Prospective elementary teachers' experiences with and perspectives on grouping by ability in mathematics

Corey M Webel, Amy Dwiggins

Abstract


Within-class ability grouping (WCAG) is widely used in elementary mathematics instruction in the United States, yet it has drawn criticism on the grounds that it can inequitably limit the learning opportunities of some students, not least because of its connection to between-class ability grouping (BCAG) that is more common in middle or secondary schooling. Meanwhile, some high achieving countries use relatively little ability grouping in elementary school in comparison to the United States. In this paper, we draw on qualitative data from a series of assignments in four sections of an elementary mathematics methods course in the beginning teacher education programme at a United States university. These assignments were designed to explore the potential of using preservice teachers' (PSTs') memories of and experiences with ability grouping in their own schooling to support critical reflection about the possible negative consequences of within-class ability grouping practices. We found that while many PSTs reported negative personal experiences with ability grouping in mathematics, they often remained uncritical when reflecting on the use of ability grouping in the elementary classes they visited as part of their teacher education programme.


Keywords


teacher education; elementary; ability grouping; tracking; cognitive conflict

References


Aguirre, J., Mayfield-Ingram, K., & Martin, D. B. (2013). The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices. Reston, VA: National Council of Teachers of Mathematics.

Arbaugh, F., Lannin, J., Jones, D. L., & Park-Rogers, M. (2006). Examining instructional practices in Core-Plus lessons: Implications for professional development. Journal of Mathematics Teacher Education, 6, 517-550.

Archer, L., Francis, B., Miller, S., Taylor, B., Tereshchenko, A., Mazenod, A., . . . Travers, M.-C. (2018). The symbolic violence of setting: A Bourdieusian analysis of mixed methods data on secondary students' views about setting. British Educational Research Journal, 44(1), 119-140.

Association of Mathematics Teacher Educators. (2017). Standards for Preparing Teachers of Mathematics. Retrieved from amte.net/standards

Battey, D., Llamas-Flores, S., Burke, M., Guerra, P., Kang, H. J., & Kim, S. H. (2013). ELL policy and mathematics professional development colliding: Placing teacher experimentation within a sociopolitical context. Teachers College Record, 115(6), 1-44.

Belfi, B., Goos, M., De Fraine, B., & Van Damme, J. (2012). The effect of class composition by gender and ability on secondary school students' school well-being and academic self-concept: A literature review. Educational Research Review, 7, 62-74.

Boaler, J. (2008). What's math got to do with it? How parents and teachers can help children learn to love their least favorite subject: Penguin Books.

Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645.

Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43(1), 105-136.

Chiu, D., Beru, Y., Watley, E., Wubu, S., & Simson, E. (2008). Influence of math tracking on seventh-grade students' self-beliefs and social comparisons. The Journal of Educational Research, 102(2), 125-135.

Crespo, S. (2016). Why are you asking for these impossible math lessons? In D. Y. White, S. Crespo, & M. Civil (Eds.), Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (pp. 63-70). Charlotte, NC: Information Age Publishing.

Dunne, M., Humphreys, S., Dyson, A., Sebba, J., Gallannaugh, F., & Muijs, D. (2011). The teaching and learning of pupils in low-attainment sets. The Curriculum Journal, 22(4), 485-513.

Forgasz, H. (2010). Streaming for mathematics in Years 7-10 in Victoria: An issue of equity? Mathematics Education Research Journal, 22(1), 57-90.

Francis, B., Archer, L., Hodgen, J., Pepper, D., Taylor, B., & Travers, M.-C. (2017). Exploring the relative lack of impact of research on 'ability grouping' in England: a discourse analytic account. Cambridge Journal of Education, 47(1), 1-17.

Francis, B., Connolly, P., Hodgen, J., Mazenod, A., Pepper, D., Sloan, S., . . . Travers, M.-C. (2017). Attainment grouping as self-fulfilling prophesy? A mixed methods exploration of self confidence and set level among Year 7 students. International Journal of Educational Research, 86, 96-108.

Franke, M. (2016). Identifying and supporting the next small step together: A commentary on Crespo's case. In D. Y. White, S. Crespo, & M. Civil (Eds.), Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (pp. 71-74). Charlotte, NC: Information Age Publishing.

Gallagher, S., Smith, S. R., & Merrotsy, P. (2011). Teachers' perceptions of the socioemotional development of intellectually gifted primary aged students and their attitudes towards ability grouping and acceleration. Gifted and Talented International, 26(1), 11-24.

Gamoran, A. (1992). Is ability grouping equitable? Educational Leadership, 50(2), 11-17.

Givvin, K. B., Hiebert, J., Jacobs, J. K., Hollingsworth, H., & Gallimore, R. (2005). Are there national patterns of teaching? Evidence from the TIMSS 1999 video study. Comparative Education

Review, 49(3), 311-343.

Goffney, I., & Crespo, S. (2016). Conversations about inequities in mathematics methods courses. In D. Y. White, S. Crespo, & M. Civil (Eds.), Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms. Charlotte, NC: Information Age Publishing.

Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258-291.

Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2008). Constructing competence: An analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematics, 70, 49-70.

Haimes, D. (1999). Teachers' strategies for implementation of de-streaming in secondary mathematics classes. Mathematics Education Research Journal, 11(2), 94-108.

Herbel-Eisenmann, B., Bartell, T. G., Breyfogle, L., Bieda, K., Crespo, S., Dominguez, H., & Drake, C. (2013). Strong is the silence: Challenging interlocking systems of privilege and oppression in mathematics teacher education. Journal of Urban Mathematics Education, 6(1), 6-18.

Hiebert, J. (2013). The constantly underestimated challenge of improving mathematics instruction. In K. R. Leatham (Ed.), Vital Directions for Mathematics Education Research (pp. 45-56). New York: Springer.

Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester, Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Pub Inc.

Ireson, J., Hallam, S., & Hurley, C. (2007). What are the effects of ability grouping on GCSE attainment? British Educational Research Journal, 31(4), 443-458.

Jackson, C. (2016). Equitable mathematics teaching for all students: A commentary on Crespo's case In D. Y. White, S. Crespo, & M. Civil (Eds.), Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (pp. 75-78). Charlotte, NC: Information Age Publishing.

Johnston, O., & Wildy, H. (2016). The effects of streaming in the secondary school on learning outcomes for Australian students - A review of the international literature. Australian Journal of Education.

Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102(1), 59-80.

LeTendre, G. K., Hofer, B. K., & Shimizu, H. (2003). What is tracking? Cultural expectations in the United States, Germany, and Japan. American Educational Research Journal, 40(1), 43-89.

Linchevski, L., & Kutscher, B. (1998). Tell me with whom you're learning, and I'll tell you how much you've learned: Mixed-ability versus same-ability grouping in mathematics. Journal for Research in Mathematics Education, 29(5), 533-554.

Loveless, T. (2013). The 2013 Brown Center Report on American Education: How well are American students learning? (Vol. 3). Washington D.C.: The Brookings Institution.

Macqueen, S. E. (2010). Primary teachers attitudes in achievement-based literacy classes. Issues in Educational Research, 20(2), 118-136.

Macqueen, S. E. (2012). Academic outcomes from between-class achievement grouping: the Australian primary context. The Australian Educational Researchers, 39(1), 59-73.

Macqueen, S. E. (2013). Grouping for inequity. International Journal of Inclusive Education, 17(3), 295-309.

Moshman, D. (2005). Piaget's theory of formal operations. In Adolescent Psychological Development (pp. 3-15). Mahwah, NJ: Lawrence Erlbaum.

Mujis, D., & Dunne, M. (2010). Setting by ability--or is it? A quantitative study of determinants of set placement in English secondary schools. Educational Research, 52(4), 391-407. doi:10.1080/00131881.2010.524750

Munter, C., Stein, M. K., & Smith, M. S. (2015). Dialogic and direct instruction: Two distinct models of mathematics instruction and the debate(s) surrounding them. Teachers College Record, 117(11), 1-32.

Murata, A. (2013). Diversity and high academic expectations without tracking: Inclusively responsive instruction. Journal of the learning sciences, 22(2), 312-335.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

Neumayer-Depiper, J. (2013). Teacher identity work in mathematics teacher education. For the Learning of Mathematics, 33(1), 9-15.

Oakes, J. (2005). Keeping Track: How Schools Structure Inequality (2nd ed.): Yale University Press.

Shilling-Traina, L. N., & Stylianides, G. J. (2013). Impacting prospective teachers' beliefs about mathematics. ZDM Mathematics Education, 45(3), 393-407.

Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501-531.

Sleeter, C. E. (2001). Preparing teachers for culturally diverse schools: Research and the overwhelming presence of whiteness. Journal of Teacher Education, 52(2), 94-106.

Staples, M. (2008). Promoting student collaboration in a detracked, heterogenous secondary mathematics classroom. Journal of Mathematics Teacher Education, 11, 349-371.

Stinson, D. W. (2016). Turning disappointing student emails into teachable moments: A commentary on Crespo's case. In D. Y. White, S. Crespo, & M. Civil (Eds.), Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (pp. 79-83). Charlotte, NC: Information Age Publishing.

Stoehr, K. J. (2017). Building the wall brick by brick: one prospective teacher's experiences with mathematics anxiety. Journal of Mathematics Teacher Education, 20(2), 119-139.

Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40(3), 314-352.

Turner, E., Drake, C., Roth McDuffie, A., Aguirre, J., Bartell, T. G., & Foote, M. Q. (2012). Promoting equity in mathematics teacher preparation: a framework for advancing teacher learning of children's multiple mathematics knowledge bases. Journal of Mathematics Teacher Education, 15, 67-82.

Welder, R. M., & Champion, J. (2011). Toward an understanding of graduate preservice elementary teachers as adult learners of mathematics. Adults Learning Mathematics: An International Journal, 6(1), 20-40.

White, D. Y., Crespo, S., & Civil, M. (Eds.). (2016). Cases for mathematics teacher educators: Facilitating conversations about inequities in mathematics classrooms (Vol. 1). Charlotte, NC: Information Age Publishing.

Zevenberger, R. (2005). The construction of a mathematical habitus: Implications of ability grouping in the middle years. Journal of Curriculum Studies, 37(5), 607-619.


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