The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration

Educational Studies in Mathematics

Volumn 47, Issue 2, 2001, Pages 199-221

  Stacey, Kaye ^a   Helme, Sue ^a   Archer, Shona ^a   Condon, Caroline ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Accessibility; Decimal numeration; Epistemic fidelity; Models; Physical materials; Transparency

Indexed keywords

EID: 52549104785     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1014590319667     Document Type: Article

References (19)

1. Archer, S.: 1999, The Comparative Effectiveness of Linear Arithmetic Blocks and Multibase Arithmetic Blocks in Addressing Students' Misconceptions about Decimals, University of Melbourne, Unpublished Honours Thesis.
2. Archer, S. and Condon, C.: 1999, Linear Arithmetic Blocks: A Concrete Model for Teaching Decimals, Department of Science and Mathematics Education, University of Melbourne.
3. Ball, D.: 1992, 'Manipulatives and the reform of math education', American Educator Summer, 14-18, 46-47.
4. Battista, M. and Clements, D.: 1996, 'Students' understanding of three-dimensional rectangular arrays of cubes', Journal For Research in Mathematics Education 27(3), 258-292.
5. Booker, G., Briggs, J., Davey, G. and Nisbet, S.: 1996, Teaching Primary Mathematics, Longman, Melbourne.
6. Condon, C. and Archer, S.: 1999, Lesson Ideas and Activities for Teaching Decimals, Department of Science and Mathematics Education, University of Melbourne.
7. Condon, C.: 1999, The Comparison of Two Decimal Models - The MAB and LAB, University of Melbourne, Unpublished Honours Thesis.
8. Dienes, Z.: 1964. Mathematics in the Primary Classroom, St. Martin's Press, New York.
9. English, L. and Halford, G.: 1995, Mathematics Education: Models and Processes, Lawrence Erlbaum, Mahwah, NJ.
10. Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structure, Kluwer, Dordrecht.
11. Hiebert, J., Wearne, D. and Taber, S.: 1991, 'Fourth graders' gradual construction of decimal fractions during instruction using different physical representations', The Elementary School Journal 91(4), 321-341.
12. Lave, J. and Wenger, E.: 1991, Situated Learning: Legitimate Peripheral Participation, Cambridge University Press, Cambridge.
13. Lesh, R., Behr, M. and Post, T.: 1987, 'Rational number relations and proportions', in C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics, Erlbaum, Hillsdale, NJ, pp. 41-58.
14. Meira, L.: 1998, 'Making sense of instructional devices: The emergence of transparency in mathematical activity', Journal for Research in Mathematics Education 29(2), 121-142.
15. National Council of Teachers of Mathematics: 2000, Principles and Standards for School Mathematics, NCTM, Reston, VA.
16. Sowell, E.: 1989, 'Effects of manipulative materials in mathematics instruction', Journal for Research in Mathematics Education 20(5), 498-505.
17. Stacey, K. and Steinle, V.: 1998, 'Refining the classification of students' interpretations of decimal notation', Hiroshima Journal of Mathematics Education 6, 1-21.
18. Stacey, K. and Steinle, V.: 1999, 'A longitudinal study of children's thinking about decimals: A preliminary analysis', in O. Zaslavsky (ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Haifa, Israel.
19. Thompson, P.W.: 1992, 'Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics, Journal for Research in Mathematics Education 23(2), 123-147.