Children's strategies for division by fractions in the context of the area of a rectangle

Educational Studies in Mathematics

Volumn 73, Issue 2, 2010, Pages 105-120

  Yim, Jaehoon ^a  

^a Gyeongin National University of Education   (South Korea)

Author keywords

Algorithm; Children's construction; Division by fractions; The area of a rectangle; The inverse of a Cartesian product

Indexed keywords

EID: 77951878217     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-009-9206-0     Document Type: Article

References (35)

1. Behr, M., & Post, T. (1992). Teaching rational number and decimal concepts. In T. R. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (pp. 201-248). Boston: Allyn and Bacon.
2. Bezuk, N. S., & Armstrong, B. E. (1993). Understanding division of fractions. The Mathematics Teacher, 86, 43-46.
3. Boero, P., Ferrari, P. L., & Ferrero, E. (1989). Division problems: meanings and procedures in the transition to a written algorithm. For the Learning of Mathematics, 9(3), 17-25.
4. Brendefur, J. L., & Pitingoro, R. C. (1998). Dividing fractions by using the ratio table. In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 204-207). Reston: National Council of Teachers of Mathematics.
5. Bulgar, S. (2003). Children's sense-making of division of fractions. The Journal of Mathematical Behavior, 22, 319-334. doi: 10. 1016/S0732-3123(03)00024-5.
6. Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3-17. doi: 10. 2307/748969.
7. Flores, A., Turner, E. E., & Bachman, R. C. (2005). Posing problems to develop conceptual understanding: two teachers make sense of division of fractions. Teaching Children Mathematics, 12(3), 117-121.
8. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.
9. Graeber, A. O., & Tirosh, D. (1990). Insights fourth and fifth graders bring to multiplication and division with decimals. Educational Studies in Mathematics, 21, 565-588. doi: 10. 1007/BF00315945.
10. Gregg, J., & Gregg, D. U. (2007). Measurement and fair-sharing models for dividing fractions. Mathematics Teacher in the Middle School, 12, 490-496.
11. Hatfield, M. M., Edwards, N. T., & Bitter, G. G. (1997). Mathematics methods for the elementary and middle school teachers (3rd ed.). Massachusetts: Allyn and Bacon.
12. Huinker, D. (1998). Letting fraction algorithms emerge through problem solving. In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 170-182). Reston: National Council of Teachers of Mathematics.
13. Kamii, C., & Warrington, M. A. (1999). Teaching fractions fostering children's own reasoning. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in grades k-12 (pp. 82-92). Reston: National Council of Teachers of Mathematics.
14. Lee, Y. R. (2001). Jido Naiyongui Haiksim Gwaje 99 (The 99 core tasks of elementary school) mathematics. Seoul: Kyungmoon.
15. Lubinski, C. A., Thomason, R., & Fox, T. (1998). Learning to make sense of division of fractions: One K-8 preservice teacher's perspective. School Science and Mathematics, 98(5), 247-253.
16. Ma, L. (1999). Knowing and teaching elementary school mathematics. Mahwah: Lawrence Erlbaum.
17. Musser, G. L., & Burger, W. F. (1988). Mathematics for elementary teachers. New York: Macmillian.
18. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
19. Okazaki, M., & Koyama, M. (2005). Characteristics of 5th graders' logical development through learning division with decimals. Educational Studies in Mathematics, 60, 217-251. doi: 10. 1007/s10649-005-8123-0.
20. Ott, J. M., Snook, D. L., & Gibson, D. L. (1991). 'Understanding partitive division of fractions. The Arithmetic Teacher, 39(2), 7-11.
21. Pagni, D. (1998). Giving meaning to multiplication and division of fractions. Australian Mathematics Teacher, 54(4), 11-13.
22. Perlwitz, M. D. (2004). Two students' constructed strategies to divide fractions. Mathematics Teacher in the Middle School, 10, 122-126.
23. Perlwitz, M. D. (2005). Dividing fractions: Reconciling self-generated solutions with algorithmic answers. Mathematics Teacher in the Middle School, 10, 278-283.
24. Pirie, S. E. B. (1988). Understanding: Instrumental, relational, intuitive, constructed, formalised...? How can we know? For the Learning of Mathematics, 8(3), 2-6.
25. Sharp, J. (1998). A constructed algorithm for the division of fractions. In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 198-203). Reston: National Council of Teachers of Mathematics.
26. Sharp, J., & Adams, B. (2002). Children's constructions of knowledge for fraction division after solving realistic problems. The Journal of Educational Research, 95, 333-347.
27. Shimizu, Y. (1996). High achievement versus rigidity: Japanese students' thinking on division of fractions. Paper presented at the China-Japan-U. S. seminar on mathematics education, ERIC document reproduction service No. ED395776.
28. Siebert, I. (2002). Connecting informal thinking and algorithms: The case of division of fractions. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 247-256). Reston: National Council of Teachers of Mathematics.
29. Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 153-161). Reston: National Council of Teachers of Mathematics.
30. Thompson, C. (1979). Teaching division by fractions with understanding. The Arithmetic Teacher, 26, 24-27.
31. Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95-113). Reston: National Council of Teachers of Mathematics.
32. Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31, 5-25. doi: 10. 2307/749817.
33. Tirosh, D., & Graeber, A. O. (1989). Preservice elementary teachers' explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20, 79-96. doi: 10. 1007/BF00356042.
34. van de Walle, J. A. (1998). Elementary and middle school mathematics: Teaching developmentally (3rd ed.). New York: Addison Wesley Longman.
35. Warrington, M. A. (1997). How children think about division with fractions. Mathematics Teacher in the Middle School, 2, 390-394.