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Research papers

Algebraic thinking from a cultural semiotic perspective

Pages 1-19 | Published online: 12 Feb 2010

References

  • Ali Fernandes , S. 2008 . Das experiências sensoriais aos conhecimentos matemáticos . PhD diss. Pontifícia Universidade Católica de São Paulo , São Paulo , Brazil .
  • Arzarello , F. 2006 . Semiosis as a multimodal process . Revista Latinoamericana de Investigación en Matemática Educativa , special issue on semiotics, culture, and mathematical thinking : 267 99 .
  • Balacheff , N. 2001 . Postscript In Perspectives in school algebra R. Sutherland , T. Rojano , A. Bell , R. Lins : 249 60 . Dordrecht : Kluwer .
  • Barallobres , G. 2007 . Introduction à l'algèbre par la généralisation: Problèmes didactiques soulevés . For the Learning of Mathematics , 27 ( 1 ) : 39 – 44 .
  • Becker , J. , F. Rivera 2008 . Generalization in algebra: The foundation of algebraic thinking and reasoning across the grades . ZDM – The International Journal on Mathematics Education 40 , no. 1 .
  • Bednarz , N. , C. Kieran , L. Lee 1996 . Approaches to algebra: Perspectives for research and teaching . Dordrecht : Kluwer .
  • Benson , D. 1994 . The neurology of thinking , New York : Oxford University Press .
  • Bills , L. and Rowland , T. 1999 . Examples, generalisation and proof . Research in Mathematics Education , 1 ( 1 ) : 103 – 116 .
  • Coles , A. and Brown , L. 2001 . Needing to use algebra . Research in Mathematics Education , 3 ( 1 ) : 23 – 36 .
  • Cortes , A. , G. Vergnaud , N. Kavafian . 1990 . From arithmetic to algebra: Negotiating a jump in the learning process . Proceedings of the l4th Conference of the International Group for the Psychology of Mathematics Education G. Brooker , P. Cobb , T. de Mendicuti , 2 , 27 34 . Oaxtepex, , Mexico : PME .
  • Ernest , P. 2008 . Towards a semiotics of mathematical text (part 1) . For the Learning of Mathematics , 28 ( 1 ) : 2 – 8 .
  • Filloy , E. , T. Rojano . 1984a . From an arithmetical to an algebraic thought. (A clinical study with 12–13 years old) In Proceedings of the 6th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter J.M. Moser , 51 56 . Madison, Wisconsin .
  • Filloy , E. , T. Rojano . 1984b . La aparición del lenguaje aritmético-algebraico . L'Educazione Matematica 5 , 3 : 278 306 .
  • Filloy , E. , T. Rojano . 1989 . Solving equations: The transition from arithmetic to algebra . For the Learning of Mathematics 9 , 2 : 19 25 .
  • Gallese , V. and Lakoff , G. 2005 . The brain's concepts: The role of the sensory-motor system in conceptual knowledge . Cognitive Neuropsychology , 22 ( 3/4 ) : 455 – 479 .
  • Gehlen , A. 1988 . Man. His nature and place in the world , New York : Columbia University Press .
  • Glaeser , G. 1999 . Une introduction à la didactique expérimentale des mathématiques , Grenoble : La pensée sauvage .
  • Hoch , M. , T. Dreyfus . 2006 . Structure sense versus manipulation skills: An unexpected result In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education J. Novotná , H. Moraová , M. Krátká , N. Stehlíková , 3 , 305 12 . Prague, , Czech Republic : Charles University .
  • H⊘yrup , J. 2008 . The tortuous ways toward a new understanding of algebra in the Italian abacus school (14th–16th centuries) In Proceedings of the Joint 32nd Conference of the International Group for the Psychology of Mathematics Education and the 30th North American Chapter O. Figueras , J.L. Cortina , S. Alatorre , T. Rojano , A. Sepúlveda , 1 , 1 15 . Morelia, , Mexico : PME .
  • Husserl , E. 1954 . The crisis of European sciences and transcendental phenomenology , 1970 ed Northwestern University Press Evanston http://www.marxists.org/reference/subject/philosophy/works/ge/husserl.htm .
  • Husserl , E. . 1970 . Logical investigations . London : Routledge and Kegan Paul .
  • Kieran , C. 1989 . The early learning of algebra: A structural perspective In Research issues in the learning and teaching of algebra , S. Wagner C. Kieran , 33–56. Virginia : Lawrence Erlbaum Associates and National Council of Teachers of Mathematics .
  • Kieran , C. . 1990 . A procedural-structural perspective on algebra research In Proceedings of the 15th Conference of the International Group for the Psychology of Mathematics Education , F. Furinghetti 2 , 245 53 . Assisi, , Italy : Università di Genova .
  • Kieran , C. . 2006 . Research on the learning and the teaching of algebra: A broadening of sources of meaning In Handbook of research on the psychology of mathematics education: Past, present, future A. Gutiérrez P. Boero , 23 49 . Rotterdam, , The Netherlands : Sense Publishers .
  • Kirshner , D. 2001 . The structural algebra option revisited In Perspectives on school algebra R. Sutherland , T. Rojano , R. Lins , A. Bell , 83 98 . Dordrecht : Kluwer .
  • Linchevski , L. 1995 . Algebra with numbers and arithmetic with letters: A definition of pre-algebra . Journal of Mathematical Behavior , 14 : 113 – 120 .
  • Mason , J. 1990 . Algebra , Milton Keynes : Centre for Mathematics Education, The Open University .
  • Mason , J. 1996 . Expressing generality and roots of algebra In Approaches to algebra N. Bednarz , C. Kieran , L. Lee , 65 86 . Dordrecht : Kluwer .
  • Merleau-Ponty , M. 1945 . Phénomenologie de la perception , Paris : Gallimard .
  • Nemirovsky , R. 1994 . On ways of symbolizing: The case of Laura and the velocity sign . Journal of Mathematical Behavior , 13 : 389 – 422 .
  • Nemirovsky , R. . 2003 . Three conjectures concerning the relationship between body activity and understanding mathematics In Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education N. Pateman , B. Dougherty J. Zilliox , 1 , 105 109 . Hawaii : PME .
  • Puig , L. 2004 . History of algebraic ideas and research on educational algebra. Regular Lecture at the 10th International Congress on Mathematical Education , Copenhagen . http://www.uv.es/puigl/ .
  • Radford , L. 2000 . Signs and meanings in students' emergent algebraic thinking: A semiotic analysis . Educational Studies in Mathematics , 42 ( 3 ) : 237 – 268 .
  • Radford , L. 2001 . The historical origins of algebraic thinking In Perspectives in school algebra Sutherland , R. Rojano , T. Bell , A. Lins , R. 13 63 . Dordrecht : Kluwer .
  • Radford , L. 2002a . The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge . For the Learning of Mathematics 22 , 2 : 14 23 .
  • Radford , L. 2002b . Algebra as tekhnē. Artefacts, symbols and equations in the classroom . Mediterranean Journal for Research in Mathematics Education 1 , 1 : 31 56 .
  • Radford , L. . 2002c . On heroes and the collapse of narratives. A contribution to the study of symbolic thinking In Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education A.D. Cockburn E. Nardi , 4 , 81 8 . University of East Anglia , UK .
  • Radford , L. 2003 . Gestures, speech and the sprouting of signs . Mathematical Thinking and Learning 5 1 : 37 70 .
  • Radford , L. 2006 . Algebraic thinking and the generalization of patterns: A semiotic perspective In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter S. Alatorre , J.L. Cortina , M. Sáiz , A. Méndez 1 , 2 21 . Mérida, Mexico .
  • Radford , L. 2008a . The ethics of being and knowing: Towards a cultural theory of learning In Semiotics in mathematics education: Epistemology, history, classroom, and culture L. Radford , G. Schubring F. Seeger , 215 34 . Rotterdam : Sense Publishers .
  • Radford , L. 2008b . Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts . ZDM – The International Journal on Mathematics Education 40 , 1 : 83 96 .
  • Radford , L. 2009a . Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings . Educational Studies in Mathematics 70 , 2 : 111 26 .
  • Radford , L. . 2009b . “No! He starts walking backwards!”: Interpreting motion graphs and the question of space, place and distance . ZDM – The International Journal on Mathematics Education , 41 , 4 : 467 80 .
  • Radford , L. , Bardini , C. and Sabena , C. 2007 . Perceiving the general: The multisemiotic dimension of students’ algebraic activity . Journal for Research in Mathematics Education , 38 : 507 – 530 .
  • Radford , L. , Demers , S. and Miranda , I. 2009 . Processus d'abstraction en mathématiques , Ottawa : Centre Franco-Ontarien de Ressources Pédagogiques, Imprimeur de la Reine pour l'Ontario .
  • Radford , L. , Edwards , L. and Arzarello , F. 2009 . Beyond words . Educational Studies in Mathematics , 70 ( 2 ) : 91 – 95 .
  • Radford , L. and Puig , L. 2007 . Syntax and meaning as sensuous, visual, historical forms of algebraic thinking . Educational Studies in Mathematics , 66 ( 2 ) : 145 – 164 .
  • Russell , B. 1976 . An inquiry into meaning and truth , London : George Allen and Unwin Ltd .
  • Serfati , M. 1999 . La dialectique de l'indéterminé, de Viète à Frege et Russell In La recherche de la vérité M. Serfati , 145 74 . Paris : ACL – Les éditions du kangourou .
  • Serfati , M. . 2006 . La constitution de l'ecriture symbolique mathematique. Symbolique et invention . SMF – Gazette 108 , 101 18 .
  • Staats , S. and Batteen , C. 2009 . Stretching, sliding and strategy: Indexicality in algebraic explanations . Research in Mathematics Education , 11 ( 1 ) : 57 – 71 .
  • Sutherland , R. , T. Rojano , A. Bell , R. Lins 2001 . Perspectives in school algebra . Dordrecht : Kluwer .
  • Vergnaud , G. 1996 . Au fond de l'apprentissage, la conceptualisation In Actes de la 8ème école d’été de didactique des mathématiques , 174 85 . Clermont-Ferrand : IREM de Clermont-Ferrand .
  • Vygotsky , L.S. 1981 . The instrumental method in psychology In The concept of activity in Soviet psychology J.V. Wertsch , 135 43 . Armonk, NY : Sharpe .

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