Using Mathematics-Pedagogy Tasks to Facilitate the Professional Growth of Pre-service Elementary Teachers
We used mathematics-pedagogy tasks (MPTs) to design content and methods (pedagogy) courses to facilitate the professional growth of pre-service elementary teachers, especially those who did not study in mathematics-related areas. MPTs, together with the use of relevant theories, enable pre-service elementary teachers to coordinate the learning of mathematics, student cognition, the sequence of mathematics content arranged in the curriculum, and teaching activities designed in textbooks. For those pre-service teachers studying in non-mathematics areas, the learning of mathematics should be the starting point, as it enables them not only to understand the mathematics but also to build personal learning theories that can subsequently be applied to realize student cognition. The integration of mathematics and student cognition becomes the foundation for pre-service elementary teachers to comprehend curriculum arrangement and textbook design. In this chapter, we discuss and exemplify the notion of MPTs using examples implemented in two teacher education courses (one content course and one methods course).
KeywordsMathematics-pedagogy task (MPT) Pre-service elementary teachers Professional growth Content course Methods course
- Artzt, A. F. (1999). A structure to enable preservice teachers of mathematics to reflect on their teaching. Journal of Mathematics Teacher Education, 2, 143–166.Google Scholar
- Ball, D. Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis, & E. Simmt (Eds.), 2002 Annual Meeting of the Canadian Mathematics Education Study Group, Edmonton, AB, 2003 (pp. 3–14): CMESG/GCEMD.Google Scholar
- Ball, D., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of teacher education, 59(5), 389–407, doi: 10.1177/0022487108324554.
- Baturo, A., Cooper, T., Doyle, K., & Grant, E. (2007). Using three levels in design of effective teacher-education tasks: The case of promoting conflicts with intuitive understandings in probability. Journal of Mathematics Teacher Education, 10(4), 251–259, doi: 10.1007/s10857-007-9042-z.
- Bell, A. (1993). Principles for the design of teaching. Educational Studies in Mathematics, 24(1), 5–34.Google Scholar
- Boyd, D. J., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4), 416–440.Google Scholar
- Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University.Google Scholar
- Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.Google Scholar
- Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.Google Scholar
- Dienes, Z. (1973). The six stages in the process of learning mathematics. Slough: NFER-Nelson.Google Scholar
- Freeman, D. J., & Porter, A. C. (1989). Do textbooks dictate the content of mathematics instruction in elementary schools? American Educational Research Journal, 26(3), 403–421.Google Scholar
- Fuller, F. F. (1969). Concerns of Teachers: A Developmental Conceptualization. American Educational Research Journal, 6(2), 207–226, doi: 10.3102/00028312006002207.
- Fwu, B.-j., & Wang, H.-h. (2002). From uniformity to diversification: transformation of teacher education in pursuit of teacher quality in Taiwan from 1949 to 2000. International Journal of Educational Development, 22(2), 155–167, doi:http://dx.doi.org/10.1016/S0738-0593(01)00019-0.
- Hill, H. C., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.Google Scholar
- Li, Y., Ma, Y., & Pang, J. (2008). Mathematical preparation of prospective elementary teachers. In P. Sullivan, & T. Wood (Eds.), Knowledge and beliefs in mathematics teaching and teaching development (Vol. 1, pp. 37–62, Vol. The international handbook of mathematics teacher education). Rotterdam: Sense Publishers.Google Scholar
- Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, New Jersey: Lawrence Erlbaum Associates Inc.Google Scholar
- Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Wokingham, England: Addison-Wesley Publishing Company.Google Scholar
- Mason, J., & Davis, B. (2013). The Importance of Teachers’ Mathematical Awareness for In-the-Moment Pedagogy. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 182–197, doi: 10.1080/14926156.2013.784830.
- Mason, J., & Pimm, D. (1984). Generic example: Seeing the general in particular. Educational Studies in Mathematics, 15(3), 277–289.Google Scholar
- Perry, W. G. (1981). Cognitive and ethical growth: The making of meaning. In A. W. Chickering (Ed.), The modern American college (pp. 76–116). San Francisco: Jossey-Boss.Google Scholar
- Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8–27.Google Scholar
- Shinno, Y., Yanagimoto, T., & Uno, K. (This Volume). An investigation of prospective primary teachers’ argumentation: From the perspective of mathematical knowledge for teaching and evaluating. In 13th Conference of ICME: Monograph for TSG 47.Google Scholar
- Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
- Simon, M. (1994). Learning mathematics and learning to teach: Learning cycles in mathematics teacher education. Educational Studies in Mathematics, 26(1), 71–94, doi: 10.1007/BF01273301.
- Skemp, R. (1983). Lecture note in Taiwan. National Taiwan Normal University.Google Scholar
- Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Charlotte, NC: Information Age Publishers.Google Scholar
- Stylianides, G. J., & Stylianides, A. J. (2010). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education, 26(2), 161–172, doi:http://dx.doi.org/10.1016/j.tate.2009.03.022.
- Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: a design research study. Journal of Mathematics Teacher Education, 10(4), 217–237, doi: 10.1007/s10857-007-9038-8.
- Watson, A., & Mason, J. (2007). Taken-as-shared: a review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education, 10(4–6), 205–215, doi: 10.1007/s10857-007-9059-3.
- Wilson, S. M., Floden, R. E., & Ferrini-Mundy, J. (2001). Teachers preparation research: Current knowledge, gaps and recommendations. A research report prepared for the U.S. Department of Education. Seattle: Center for the Study of Teaching and Policy, University of Washington.Google Scholar
- Yang, K.-L., & Lin, F.-L. (2012). Effects of reading-oriented tasks on students’ reading comprehension of geometry proof. Mathematics Education Research Journal, 24(2), 215.Google Scholar