Publication Cover
Educational Research and Evaluation
An International Journal on Theory and Practice
Volume 15, 2009 - Issue 1
1,227
Views
33
CrossRef citations to date
0
Altmetric
Articles

Are representations to be provided or generated in primary mathematics education? Effects on transfer

, , &
Pages 25-44 | Received 30 Mar 2008, Published online: 09 Feb 2009

References

  • Ainsworth , S. 2006 . DeFT: A conceptual framework for considering learning with multiple representations . Learning and Instruction , 16 ( 3 ) : 183 – 198 .
  • Anderson , J. R. 1995 . Cognitive psychology and its implications , 4th ed. , New York : Freeman and Company .
  • Ausubel , D. P. 1968 . Educational psychology: A cognitive view , New York : Holt, Rinehart & Winston .
  • Brown , A. L. and Palincsar , A. S. 1989 . “ Guided, cooperative learning and individual knowledge acquisition ” . In Knowing, learning and instruction: Essays in the honor of Robert Glaser , Edited by: Resnick , L. B. 393 – 451 . Hillsdale, NJ : Erlbaum Associates .
  • Cohen , J. 1988 . Statistical power analysis for the behavioral sciences , Hillsdale, NJ : Lawrence Erlbaum Associates .
  • De Bock , D. , Verschaffel , L. , Janssens , D. , Van Dooren , W. and Claes , K. 2003 . Do realistic contexts and graphical representations always have beneficial impact on students performance? Negative evidence from a study on modelling non-lineair geometry problems . Learning and Instruction , 13 ( 4 ) : 441 – 463 .
  • diSessa , A. A. 2002 . “ Students' criteria for representational adequacy ” . In Symbolizing, modelling and tool use in mathematics education , Edited by: Gravemeijer , K. , Lehrer , R. , van Oers , B. and Verschaffel , L. 105 – 130 . Dordrecht, , The Netherlands : Kluwer Academic Publishers .
  • diSessa , A. A. 2004 . Metarepresentation: Native competence and targets for instruction . Cognition and Instruction , 22 : 293 – 331 .
  • diSessa , A. A. , Hammer , D. , Sherin , B. and Kolpakowski , T. 1991 . Inventing graphing: Meta-representational expertise in children . Journal of Mathematical Behavior , 10 ( 2 ) : 117 – 160 .
  • Freudenthal , H. 1991 . Revisiting mathematics education. China lectures , Dordrecht, , The Netherlands : Kluwer Academic Publishers .
  • Gilbert J. K. Boulter C. J. Developing models in science education Kluwer Academic Publishers Dordrecht, , The Netherlands/Boston/London 2000
  • Gravemeijer K. Lehrer R. Van Oers B. Verschaffel L. Symbolizing, modelling and tool use in mathematics education 105 130 Kluwer Academic Publishers Dordrecht, , The Netherlands 2003
  • Gravemeijer , K. P.E. and Terwel , J. 2000 . Hans Freudenthal a mathematician on didactics and curriculum theory . Journal of Curriculum Studies , 32 : 777 – 796 .
  • Greeno , J. G. 1997 . On claims that answer the wrong questions . Educational Researcher , 26 ( 1 ) : 5 – 17 .
  • Greeno , J. G. 2006 . Authoritative, accountable positioning and connected, general knowing: Progressive themes in understanding transfer . Journal of the Learning Sciences , 15 ( 4 ) : 537 – 547 .
  • Greeno , J. G. , Smith , D. R. and Moore , J. L. 1993 . “ Transfer of situated learning ” . In Transfer on trial: Intelligence, cognition, and instruction , Edited by: Detterman , D. K. and Sternberg , R. J. 99 – 167 . Norwood, NJ : Ablex .
  • Greer , B. 1997 . Modelling reality in mathematics classrooms: The case of word problems . Learning and Instruction , 7 ( 4 ) : 293 – 307 .
  • Hattie , J. , Biggs , J. and Purdie , N. 1996 . Effects of learning skills interventions on student learning: A meta-analysis . Review of Educational Research , 66 ( 2 ) : 99 – 136 .
  • Herfs , P. G.P. , Mertens , E. H.M. , Perrenet , J.Chr. and Terwel , J. 1991 . Leren door samenwerken [Learning through co-operation] , Amsterdam/Lisse, , The Netherlands : Swets & Zeitlinger .
  • Judd , C. H. 1908 . The relation of special training to general intelligence . Educational Review , 36 : 28 – 42 .
  • Katona , G. 1940 . Organizing and memorizing: Studies in the psychology of learning and teaching , New York : Columbia University Press .
  • Keijzer , R. and Terwel , J. 2003 . Learning for mathematical insight: A longitudinal comparative study on modelling . Learning and Instruction , 13 ( 3 ) : 285 – 304 .
  • Keijzer , R. , Van Galen , F. and Oosterwaal , L. . Reinvention revisited. Learning and teaching decimals as example . Paper presented at the International Congress on Mathematical Education . Copenhagen, Denmark. July ,
  • Lehtinen , E. and Hannula , M. M. 2006 . “ Attentional processes, abstraction and transfer in early mathematical processes ” . In Instructional psychology: Past, present and future trends , Advances in learning and instruction series Edited by: Verschaffel , L. , Dochy , F. , Boekaerts , M. and Vosniadou , S. 39 – 55 . Amsterdam : Elsevier .
  • Lewin , K. 1943 . Defining the “field at a given time” . Psychological Review , 50 ( 3 ) : 292 – 310 .
  • Lobato , J. 2003 . How design experiments can inform a rethinking of transfer and vice versa . Educational Researcher , 32 ( 1 ) : 17 – 20 .
  • Lobato , J. 2006 . Alternative perspectives on the transfer of learning: History, issues, and challenges for future research . The Journal of the Learning Sciences , 15 ( 4 ) : 431 – 449 .
  • Marton . 2006 . Sameness and difference in transfer . Journal of the Learning Sciences , 15 ( 4 ) : 499 – 535 .
  • Mayer , R. E. 1989 . Models for understanding . Review of Educational Research , 59 ( 1 ) : 43 – 64 .
  • Perkins , D. N. and Unger , Chr. 1999 . “ Teaching and learning for understanding ” . In Instructional-design theories and models. Volume II. A new paradigm of instructional theory , Edited by: Reigeluth , C. M. 91 – 114 . Mahwah, NJ : Lawrence Erlbaum Associates .
  • Rosenshine , B. , Meister , C. and Chapman , S. 1996 . Teaching students to generate questions: A review of the intervention studies . Review of Educational Research , 66 : 181 – 221 .
  • Säljö , R. 2003 . “ Epilogue: From transfer to boundary-crossing ” . In Between school and work. New perspectives on transfer and boundary-crossing , Edited by: Tuomi-Grön , T. and Egeström , Y. 311 – 321 . Amsterdam : Pergamon/Elsevier Science .
  • Schnotz , W. and Bannert , B. 2003 . Construction and interference in learning from multiple representations . Learning and Instruction , 13 ( 2 ) : 141 – 156 .
  • Schwartz , D. L. 1995 . The emergence of abstract representations in dyad problem solving . The Journal of the Learning Sciences , 4 ( 3 ) : 321 – 351 .
  • Sfard , A. 1998 . On two metaphors for learning and the dangers of choosing just one . Educational Researcher , 27 ( 2 ) : 4 – 13 .
  • Sternberg R. J. Thinking and problem solving Academic Press San Diego, CA 1994
  • Streefland , L. 1990 . Fractions in realistic mathematics education, a paradigm of developmental research , Dordrecht, , The Netherlands : Kluwer Academic Publishers .
  • Thorndike , E. L. 1922 . The psychology of arithmetic , New York : Macmillan .
  • Van Dijk , I. M.A.W. , Van Oers , B. and Terwel , J. 2003 . Providing or designing? Constructing models in primary maths education . Learning and Instruction , 13 ( 1 ) : 53 – 72 .
  • Van Dijk , I. M.A.W. , Van Oers , B. , Terwel , J. and Van den Eeden , P. 2003 . Strategic learning in primary mathematics education. Evaluation of a program in modelling . Educational Research and Evaluation , 9 : 161 – 187 .
  • Van Oers , B. 1998 . From context to contextualizing . Learning and Instruction , 8 ( 6 ) : 473 – 488 .
  • Van Oers , B. 2001 . Contextualisation for abstraction . Cognitive Science Quarterly , 1 ( 3/4 ) : 279 – 306 .
  • Van Parreren , C. F. 1966 . Psychologie van het leren II [Psychology of learning II] , Arnhem, , The Netherlands : Van Lochum Slaterus .
  • Van Parreren , C. F. 1993 . Ontwikkelend onderwijs [Developmental Education] , Amersfoort, , The Netherlands/Leuven, Belgium : Acco .
  • Vygotsky , L. 1978 . Mind in society , London : Harvard University Press .
  • Wells , G. 1999 . Dialogic inquiry , Cambridge, , UK : Cambridge University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.