591
Views
10
CrossRef citations to date
0
Altmetric
Articles

Pupils’ visual representations in standard and problematic problem solving in mathematics: their role in the breach of the didactical contract

, , , &
Pages 95-110 | Published online: 26 Mar 2009

References

  • Baldisseri , F. , D’Amore , B. , Fascinelli , E. , Fiori , M. , Gastaldelli , B. and Golinelli , P. 1994 . “ Greta’s ballons ” . In Didactics of mathematics , Edited by: Gagatsis , A. 571 – 8 . Thessaloniki : ERASMUS ICP‐93‐2001‐11 .
  • Bishop , A. 1989 . Review of research on visualization in mathematics education . Focus on Learning Problems in Mathematics , 11 ( 1 ) : 7 – 15 .
  • Brousseau , G. 1997 . Theory of didactical situations in mathematics , Dordrecht, , The Netherlands : Kluwer .
  • Brown , D. and Wheatly , G. 1997 . Components of imagery and mathematical understanding . Focus on Learning Problems in Mathematics , 19 ( 1 ) : 45 – 70 .
  • Bruner , J. 1961 . The process of education , Cambridge, MA : Harvard University Press .
  • Carney , N.R. and Levin , R.J. 2002 . Pictorial illustrations still improve students’ learning from text . Educational Psychology Review , 14 ( 1 ) : 5 – 26 .
  • DeFranco , T.C. and Curcio , F.R. 1997 . A division problem with a remainder embedded across two contexts: Children’s solutions in restrictive versus real‐world settings . Focus on Learning Problems in Mathematics , 19 ( 2 ) : 58 – 72 .
  • DeLoache , J.S. 1991 . Symbolic functioning in very young children: understanding of picture and models . Child Development , 62 ( 4 ) : 736 – 52 .
  • DeWindt‐King , A.M. and Goldin , G.A. 2003 . Children’s visual imagery: aspects of cognitive representation in solving problems with fractions . Mediterranean Journal for Research in Mathematics Education , 2 ( 1 ) : 1 – 42 .
  • Diezmann , C. and English , L. 2001 . The roles of representation in school mathematics: 2001 Year Book , Virginia : NCTM .
  • Dreyfus , T. and Eisenberg , T. . On difficulties with diagrams: Theoretical issues . Proceedings of the 14th Annual Conference of the International Group for the Psychology of Mathematics Education . Edited by: Booker , G. , Cobb , P. and De Mendicuti , T.N. Vol. I , pp. 27 – 36 . Oaxtepex, , Mexico : PME .
  • Elia , I. , Gagatsis , A. and Deliyianni , E. . A review of the effects of different modes of representation in mathematical problem solving . Proceedings of the 4th Mediterranean Conference on Mathematics Education . Edited by: Gagatsis , A. , Spagnolo , F. , Makrides , Gr. and Farmaki , V. Vol. I , pp. 271 – 86 . Palermo, , Italy : University of Palermo, Cyprus Mathematical Society .
  • Elia , I. , Gagatsis , A. and Demetriou , A. 2007 . The effects of different modes of representation on the solution of one‐step additive problems . Learning and Instruction , 17 : 658 – 72 .
  • Elia , I. and Philippou , G. . The functions of pictures in problem solving . Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education . Edited by: Johnsen Hoines , M. and Berit Fuglestad , A. Vol. 2 , pp. 327 – 34 . Bergen, , Norway : Bergen University College .
  • Fennema , E. and Tartre , L.A. 1985 . The use of spatial visualization in mathematics by girls and boys . Journal for Research in Mathematics Education , 16 ( 3 ) : 184 – 206 .
  • Gagatsis , A. 1992 . “ Introduction: Concepts and methods of didactics of mathematics – Relations between history and didactics of mathematics ” . In Topics on didactics of mathematics , Edited by: Gagatsis , A. 11 – 28 . Thessaloniki, , Greece : Erasmus ICP‐91‐G‐0027/11 .
  • Greer , B. 1997 . Modeling reality in mathematics classrooms: The case of word problems . Learning and Instruction , 7 ( 4 ) : 293 – 307 .
  • Hegarty , M. and Kozhevnikov , M. 1999 . Types of visual‐spatial representations and mathematical problem solving . Journal of Educational Psychology , 19 : 684 – 9 .
  • Hitt , F. 2006 . Students’ functional representations and conceptions in the construction of mathematical concepts. An example: The concept of limit . Annales de Didactique et de Sciences Cognitives , 11 : 253 – 68 .
  • Levie , W.H. and Lentz , R. 1982 . Effects of text illustrations: A review of research . Educational Communication and Technology Journal , 30 ( 4 ) : 195 – 232 .
  • Marcou , A. and Gagatsis , A. . ‘Didactical contract’ and word problems: Influences and breach of contract in primary school . Proceedings of the 3rd Mediterranean Conference on Mathematical Education . Edited by: Gagatsis , A. and Papastavridis , S. pp. 247 – 56 . Athens : Hellenic Mathematical Society, Cyprus Mathematical Society .
  • National Council of Teachers of Mathematics (NCTM) . 2000 . Principles and standards for school mathematics , Reston, VA : NCTM .
  • Presmeg , N. 2006 . “ Research on visualization in learning and teaching mathematics ” . In Handbook of research on the psychology of mathematics education: Post, past and future , Edited by: Gutierrez , A. and Boero , P. 205 – 35 . Rotterdam, , The Netherlands : Sense Publishers .
  • Reusser , K. and Stebler , R. 1997a . Every word problem has a solution – The social rationality of mathematical modeling in schools . Learning and Instruction , 7 ( 4 ) : 309 – 27 .
  • Reusser , K. and Stebler , R. . Realistic mathematical modeling through the solving of performance tasks . Paper presented at the Seventh European Conference on Learning and Instruction . August 26–30 , Athens, Greece.
  • Schnotz , W. 2002 . Towards an integrated view of learning from text and visual displays . Educational Psychology Review , 14 ( 1 ) : 101 – 20 .
  • Seeger , F. 1998 . “ Representations in the mathematical classroom: Reflections and constructions ” . In The culture of the mathematics classroom , Edited by: von Seeger , F. , Voigt , J. and Waschescio , U. 308 – 43 . Cambridge : Cambridge University Press .
  • Theodoulou , R. , Gagatsis , A. and Theodoulou , A. 2004 . Un’ imagine vale piu di mille parole… Ma che tipo di imagine risulta piu efficace nell attivita di problem solving matematico degli studenti? . La matematica e la sua didattica , 2 : 4 – 32 .
  • van Garderen , D. and Montague , M. 2003 . Visual‐spatial representation, mathematical problem solving, and students of varying abilities . Learning Disabilities Research and Practice , 18 ( 4 ) : 246 – 54 .
  • Verschaffel , L. , De Corte , E. and Lasure , S. 1994 . Realistic considerations in mathematical modeling of school arithmetic word problems . Learning and Instruction , 4 : 273 – 94 .
  • Verschaffel , L. , Greer , B. and De Corte , E. 2000 . Making sense of word problems , The Netherlands : Swets and Zeitlinger .
  • Wyndhamn , J. and Säljö , R. 1997 . Word problems and mathematical reasoning – A study of children’s mastery of reference and meaning in textual realities . Learning and Instruction , 7 ( 4 ) : 361 – 82 .
  • Yoshida , H. , Verschaffel , L. and De Corte , E. 1997 . Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? . Learning and Instruction , 7 ( 4 ) : 329 – 38 .

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.