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Issues Regarding the Concept of Mathematical Practices

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Proficiency and Beliefs in Learning and Teaching Mathematics

Part of the book series: Mathematics Teaching and Learning ((MTAL))

Abstract

In the first chapter of Alan Schoenfeld’s 2011 book How we think, he describes his original framework (1985) for the study of mathematical problem solving as having four components: knowledge base, problem solving strategies, metacognition, and beliefs.

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References

  • Barwell, R. (2005). Ambiguity in the mathematics classroom. Language and Education, 19(2), 117–125.

    Article  Google Scholar 

  • Barwell, R., Leung, C., Morgan, C., & Street, B. (2005). Applied linguistics and mathematics education: More than words and numbers. Language and Education, 19(2), 141–146.

    Article  Google Scholar 

  • Breidenbach, D., Dubinsky, E., Nichols, D., & Hawks, J. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247–285.

    Article  Google Scholar 

  • Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics. Educational Studies in Mathematics, 37(2), 121–143.

    Article  Google Scholar 

  • Byers, W. (2007). How mathematicians think: Using ambiguity, contradiction, and paradox to create mathematics. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21–29.

    Article  Google Scholar 

  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1&2), 113–164.

    Article  Google Scholar 

  • Cobb, P., Wood, T. & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In E. Forman,N.Minick, &C.A.Stone (Eds), Contexts for learning: Sociocultural dynamics in children’s development (pp. 91–119). New York, NY: Oxford University Press.

    Google Scholar 

  • Davis, P. J., & Hersch, R. (1982). The mathematical experience. Boston: Houghton Mifflin Co.

    Google Scholar 

  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21, 521–544.

    Article  Google Scholar 

  • Forman, E. (1996). Learning mathematics as participation in classroom practice: Implications of sociocultural theory for educational reform. In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 115–130). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Gee, J. (1999). An introduction to Discourse analysis: Theory and method. New York: Routledge.

    Google Scholar 

  • GutiĂ©rrez, K. D., Sengupta-Irving, T., & Dieckmann, J. (2010). Developing a mathematical vision: Mathematics as a discursive and embodied practice. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Hadamard, J. (1945). The psychology of invention in the mathematical field. New York: Princeton University Press.

    Google Scholar 

  • Hardy, G. H. (1940). A mathematician’s apology. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hersh, R. (2007). Book review: How mathematicians think. Notices of the AMS, 54(11), 1496–1499.

    Google Scholar 

  • Høyrup, J. (1994). In measure, number, and weight: Studies in mathematics and culture. Albany: SUNY Press.

    Google Scholar 

  • Lakatos, I. (1976). Proofs and refutations (Rev. ed.). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Lampert, M. (1986). Knowing, doing and teaching multiplication. Cognition and Instruction, 3(4), 305–342.

    Article  Google Scholar 

  • 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), 29–64.

    Article  Google Scholar 

  • Latour, B. (1987). Science in action. Cambridge: Harvard University Press.

    Google Scholar 

  • Latour, B., & Woolgar, S. (1986). Laboratory life: The construction of scientific facts. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation.New York: Cambridge University Press.

    Google Scholar 

  • Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Mendez, E. P. (2001.) A history of mathematical dialogue in textbooks and classrooms. Mathematics Teacher, 94, 170–173.

    Google Scholar 

  • Morgan, C. (2004). Word, definitions and concepts in discourses of mathematics, teaching and learning. Language and Education, 18, 1–15.

    Article  Google Scholar 

  • Moschkovich, J. N. (2002). An Introduction to examining everyday and academic mathematical practices. In M. Brenner & J. Moschkovich (Eds.), Everyday and academic mathematics: Implications for the classroom. Journal for Research in Mathematics Education, Monograph Number 11, 1–11.

    Google Scholar 

  • Moschkovich, J. N. (2004). Appropriating mathematical practices: A case study of learning to use and explore functions through interaction with a tutor. Educational Studies in Mathematics, 5, 49–80.

    Article  Google Scholar 

  • Moschkovich, J. N. (2007). Examining mathematical Discourse practices. For the Learning of Mathematics, 27(1), 24–30.

    Google Scholar 

  • Moschkovich, J. N. (2008). “I went by twos, he went by one:” Multiple interpretations of inscriptions as resources for mathematical discussions. The Journal of the Learning Sciences, 17(4), 551–587.

    Article  Google Scholar 

  • Moschkovich, J. N. (2010). Language and mathematics education: Multiple perspectives and directions for research. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Moschkovich, J. N., & Brenner, M. (2000). Integrating a naturalistic paradigm into research on mathematics and science cognition and learning. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics & science education (pp. 457-486). New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations, and connections among them. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 69–100). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Newman, D., Griffin, P., & Cole, M. (1989). The construction zone: Working for cognitive change in school. Cambridge: Cambridge University Press.

    Google Scholar 

  • Nunes, T., Schliemann, A., & Carraher, D. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.

    Google Scholar 

  • O’Halloran, K. L. (1999). Towards a systemic functional analysis of multisemiotic mathematics texts. Semiotica, 124(1/2), 1–29.

    Article  Google Scholar 

  • O’Halloran, K. L. (2000). Classroom discourse in mathematics: A multisemiotic analysis. Linguistics and Education, 10(3), 359–388.

    Article  Google Scholar 

  • O’Connor, M. C. (1999). Language socialization in the mathematics classroom. Discourse practices and mathematical thinking. In M. Lampert & M. Blunk (Eds.), Talking mathematics (pp. 17–55). New York: Cambridge University Press.

    Google Scholar 

  • Ochs, E., Gonzales, P., and Jacoby, S., (1996). “When I come down I’m in the domain state”: Grammar and graphic representation in the interpretive activity of physicists. In E. Ochs, E. Schegloff, & S. Thompson (Eds.), Interaction and grammar (pp. 328–369). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Ochs, E., Jacoby, S., & Gonzales, P. (1994). Interpretive journeys: How physicists talk and travel through graphic space. Configurations, 2(1), 151–171.

    Article  Google Scholar 

  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge.

    Google Scholar 

  • Polya, G. (1957). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Radford, L. (2001). Signs and meanings in students’ emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42(3), 237–268.

    Article  Google Scholar 

  • Restivo, S. (1993). The social life of mathematics. In S. Restivo, J. P. Van Bendegem, & R. Fischer (Eds.), Math worlds: Philosophical and social studies of mathematics and mathematics education (pp. 247–278). Albany: SUNY Press.

    Google Scholar 

  • Richards, J. (1991). Mathematical discussions. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 13–51). Dordrecht, the Netherlands: Kluwer.

    Google Scholar 

  • Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context.New York: Oxford University Press.

    Google Scholar 

  • Rowland, T. (1999). The pragmatics of mathematics education: Vagueness in mathematical discourse. New York: Routledge, Taylor & Francis Group.

    Google Scholar 

  • Saxe, G. (1991). Culture and cognitive development. New Jersey: Erlbaum.

    Google Scholar 

  • Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

    Google Scholar 

  • Schoenfeld, A. (1990). GRAPHER: A case study in educational technology, research, and development. In A. DiSessa, M. Gardner, J. Greeno, F. Reif, A. Schoenfeld, & E. Stage (Eds.), Toward a scientific practice of science education (pp. 281–300). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.

    Google Scholar 

  • Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: Research and theory, practice and politics. ZDM – The International Journal on Mathematics Education, 39(5–6), 537–551.

    Article  Google Scholar 

  • Schoenfeld, A. S. (2011). How we think: A theory of goal-oriented decision making and its educational applications, Studies in Mathematical Thinking and Learning Series. New York: Routledge.

    Google Scholar 

  • Schoenfeld, A., Arcavi, A. & Smith, J. (1993). Learning. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55–175). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Schwarz, J., & Yerushalmy, M. (1992). Getting students to function in and with algebra. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 261–289). MAA Notes, Vol. 25. Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Schleppegrell, M. J. (2010). Language in mathematics teaching and learning: A research review. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for fesearch. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 9–40). Cambridge: Harvard University Press.

    Google Scholar 

  • Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-the case of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 261–289). MAA Notes, Vol 25. Washington DC: Mathematical Association of America.

    Google Scholar 

  • Traweek, S. (1988). Beam times and lifetimes: The world of high energy physicists. Cambridge: Harvard University Press.

    Google Scholar 

  • Tymoczo, T. (Ed.). (1986). New directions in the philosophy of mathematics. Basel: Birkhauser.

    Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds.). Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Vygotsky, L. S. (1979). The genesis of higher mental functions. In J. V. Wertsch (Ed. & Trans.), The concept of activity in Soviet psychology (pp. 144–188). Armonk, NY: M. E. Sharpe.

    Google Scholar 

  • Vygotsky, L. S. (1987). The collected work of L. S. Vygotsky (R. W. Rieber, Ed., & N. Minick, Trans.). New York: Plenum Press.

    Google Scholar 

  • Wertsch, J. V. (1979a). The concept of activity in soviet psychology: An introduction. In J. V. Wertsch (Ed. & Trans.), The concept of activity in soviet psychology (pp. 3–35). Armonk, NY: M. E. Sharpe.

    Google Scholar 

  • Wertsch, J. V. (1979b). From social interaction to higher psychological processes: A clarification and application of Vygotsky’s theory. Human Development, 22(1), 1–22.

    Article  Google Scholar 

  • Wertsch, J. V. (1984). The zone of proximal development: Some conceptual issues. In B. Rogoff & J. V. Wertsch (Eds.), Children’s learning in the zone of proximal development (pp. 7–18). New Directions for Child Development Series, No. 22. San Francisco: Jossey-Bass Inc.

    Google Scholar 

  • Wertsch, J. (1985). Vygotsky and the social formation of mind. Cambridge: Harvard University Press.

    Google Scholar 

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Authors and Affiliations

  1. University of California, Santa Cruz, USA

    Judit N. Moschkovich

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  1. Judit N. Moschkovich
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Editors and Affiliations

  1. Texas A&M University, USA

    Yeping Li

  2. University of California, Santa Cruz, USA

    Judit N. Moschkovich

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Moschkovich, J.N. (2013). Issues Regarding the Concept of Mathematical Practices. In: Li, Y., Moschkovich, J.N. (eds) Proficiency and Beliefs in Learning and Teaching Mathematics. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6209-299-0_15

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