Abstract
As a young field in its own right (unlike the ancient discipline of mathematics), mathematics education research has been eclectic in drawing upon the established knowledge bases and methodologies of other fields. Psychology served as an early model for a paradigm that valorized psychometric research, largely based in the theoretical frameworks of cognitive science. More recently, with the recognition of the need for sociocultural theories, because mathematics is generally learned in social groups, sociology and anthropology have contributed to methodologies that gradually moved away from psychometrics towards qualitative methods that sought a deeper understanding of issues involved. The emergent perspective struck a balance between research on individual learning (including learners’ beliefs and affect) and the dynamics of classroom mathematical practices. Now, as the field matures, the value of both quantitative and qualitative methods is acknowledged, and these are frequently combined in research that uses mixed methods, sometimes taking the form of design experiments or multi-tiered teaching experiments. Creativity and rigor are required in all mathematics education research, thus it is argued in this paper, using examples, that characteristics of both the arts and the sciences are implicated in this work.
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Ball, D. L. (2000). Working on the inside: using one’s own practice as a site for studying teaching and learning. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 365–402). Mahwah: Lawrence Erlbaum Associates.
Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht: Kluwer Academic Publishers.
Bishop, A. J. (2004). Mathematics education in its cultural context. In T. P. Carpenter, J. A. Dossey, & J. L. Koehler (Eds.), Classics in mathematics education research (pp. 201–207). Reston, VA: National Council of Teachers of Mathematics. Reprinted from Educational Studies in Mathematics, 19 (1988), 179–191.
Brown, T. (1997). Mathematics education and language: Interpreting hermeneutics and post-structuralism. Dordrecht: Kluwer.
Bruner, J. (1986). Actual minds, possible worlds. Cambridge: Harvard University Press.
Cobb, P. (2007). Putting philosophy to work. In F. K. Lester Jr (Ed.), Second handbook of research in mathematics teaching and learning (pp. 3–38). Charlotte: Information Age Publishing.
Cobb, P. Yackel, E., & McClain, K. (Eds.) (2000). Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah: Lawrence Erlbaum Associates.
Confrey, J. (1991). Steering a course between Piaget and Vygotsky. Educational Researcher, 20(8), 28–32.
De Bono, E. (1970). Lateral thinking: A textbook of creativity. London: Pelican.
Dörfler, W. (2000). Means for meaning. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 99–131). Mahwah: Lawrence Erlbaum Associates.
Dukas, H. & Hoffmann, B. (Eds.) (1979). Albert Einstein: The human side. Princeton, NJ: Princeton University Press.
Duval, R. (1999). Representations, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3–26). Columbus: ERIC Clearinghouse for Science, Mathematics, & Environmental Education.
Einstein, A. (1970). Out of my later years. New York: Greenwood Press.
Einstein, A. (1973). Ideas and opinions. London: Souvenir Press.
Einstein, A. (1976). Relativity: The special and the general theory. London: Methuen.
Einstein, A. (1979). The world as I see it. New York: Citadel Press.
Eisenhart, M. A. (1988). The ethnographic research tradition and mathematics education research. Journal for Research in Mathematics Education, 19(2), 99–114.
Ewert, G. D. (1991). Habermas and education: A comprehensive overview. Review of Educational Research, 61(3), 345–378.
Gagatsis, A., Sriraman, B., Elia, I., & Modestou, M. (2006). Exploring young children’s geometrical strategies. Nordic Studies in Mathematics Education, 11(2), 23–50.
Grundy, S. (1990). Curriculum: Product of praxis. New York: The Falmer Press.
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York: Routledge.
Habermas, J. (1978). Knowledge and human interests. London: Heinemann.
Hall, M. (2000). Bridging the gap between everyday and classroom mathematics: An investigation of two teachers’ intentional use of semiotic chains. Unpublished doctoral dissertation, The Florida State University.
Hartnett, A. E. (1982). The social sciences in educational studies: A selective guide to the literature. London: Heinemann.
Holton, G. (1973). Thematic origins of scientific thought: Kepler to Einstein. Cambridge: Harvard University Press.
Hostetler, K. (2005). What is “good” educational research? Educational Researcher, 34(6), 16–21.
Johnson, R. K., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14–26.
Keats, J. (1880/1953). Ode on a Grecian urn. In H. B. Forman (Ed.), The poetical works of John Keats (pp. 233–234). London: Oxford University Press.
Kemmis, S. (1999). Action research. In J. P. Keeves & G. Lakomski (Eds.), Issues in educational research (pp. 150–160). New York: Pergamon.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Leder, G. C., Pehkonen, E., & Törner, G., (Eds.) (2002). Beliefs: A hidden variable in mathematics education? Dordrecht, The Netherlands: Kluwer Academic Publishers.
Lester, F. K. Jr. (Ed.) (2007). Second handbook of research on mathematics teaching and learning. Charlotte: Information Age Publishing.
McCormick, R., Bynner, J., Clift, P., James, M., & Brown, C. M. (Eds.) (1977).Calling education to account. London: Heinemann.
Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology, 27(1), 75–92.
Millroy, W. L. (1992). An ethnographic study of the mathematics of a group of carpenters. Reston: National Council of Teachers of Mathematics, Monograph 5.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: The Council.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: The Council.
Nickson, M. (1992). The culture of the mathematics classroom: An unknown quantity? In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 101–114). New York: Macmillan.
Ontiveros, J. Q. (1991). Piaget and Vygotsky: Two interactionist perspectives in the construction of knowledge. In Paper presented at the fifth international conference on theory of mathematics education, Paderno Del Grappa, 20–27 June 1991.
Peirce, C. S. (1992). The essential Peirce (Vol. 1). In N. Houser & C. Kloesel (Eds.) Bloomington: Indiana University Press.
Peirce, C. S. (1998). The essential Peirce (Vol. 2). In The Peirce Edition Project (Ed.). Bloomington: Indiana University Press.
Presmeg, N. C. (1985), The role of visually mediated processes in high school mathematics: A classroom investigation. Unpublished Ph.D. dissertation, University of Cambridge.
Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595–610.
Presmeg, N. C. (1993). Mathematics—‘A bunch of formulas’? Interplay of beliefs and problem solving styles. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F.-L. Lin (Eds.), Proceedings of the 17th annual meeting of the international group for the psychology of mathematics education, Tsukuba, Japan, July 18–23, Vol. 3 (pp. 57–64).
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). Hillsdale: Lawrence Erlbaum Associates.
Presmeg, N. C. (1997b). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299–312). Hillsdale: Lawrence Erlbaum Associates.
Presmeg, N. C. (1998a). Balancing complex human worlds: Mathematics education as an emergent discipline in its own right. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (Vol. 1, pp. 57–70). International Commission on Mathematical Instruction Study Publication. Dordrecht: Kluwer.
Presmeg, N. C. (1998b). Metaphoric and metonymic signification in mathematics. The Journal of Mathematical Behavior, 17(1), 25–32.
Presmeg, N. C. (2006a). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–235). Rotterdam: Sense Publishers.
Presmeg, N. C. (2006b). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. Plenary Paper. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th annual meeting of the international group for the psychology of mathematics education, Vol. 1 (pp. 19–34). Prague, 16–21 July 2006.
Presmeg, N. C. (2006c). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61(1–2), 163–182.
Presmeg, N. C. (2008). Trigonometric connections through a semiotic lens. In L. Radford, G. Schubring & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture. Rotterdam: Sense Publishers.
Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: The multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, 38(5), 507–530.
Roth, W.-M. (2008). Editorial power/authorial suffering. RISE special issue on peer review (to appear).
de Saussure, F. (1959). Course in general linguistics. New York: McGraw-Hill.
Schilpp, P. A. (Ed.) (1959). Albert Einstein: Philosopher-scientist. Vol. I & II, Library of Living Philosophers. London: Harper & Rowe.
Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14(1), 44–55.
Sfard, A. (2000). Symbolizing mathematical reality into being—or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 37–98). Mahwah: Lawrence Erlbaum Associates.
Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22.
Sierpinska, A., & Kilpatrick, J. (Eds.). (1998). Mathematics education as a research domain: A search for identity. Dordrecht: Kluwer.
Sriraman, B. (Ed.). (2007). International perspectives on social justice in mathematics education. The University of Montana Press: Monograph 1, The Montana Mathematics Enthusiast (http://www.math.umt.edu/TMME/Monograph1/).
Steen, L. A. (1990). On the shoulders of Giants: New approaches to numeracy. Washington, DC: National Academy Press.
US Congress. (2001). No child left behind Act of 2001. Washington, DC: Author.
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Presmeg, N. Mathematics education research embracing arts and sciences. ZDM Mathematics Education 41, 131–141 (2009). https://doi.org/10.1007/s11858-008-0136-6
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DOI: https://doi.org/10.1007/s11858-008-0136-6