Young children'S notations for fractions

Educational Studies in Mathematics

Volumn 62, Issue 3, 2006, Pages 281-305

  Brizuela, Bárbara M ^a  

^a TUFTS UNIVERSITY   (United States)

Author keywords

Fractional numbers; Notations; Representations; Young children

Indexed keywords

EID: 33747735647     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-005-9003-3     Document Type: Review

References (41)

1. Alvarado, M.: 2002, La Construcción del Sistema Gráfico Numérico en los Momentos Iniciales de la Adquisición del Sistema Gráfico Alfabético [The Construction of the Numerical Graphical System in the Initial Moments of the Acquisition of the Alphabetic Graphic System], Unpublished Doctoral Dissertation, CINVESTAV, IPN, Departamento de Investigaciones Educativas, México.
2. Ball, D.L.: 1993, 'Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions', in T.P. Carpenter, E. Fennema and T.A. Romberg (eds.), Rational Numbers: An Integration of Research, Lawrence Erlbaum and Associates, Hillsdale, NJ, pp. 157-195.
3. Behr, M.J. and Bright, G.W.: 1984, Identifying Fractions on Number Lines, Paper presented at the Annual Meeting of the American Educational Research Association, ERIC document ED248 148, New Orleans, LA.
4. Behr, M.J., Lesh, R., Post, T.R. and Silver, E.A.: 1983, 'Rational-Number Concepts', in R. Lesh and M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York, pp. 91-126.
5. Brizuela, B.M.: 2001, Children's Ideas About the Written Number System, Unpublished Doctoral Dissertation, Harvard University Graduate School of Education, Cambridge, MA.
6. Brizuela, B.M.: 2004, Mathematical Development in Young Children: Exploring Notations, Teachers College Press, New York.
7. Carpenter, T.P, Fennema, E. and Romberg, T.A.: 1993, 'Towards a unified discipline of scientific inquiry', in T.P. Carpenter, E. Fennema and T.A. Romberg (eds.), Rational Numbers: An Integration of Research, Lawrence Erlbaum and Associates, Hillsdale, NJ, pp. 1-11.
8. Carraher, D.W.: 1996, 'Learning about fractions', in L. Steffe, P. Nesher, P. Cobb, G. Goldin and B. Greer (eds.), Theories of Mathematical Learning, Lawrence Erlbaum and Associates, Mahwah, NJ, pp. 241-266.
9. Cobb, P., Gravemeijer, K., Yackel, E., McClain, K. and Whitenack, J.: 1997, 'Mathematizing and symbolizing: The emergence of chains of signification in one first-grade class-room', in D. Kirshner and J. Whitson (eds.), Situated Cognition: Social, Semiotic, and Psychological Perspectives, Lawrence Erlbaum Associates, Inc., Mahwah, NJ, pp. 151-234.
10. Empson, S.B.: 1995, 'Using sharing situations to help children learn fractions', Teaching Children Mathematics 2(2), 110-114.
11. 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.
12. Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, Kluwer Academic Publishers, Dordrecht, The Netherlands.
13. Goldin, G.: 1998, 'Representational systems, learning, and problem solving in mathematics', Journal of Mathematical Behavior 17(2), 137-165.
14. Goldin, G. and Shteingold, N.: 2001, 'Systems of representations and the development of Mathematical Concepts', in A.A. Cuoco and F.R. Curcio (eds.), The Roles of Representation in School Mathematics. NCTM 2001 Yearbook, National Council of Teachers of Mathematics, Reston, Virginia, pp. 1-23.
15. Gunderson, A.G. and Gunderson, E.: 1957, 'Fraction concepts held by young children', Arithmetic Teacher 4, 168-174.
16. Hiebert, J. and Wearne, D.: 1987, 'Cognitive effects of instruction designed to promote meaning for written mathematical symbols', in J. Bergeron, N. Herscovics and C. Kieran (eds.), Psychology of Mathematics Education 11(1), 391-398.
17. Hunting, R.: 1987, What Does the Last Decade of Rational Number Research Offer the Elementary Teacher?, Paper presented at the annual meeting of the National Council of Teachers of Mathematics, Anaheim, CA.
18. Kamii, C.: 2000, Young Children Reinvent Arithmetic: Implications of Piaget's Theory (2nd ed.), Teachers College Press, New York.
19. Keijzer, R. and Terwel, J.: 2000, Learning for Mathematical Insight: A Longitudinal Comparison of Two Dutch Curricula on Fractions, Paper presented at the Annual Meeting of the American Educational Research Association, ERIC document ED 440 865, New Orleans, LA.
20. Kieren, T.E.: 1980, 'The rational number construct - Its elements and mechanisms', in T.E. Kieren (ed.), Recent Research on Number Learning, ERIC/SMEAC, Columbus, OH, pp. 125-150.
21. Kieren, T.E.: 1992, 'Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction', in R. Leinhardt, R. Putnam and R.A. Hattrup (eds.), Analysis of Arithmetic Mathematics Teaching, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 323-371.
22. Lamon, S.J.: 1994, 'Ratio and proportion: Cognitive foundations of unitizing and norming', 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. 89-120.
23. Lamon, S.J.: 1999, Teaching Fractions and Ratios for Understanding, Lawrence Erlbaum and Associates, Mahwah, NJ.
24. Lee, K. and Karmiloff-Smith, A.: 1996, The development of external symbol systems: the child as notator', in R. Goelman and T. Kit-Fong Au (eds.), Perceptual and Cognitive Development, Academic Press, San Diego, CA, pp. 185-211.
25. Mack, N.K.: 1990, 'Learning fractions with understanding: Building on informal knowledge', Journal for Research in Mathematics Education, 21(1), 16-32.
26. Mack, N.K.: 1993, 'Making connections to understand fractions', Arithmetic Teacher 40(6), 362-364.
27. Martí, E. and Pozo, J.I.: 2000, 'Mas Allá de las representaciones mentales: La adquisición de los sistemas externos de representación [Beyond mental representations: The acquisition of external systems of representation] ', Infancia y Aprendizaje 90, 11-30.
28. Moss, J. and Case, R.: 1999, 'Developing children's rational number understanding of the rational numbers: A new model and an experimental curriculum', Journal for Research in Mathematics Education 30(2), 122-147.
29. Piaget, J.: 1929, The Child's Conception of the World (J. and A. Tomlinson, trans.), Littlefield Adams, Savage, MD. (Original work published 1926)
30. Piaget, J., Inhelder, B. and Szeminska, A.: 1960, The Child's Conception of Geometry, Routledge & Kegan Paul, London.
31. Pitkethly, A. and Hunting, R.: 1996, 'A review of recent research in the area of initial fraction concepts', Educational Studies in Mathematics 30, 5-38.
32. Polkinghorne, A.R.: 1935, 'Young children and fractions', Childhood Education 11, 354-358.
33. Pothier, Y. and Sawada, D.: 1983, 'Partitioning: The emergence of rational number ideas in young children', Journal for Research in Mathematics Education 14(5), 307-317.
34. Quinteros, G.: 1997, El Uso y Función de las Letras en el Período Pre-Alfabético [The Use and Role of Letters in the Pre-Alphabetic Period], DIE/CINVESTAV (Thesis no. 27), Mexico.
35. Sáenz-Ludlow, A.: 1994, 'Michael's fraction schemes', Journal for Research in Mathematics Education 25(1), 50-85.
36. Sáenz-Ludlow, A.: 1995, 'Ann's fraction schemes', Educational Studies in Mathematics 28, 101-132.
37. Siegal, M. and Smith, J.A.: 1997, 'Toward making representation count in children's conceptions of fractions', Contemporary Educational Psychology 22, 1-22.
38. Smith, J.P.: 2002, 'The development of students' knowledge of fractions and ratios', in B. Litwiller (ed.), Making Sense of Fractions, Ratios, and Proportions. 2002 Yearbook, NCTM: Reston, VA, pp. 3-17.
39. Spinillo, A.G. and Bryant, P.: 1991, 'Children's proportional judgments: The importance of "half", Child Development 62, 427-440.
40. Steffe, L.P. and Olive, J.: 1991, 'The problem of fractions in the elementary school', Arithmetic Teacher 38(9), 22-24.
41. Vergnaud, G.: 1983, 'Multiplicative structures', in R. Lesh and M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York, pp. 127-174.