Abstract
In this chapter, we discuss research that investigated what, how, and with what possible effects, mathematical knowledge and related practices are constituted in and across a range of programmes, across diverse teacher training institutions in South Africa. Our study includes three cases from three different teacher education sites where teachers were enrolled in in-service upgrading programmes. Our focus is on what comes to be the content of mathematics for teaching; that is, the mathematical content and practices offered in these courses, and how this occurs. In the chapter, we describe our observations and the analytic resources recruited to that end, building on our previous work. We argue that three different orientations to learning mathematics for teaching are exhibited across our cases and present different opportunities for learning mathematics in and for teaching.
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Notes
- 1.
QUANTUM is the name given to a Research and Development project on quality mathematical education for teachers in South Africa. The development arm of QUANTUM focused on qualifications for teachers underqualified in mathematics (hence the name) and completed its tasks in 2003. QUANTUM continues as a research project.
- 2.
In South Africa, teachers are required to obtain a 4-year post-school qualification in education to practice. Those teachers who obtained only 3 (or fewer) year qualifications under previous dispensations are now required to enrol for further study on in-service programmes to ‘upgrade’ their teaching qualifications.
- 3.
- 4.
Most of the teachers on this programme were initially trained to teach in primary schools and were upgrading a 3-year qualification and improving their level of teaching. A design principle of the course was that by learning to teach algebra, the teachers would themselves have opportunities to (re)learn algebra.
- 5.
More generally, it is interesting to note that in instances such as these there is a question of the integrity of the metaphor with respect to the mathematical idea being ‘exemplified’. This specific point is a general concern in mathematics education where the everyday is frequently recruited to invest mathematical objects and notions with meaning. Given the intelligible nature of mathematical ideas, this presents teachers with difficulties of finding useful and meaningful metaphors.
- 6.
For example, a deep knowledge of the school mathematics required by the new curriculum, or professional competence such as an ability to produce a year plan based on a curriculum document.
References
Adler, J. (2002). Global and local challenges of teacher development. In J. Adler & Y. Reed (Eds.), Challenges of teacher development: An investigation of take-up in South Africa (pp. 1–16). Pretoria: Van Schaik.
Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270–296.
Adler, J., & Huillet, D. (2008). The social production of mathematics for teaching. In T. Wood S. & P. Sullivan (Eds.), International handbook of mathematics teacher education: Vol. 1. Knowledge and beliefs in mathematics teaching and teaching development (pp. 195–222). Rotterdam: The Netherlands: Sense Publishers.
Ball, D., Bass, H., & Hill, H. (2004). Knowing and using mathematical knowledge in teaching: Learning what matters. In A. Buffler & R. Lausch (Eds.), Proceedings of the 12th Annual Conference of the South African Association for Research in Mathematics, Science and Technology Education (SAARMSTE). Cape Town.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.
Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory, research and critique (Revised Edition). Lanham: Rowman & Littlefield Publishers, Inc.
Carnoy, M., Chisholm, L., et al. (2008). Towards understanding student academic performance in South Africa: A Pilot Study of Grade 6 Mathematics Lessons in South Africa. Pretoria: HSRC.
Davis, Z. (2001). Measure for measure: Evaluative judgement in school mathematics pedagogic texts. Pythagoras, 56, 2–11.
Davis, Z. (2005). Pleasure and pedagogic discourse in school mathematics: A case study of a problem-centred pedagogic modality. Unpublished PhD thesis, University of Cape Town, Cape Town.
Davis, Z., Adler, J., & Parker, D. (2007). Identification with images of the teacher and teaching in formalized in-service mathematics teacher education and the constitution of mathematics for teaching. Journal of Education, 42, 33–60.
Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). “Mathematical knowledge for teaching”: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171–197.
Ensor, P. (2004). Modalities of teacher education discourse and the education of effective practitioners. Pedagogy, Culture and Society, 12(2), 217–232.
Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521–544.
Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116.
Hill, H., Blunk, M., Charalambos, Y., Lewis, J., Phelps, G., Sleep, L., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26, 430–511.
Krauss, S., Neubrand, M., Blum, W., & Baumert, J. (2008). The professional knowledge of German secondary mathematics teachers: Investigations in the context of the COACTIV project. Unpublished paper presented to Topic Study Group 27, ICME12, Mexico.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States New Jersey, NJ: Lawrence Erlbaum.
Marks, R. (1992). Pedagogical content knowledge: From a mathematics case to a modified conception. Journal of Teacher Education, 4(3), 3–11.
Parker, D. (2009). The specialisation of pedagogic identities in initial mathematics teacher education in post-apartheid South Africa. Unpublished PhD thesis, University of the Witwatersrand, Johannesburg, South Africa.
Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of a new reform. Harvard Educational Review, 57(1), 1–22.
Welch, T. (2002). Teacher education in South Africa before, during and after apartheid: An overview. In J. Adler & Y. Reed (Eds.), Challenges of teacher development: An investigation of take-up in South Africa (pp. 17–35). Pretoria, South Africa: Van Schaik.
Acknowledgement
This chapter forms part of the QUANTUM research project on Mathematics for Teaching, directed by Jill Adler, at the University of the Witwatersrand. This material is based upon work supported by the National Research Foundation (NRF) under Grant number FA2006031800003. Any opinion, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NRF.
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Adler, J., Davis, Z. (2011). Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching. In: Rowland, T., Ruthven, K. (eds) Mathematical Knowledge in Teaching. Mathematics Education Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9766-8_9
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