Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children's thinking

Educational Studies in Mathematics

Volumn 63, Issue 1, 2006, Pages 1-28

  Empson, Susan B ^a   Junk, Debra ^a   Dominguez, Higinio ^a   Turner, Erin ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

Children's strategies; Distributed thinking; Elementary K 8; Equal sharing; Fractions; Multiplicative structure; Problem solving; Rational number

Indexed keywords

EID: 33748995349     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-005-9000-6     Document Type: Review

References (25)

1. Behr, M., Harel, G., Post, T. and Lesh, R.: 1992, 'Rational number, ratio, and proportion', in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 296-333.
2. Carpenter, T.P., Ansell, E., Franke, M.L., Fennema, E. and Weisbeck, L.: 1993, 'Models of problem solving: A study of kindergarten children's problem-solving processes', Journal for Research in Mathematics Education 24(5), 427-440.
3. Charles, K. and Nason, R.: 2000, 'Young children's partitioning strategies', Educational Studies in Mathematics 43, 191-221.
4. Courant, R. and Robbins, H.: 1996, What is mathematics? 2nd ed., Oxford, New York.
5. Dienes, Z.P.: 1967, Fractions: An Operational Approach, Herder and Herder, New York.
6. Empson, S.B.: 1999, 'Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom', Cognition and Instruction 17(3), 283-342.
7. Empson, S.B.: 2003, 'Low-performing students and teaching fractions for understanding: An interactional analysis', Journal for Research in Mathematics Education 34, 305-343.
8. Ginsburg, H., Kossan, N., Schwartz, R. and Swanson, D.: 1983, in H. Ginsburg (ed.), The Acquisition of Mathematical Concepts and Processes, Academic, New York, pp. 8-46.
9. Greeno, J., Collins, A. and Resnick, L. (1996). 'Cognition and learning', in D. Berliner and R. Calfee (eds.), Handbook of Educational Psychology, Macmillan, New York, pp. 15-46.
10. Greer, B.: 1992, 'Multiplication and division as models of situations', in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York.
11. Kieren, T.: 1988, 'Personal knowledge of rational numbers: Its intuitive and formal development', in J. Hiebert and M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Lawrence Erlbaum, Hillsdale, NJ, pp. 162-181.
12. Kieren, T.: 1995, 'Creating spaces for learning fractions', in J. Sowder and B. Schappelle (eds.), Providing a Foundation for Teaching Mathematics in the Middle Grades, State University of New York Press, New York, pp. 31-65.
13. Lamon, S.: 1996, The development of unitizing: Its role in children's partitioning strategies', Journal for Research in Mathematics Education 271(2), 170-193.
14. Nunes, T. and Bryant, P.: 1996, Children Doing Mathematics, Blackwell, Cambridge, MA.
15. Piaget, J., Inhelder, B. and Szeminska, A.: 1960, The Child's Conception of Geometry (E.A. Lunzer, Trans.), Basic, New York.
16. Pothier, Y. and Sawada, D.: 1983, 'Partitioning: The emergence of rational number ideas in young children', Journal for Research in Mathematics Education 14, 307-317.
17. Saxe, G., Taylor, E., McIntosh, C. and Gearhart, M.: in press, 'Representing fractions with standard notation: A developmental analysis', Journal of Research in Mathematics Education.
18. Schwartz, D.L., Martin, T. and Pfaffman, J.: in press, 'How mathematics propels the development of physical knowledge', Journal of Cognition and Development. Manuscript in press.
19. Schwartz, J.: 1988, 'Intensive quantity and referent transforming arithmetic operations', in J. Hiebert and M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Lawrence Erlbaum, Hillsdale, NJ, pp. 53-92.
20. Steffe, L.P.: 2002, 'A new hypothesis concerning children's fractional knowledge', Journal of Mathematical Behavior 2, 267-307.
21. Steffe, L.P.: 1994, 'Children's multiplying schemes', in G. Harel and J. Confrey (eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics, State University of New York Press, Albany, NY, pp. 3-40.
22. Streefland, L.: 1991, Fractions in Realistic Mathematics Education, Kluwer, Boston.
23. Streefland, L.: 1993, 'Fractions: A realistic approach', in T.P. Carpenter, E. Fennema and T. Romberg (eds.), Rational Numbers: An Integration of Research, Lawrence Erlbaum, Hillsdale, NJ, pp. 289-325.
24. Thompson, P. and Saldanha, L.: 2003, Fractions and multiplicative reasoning', in J. Kilpatrick, W.G. Mateo and D. Schifter (eds.), A Research Companion to Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, Reston, VA, pp. 95-113.
25. Vergnaud, G.: 1988, 'Multiplicative structures', in J. Hiebert and M. Behr (eds.), Number Concepts and Operations in the Middle Grades, Lawrence Erlbaum, Hillsdale, NJ, pp. 141-161.