Critical Praxis Research pp 193-208 | Cite as

# The Interplay of Identity, Context, and Purpose in a Study of Mathematics Teaching and Learning

## Abstract

In this chapter, Roser Giné connects her experiences as a mathematics student and educator to the research process she engaged in during her doctoral dissertation. Specifically, she shows how her identity and her beliefs about teaching and learning, influenced in part by her peripheral participation in the mathematics community as a young child, guided her research choices, from the formation of researchable questions, through the theoretical lenses appropriated, to the data collection and analysis processes. Her work attempts to reveal how students make sense of mathematics in the setting where their learning occurs, through interactions with their teacher and peers, through the enactment of curriculum, and in their development of disciplinary tools. Her views on the humanistic nature of the development of mathematical thinking leads to her use of a bricolage of socio-cultural theories, including Activity Theory, Structure Theory, and socio-semiotics. The chapter details the interplay between the author’s identity, the context in which she conducts her work, and her purpose as an educator and a mathematics education researcher.

## Keywords

Activity Theory Mathematics Classroom Mathematical Thinking Epistemological Belief Charter School## References

- Barab, S., & Duffy, T. (1998). From practice fields to communities of practice. In D. Jonassen & S. Land (Eds.),
*Theoretical foundations of learning environments*(pp. 25–55). Bloomington, IN: Lawrence Erlbaum Associates.Google Scholar - Beaton, A. E., Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1998).
*Mathematics achievement in the final year of secondary school: IEA’s Third International Mathematics and Science Study (TIMSS)*. Chestnut Hill, MA: Boston College.Google Scholar - Benne, K. (1970). Authority in education.
*Harvard Educational Review, 40*(3), 385–410.Google Scholar - Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.),
*Advanced mathematical thinking*(pp. 95–123). Dordrecht: Kluwer.Google Scholar - Engeström, Y. (2001). Expansive learning at work: Toward and activity-theoretical reconceptualization.
*Journal of Education and Work, 14*(1), 133–156.Google Scholar - Giné, E. (2008). Learning mathematics. In R. Giné (Ed.),
*Email communication and conversation*.Google Scholar - Giné, R. (2009).
*Transforming figures: The mathematics of animation*. Newton, MA: Education Development Center.Google Scholar - Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving.
*Educational Studies in Mathematics, 49*, 193–223.CrossRefGoogle Scholar - Gray, E., & Tall, D. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In
*Proceedings of PME25*(pp. 65–72). Utrecht, Holland: University of Utrecht.Google Scholar - Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th century.
*Mathematical Cognition*. Retrieved October 13, 2006 from http://www.csun.edu/~vcmth00m/AHistory.html - Kuutti, K. (1995). Activity theory as a potential framework for human-computer interaction research. In B. Nardi (Ed.),
*Context and consciousness: Activity theory and human interaction*(pp. 17–44). Cambridge: MIT Press.Google Scholar - Martin, D. B. (2004).
*Optimizing minority achievement in rigorous mathematics courses: Challenging what we think we know*. Paper prepared for Maryland Institute for Minority Achievement and Urban Education, Maryland.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. Reston, VA: NCTM.Google Scholar - Oakes, J. (1990).
*Multiplying inequalities: The effects of race, social class, and tracking on opportunities to learn mathematics and science*. Santa Monica, CA: The RAND Corporation.Google Scholar - Remillard, J., Stein, M. K., & Smith, M. (2007). How curriculum influences student learning. In F. Lester (Ed.),
*Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics*(pp. 319–369). Charlotte, NC: Information Age Publishing.Google Scholar - Saka, Y., Southerland, S., & Brooks, J. (2009, March 11). Becoming a member of a school community while working toward science education reform: Teacher induction from a Cultural Historical Activity Theory (CHAT) perspective.
*Science Education,**93*(6), 996–1025.CrossRefGoogle 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 - Secada, W. G. (1992). Race, ethnicity, social class, language, and achievement in mathematics. In D. A. Grouws (Ed.),
*Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of mathematics*(pp. 623–660). New York: Macmillan.Google Scholar - Sewell, W. (1992). A theory of structure: Duality, agency, and transformation.
*American Journal of Sociology, 98*(1), 1–29.CrossRefGoogle Scholar - Thurston, W. (1990). Mathematical education.
*Notices of the AMS, 37*, 844–850.Google Scholar - Van Oers, B. (2000). The appropriation of mathematical symbols: A psychosemiotic approach to mathematics learning. In P. Cobb, E. Yackel, & K. McClain (Eds.),
*Symbolizing and communicating in mathematics classrooms*(pp. 133–177). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Vygotsky, L. S. (1978).
*Mind in society: The development of higher psychological processes*. Cambridge: Harvard University Press.Google Scholar - Yin, R. (2003).
*Case study research: Design and methods*(3rd ed.) Thousand Oaks, CA: Sage.Google Scholar