The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage

Educational Studies in Mathematics

Volumn 54, Issue 1, 2003, Pages 9-35

  Van Den Heuvel Panhuizen, Marja ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Contexts; Curriculum design; Mathematics education; Models; Percentage; Primary school; Shift in levels of understanding

Indexed keywords

EID: 3843119950     PISSN: 00131954     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:EDUC.0000005212.03219.dc     Document Type: Conference Paper

References (50)

1. Abels, M.: 1991, 'Procenten in W12-16', Nieuwe Wiskrant 10(3), 20-25.
2. De Lange, J.: 1987, Mathematics, Insight and Meaning, OW&OC, Utrecht University, Utrecht, The Netherlands.
3. Freudenthal, H.: 1968, 'Why to teach mathematics so as to be useful?', Educational Studies in Mathematics 1, 3-8.
4. Freudenthal, H.: 1971, 'Geometry between the devil and the deep sea', Educational Studies in Mathematics 3, 413-435.
5. Freudenthal, H.: 1973, Mathematics as an Educational Task, Riedel Publishing Company, Dordrecht, The Netherlands.
6. Freudenthal, H.: 1975, 'Voorwoord', in R. de Jong, A. Treffers and E. Wijdeveld (eds.), Overzicht van Wiskundeonderwijs op de Basisschool. Leerplanpublikatie 2, IOWO, Utrecht, The Netherlands.
7. Freudenthal, H.: 1977, 'Antwoord door Prof. Dr H. Freudenthal na het verlenen van het eredoctoraat' [Answer by Prof. Dr H. Freudenthal upon being granted an honorary doctorate], Euclides 52, 336-338.
8. Freudenthal, H.: 1978, Weeding and Sowing. Preface to a Science of Mathematical Education, Reidel Publishing Company, Dordrecht, The Netherlands.
9. Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, Riedel Publishing Company, Dordrecht, The Netherlands.
10. Freudenthal, H.: 1987, 'Mathematics starting and staying in reality', in I. Wirszup and R. Street (eds.), Proceedings of the USCMP Conference on Mathematics Education on Development in School Mathematics around the World, NCTM, Reston, VA.
11. Freudenthal, H.: 1991, Revisiting Mathematics Education. China Lectures, Kluwer Academic Publishers, Dordrecht, The Netherlands.
12. Gravemeijer, K.: 1982, 'Het gebruik van contexten', Willem Bartjens 1(4), 192-197.
13. Gravemeijer, K.P.E.: 1994a, Developing Realistic Mathematics Education, CD-ß Press / Freudenthal Institute, Utrecht, The Netherlands.
14. Gravemeijer, K.P.E.: 1994b, 'Educational development and developmental research in mathematics education', Journal for Research in Mathematics Education 25(5), 443-471.
15. Gravemeijer, K.P.E.: 1997, 'Mediating between concrete and abstract', in T. Nunes and P. Bryant (eds.), Learning and Teaching Mathematics: An International Perspective, Lawrence Erlbaum, Hove, Sussex, United Kingdom, pp. 315-343.
16. Gravemeijer, K: 1999, 'How emergent models may foster the constitution of formal mathematics', Mathematical Thinking and Learning 1(2), 155-177.
17. Gravemeijer, K. and Doorman, D.: 1999, 'Context problems in Realistic Mathematics Education: A calculus course as an example', Educational Studies in Mathematics 39, 111-129.
18. Keijzer, R., Van den Heuvel-Panhuizen, M., Wijers, M., Shew, J., Brinker, L.J., Pligge, M.A., Shafer, M.C. and Brendefur, J.: 1998a: 'More or Less', in T.A. Romberg (ed.), Mathematics in Contexts: A Connected Curriculum for Grade 5-8, Encyclopaedia Britannica Educational Corporation, Chicago, IL.
19. Keijzer, R., Van Galen, F., Gravemeijer, K., Shew, A., Cole, B.R. and Brendefur, J.: 1998b, 'Fraction Times', in T.A. Romberg (ed.), Mathematics in Contexts: A Connected Curriculum for Grade 5-8, Encyclopaedia Britannica Educational Corporation, Chicago, IL.
20. Lesh, R. and Doerr, H. M.: 2000, 'Symbolizing, communication and mathematizing: Key components of models and modeling', in P. Cobb, E. Yackel and K. McClain (eds.), Symbolizing and Communicating in Mathematics Classrooms, Lawrence Erlbaum Associates, Mahwah, NJ, pp. 361-383.
21. National Council of Teachers of Mathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston VA.
22. Middleton, J.A., Van den Heuvel-Panhuizen, M. and Shew, J.A.: 1998, 'Using bar representations as a model for connecting concepts of rational number', Mathematics Teaching in the Middle School 3(4), 302-311.
23. Middleton, J.A. and Van den Heuvel-Panhuizen, M.: 1995, 'The ratio table', Mathematics Teaching in the Middle School 1(4), 282-288.
24. Romberg, T.A. (ed.): 1997-1998, Mathematics in Contexts: A Connected Curriculum for Grade 5-8, Encyclopaedia Britannica Educational Corporation, Chicago, IL.
25. Streefland, L.: 1985a, 'Wiskunde als activiteit en de realiteit als bron', Nieuwe Wiskrant 5(1), 60-67.
26. Streefland, L.: 1985b, 'Vorgreifendes Lernen zum Steuern Langfristiger Lernprozesse', in W. Dörfler and R. Fischer (eds.), Empirische Untersuchungen zum Lehren und Lernen von Mathematik. Beiträge zum 4. Internationalen Symposium für Didaktik der Mathematik in Klagenfurt in 1984, Hölder-Pichler-Tempsky, Wien, Austria, pp. 271-285.
27. Streefland, L.: 1988, 'Reconstructive learning', in Proceedings of the XII PME Conference, Veszprein, Hungary, Vol. I, pp. 75-91.
28. Streefland, L.: 1991, Fractions in Realistic Mathematics Education. A Paradigm of Developmental Research, Kluwer Academic Publisher, Dordrecht.
29. Streefland, L.: 1992, 'Het ontwerpen van een wiskundeleergang', Tijdschrift voor Nascholing en Onderzoek van het Reken-Wiskundeonderwijs 10(4), 3-14.
30. Streefland, L. and Van den Heuvel-Panhuizen, M.: 1992, 'Evoking pupils' informal knowledge on percents', Proceedings of the Sixteenth PME Conference, University of New Hampshire, Durham, NH, Vol. III, pp. 51-57.
31. Streefland, L.: 1993, 'The design of a mathematics course. A theoretical reflection', Educational Studies in Mathematics 25(1-2), 109-135.
32. Streefland, L.: 1996, Learning from History for Teaching in the Future, Utrecht, Freudenthal Institute, Utrecht University, The Netherlands. (Regular lecture held at the ICME-8 in Sevilla, Spain)
33. Treffers, A. and Goffree, F.: 1985, 'Rational analysis of realistic mathematics education - the Wiskobas program', in L. Streefland (ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, OW&OC, Utrecht University, Utrecht, The Netherlands, Vol. II, pp. 97-121.
34. Treffers, A.: 1978, Wiskobas Doelgericht, IOWO, Utrecht, The Netherlands.
35. Treffers, A.: 1987, Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction - The Wiskobas Project, Reidel Publishing Company, Dordrecht, The Netherlands.
36. Treffers, A.: 1991, 'Didactical background of a mathematics programm for primary education', in L. Streefland (ed.), Realistic Mathematics Education in Primary School, CD-ß Press / Freudenthal Institute, Utrecht University, Utrecht, The Netherlands, pp. 21-56.
37. Van Amerom, B.: 2002, Reinvention Early Algebra. Developmental Research on the Transition from Arithmetic to Algebra, CD-ß Press / Freudenthal Institute, Utrecht, The Netherlands.
38. Van den Brink, J.: 1973, 'Bijna noemen', Wiskobasbulletin 3, 129-131.
39. Van den Brink, J.: 1984, 'Numbers in contextual frameworks', Educational Studies in Mathematics 15, 239-257.
40. Van den Heuvel-Panhuizen, M. and Streefland, L.: 1993, 'Per Sense - Een onder-wijspakketje over procenten', in M. Dolk and W. Uittenbogaard (eds.), Procenten - Op de grens van basisschool en basisvorming, Panama / HMN & Freudenthal Instituut, Utrecht, The Netherlands, pp. 25-48.
41. Van den Heuvel-Panhuizen, M.: 1994, 'Improvement of (didactical) assessment by improvement of the problems: An attempt with respect to percentage', Educational Studies in Mathematics 27(4), 341-372.
42. Van den Heuvel-Panhuizen, M.: 1995, 'A representional model in a long term learning process - the didactical use of models in Realistic Mathematics Education' paper presented at the AERA conference, San Francisco, CA.
43. Van den Heuvel-Panhuizen, M.: 1996, Assessment and Realistic Mathematics Education, CD-ß Press Utrecht University, Utrecht, The Netherlands.
44. Van den Heuvel-Panhuizen, M., Streefland, L., Meyer, M., Middleton, J.A. and Browne, J.: 1997, 'Per Sense', in T.A. Romberg (ed.), Mathematics in Contexts: A Connected Curriculum for Grade 5-8, Encyclopaedia Britannica Educational Corporation, Chicago, IL.
45. Van den Heuvel-Panhuizen, M.: 2001, 'Realistic Mathematics Education in the Netherlands', in J. Anghileri (ed.), Principles and Practices in Arithmetic Teaching. Innovative Approaches for the Primary Classroom, Open University Press, Buckingham, United Kingdom, pp. 49-63.
46. Van den Heuvel-Panhuizen, M.: 2002, 'Realistic Mathematics Education as work in progress', in F.L. Lin (ed.), Common Sense in Mathematics Education. Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education, Taipei, Taiwan, National Taiwan Normal University, Taipei, Taiwan, pp. 1-42.
47. Vygotsky, L.S.: 1978, Mind in Society: The Development of Higher Psychological Processes, Harvard University Press, Cambridge, MA.
48. Wijdeveld, E.: 1980, 'Zich realiseren', in IOWO, De Achterkant van de Möbiusband, IOWO, Utrecht, The Netherlands, pp. 23-26.
49. Wijers, M. and Van Galen, F.: 1995, 'Breuken, procenten en kommagetallen in het Middle School Project', in C. van den Boer and M. Dolk (eds.), Rekenen in de Bovenbouw van de Basisschool, Panama / HvU & Freudenthal Institute, Utrecht University, Utrecht, The Netherlands, pp. 65-74.
50. Yackel, E., Underwood, D., Stephan, M. and Rasmussen, Ch.: 2001, 'Didactising: Continuing the work of Leen Streefland', in M. van den Heuvel-Panhuizen (ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Freudenthal Institute, Utrecht University, Utrecht, The Netherlands, Vol. 1, pp. 239-249 and 251-253.