Abstract
Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields, which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexander, P. A., & Winne, P. H. (2006). Afterword. In P. A. Alexander & P. H. Winne (Eds.), Handbook of Educational Psychology (2nd ed., pp. 981–984). Mahwah, NJ: Lawrence Erlbaum Associates.
Artigue, M. (1994). Didactical engineering as a framework for the conception of teaching products. In I. R. Biehler, R. W. Scholtz, R. Sträßer, & B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 247–261). Dordrecht: Kluwer.
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work.
Assude, T., Boero, P., Herbst, P., Lerman, S., & Radford, L. (2008). The notion and roles of theory in mathematics education research. Paper presented at the 10th International Congress on Mathematical Education, Monterrey, Mexico, July 6–13.
Bachelard, G. (1938). La formation de l’esprit scientifique. Paris: J. Vrin.
Balacheff, N. (1999). Contract and custom: Two registers of didactical interactions. The Mathematics Educator, 9(2), 23–29.
Bell-Gredler, M. E. (1986). Learning and Instruction: Theory Into Practice. New York: Macmillan.
Berliner, D. C. (2006). Educational psychology: Searching for essence throughout a century of influence. In P. A. Alexander & P. H. Winne (Eds.), Handbook of Educational Psychology (2nd ed., pp. 3–28). Mahwah, NJ: Lawrence Erlbaum Associates.
Bishop, A. (1992). International perspectives on research in mathematics education. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 710–723). Reston, NY: Simon & Schuster Macmillan.
Boaler, J. (2008). What’s Math Got to Do With It? Helping Children Learn to Love Their Least Favorite Subject—and Why It’s Important for America. Baltimore: Viking/Penguin.
Bosch, M., Chevallard, Y., & Gascon, J. (2005). Science or magic? The use of models and theories in didactics of mathematics. In Proceedings of CERME4, Spain.
Bourbaki, N. (1970). Théorie des ensembles dela collection elements de mathématique. Paris: Hermann.
Brantlinger, E. (2003). Dividing Classes: How the Middle Class Negotiates and Rationalizes School Advantage. London: Routledge Falmer Press, Taylor and Francis.
Brousseau, G. (1981). Problèmes de didactique des décimaux. Recherches en Didactique des Mathématiques, 2, 37–127.
Brousseau, G. (1986). Fondemonts et methods de la didactique des mathématiques. Recherches en Didactique des Mathématiques, 7(2), 33–115.
Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer.
Brousseau, G. (1999a). Research in mathematics education: Observation and … mathematics. In Schwank (Ed.), Proceedings of CERME 1 (Vol. 1, pp. 35–49). Osnabrueck: Forschungs Institut fuer Mathematikdidaktik.
Brousseau, G. (1999b). Education and didactique of mathematics. Plenary Lecture at Congress of Aguas Calientes, Mexico, October 1999. Pre-print obtained from Author. 42 pages.
Brunschwicg, L. (1912). Les etapes de la philosophie mathématique. Paris: F. Alcan.
Burton, L. (2004). Mathematicians as Enquirers. Dordrecht: Kluwer.
Calfee, R. (2006). Educational psychology in the 21st century. In P. A. Alexander & P. H. Winne (Eds.), Handbook of Educational Psychology (2nd ed., pp. 29–42). Mahwah, NJ: Lawrence Erlbaum Associates.
Campbell, S. R. (2006). Educational neuroscience: New horizons for research in mathematics education. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 257–264). Prague: PME.
Chevallard, Y. (1985). La transposition didactique. Du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage.
Chevallard, Y. (1992a). Fondamentals concepts of didactics: Perspectives given by an anthropological approach. Recherches en Didactique des Mathématiques, 12(1), 73–112.
Chevallard, Y. (1992b). A theoretical approach to curricula. Journal für Mathematik Didaktik, 2/3, 215–230.
Chevallard, Y. (1999a). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.
Chevallard, Y. (1999b). Didactique? You must be joking! A critical comment on terminology. Instructional Science, 27, 5–7.
Cobb, P. (2007). Putting philosophy to work. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 3–38). Charlotte, NC: Information Age Publishing and Reston, VA: National Council of Teachers of Mathematics.
D’Ambrosio, U. (1999). Literacy, matheracy, and technoracy: A trivium for today. Mathematical Thinking and Learning, 1(2), 131–154.
Davis, R., Maher, C., & Noddings, N. (Eds.) (1990). Constructivist Views on the Teaching and Learning of Mathematics. Reston, VA: NCTM.
Dieudonné, J. (1961). New thinking in school mathematics. In New Thinking in School Mathematics (pp. 31–46). Paris: OEEC.
Dieudonné, J. (1992). Mathematics—The Music of Reason. New York: Springer-Verlag.
Eisenberg, T., & Fried, M. (2008). Dialogue on mathematics education: The state of the art through different lenses. ZDM—The International Journal on Mathematics Education, 40(2), 165–178.
Eisenberg, T., & Fried, M. (2009). Dialogue on mathematics education: Two points of view on the state of the art through different lenses. ZDM—The International Journal on Mathematics Education, 41(1&2), 143–149.
English, L. D. (Ed.) (2002). Handbook of International Research in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum.
English, L. D. (2007). Complex systems in the elementary and middle school mathematics curriculum: A focus on modeling. In B. Sriraman (Ed.), The Montana Mathematics Enthusiast Monograph : Vol. 3. Festschrift in Honor of Gunter Torner (pp. 139–156). Charlotte, NC: Information Age Publishing.
English, L. D. (2008a). Handbook of International Research in Mathematics Education (2nd ed.). London: Routledge, Taylor & Francis.
English, L. D. (2008b). Mathematical modeling: Linking mathematics, science, and the arts in the elementary curriculum. In B. Sriraman, C. Michelsen, A. Beckmann, & V. Freiman (Eds.), Proceedings of the Second International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2) (pp. 5–36). Odense: University of Southern Denmark Press.
English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling. ZDM: The International Journal on Mathematics Education, 41(1), 161–181.
English, L. D., & Mousoulides, N. (2009). Integrating engineering education within the elementary and middle school mathematics curriculum. In B. Sriraman, V. Freiman, & N. Lirette-Pitre (Eds.), Interdisciplinarity, Creativity and Learning: Mathematics with Literature, Paradoxes, History, Technology and Modeling (pp. 165–176). Charlotte, NC: Information Age Publishing.
Ernest, P. (1991). The Philosophy of Mathematics Education. Briston, PA: The Falmer Press.
Ernest, P. (1994). Conversation as a metaphor for mathematics and learning. In Proceedings of the British Society for Research into Learning Mathematics Day Conference, Manchester Metropolitan University (pp. 58–63). Nottingham: BSRLM.
Furinghetti, F. (2003). Mathematical instruction in an international perspective: The contribution of the journal L’Enseignement Mathématique. In D. Coray, F. Furinghetti, H. Gispert, B. Hodgson, & G. Schubring (Eds.), One Hundred Years of l’Enseignement Mathématique, Monograph No. 39 (pp. 19–46). Geneva.
Gascón, J. (2003). From the cognitive program to the epistemological program in didactics of mathematics. Two incommensurable scientific research programs? For the Learning of Mathematics, 23(2), 44–55.
Goldin, G. A. (2003). Developing complex understandings: On the relation of mathematics education research to mathematics. Educational Studies in Mathematics, 54, 171–202.
Guerra, J. C. (1998). Close to Home: Oral and Literate Practices in a Transnational Mexicano Community. New York: Teachers College Press.
Hall, R. (1999). Case studies of math at work: Exploring design-oriented mathematical practices in school and work settings (NSF Rep. No. RED-9553648). Arlington, VA: National Science Foundation.
Hersh, R. (1978). Introducing Imre Lakatos. Mathematical Intelligencer, 1(3), 148–151.
Hersh, R. (1997). What is Mathematics, Really? New York: Oxford University Press.
Hersh, R. (2006). 18 Unconventional Essays on the Nature of Mathematics. New York: Springer Science & Business Media Inc.
Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 371–404). Charlotte, NC: Information Age Publishing.
Kaiser, G. (2002). Educational philosophies and their influence on mathematics education—An ethnographic study in English and German classrooms. International Reviews on Mathematical Education (ZDM), 34(6), 241–257.
Kilpatrick, J. (1981). The reasonable ineffectiveness of research in mathematics education. For the Learning of Mathematics, 2(2), 22–29.
Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 3–38). New York: Simon & Schuster Macmillan.
King, K. D., & McLeod, D. (1999). Coming of age in academe—A review of Mathematics Education as a Research Identity. Journal for Research in Mathematics Education, 30(2), 227–234.
Kuhn, T. S. (1966). The Structure of Scientific Revolutions (3rd ed.). Chicago: University of Chicago Press.
Lakatos, I. (1970). Criticism and Growth of Knowledge. New York: Cambridge Press.
Lakatos, I. (1976). Proofs and Refutations. Cambridge, UK: Cambridge University Press.
Lakoff, G., & Núñez, R. (2000). Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being. New York: Basic Books.
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(1), 29–63.
Lenoir, T. (1981). Review of Imre Lakatos’ Proofs and Refutations. Historia Mathematica, 8, 99–104.
Lerman, S. (1998). Research on socio-cultural perspectives of mathematics teaching and learning. In J. Kilpatrick & A. Sierpinska (Eds.), Mathematics Education as a Research Domain: A Search for Identity (Vol. 1, pp. 333–350). London: Kluwer.
Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning. Westport, CT: Ablex Publishing.
Lesh, R. A. (2007). Foundations for the future in engineering and other fields that are heavy users of mathematics, science, and technology. In R. A. Lesh, E. Hamilton, & J. J. Kaput (Eds.), Foundations for the Future in Mathematics Education. Mahwah, NJ: Lawrence Erlbaum Associates.
Lesh, R. (2008). Directions for future research and development in engineering education. In J. Zawojewski, H. Diefes-Dux, & K. Bowman (Eds.), Models and Modeling in Engineering Education: Designing Experiences for All Students (pp. 271–291). Rotterdam: Sense Publications.
Lesh, R., & Sriraman, B. (2005). Mathematics education as a design science. Zentralblatt für Didaktik der Mathematik, 37(6), 490–505.
Lester, F. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. Zentralblatt für Didaktik der Mathematik, 37(6), 457–467.
Lincoln, Y. S., & Guba, E. G. (1994). Competing paradigms in qualitative research. In N. Denzin & Y. Lincoln (Eds.), Handbook of Qualitative Research (pp. 105–117). Thousand Oaks, CA: Sage Publications.
Malara, N., & Zan, R. (2008). The complex interplay between theory in mathematics education and teacher’s practice: Reflections and examples. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 535–560). London: Routledge, Taylor & Francis.
Moon, B. (1986). The ‘New Maths’ Curriculum Controversy: An International Story. London: The Falmer Press.
OEEC (1961). New Thinking in School Mathematics. Paris: OEEC.
Pepin, B. (1998). Mobility of mathematics teachers across England, France and Germany: Any problems? Paper presented at the European Conference for Educational Research, University of Ljubljana, Slovenia September 1998. http://www.leeds.ac.uk/educol/documents/000000871.htm, accessed November 12, 2006.
Pepin, B. (1999a). The influence of national cultural traditions on pedagogy: Classroom practices in England, France and Germany. In J. Leach & B. Moon (Eds.), Learners and Pedagogy (pp. 237–252). London: Sage.
Pepin, B. (1999b). Epistemologies, beliefs and conceptions of mathematics teaching and learning: the theory, and what is manifested in mathematics teachers’ work in England, France and Germany (The Open University, UK). TNTEE Publications, 2, 127–146.
Pepin, B. (2002). Different cultures, different meanings, different teachings. In L. Haggarty (Ed.), Teaching Mathematics in Secondary Schools (pp. 245–258). London: Routledge.
Piaget, J. (1955). The Child’s Construction of Reality. London: Routledge and Kegan Paul.
Piaget, J. (1972). Intellectual evolution from adolescence to adulthood. Human Development, 15(1), 1–12.
Pimm, D., Beisiegel, M., & Meglis, I. (2008). Would the real Lakatos please stand up? Interchange: A Quarterly Review of Education, 39(4), 469–481.
Pitman, A. (1989). Mathematics education reform in its social, political and economic contexts. In N. F. Ellerton & M. A. Clements (Eds.), School Mathematics: The Challenge to Change (pp. 102–119). Geelong, Vic, Australia: Deakin University Press.
Poincaré, H. (1908). L’invention mathématique. L’Enseignment Mathématique, 10, 357–371.
Prediger, S., Ferdinando, A., Bosch, M., & Lenfant, A. (Issue Editors) (2008a). Comparing combining, co-ordinating—networking strategies for connecting theoretical approaches. ZDM—The International Journal on Mathematics Education, 40(2), 163–340.
Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (Eds.) (2008b). Comparing, combining, coordinating—Networking strategies for connecting theoretical approaches. Thematic Issue of ZDM—The International Journal on Mathematics Education, 40(2), 163–327.
Presmeg, N. (2009). Mathematics education research embracing arts and sciences. ZDM—The International Journal on Mathematics Education, 41(1&2), 131–141.
Roth, W.-M. (2007). Emotions at work: A contribution to third-generation cultural historical activity theory. Mind, Culture and Activity, 14, 40–63.
Roth, W. M. (2009). Mathematical Representations at the Interface of Body and Culture. Charlotte, NC: Information Age Publishing.
Rotman, B. (2000). Mathematics as Sign: Writing, Imagining, Counting. Stanford: Stanford University Press.
Sanders, D. P. (1981). Educational inquiry as developmental insight. Educational Researcher, 10(3), 8–13.
Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. Notices of the AMS, 47(6), 641–649.
Schoenfeld, A. H. (2002). Research methods in (mathematics) education. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 435–487). Mahwah, NJ: Lawrence Erlbaum Associates.
Secada, W. (1995). Social and critical dimensions for equity in mathematics education. In W. Secada, E. Fennema, & L. Byrd Adajian (Eds.), New Directions for Equity in Mathematics Education (pp. 147–164). Cambridge: Cambridge University Press.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.
Sfard, A. (2008). Thinking as Communicating. Cambridge: Cambridge University Press.
Sierpinska, A., & Kilpatrick, J. (1998). Mathematics Education as a Research Domain: A for Identity (Vols. 1 & 2). London: Kluwer.
Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and mathematics education. In A. J. Bishop, M. A. Clements, C. Keital, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 827–876). Springer.
Silver, E. A., & Herbst, P. (2004, April). “Theory” in mathematics education scholarship. Paper presented at the research pre-session of the annual meeting of the National Council of Teachers of Mathematics, Philadelphia, PA.
Silver, E. A., & Herbst, P. (2007). Theory in mathematics education scholarship. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 39–67). Charlotte, NC: Information Age Publishing and Reston, VA: National Council of Teachers of Mathematics.
Skovsmose, O. (1997). Critical mathematics education: Some philosophical remarks. The Royal Danish School of Educational Studies, Copenhagen (Denmark). Dept. of Mathematics, Physics, Chemistry and Informatics), 12 pp.
Skovsmose, O. (2004). Mathematics: Insignificant? Philosophy of Mathematics Education Journal (Oct 2004) (no. 18), 19 p.
Skovsmose, O. (2005). Traveling through Education. Rotterdam: Sense Publishers.
Skovsmose, O., & Valero, P. (2008). Democratic access to powerful mathematics ideas. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 383–408). London: Routledge, Taylor & Francis.
Sriraman, B. (2006). An ode to Imre Lakatos: Quasi-thought experiments to bridge the ideal and actual mathematics classrooms. Interchange: A Quarterly Review of Education, 37(1–2), 151–178.
Sriraman, B. (2008). Let Lakatos be! A commentary on “Would the real Lakatos Please Stand up”. Interchange: A Quarterly Review of Education, 39(4), 483–492.
Sriraman, B. (2009a). On the identities of mathematics education. Interchange: A Quarterly Review of Education, 40(1), 119–135.
Sriraman, B. (2009b). A historic overview of the interplay of theology and philosophy in the arts, mathematics and sciences. ZDM—The International Journal on Mathematics Education, 41(1 & 2), 75–86.
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 (International Reviews on Mathematical Education), 37(6), 450–456.
Sriraman, B., & Strzelecki, P. (2004). Playing with powers. The International Journal for Technology in Mathematics Education, 11(1), 29–34.
Sriraman, B., & Törner, G. (2008). Political union/mathematical education disunion. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 656–690). London: Routledge, Taylor & Francis.
Steen, L. (1999). Review of mathematics education as research domain. Journal for Research in Mathematics Education, 30(2), 235–41.
Steffe, L. (1992). Building a foundation. Journal for Research in Mathematics Education, 23(2), 182–186.
Steffe, L., Nesher, P., Cobb, P., Greer, B., & Goldin, J. (Eds.) (1996). Theories of Mathematical Learning. Mahwah, NJ: Lawrence Erlbaum.
Steiner, H.-G. (1985). Theory of mathematics education (TME): An introduction. For the Learning of Mathematics, 5(2), 11–17.
Steiner, H. G., & Vermandel, A. (1988). Foundations and methodology of the discipline of mathematics education. In Proceedings of the TME Conference. Antwerp, Belgium.
Stevens, R. (2000). Who counts what as mathematics? Emergent and assigned mathematics problems in a project-based classroom. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning (pp. 105–144). Westport: Ablex Publishing.
Stewart, I. (1995). Bye-bye Bourbaki—paradigm shifts in mathematics. Mathematical Gazette, 79(486), 496–498.
Thom, R. (1973). Modern mathematics: Does it exist? In A. G. Howson (Ed.), Developments in Mathematical Education. Proceedings of the Second International Congress on Mathematical Education (pp. 194–209). Cambridge: Cambridge University Press.
Törner, G., & Sriraman, B. (2007). A contemporary analysis of the six “Theories of Mathematics Education” theses of Hans-Georg Steiner. ZDM—The International Journal on Mathematics Education, 39(1&2), 155–163.
Von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzlawick (Ed.), The Invented Reality (pp. 17–40). New York: Norton.
Von Glasersfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 3–18). Hillsdale, NJ: Lawrence Erlbaum Associates.
Von Glasersfeld, E. (1989). Constructivism. In T. Husen & T. N. Postlewaithe (Eds.), The International Encyclopedia of Education (1st ed., supplement Vol. 1, pp. 162–163). Oxford: Pergamon.
Vygotsky, L. S. (1978). Mind and Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sriraman, B., English, L. (2010). Surveying Theories and Philosophies of Mathematics Education. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-00742-2_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00741-5
Online ISBN: 978-3-642-00742-2
eBook Packages: Humanities, Social Sciences and LawEducation (R0)