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Cognitive psychology, developmental psychology, and educational psychology are general fields of research for which mathematics education naturally seems one among many domains of application. However, the history of these domains of research and of the development of research in mathematics education is much more complex, and not at all hierarchical. For example, in their monumental Human Problem Solving (Newell and Simon 1972), Newell and Simon acknowledged that many of their ideas (which became among the fundamentals of Cognitive Psychology) were largely inspired from George Pólya’s How to Solve It (Pólya 1945). Another prestigious link is of course Piaget’s Epistémologie Génétique – his theory of human development: the theory was based on memorable experiments in which Piaget designed conservation tasks in which mathematical entities were focused on (number, quantity, length, proportions, etc.). Also Cole’s Cultural Psychology (1996) is largely based on the...
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References
Bauersfeld H (1988) Interaction, construction, and knowledge: alternative perspectives for mathematics education. In: Grouws DA, Cooney TJ (eds) Perspectives on research on effective mathematics teaching. Lawrence Erlbaum, Hillsdale, pp 27–46
Cobb P, Bauersfeld H (1995) The emergence of mathematical meaning: interaction in classroom cultures. Erlbaum, Hillsdale
Cobb P, Stephen M, McClain K, Gravemeijer K (2001) Participating in classroom mathematical practices. J Learn Sci 10(1&2):113–163
Cole M (1996) Cultural psychology: a once and future discipline. The Belknap Press of Harvard University Press, Cambridge, MA
Collins A, Joseph D, Bielaczyc K (2004) Design research: theoretical and methodological issues. J Learn Sci 13:15–42
Collis K (1975) A study of concrete and formal operations in school mathematics: a Piagetian viewpoint. Australian Council for Educational Research, Hawthorn
Dienes ZP (1971) Building up mathematics, 4th edn. Hutchinson, London
Douady R (1986) Jeux de cadres et dialectique outil-objet. Rech didact des math 7(2):5–31
Dubinsky E (1991) Reflective abstraction in advanced mathematical thinking. In: Tall D (ed) Advanced mathematical thinking. Kluwer, Dordrecht, pp 95–125
Engeström Y (1987) Learning by expanding: an activity-theoretical approach to developmental research. Orienta-Konsultit, Helsinki
Fischbein E (1987) Intuition in science and mathematics. Kluwer, Dordrecht
Fischbein E (1989) Tactic models and mathematical reasoning. Learn Math 9(2):9–14
Foucault M (1969) L’archéologie du savoir. Librairie Gallimard, Paris
Hartnett PM, Gelman R (1998) Early understandings of number: paths or barriers to the construction of new understandings? Learn Instr 8:341–374
Kieran C (1992) The learning and teaching of school algebra. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 390–419
Kieran C, Forman EA, Sfard A (eds) (2002) Learning discourse: discursive approaches to research in mathematics education. Kluwer, Dordrecht
Lerman S (2001) Cultural, discursive psychology: a sociocultural approach to studying the teaching and learning of mathematics. Educ Stud Math 46:87–113
Merenluoto K, Lehtinen E (2002) Conceptual change in mathematics: understanding the real numbers. In: Limon M, Mason L (eds) Reconsidering conceptual change: issues in theory and practice. Kluwer, Dordrecht, pp 233–258
Michaels S, O’Connor C, Resnick L (2009) Deliberative discourse idealized and realized: accountable talk in the classroom and in civic life. Stud Philos Educ 27(4):283–297
Newell A, Simon HA (1972) Human problem solving. Prentice-Hall, Englewood Cliffs
Nunes T, Schliemann A, Carraher D (1993) Street mathematics and school mathematics. Cambridge University Press, New York
Pólya G (1945) How to solve it. Princeton University Press, Princeton
Rogoff B (1990) Apprenticeship in thinking: cognitive development in social context. Oxford University Press, Oxford, UK
Schoenfeld AH (2002) Research methods in (mathematics) education. In: English L (ed) Handbook of international research in mathematics education. Erlbaum, Mahwah, pp 435–487
Schwarz BB, Dreyfus T, Hershkowitz R (2009) The nested epistemic actions model for abstraction in context. In: Schwarz BB, Dreyfus T, Hershkowitz R (eds) Transformation of knowledge through classroom interaction, New perspectives on learning and instruction. Routledge, London, pp 11–41
Sfard A (1991) On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educ Stud Math 22:1–36
Sfard A (2008) Thinking as communicating: human development, the growth of discourses, and mathematizing. Cambridge University Press, Cambridge, UK
Skemp RR (1971) The psychology of learning mathematics. Penguin, Harmondsworth
Smith JP, diSessa AA, Rochelle J (1993) Misconceptions reconceived: a constructivist analysis of knowledge in transition. J Learn Sci 3(2):115–163
Stahl G (2012) Dynamic-geometry activities with GeoGebra for virtual math teams. Web: http://GerryStahl.net/pub/activities_OnlinePDF.pdf
Stahl G (2013) Translating Euclid. Designing a human-centered mathematics. Morgan & Claypool, San Rafael
Stavy R, Tirosh D (2000) How students (mis)understand science and mathematics: intuitive rules. Teachers College Press, New York
Steffe LP, Thompson PW, von Glasersfeld E (2000) Teaching experiment methodology: underlying principles and essential elements. In: Kelly EA, Lesh RA (eds) Handbook of research design in mathematics and science education. Erlbaum, Mahwah, pp 267–306
Tall D, Vinner S (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity. Educ Stud Math 12:151–169
van Hiele PM (2004) A child’s thought and geometry. In: Carpenter TP, Dossey JA, Koelher JL (eds) Classics in mathematics education research. National Council of Teachers of Mathematics, Reston, pp 60–67
Vergnaud G (1983) Multiplicative structures. In: Lesh R, Landau M (eds) Acquisition of mathematics concepts and processes. Academic, New York, pp 127–174
Verschaffel L, De Corte E (1993) A decade of research on word-problem solving in Leuven: theoretical, methodological and practical outcomes. Educ Psychol Rev 5:239–256
Von Glasersfeld E (1989) Constructivism in education. In: Husen T, Postlethwaite TN (eds) The international encyclopedia of education, supplement, vol 1. Pergamon Press, Oxford/New York, pp 162–163
Wertsch JV (1998) Mind as action. Oxford University Press, New York
Yackel E, Cobb P (1996) Sociomathematical norms, argumentation, and autonomy in mathematics. J Res Math Educ 27(4):58–477
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Schwarz, B.B. (2014). Psychological Approaches in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_167
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