Reflective Awareness in Mathematics Teachers’ Learning and Teaching

Olive Chapman

doi:10.12973/eurasia.2015.1334a

Full Text (PDF)

Olive Chapman ¹ ^*

More Detail

¹ University of Calgary, CANADA
^* Corresponding Author

Abstract

The nature of mathematics teachers’ knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness as a central aspect of MTK based on a study of elementary school mathematics teachers’ learning and teaching associated with a self-directed professional development initiative to transform their teaching to an inquiry-based perspective. Research questions focused on how this initiative supported reflective awareness in the teachers’ learning and teaching. Findings indicated that engaging in self-based and meaning-based questioning and creating pedagogical models were central to the teachers’ learning and use of reflective awareness. Their knowledge of reflective awareness as a way of knowing was important to their development of an inquiry stance and knowledge of mathematics for teaching and mathematics pedagogy.

Keywords

mathematics teachers’ knowledge
mathematics teachers’ learning
pedagogical models
questioning
reflective awareness

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

https://doi.org/10.12973/eurasia.2015.1334a

EURASIA J Math Sci Tech Ed, 2015 - Volume 11 Issue 2, pp. 313-324

Publication date: 12 Apr 2015

Article Views: 1438

Article Downloads: 600

Open Access References How to cite this article

References

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 5, 389-407.
Barton, B. (2009). Being Mathematical, Holding Mathematics: Further steps in mathematical knowledge for teaching. In R. Hunter, B. Bicknell & T. Burgess (Eds.), Crossing Divides: Proceedings of the Mathematics Education Research Group of Australasia (vol. 1). Palmerston North, NZ: MERGA.
Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33, 8, 3–15.
Chapman, O. (2013). Mathematics teachers’ learning through inquiry. Sisyphus-Journal of Education, 1, 3, 122-150.
Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: an integrative model for teacher preparation. Journal of Teacher Education, 44, 263- 272.
Davis, B., & Renert, M. (2009). Mathematics-for-Teaching as shared dynamic participation. For the Learning of Mathematics. 29, 3, 37–43.
Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process (revised edition). Boston: Heath.
Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24, 1, 8-40.
Ernest, P. (1991). The philosophy of mathematics education. London: Falmer.
Fennema, E., & Franke, L. M. (1992). Teachers’ knowledge and its impact. In D.A. Grouws (Ed) Handbook of research on mathematics teaching and learning (pp. 147-164). New York, Macnillan Publishing Co.
Handal, B. (2003). Teachers' mathematical beliefs: A review. Mathematics Educator, 13, 2, 47-57.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs. ZDM, 40, 5, 873-892.
Ma, L. (1999). Knowing and teaching elementary mathematics. Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, New Jersey: Lawrence Erlbaum Associates, Inc.
Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1, 3, 243–267.
Mason, J. (2008). Being mathematical with and in front of learners: Attention, awareness, and attitude as sources of difference between teacher educators, teachers and learners. In B. Jaworski & T. Wood (Eds.), International handbook of mathematics teacher education: Vol. 4: The Mathematics teacher educator as a developing professional (pp. 31-56). Rotterdam, The Netherlands: Sense.
Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. New York: Prentice Hall.
Mayer, R. E., & Wittrock, R. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ: Erlbaum.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (2000). Principals and Standards for School Mathematics. Reston, VA: NCTM.
Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 461–494). Rotterdam, The Netherlands: Sense.
Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the knowledge quartet. London: Sage Publications.
Rowland, T., & Ruthven, K. (Eds.). (2011). Mathematical knowledge in teaching. New York: Springer.
Ruthven, K. (2011). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical Knowledge in Teaching (pp. 83-96). Dordrecht: Springer.
Scherrer, J., & Stein, M.K. (2012). Effects of a coding intervention on what teachers learn to notice during whole group discussion. Journal of Mathematics Teacher Education, 16, 105-124.
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.
Schön, D. A. (1983). The reflective practitioner: How professionals think in action. Aldershot Hants: Avebury.
Schön, D. A. (1987). Educating the reflective practitioner. Oxford: Jossey-Bass.
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.) (2010). Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–13). New York, NY: Routledge
Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers' ability to notice classroom interactions. Journal of Technology and Teacher Education, 13, 475-491.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Senge, P.M., Scharmer, C.O., Jaworski, J., & Flowers, B.S. (2005). Presence: An exploration of profound change in people, organizations, and society. New York: Doubleday.
Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers' ability to notice. Journal of Mathematics Teacher Education, 11, 107–125.
Tatto, M.T., Peck, R., Schwille, J., Bankov, K., Senk, S.L., Rodriguez, M., et al. (2012). Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries. Amsterdam, the Netherlands: International Association for the Evaluation of Educational Achievement.
Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 127-146). New York, NY:Macmillan.
van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers' "learning to notice" in the context of a video club. Teaching and Teacher Education, 24, 244-276.
Watson, A. (2008). School mathematics as a special kind of mathematics. For the Learning of Mathematics, 28, 3, 3-7.
Wells, G. (1999). Dialogic inquiry: Toward a sociocultural practice and theory of education. Cambridge: Cambridge University Press.

How to cite this article

APA

Chapman, O. (2015). Reflective Awareness in Mathematics Teachers’ Learning and Teaching. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 313-324. https://doi.org/10.12973/eurasia.2015.1334a

Vancouver

Chapman O. Reflective Awareness in Mathematics Teachers’ Learning and Teaching. EURASIA J Math Sci Tech Ed. 2015;11(2):313-24. https://doi.org/10.12973/eurasia.2015.1334a

AMA

Chapman O. Reflective Awareness in Mathematics Teachers’ Learning and Teaching. EURASIA J Math Sci Tech Ed. 2015;11(2), 313-324. https://doi.org/10.12973/eurasia.2015.1334a

Chicago

Chapman, Olive. "Reflective Awareness in Mathematics Teachers’ Learning and Teaching". Eurasia Journal of Mathematics, Science and Technology Education 2015 11 no. 2 (2015): 313-324. https://doi.org/10.12973/eurasia.2015.1334a

Harvard

Chapman, O. (2015). Reflective Awareness in Mathematics Teachers’ Learning and Teaching. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), pp. 313-324. https://doi.org/10.12973/eurasia.2015.1334a

MLA

Chapman, Olive "Reflective Awareness in Mathematics Teachers’ Learning and Teaching". Eurasia Journal of Mathematics, Science and Technology Education, vol. 11, no. 2, 2015, pp. 313-324. https://doi.org/10.12973/eurasia.2015.1334a