324
Views
4
CrossRef citations to date
0
Altmetric
Research papers

Normalising geometrical figures: dynamic manipulation and construction of meanings for ratio and proportion

&
Pages 149-166 | Published online: 22 Jul 2009

References

  • Ainley , J. , Pratt , D. and Nardi , E. 2001 . Normalising: Children's activity to construct meanings for trend . Educational Studies in Mathematics , 45 : 131 – 146 .
  • Ainley , J. , Pratt , D. and Hansen , A. 2006 . Connecting engagement and focus in pedagogic task design . British Educational Research Journal , 32 ( 1 ) : 23 – 38 .
  • Artigue , M. 2002 . Learning Mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work . International Journal of Computers for Mathematical Learning , 7 ( 3 ) : 245 – 274 .
  • Behr , M. , Harel , G. , Post , T. and Lesh , R. 1992 . “ Rational number, ratio and proportion ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. 296 – 333 . New York : MacMillan .
  • Clarkson , R. 1989 . “ Ratio: Enlargement ” . In Children's mathematical frameworks 8–13: A study of classroom teaching , Edited by: Johnson , D.C. 191 – 217 . Windsor : NFER-Nelson .
  • Cobb , P. , Confrey , J. , diSessa , A. , Lehrer , P. and Schauble , L. 2003 . Design experiments in educational research . Educational Researcher , 32 ( 1 ) : 9 – 13 .
  • Drijvers , P. and Trouche , L. 2008 . “ From artifacts to instruments: A theoretical framework behind the orchestra metaphor ” . In Research on technology and the teaching and learning of mathematics: Vol 2. Cases and perspectives , Edited by: Blume , G.W. and Heid , M.K. 363 – 391 . Charlotte, NC : Information Age .
  • Guin , D. and Trouche , L. 1999 . The complex process of converting tools into mathematical instruments: The case of calculators . International Journal of Computers for Mathematical Learning , 3 ( 3 ) : 195 – 227 .
  • Hadas , N. , Hershkowitz , R. and Schwarz , B.B. 2000 . The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments . Educational Studies in Mathematics , 44 : 127 – 150 .
  • Harel , I. and S. Papert 1991 . Constructionism: Research reports and essays . Norwood, NJ : Ablex Publishing Corporation .
  • Hart , K. 1981 . “ Ratio and proportion ” . In Children's understanding of mathematics: 11–16 , Edited by: Hart , K. , Brown , M.L. , Kuchemann , D. , Kerslake , D. , Ruddock , G. and McCartney , M. 88 – 101 . London : John Murray .
  • Hart , K. 1984 . Ratio: Children's strategies and errors , Windsor : NFER-Nelson .
  • Hölzl , R. 1996 . How does ‘dragging’ affect the learning of geometry? . International Journal of Computers for Mathematical Learning , 1 ( 2 ) : 169 – 187 .
  • Hoyles , C. and Noss , R. 1989 . The computer as a catalyst in children's proportion strategies . Journal of Mathematical Behavior , 8 : 53 – 75 .
  • Hoyles , C. , Noss , R. and Sutherland , R. 1989 . “ A Logo-based microworld for ratio and proportion ” . In Proceedings of the 13th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Vergnaud , G. , Rogalski , J. and Artique , M. Vol. 2 , 115 – 122 . Paris : Laboratoire PSYDEE .
  • Kaput , J. and West , M. 1994 . “ Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns ” . In The development of multiplicative reasoning in the learning of mathematics , Edited by: Harel , G. and Confrey , J. 235 – 287 . Albany, NY : State University of New York Press .
  • Karplus , R. , Pulos , S. and Stage , E.K. 1983 . “ Proportional reasoning of early adolescents ” . In Acquisition of mathematical concepts and processes , Edited by: Lesh , R. and Landau , M. 45 – 90 . Orlando, FL : Academic Press .
  • Kuchemann , D. 1989 . “ The effect of setting and numerical content on the difficulty of ratio tasks ” . In Proceedings of the 13th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Vergnaud , G. , Rogalski , J. and Artigue , M. Vol. 2 , 180 – 86 . Paris : Laboratoire PSYDEE .
  • Kynigos , C. 2004 . A “black-and-white box” approach to user empowerment with component computing . Interactive Learning Environments , 12 ( 1–2 ) : 27 – 71 .
  • Lamon , S. J. 1993 . Ratio and proportion: Connecting content and children's thinking . Journal for Research in Mathematics Education 24 , no. 1 : 41 – 61 .
  • Noss , R. and Hoyles , C. 1996 . Windows on mathematical meanings. Learning cultures and computers , Dordrecht : Kluwer Academic Press .
  • Papert , S. 1980 . Mindstorms. Children, computers and powerful ideas , New York : Basic Books .
  • Papert , S. 1996 . An exploration in the space of mathematics educations . International Journal of Computers for Mathematical Learning 1 , no. 1 : 95 – 123 .
  • Post , T. , Behr , M. and Lesh , R. 1988 . “ Proportionality and the development of prealgebra understandings ” . In The ideas of algebra, K-12 , Edited by: Coxford , A.F. and Shulte , A.P. 78 – 90 . Reston, VA : National Council of Teachers of Mathematics .
  • Psycharis , G. and Kynigos , C. 2004 . “ Normalising geometrical constructions: A context for the generation of meanings for ratio and proportion ” . In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , Edited by: H⊘ines , M. J. and Fuglestad , A.B. Vol. 4 , 65 – 72 . Bergen, , Norway : University of Bergen .
  • Singh , P. 2000 . Understanding the concepts of proportion and ratio constructed by two grade six students . Educational Studies in Mathematics , 43 : 271 – 292 .
  • Strauss , A. and Corbin , J. 1998 . Basics of qualitative research , Sage Publications .
  • Vergnaud , G. 1980 . “ Didactics and acquisition of “multiplicative structures” in secondary schools ” . In Cognitive development research in science and mathematics , Edited by: Archenhold , W.F. , Driver , R.H. , Orton , A. and Wood-Robinson , C. 190 – 200 . Leeds, , UK : Leeds University Press .
  • Vergnaud , G. 1983 . “ Multiplicative structures ” . In Acquisition of mathematical concepts and processes , Edited by: Lesh , R. and Landau , M. 127 – 174 . Orlando, FL : Academic 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.