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Articles

A Symbolic Dance: The Interplay Between Movement, Notation, and Mathematics on a Journey Toward Solving Equations

REFERENCES

  • Bills , L. , Ainley , J. and Wilson , K. 2006 . Modes of algebraic communication—Moving from spreadsheets to standard notation . For the Learning of Mathematics , 26 ( 1 ) : 41 – 47 .
  • Blanton , M. L. and Kaput , J. J. 2004 . Elementary grades students’ capacity for functional thinking , 135 – 142 . Norway , 2 : Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergan .
  • Booth , L. R. 1984 . Algebra: Children's strategies and errors , Windsor , UK : NFER-Nelson .
  • Brizuela , B. and Schliemann , A. 2004 . Ten-year-old students solving linear equations . For the Learning of Mathematics , 24 ( 2 ) : 33 – 40 .
  • Bruner , J. 1966 . Toward a theory of instruction , Cambridge , MA : The Belknap Press of Harvard University Press .
  • Caglayan , G. and Olive , J. 2010 . Eighth grade students’ representations of linear equations based on a cups and tiles model . Educational Studies in Mathematics , 74 : 143 – 162 .
  • Camtasia . Version 8.0) [Computer software]. Okemos, MI: TechSmith
  • Carraher , D. , Schliemann , A., D. and Brizuela , B., M. 2001 . Can young students operate on unknowns? Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Utrecht 130 – 140 . The Netherlands , 1
  • Clement , J. , Lochhead , J. and Monk , G. S. 1981 . Translation difficulties in learning mathematics . American Mathematical Monthly , 88 ( 4 ) : 286 – 290 .
  • Collins , A. , Brown , J. S. and Newman , S. E. 1989 . “ Cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics ” . In Knowing, learning, and instruction: Essays in honor of Robert Glaser , Edited by: Resnick , L. B. 453 – 494 . Hillsdale , NJ : Lawrence Erlbaum Associates . InEd.pp.
  • Cook , S. W. , Mitchell , Z. and Goldin-Meadow , S. 2008 . Gesturing makes learning last . Cognition , 106 ( 2 ) : 1047 – 1058 .
  • Drouhard , J.-P. and Teppo , A. R. 2004 . “ Symbols and language ” . In The future of the teaching and learning of algebra: The 12th ICMI study , Edited by: Stacey , K. , Chick , H. and Kendal , M. 227 – 264 . Dordrecht : The Netherlands: Kluwer Academic Publishers . InEds.pp.
  • Edwards , L. D. 2009 . Gestures and conceptual integration in mathematical talk . Educational Studies in Mathematics , 70 : 127 – 141 .
  • Fauconnier , G. and Turner , M. 2002 . The way we think: Conceptual blending and the mind's hidden complexities , New York , NY : Basic Books .
  • Gray , E. M. and Tall , D. O. 1994 . Duality, ambiguity and flexibility: A proceptual view of simple arithmetic . Journal for Research in Mathematics Education , 25 ( 2 ) : 115 – 141 .
  • Hatsell, M., Butler, D.Couzens, P.2004Autograph version 3. Retrieved from http://www.autograph-math.com (http://www.autograph-math.com)
  • Herscovics , N. 1989 . “ Cognitive obstacles encountered in the learning of algebra ” . In Research issues in the learning and teaching of algebra , Edited by: Wagner , S. and Kieran , C. 60 – 86 . Reston , VA : National Council of Teachers of Mathematics, Lawrence Erlbaum Associates . InEds.pp.
  • Herscovics , N. and Linchevski , L. 1994 . A cognitive gap between arithmetic and algebra . Educational Studies in Mathematics , 27 : 59 – 78 .
  • Hewitt, D. (n. d.) Grid Algebra (Version 1.0) [Computer software]. Derby, UK: Association of Teachers of Mathematics.
  • Hewitt , D. 2012 . Young students learning formal algebraic notation and solving linear equations: Are commonly experienced difficulties avoidable? . Educational Studies in Mathematics , 81 ( 2 ) : 139 – 159 . doi:10.1007/s10649-012-9394-x.
  • Holton , D. and Clarke , D. 2006 . Scaffolding and metacognition . International Journal of Mathematical Education in Science and Technology , 37 ( 2 ) : 127 – 143 .
  • Kaput , J. J. , Blanton , M. L. and Moreno , L. 2008 . “ Algebra from a symbolization point of view ” . In Algebra in the early grades , Edited by: Kaput , J. J. , Carraher , D. W. and Blanton , M. L. 19 – 55 . New York , NY : LEA & NCTM . InEds.pp.
  • Lee , M. A. and Messner , S. J. 2000 . Analysis of concatenations and order of operations in written mathematics . School Science and Mathematics , 100 ( 4 ) : 173 – 180 .
  • MacGregor , M. and Stacey , K. 1996 . Origins of students’ interpretations of algebraic notation. Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education, Valencia 297 – 304 . Spain , 3
  • MacGregor , M. and Stacey , K. 1997 . Students’ understanding of algebraic notation: 11–15 . Educational Studies in Mathematics , 33 : 1 – 19 .
  • Mason , J. 1980 . When is a symbol symbolic? . For the learning of mathematics , 1 ( 2 ) : 8 – 12 .
  • Mason , J. 2000 . Asking mathematical questions mathematically . International Journal of Mathematical Education in Science and Technology , 31 ( 1 ) : 97 – 111 .
  • Mercer , N. 2000 . Words and minds , London , UK : Routledge .
  • Moss , J. and Beatty , R. 2006 . Knowledge building in mathematics: Supporting collaborative learning in pattern problems . International Journal of Computer-Supported Collaborative Learning , 1 ( 4 ) : 441 – 465 . doi:10.1007/s11412-006-9003-z.
  • Núñez , R. , Edwards , L. D. and Matos , J. F. 1999 . Embodied cognition as grounding for situatedness and context in mathematics education . Educational Studies in Mathematics , 39 : 45 – 65 .
  • Radford , L. 2009 . Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings . Educational Studies in Mathematics , 70 ( 2 ) : 111 – 126 .
  • Radford , L. 2010 . Algebraic thinking from a cultural semiotic perspective . Research in Mathematics Education , 12 ( 1 ) : 1 – 19 .
  • Radford , L. and Puig , L. 2007 . Syntax and meaning as sensuous, visual, historical forms of algebraic thinking . Educational Studies in Mathematics , 66 : 145 – 164 .
  • Schliemann , A. , Carraher , D. , Brizuela , B. , Earnest , D. , Goodrow , A. , Lara-Roth , S. and Peled , I. 2003 . Algebra in elementary school , Vol. 4 , 127 – 134 . Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of PME-NA, Hawai'i .
  • Schmittau , J. 2005 . The development of algebraic thinking . ZDM , 37 ( 1 ) : 16 – 22 .
  • Schwartz , J. L. and Yerushalmy , M. 1992 . The Function Supposer: Symbols and graphs , Pleasantville , NY : Sunburst Communications .
  • Seeley Brown , J. , Collins , A. and Duguid , P. 1989 . Situated cognition and the culture of learning . Educational Researcher , 18 ( 1 ) : 32 – 42 .
  • Sfard , A. and Linchevski , L. 1994 . The gains and pitfalls of reification—The case of algebra . Educational Studies in Mathematics , 26 : 191 – 228 .
  • Strauss , A. and Corbin , J. 1990 . Basics of qualitative research: Grounded theory procedures and techniques , London , UK : Sage .
  • Studiocode (Version 5.0) [Computer Software]. Camatrillo, CA: Studiocode Business Group.
  • Sutherland , R. and Balacheff , N. 1999 . Didactical complexity of computational environments for the learning of mathematics . International Journal of Computers for Mathematical Learning , 4 ( 1 ) : 1 – 26 .
  • Tall , D. 2004 . Thinking through three worlds of mathematics , Vol. 4 , 281 – 288 . Norway : Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergan .
  • Wilensky , U. 1991 . “ Abstract meditations on the concrete and concrete implications for mathematical education ” . In Constructionism , Edited by: Harel , I. and Papert , S. 193 – 203 . Norwood , NJ : Ablex Publishing Corporation . InEds.pp.
  • Wood , D. , Bruner , J. S. and Ross , G. 1976 . The role of tutoring in problem solving . Journal of child psychology and psychiatry , 17 : 89 – 100 .
  • Yelland , N. and Masters , J. 2007 . Rethinking scaffolding in the information age . Computers & Education , 48 : 362 – 382 .

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