Abstract
The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. (Journal for Research in Mathematics Education 43(5) 584–615, 2012) of two primary ways teachers use their content knowledge—decompressing and trimming—this paper differentiates between micro- and macro-levels of mathematical complexity as a way to extend and further conceptualize the moves that teachers make at a more nuanced grain size. This paper explains and portrays their counterparts, micro-level trimming and macro-level decompressing, which we discuss as concealing and foreshadowing complexity, respectively. Support for their use in teachers’ work is provided through specific examples. Implications for the mathematical preparation and professional development of teachers are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Multiplying by 0 and 1 also do not make things bigger, but likely could be considered special cases from the identity and zero-product properties.
References
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.
Askew, M., Brown, M., Rhodes, V., Wiliam, D., & Johnson, D. (1997). Effective teachers of numeracy. London: King’s College, University of London.
Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90(4), 449–466.
Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport: Ablex.
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.
Begle, E. G. (1972). Teacher knowledge and pupil achievement in algebra (NLSMA Technical Report Number 9). Palo Alto: Stanford University, School Mathematics Study Group.
Bruner, J. S. (1960). The process of education. Cambridge: Harvard University Press.
Cochran-Smith, M., & Lytle, S. L. (1999). Relationships of knowledge and practice: Teacher learning in communities. Review of Research in Education, 24(1), 249–305.
Cohen, D. K. (2004). Teaching and its predicaments. Cambridge: Harvard University Press.
Common Core State Standards in Mathematics (CCSS-M). (2010). Retrieved from http://www.corestandards.org/the-standards/mathematics
Eisenberg, T. A. (1977). Begle revisited: Teacher knowledge and student achievement in algebra. Journal for Research in Mathematics Education, 8(3), 216–222.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.
Mamolo, A., & Zazkis, R. (2012). Stuck on convention: A story of derivative relationships. Educational Studies in Mathematics, 81(2), 161–177.
Marton, F., & Tsui, A. (Eds.). (2004). Classroom discourse and the space for learning. Mahwah: Lawrence Erlbaum.
Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32.
McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584–615.
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.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Somayajulu, R. B. (2012). Building pre-service teacher’s mathematical knowledge for teaching of high school geometry (Doctoral dissertation). Retrieved from ProQuest Digital Dissertations. (AAT 3535102).
Wasserman, N. (2014). Introducing algebraic structures through solving equations: Vertical content knowledge for K-12 mathematics teachers. PRIMUS, 24(3), 191–214.
Wasserman, N., & Stockton, J. (2014). The impact of teachers’ knowledge of group theory on early algebra teaching practices. Paper presented at the meeting of Association of Mathematics Teacher Educators (AMTE) Annual Conference, Irvine, CA.
Wertheimer, M. (1959). Productive thinking. New York: Harper & Row.
Zazkis, R., Sinitsky, I., & Leikin, R. (2013). Derivative of area equals perimeter—coincidence or rule? Mathematics Teacher, 106(9), 686–692.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wasserman, N.H. Unpacking teachers’ moves in the classroom: navigating micro- and macro-levels of mathematical complexity. Educ Stud Math 90, 75–93 (2015). https://doi.org/10.1007/s10649-015-9615-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-015-9615-1