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Theory usage and theoretical trends in Europe: A survey and preliminary analysis of CERME4 research reports

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An Erratum to this article was published on 01 February 2006

Abstract

The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports1 on theory usage by European researchers inseven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance on ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner's vision of bridging theoretical traditions which are independently formulated in different regions of the world.

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References

  • Alro, H. & Skovsmose, O.: 2002,Dialogue and learning in Mathematics education, Kluwer Academics Publishers, Dordrecht-Boston-London.

    Google Scholar 

  • Arcavi, A. (2003): The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.

    Google Scholar 

  • Arcavi, A.: 1994, ‘Symbol Sense Informal Sense Making in Formal Mathematics’,For the learning of Mathematics, vol 14(3), 24–35.

    Google Scholar 

  • Australian Education Council (1990),A national statement on mathematics for Australian schools. Melbourne, VC: Australian Educational Council.

    Google Scholar 

  • Auslander, J. (2001). Review of G. Lakoff & R. Núñez, Where Mathematics Comes From.The American Scientist.

  • Bachelard, G. (1949). Le rationalisme appliqué, Collection PUF, Paris, 1986.

    Google Scholar 

  • Balacheff, N. (1988). Aspects of Proof in Pupils' Practice of School Mathematics. In: D. Pimm (ed.), Mathematics, Teachers and Children. London, Hodder & Stoughton: 216–238.

    Google Scholar 

  • Balacheff N (1991). The benefits and limits of social interaction: the case of mathematical proof In A. J. Bishop et al (Eds). Mathematical knowledge: its growth through teaching, pp. 175~192. Kluwer Academic Publishers.

  • Balacheff, N. (1991b). Construction et anlyse d'une situation didactique. Le cas de ‘la somme des angles d'un triangle’. Journal für Mathematik-Didaktik 12(2/3): 199–264.

    Google Scholar 

  • Battista, M. T. and Clements, D. H.: 1996, ‘Students’ understanding of three-dimensional rectangular arrays of cubes',Journal for Research in Mathematics Education 27 (3), 258–292.

    Google Scholar 

  • Bell, A. (1993). Principles for the design of teaching.Educational Studies in Mathematics, 24, 5–34.

    Google Scholar 

  • Bell-Gredler, M. E. (1986).Learning and instruction (pp. 191–224). New York, NY: Macmillan.

    Google Scholar 

  • Beth, E. W. and Piaget, J. (1966).Mathematical Epistemology and Psychology. D. Reidel, Dordrecht, The Netherlands.

    Google Scholar 

  • Birkhoff, G. (1969). Mathematics and psychology.SLAM Review, 11, 429–469.

    Google Scholar 

  • Bikner-Ahsbahs, A. (2003). A social extension of a psychological interest theory. In:Proceedings PME 27,http://onlinedb.terc.edu/PME2003/PDF/RR biknerashbahs.pdf.

  • Bonotto, C. (1999). About the use of cultural artifacts in the teaching/learning of mathematics'.L'Educazione matematica, Anno XX, Vol. 1, (2), 62–95.

    Google Scholar 

  • Bolhuis, S. & Voeten, J.M. (2004). Teachers' Conceptions of Student Learning and Own Learning'.Teachers and Teaching: theory and practice, 10 (1), 77–98.

    Google Scholar 

  • Boole, G. (1854).An Investigation of The Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Macmillan. London.

    Google Scholar 

  • Booth, L. (1988). Children's difficulties in beginning algebra', in A.F. Coxford and A.P. Schulte (eds.), The ideas of algebra, K-12, Yearbook. National Council of Teachers of Mathematics, Reston, VA.

    Google Scholar 

  • Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes in mathématiques. Recherches en Didactique des Mathématiques, 4, 2, 165–198.

    Google Scholar 

  • Brousseau, G. (1989) Les obstacles épistémologiques et la didactique des mathématiques, Bednarz, N. & Garnier, C. (Eds.), Constructions des savoirs, obstacles et conflits, Agence d'Arc, Montreal, 41–64.

    Google Scholar 

  • Brousseau G. (1998). Théorie des situations didactique, Paris: La pensée sauvage.

    Google Scholar 

  • Burton, L. (2004).Mathematicians as Enquirers. Kluwer Academic Publishers.

  • Blum, W. (1998). On the Role of ‘Grundvorstellungen” for reality-related Proofs—Examples and Reflections', in P. Galbraith, W. Blum, G. Booker and I. D. Huntley (eds.),Mathematical Modelling—Teaching and Assessment in a Technology-Rich World. Horwood, Chichester, pp. 63–74.

    Google Scholar 

  • Brinkmann, A. (1999) ‘Mathematical nets in curricular frames’, in: G. Philippon (ed.):MAVI-S Proceedings. Eighth European Workshop in Cyprus 1999. Research on Mathematical Beliefs, University of Cyprus, Nicosia, pp. 18–27.

    Google Scholar 

  • Brinkmann, A. (2001). Mind Mapping—Eine Methode zur Förderung der Kreativität und Lerneffektivität im Mathematikunterricht.Lernwelten 2/2001, Pädagogischer Zeitschriftenverlag, Berlin, pp. 101–104.

    Google Scholar 

  • Brinkmann, A. (2003a), Mind Mapping as a Tool in Mathematics Education',Mathematics Teacher, 96 (2), 96–101.

    Google Scholar 

  • Brinkmann, A. (2003b). Graphical Knowledge Display— Mind Mapping and Concept Mapping as Efficient Tools in Mathematics Education', in: P. Perks and S. Prestage (eds.),Mathematics Education Review, The Journal of Association of Mathematics Education Teachers, Number 16, pp. 39~48.

  • Bruner, J. (1986).Actual Minds. Possible Worlds. Cambridge: Harvard University Press.

    Google Scholar 

  • Bruner J. (1990).Acts of Meaning. Harvard University Press, Cambridge.

    Google Scholar 

  • Carpenter, T. P., Levi, L. (2000), Developing conceptions of algebraic reasoning in the primary grades. University of Wisconsin-Madison, Report No. 2.

  • Chevallard Y. (1991): La transposición Didáctica, Paris: La pensée sauvage.

    Google Scholar 

  • Chevallard, Y. (1995). Familière et Problématique, la figure du professeur, VIIIe Ecole d'été de didactique des mathématiques, Saint-Sauves.

  • Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique dudidactique, Recherches en didactique des mathématiques, 19 (2), 221–266.

    Google Scholar 

  • Ciompi, L. (1982),Affektlogik, Stuttgart: Klett-Cotta.

    Google Scholar 

  • Ciompi, L. 1988.Inneuwelt—Aussenwelt, Göttingen: Vandenhoeck & Ruprecht.

    Google Scholar 

  • Ciompi, L. (1991). Affects as Central Organising and Integrating Factors. A New Psychological/Biological Model of the Psyche.British Journal of Psychiatry 97~105.

  • Ciompi, L. 1999.Die emotionalen Grundlagen des Denkens. Göttingen: Vandenhoeck&Ruprecht.

    Google Scholar 

  • Clements, D. H. and Battista, M. T.: 1992, ‘Geometry and Spatial Reasoning’, in D. A. Grouws (Ed.),Handbook on Research in Mathematics Teaching and Learning, New York. Macmillan, pp. 420–464.

    Google Scholar 

  • Cobb, P. & Hodge, L. L. (press) An Interpretive Scheme for Analyzing the identities that Students Develop in Mathematics Classrooms,Journal of the Learning Sciences.

  • Coe, R. & K. Ruthven (1994). Proof practices and constructs of advanced mathematics students.British Educational Research Journal 2(1): 41–53.

    Google Scholar 

  • Cohors-Fresenborg, E. (1987) Action and Language—Two Modes of Representing Mathematical Concepts. In I. Wirszup and R. Streit (eds.),Developments in School Mathematics Education around the World, Proceedings of the UCSMP International Conference on Mathematics Education, NCTM, Reston, pp. 250~275.

  • Cohors-Fresenborg, E. and Kaune, C. (2001) Mechanisms of the Taking Effect of Metacognition in Understanding Processes in Mathematics Teaching', inDevelopments in Mathematics Education in German-speaking Countries, Selected Papers from the Annual Conference on Didatics of Mathematics, Ludwigsburg 2001, pp. 29~38.

  • Dahl, B. (2004) Analysing Cognitive Learning Processes Through Group Interviews of Successful High School Pupils: Development and Use of a Model, Educational Studies in Mathematics 56, pp. 129~155.

  • Davis, R.B. and McKnight, C. (1979) Modeling the processes of mathematical thinking',Journal of Children's Mathematical Behaviour 2, 91–113.

    Google Scholar 

  • Davis, P.J. & Hersh, R. (1981).The mathematical experience. New York: Houghton Mifflin.

    Google Scholar 

  • DeBellis, V.A. & Goldin, G.A. 1997. The Affective Domain in Mathematical Problem Solving. In: Pekhonen, E. (Ed.)Proceedings of the PME 21. Vol. 2 (pp. 209~216).

  • DeBellis V. & Goldin G.A. (1999). Aspects of affect: mathematical intimacy, mathematicalintegrity.Proceedings of PME 25 (Haifa, Israel), vol. 2, 249–256.

    Google Scholar 

  • Dewey, J. (1903). The psychological and the logical in teaching geometry.Educational Review, August 1903, 25, 387–399.

    Google Scholar 

  • Dewey, J. (1968).Philosophy and Civilization. Gloucester, MA: Peter Smith.

    Google Scholar 

  • Di Martino P., Zan R. (2001a)The problematic relationship between beliefs and attitudes' in Soro R. (Ed.) Proceedings of the Mavi X, Kristianstad, p. 17~24.

  • Di Martino P., Zan R. (2001b): ‘Attitude toward mathematics: some theoretical issues’, in van den Heuvel M. (Ed.) Proceedings of the 25th PME, vol. 3, Utrecht p. 351~358.

  • Di Martino P. & Zan R. (2002). An attempt to describe a ‘negative’ attitude toward mathematics. In P. Di Martino (Ed.)Proceedings of the MAVI-XI European Workshop, 22~29.

  • Di Martino P., Zan R. (2003)What does ‘positive’ attitude really mean?, in Pateman N., Dougherty B. & Zilliox J. (Eds.) Proceedings of the 2003 Joint Meeting of PME and PME-NA, vol. 4, Honolulu, p. 451~458.

  • Dubinsky, E. (1991). Reflective Abstraction in Advanced Mathematical Thinking. In D. Tall (Ed.). Advanced Mathematical Thinking (pp. 95–123). Kluwer: Dordrecht.

    Google Scholar 

  • Dreyfus, T. (1994). Imagery and reasoning in mathematics and mathematics education. In D. Robitaille, D. Wheeler, & C. Kieran (Eds),Selected lectures from the 7th ICME. Université laval, Quebec.

    Google Scholar 

  • Duval, R.: (2002). The cognitive analysis of problems of comprehension in the learning of mathematics',Mediterranean Journal for Research in Mathematics Education 1(2), 1–16.

    Google Scholar 

  • Duval R. (1998). Geometry from a cognitive point of view'Perspectives in the teaching of Geometry for the 21st Century Icmi Study Kluwer pp 37~51.

  • Duval, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Peter Lang, Paris.

    Google Scholar 

  • Ernest, P. (1988). The Attitudes and Practices of Student Teachers of Primary School Mathematics',Proceedings of 12th International Conference on the Psychology of Mathematics Education, Hungary, 1988, Vol. 1, A. Borbas (ed).

  • Ernest, P. (1989). The Impact of Beliefs on The Teaching of Mathematics', in P. Ernest (ed),Mathematics Teaching. The State of the Art, London. Falmer Press.

    Google Scholar 

  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.),Advanced Mathematical Thinking. (pp. 42–53), The Netherlands, Kluwer Academic Publishers.

    Google Scholar 

  • Fischbein, E. (1980, August). Intuition and proof. Paper presented at the 4th conference of the International Group for the Psychology of Mathematics Education, Berkeley, CA.

  • Fishbein, E. (1982). Intuition and Proof. For the Learning of Mathematics 3(2), 9–24.

    Google Scholar 

  • Fischbein E. (1987).Intuition in Science and Mathematics. An educational Approach. D. Reidel Publishing Company. Dordrecht.

    Google Scholar 

  • Fischbein, E. (1989). Tacit Models and Mathematical Reasoning.For the Learning of Mathematics, 9, 9–14.

    Google Scholar 

  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139–162.

    Google Scholar 

  • Freudenthal, H. (1983)Didactical Phenomenology of Mathematical Structures, Reidel, Dordrecht.

    Google Scholar 

  • Furinghetti F., Pehkonen E. (2002):Rethinking characterizations of beliefs, in Leder G., Pehkonen E., Toerner G. (Eds.) Beliefs: a hidden variable in mathematics education?, Kluwer Academic Publishers, p. 39~58.

  • Gold, B. (2001). Book Review of G. Lakoff & R. Núñez. Where does Mathematics Come FromMAA Book Reviews Online.

  • Goldin, G. (2001). Counting on the metaphorical. Book Review of G Lakoff & R. Núñez, Where does Mathematics Come From.Nature, 413, 18–19.

    Google Scholar 

  • Goldin, G. and Shteingold, N.: 2001, ‘Systems of Representations and the Development of Mathematical Concepts’, in Cuoco, A. A. and Curcio, F. R. (ed.),The Roles of Representation in School Mathematics, NCTM Yearbook. Boston, Virginia, 1–23.

    Google Scholar 

  • Goldin, G.A. (1998), Representational systems, learning and Problem Solving,Journal of Mathematical Behavior;17 (2), 137–165.

    Google Scholar 

  • Goldin, G.A. 2000. Affective Pathways and Representations in Mathematical Problem Solving.Mathematical Thinking and Learning, 17(2), (pp. 209–219).

    Google Scholar 

  • Goldin G.A. (2002). Affect, Meta-Affect, and Mathematical Belief Structures. In: Gilah C. Leder/Erkki Pehkonen/ Günter Törner 2002:Beliefs: A Hidden Variable in Mathematics Education? Dordrecht/ Boston/ London. Kluwer Academic Publishers. 59–72.

    Google Scholar 

  • Goldin, G. A. 2004. Characteristics of Affect as a System of Representation. In: M. Johnsen Hoines & A. B. Fuglestad (Eds.).Proceedings of the PME 28 Vol. 1 (pp. 109–114) Bergen, Bergen University College.

    Google Scholar 

  • Gómez-Chacón, I. M., 2000, Affective influences in the knowledge of mathematics,Educational Studies in Mathematics, 43, 149–168.

    Google Scholar 

  • Gray, E., Pinto, M., Pitta, D. & Tall, D. (1999). Knowledge Construction and Diverging Thinking in Elementary & Advance Mathematics',Educational Studies in Mathematics 38, pp. 11–133.

    Google Scholar 

  • Gray, E., Pitta, D. & Tall, D., 2000, ‘Objects, Actions and Images: A Perspective on Early Number Development’,Journal of Mathematical Behavior, 18, 4, pp. 1–13

    Google Scholar 

  • Hall, N.: 1991, ‘A procedural analogy theory: The role of concrete embodiments in teaching mathematics’, in F. Furinghetti (ed.),Proceedings of PME 15, Vol. II. Assisi, Italy, pp. 117~124.

  • Hall, N.: 1998, ‘Concrete repesentations and procedural analogy theory’,Journal of Mathematical Behavior 17, 33–51.

    Google Scholar 

  • Hadamard, J.W. (1945).Essay on the psychology of invention in the mathematical field. Princeton University Press.

  • Hanna, G. (1995). Challenges to the Importance of Proof.For the Learning of Mathematics, 15(3), 42–50.

    Google Scholar 

  • Hanna, G. & H. N. Jahnke (1993). Proof and Application. Educational Studies in Mathematics 24(4): 421–438.

    Google Scholar 

  • Hanna, G. & H. N. Jahnke (1993). Proof and proving. In: A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds.). International handbook of mathematics education. Dordrecht, Kluwer: 877–908.

    Google Scholar 

  • Hanna, G. and H. N. Jahnke (2002). Arguments from physics in mathematical proofs: An educational perspective. For the learning of mathematics 22(3): 38–45.

    Google Scholar 

  • Hannula, M. (1998). Changes of Beliefs and Attitudes. In: Pekhonen, E. & Törner, G. (Eds.) The State-of-Art in Mathematics-Related Belief Research: Results of the MAVI Activities.Research Report 184, (pp. 198~222) University of Helsinki.

  • Hannula, M./ Evans, J./ Philippou, G./ Zan, R. (2004). RF01: Affect in Mathematics Education-Exploring Theoretical Frameworks. In M. Johnsen Hoines & A. B. Fuglestad (Eds.).Proceedings of the PME 28, Vol. 1 (pp. 107–136) Bergen: Bergen University College.

    Google Scholar 

  • Hannula M. (2002). Attitude toward mathematics: emotions, expectations and values.Educational Studies in Mathematics, 49, 25–46.

    Google Scholar 

  • Healy, L. & Hoyles, C. (1998). Justifying and Proving in School Mathematics. (Technical Report on The Nationwide Survey. Institute of Education, University of London. February, 1998.

  • Healy, L. & C. Hoyles (to appear). Curriculum Change and Geometrical Reasoning. In: P. Boero (ed.), Theorems in School. Dordrecht, Kluwer

  • Hejný, M. (1999): Procept. In:Zborník bratislavského seminára z teórie vyuèovania matematiky, Comenius University, Bratislava, pp. 40–61.

    Google Scholar 

  • Hejný, M. (2002): Creating Mathematical Structure. In: Novotná, J. (ed.):European Research in Mathematics Education II, Charles University Prague 2002, pp. 14~24.

  • Hejný, M. (2003). Understanding and Structure. InCERME3 (Conference on European Research in Mathematics Education 3, Group 11), Feb. 28—March 3, Bellaria, Italy,http://www.dm.unipi.it/∼didattica/CERME3

  • Hiebert, L. (ed. 1986): Conceptual and procedural knowledge: the case for mathematics, Lawrence Erlbaum, Hillsdale NJ.

    Google Scholar 

  • Houdement C. & Kuzniak A (1998). Trois paradigmes mathématiques, in Petit x 51.

  • Houdement, C. and Kuzniak, A. (2003). Elementary Geometry Split into Different Geometrical Paradigms'Proceedings of CERME 3, Belaria, Italy.

  • Kaput, J. and J. Sims-Knight (1983). Errors In Translations To Algebraic Equations: Roots and Implications. Focus on Learning Problems in Mathematics 5: 63–78.

    Google Scholar 

  • Kaput, J. J.: 1987, ‘Representation systems and mathematics’, in C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics. Lawrence Erlbaum. Hillsdale, NJ, pp. 19–26.

    Google Scholar 

  • Kaput, J. J. (1989). Information technologies and affect in mathematical experience. In D. B. Mcleod & V.M. Adams (Eds) Affect & mathematical problem solving (pp. 87~103). Springer-Verlag.

  • Kieran, C., (1990). Cognitive Processes involved in Learning School Algebra', in Nesher P. & Kilpatrik, J. (Ed.):Mathematics and Cognition, ICMI Study Series, Cambridge University Press, 96~112.

  • Kieran, C.: 1992, ‘The Learning and Theaching of School Algebra’, in Grouws D.A., (Ed.)Handbook of Research of Mathematics Teaching and Learning, Macmillan, NY, 390–419.

    Google Scholar 

  • Lakoff, G. (1980)Metaphors we live by. University of Chicago Press, Chicago.

    Google Scholar 

  • Lakoff, G. & Núñez, R. (2000).Where Does Mathematics Come From. New York: Basic Books.

    Google Scholar 

  • Lakoff, G. & Núñez, R. Reply to B. Gold's review of Where Mathematics Comes FromMAA Book Reviews Onlin.

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal. 27, 29–36.

    Google Scholar 

  • Lave, J. and Wenger, E. (1991). Situated Learning: Legitimate Peripheral Participation, Cambridge University Press, Cambridge.

    Google Scholar 

  • Lester, F. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education.Zentralblatt für Didaktik der Mathematik, vol. 37, no. 6, pp. 457–467.

    Google Scholar 

  • Lester, F., Garofalo, J. & Kroll, D. L. (1989). Self-confidence. interest, beliefs and metacognition. In D. B. Mcleod & V. M. Adams (Eds). Affect & mathematical problem solving. (pp. 75~88). Springer-Verlag.

  • Linde, C. (1993)The Creation of Coherence. Oxford University Press, New York.

    Google Scholar 

  • Malara, N. A. (2004). From teachers education to classroom culture,regular lecture at ICME 10, (to appear).

  • Malara N. A., Navarra G. (2001). “Brioshi” and other mediation tools employed in a teaching of arithmetic with the aim of approaching algebra as a language, in Chick, E. & al (eds),proc. 12th ICMI Study on Algebra, vol. 2, 412~419

  • Malara, N.A., Navarra G. (2003a).ArAl project: arithmetic pathways towards favouring pre-algebraic thinking, Pitagora, Bologna

  • Malara, N.A., Navarra G. (2003b) Influences of a procedural vision of arithmetic in algebra learning,proc. WG 2—CERME 3, (Bellaria Italy, february 2003)

  • Mandler, G. (1984).Mind and Body: Psychology of emotion and stress. New York: Norton.

    Google Scholar 

  • Mandler, G. (1989). Affect and learning Causes and consequences of emotional interactions. In D.B. McIeod & V.M. Adams (Eds) Affect & mathematical problem solving. Springer-Verlag.

  • Manin, Y.I. (1977).A course in mathematical logic. Springer-Verlag, New York.

    Google Scholar 

  • Maslow, A.H.: 1962,Toward a psychology of being, Van Nostrand, London, New York.

    Google Scholar 

  • McIeod, D. B. (1991): Research on learning and instruction in mathematics: The role of affect. In E. Fennema, T. P. Carpenter, & S. J. Lamon (eds.),Integrating research on teaching and learming mathematics (pp. 55–82) Albany, NY: State Univ. of New York Press.

    Google Scholar 

  • Mc Leod D. (1992): Research on affect in mathematics education: a reconceptualization. In D. Grouws (Ed.),Handbook of Research on Mathematics Teaching and Learning (pp. 575~596). McMillan Publishing Company.

  • Moreno, L & Sriraman, B. (2005): The articulation of symbol and mediation in mathematics education.Zentralblatt für Didaktik der Mathematik., vol. 37, no. 6, pp. 476–486.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000).Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Nespor, J. (1987). The role of beliefs in the practice of teaching,Journal of Curriculum Studies, 19 (4), 317–328.

    Google Scholar 

  • Novak, J.: 1990, ‘Concept Mapping: A Useful tool for Science Education’,Journal of research in Science Teaching 27 (10), pp. 937–949.

    Google Scholar 

  • Novak, J. (1996): ‘Concept Mapping: A tool for Improving Science Teaching and Learning’, in: D. F. Treagust, R. Duit, B. J. Fraser (eds.),Improving Teaching and Learning in Science and Mathematics. Teachers College Press. New York.

    Google Scholar 

  • Op't Eynde, P., De Corte, E. & Verschaffel, L. (2002). Framing students' mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization. In G. Leder, E. Pehkonen & G. Törner (Eds),Beliefs: A hidden variable in mathematics education?, 13–37. Dordrecht: Kluwer.

    Google Scholar 

  • Pajares F. (1992). Teachers' Beliefs and Educational Research Cleaning Up a Messy Construct.Review of Educational Research, 62 (3), 307–332

    Google Scholar 

  • Pehkonen, E. & Pietilä, A. 2003. On Relationships between Beliefs and Knowledge in Mathematics Education. In:Proceedings of the CERME-3 (Bellaria) meeting http://www.dm.unipi.it/~didattica/CERME3/draft/proceedings_draft/TG2_draft/

  • Pegg, J. (1997) Broadening the descriptors of van Hiele's levels 2 and 3.Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia, Rotorua, MERGA, pp. 391~396.

  • Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks—Zentralblatt für Didaktik der Mathematik, Vol. 37, No. 6, pp. 468–475.

    Google Scholar 

  • Philippon, G., & Christou, C. (1998): The effects of a preparatory mathematics program in changing prospective teachers' attitudes toward mathematics.Educational Studies in Mathematics, 35, 189–206.

    Google Scholar 

  • Peirce, C.S. (1960).Collected papers, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Piaget, J. (1958):The Growth of Logical thinking from Childhood to Adolescence. Basic Books, New York, NY.

    Google Scholar 

  • Piaget, J. & Garcia, R. (1989): Psychogenesis and the History of Science, Columbia University Press, New York.

    Google Scholar 

  • Poincare, H. (1948):Science and Method. Dover: New York.

    Google Scholar 

  • Polya, G. (1954).Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. II).

  • Prawat, R.S. & Anderson, A.L.H. (1994). ‘The Affective Experiences of Students’,The Journal of Mathematical Behavior, 13, 201–221.

    Google Scholar 

  • Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics.Educational Studies in Mathematics, 23 (6), 595–610.

    Google Scholar 

  • Presmeg, N. C. (1997a). Reasoning with metaphors and metonymies in mathematics learning. In L. D. English (Ed.),Mathematical reasoning: Analogies, metaphors, and images (pp. 267–279). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Presmeg, N.C. (2001). Visualization and affect in non-routine problem solving.Mathematical thinking and Learning, 3, 289–313.

    Google Scholar 

  • Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis.Educational Studies in Mathematics 42(3): 237–268.

    Google Scholar 

  • Radford, L. (2002). 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.

    Google Scholar 

  • Radford, L. (2003). Gestures, speech and the sprouting of signs.Mathematical thinking and Learning 5(1): 37–70.

    Google Scholar 

  • Radford, L., Demers, S., Guzmán, J. and Cerulli, M. (2003) Calculators, graphs, gestures, and the production meaning, in: N. Pateman, B. Dougherty and J. Zilliox (eds.),Proceedings of PME27-PMENA25, Vol. 4, pp. 55~62.

  • Resnick, L. & Omansson S. (1987). ‘Learning to understand arithmetic’, in R. Glaser (ed.),Advances in Instructional Psychology, Vol 3, Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Ricoeur, P. (1992).Oneself as Another. Chicago: The University of Chicago Press.

    Google Scholar 

  • Rotman, B. (2000).Mathematics as Sign: Writing. Imagining. Counting. Stanford: Stanford University Press.

    Google Scholar 

  • Schlöglmann, W. (2000). Affects and mathematics learning—some remarks, In: S. Johnson/ D. Coben (Eds.):Proceedings of the sixth international conference of Adults Learning Mathematics—A Research Conference. (pp. 51~59) University of Nottingham.

  • Schlöglmann, W. (2002). Affect and mathematics learning. In A. D. Cockburn & E. Nardi (Eds.):Proceedings of the PME 26, Vol. 4 (pp. 185~192) Norwich University of East Anglia.

  • Schoenfeld, A. H. (1989). Explorations of students' mathematics beliefs and behavior.Journal for Research in Mathematics Education, 20(4), 338–355.

    Google Scholar 

  • Schubring (1986). Rupture dans le statut mathématique des nombres négatifs. Petit X, no 12, pp. 5–32.

    Google Scholar 

  • Schubring (1988). Discussions épistémologiques sur le statut des nombres négatifs et leur représentation dans les manuels allemands et français de mathématiques entre 1795 et 1845.Actes du premier colloque franco-allemand de didactique des mathématiques et de l'informatique, pp. 137–145. Paris: La Pensée Sauvage.

    Google Scholar 

  • Silver E. (Ed.),Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. Hillsdale, NJ, Erlbaum.

  • Sierpinska, A. (2004). A note from the editor.Educational Studies in Mathematics, 57 (3), p. 301.

    Google Scholar 

  • Sfard, A. (1989): Transition from operational to structural conception: The notion of function revisited. In: G. Vergnoud, J. Rogalski, and M. Artigue (Eds.):Proceedings of the 13th PME. Paris, pp. 151~158.

  • Sfard, A. (1991). On the Dual Nature of Mathematics Conception: Reflections on Processes and Objects as Different sides of the Same Coin,Educational Studies in Mathematics, 22, 1–36.

    Google Scholar 

  • Sfard, A. (1994). Reification as the birth of metaphor.For the Learning of Mathematics, 14(1), 44–54.

    Google Scholar 

  • Skemp, R. (1986).the Psychology of Learning Mathematics. 2nd Edition. Penguin Books.

  • Sriraman, B., & Törner, G. (2007, forthcoming). Political Union/Mathematical Education Disunion: Building Bridges in European Didactic Traditions. To appear in L. English (Ed).Handbook of International Research in Mathematics Education (2nd edition).

  • Sriraman, B., & English, L. (2005). Theories of mathematics education: a global survey of theoretical frameworks/trends in mathematics education research.Zentralblatt für Didaktik der Mathematik, vol. 37, no. 6, pp 450–456

    Google Scholar 

  • Steinbring, H. (1994). Die Verwendung strukturierter Diagramme im Arithmetikunterricht der Grundschule. Zum Unterschied zwischen empirischer und theoretischer Mehrdentigkeit mathematischer Zeichen'.MUP, IV. Quartal. 7~19.

  • Steinbring, H. (1998). Elements of Epistemological Knowledge for Mathematics Teachers'Journal of Mathematics Teacher Education, Vol 1/2 Kluwer, pp. 157–189.

    Google Scholar 

  • Steinbring, H. (2005). The Construction of New Mathematical Knowledge in Classroom Interaction—an Epistemological Perspective, To be published inMathematics Education Library (MELI), No. 38, Springer, Berlin, Heidelberg.

    Google Scholar 

  • Tall, D. & Vinner, S. (1981). Concept image and concept definition in Mathematics with particular reference to limits and continuity,Educational Studies in Mathematics, 12, 151–69.

    Google Scholar 

  • Tirosh D., Hadass, R., Movshovic-Hadar N. (1991), Overcoming overgeneralizations: the case of commutativity and associativity.Proce dings of PME 15, vol. 3, 310–415.

    Google Scholar 

  • Tirosh, D., Stavy, R. (1999). ‘Intuitive Rules: A Way to Explain and Predict Students' Reasoning’,Educational Studies in Mathematics, 38 51–66.

    Google Scholar 

  • Toulmin S.E. (1958),The Uses of Argtments, Cambridge University Press.

  • Van Hiele, P.M. (1986). Structure and Insight. A Theory of Mathematics Education. Academic Press, Inc., London.

    Google Scholar 

  • Vergnaud, G. (1990). La théorie des champ conceptuels,Recherches en Didactique des mathématiques, vol. 10, 133–170.

    Google Scholar 

  • Whitehead, A.N., & Russell, B. (1908).Principia Mathematica. Cambridge University Press.

  • Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra,Mathematics Education Research Journal (15) 2, 122–137.

    Google Scholar 

  • Wittgenstein, L. (1978).Remarks on the Foundations of Mathematics (Revised Edition), Cambridge, Massachusetts Institute of Technology Press.

    Google Scholar 

  • Wittmann, E. Ch. (1995). Mathematics Education as a “Design Science”.Educational Studies in Mathematics 29, 355–374.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematical Sciences, The University of Montana, 59812, Missoula, MT, USA

    Bharath Sriraman (Editor, The Montana Mathematics Enthusiast)

  2. Faculty of Education Didactics of Mathematics, University of Hamburg, Von-Melle-Park 8, 20146, Hamburg, Germany

    Gabriele Kaiser (Editor, Zentralblatt für Didaktik der Mathematik)

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  1. Bharath Sriraman
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  2. Gabriele Kaiser
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An erratum to this article is available at http://dx.doi.org/10.1007/s11858-007-0056-x.

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Sriraman, B., Kaiser, G. Theory usage and theoretical trends in Europe: A survey and preliminary analysis of CERME4 research reports. Zentralblatt für Didaktik der Mathematik 38, 22–51 (2006). https://doi.org/10.1007/BF02655904

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