem posing. In R. N. Rubenstein (Ed.), Perspectives on the teaching of mathematics: Sixty-sixth yearbook (pp. 129-140). Reston, VA: NCTM.