Self-study of a Mathematics Learning Consultant: Supporting Teachers to Plan Lessons for Implementing Differentiation in the Classroom
Keywords:
self study . differentiation . school mathematics leader . teacher knowledge . primaryAbstract
There is widespread belief that addressing differentiation within classroom practice is critical for school improvement in mathematics. School mathematics leaders and consultants are faced with the challenge of interpreting the various models of differentiation that are presented throughout professional learning programs and aligning these with existing beliefs and cultures within schools. This paper reports on a self-study of a learning consultant who supported primary mathematics teachers to plan lessons for implementing differentiation in their classrooms and aims to highlight the Mathematical Knowledge for Teaching (MKT) required to lead such planning sessions. Over three weeks, a mathematics consultant assisted teaching teams across three different schools by facilitating planning meetings. The consultant recorded self-reflections after each session and the qualitative data were coded to identify the categories of MKT the consultant relied on during her interactions with teachers. Overall, the results highlight the dominance of three categories, Knowledge of content and students (KCS), Knowledge of content and teaching (KCT) and Specialised content knowledge (SCK) emphasised by the consultant, as well as the influence different contexts had in developing a shared understanding of differentiated learning in mathematics. The findings have implications for ways in which schools and facilitators develop strategies that comprehensively support teachers to plan suitable differentiated lessons for their students. Furthermore, this study highlights the need to develop greater understanding around models of planning that adequately support teachers to plan effectively for differentiating instruction in mathematics.
References
Anthony, G., & Hunter, R. (2017). Grouping practices in New Zealand mathematics classrooms: Where are we at and where should we be? New Zealand Journal of Educational Studies, 52, 73-92. https://doi.org/10.1007/s40841-016-0054-z
Askew, M. (2015). Diversity, inclusion and equity in mathematics classrooms: From individual problems to collective possibilities. In A.
Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 129 -146). https://doi.org/10.1007/978-3-319-05978-5_8
Ball, D. L., Hill, H. C., Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-17, 20-22, 43-46. https://deepblue.lib.umich.edu/handle/2027.42/65072
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. https://doi.org/10.1177/0022487108324554
Beswick, K., & Chapman, O. (2015). Mathematics teacher educators’ knowledge for teaching. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematics Education: Intellectual and attitudinal challenges (pp. 629–633). Springer. https://doi.org/10.1007/978-3-319-12688-3
Beswick, K., Anderson, J., & Hurst, C. (2016). The education and development of practising teachers. In K. Maker, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012-2015 (pp. 329 – 352). Springer. https://doi.org/10.1007/978-981-10-1419-2
Boaler, J. (2012). From psychological imprisonment to intellectual freedom- the different roles that school mathematics can take in student’s lives. Paper presented at the 12th International Congress on Mathematics Education Korea. https://www.youcubed.org/wp-content/uploads/intellectualfreedom.pdf
Brown, L., & Coles, A. (2010). Mathematics teacher and mathematics teacher educator change: Insight through theoretical perspectives. Journal of Mathematics Teacher Education, 13, 375 – 382. https://doi.org/10.1007/s10857-010-9159-3
Cheeseman, J., & Klooger, M. (2018). Mathematics teachers: Dealing with difference. Australian Primary Mathematics Classroom, 23(3), 27-29. https://files.eric.ed.gov/fulltext/EJ1231210.pdf
Chick, H., & Beswick, K. (2018). Teaching teachers to teach Boris: A framework for mathematics teacher educator pedagogical content knowledge. Journal of Mathematics Teacher Education, 21, 475 – 499. http://doi.org/10.1007/s10857-016-9362-y
Cobb, P., & Jackson, K. (2015). Supporting teachers’ use of research-based instructional sequences. ZDM Mathematics Education, 47, 1027-1038. https://doi.org/10.1007/s11858-015-0692-5
Dack, H., O’Reilly, N., Youngs, P., & Hopper, E. (2019). Visions of differentiation: A longitudinal multicase study of preservice and beginning elementary teachers. The Elementary School Journal, 120(1), 132-175. https://doi.org/10.1086/704252
Hackenburg, A. J., Creager, M., & Eker, A. (2020). Teaching practices for differentiating mathematics instruction for middle school students. Mathematical Thinking and Learning, 23(2), 95-124. https://doi.org/10.1080/10986065.2020.1731656
Hill, H. C., Blunk, M. L., Charalambos, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430 – 511. https://doi.org/10.1080/07370000802177235
Hopkins, S. (2011). Understanding and supporting numeracy competence. In P. Foreman & A. Kelly (Eds.), Inclusion in action (3rd ed., pp. 356-399). Cengage Learning Australia.
Lambert, R. (2015). Constructing and resisting disability in mathematics classrooms: A case study exploring the impact of different pedagogies. Educational Studies in Mathematics, 89, 1-18. https://doi.org/10.1007/s10649-014-9587-6
Livy, S., & Vale, C. (2011). First year pre-service teachers’ mathematical content knowledge: Methods of solution to a ratio question. Mathematics Teacher Education and Development, 13(2), 22-44. http://dro.deakin.edu.au/view/DU:30044057
Loughran, J. (2007). Researching teacher education practices: Responding to the challenges, demands, and expectations of self-study. Journal of Teacher Education, 58(1), 12 – 20. https://doi.org/10.1177/0022487106296217
Loughran, J. (2014). Professionally developing as a teacher educator. Journal of Teacher Education, 65(4), 271-283. https://doi.org/10.1177/0022487114533386
Lynch. S. D., Hunt, J. H., & Lewis, K. E. (2018). Productive struggle for all: Differentiated instruction. Mathematics Teaching in the Middle School, 23(4), 194 – 201. https://doi.org/10.5951/mathteacmiddscho.23.4.0194
Marks, R. (2013). The blue table means you don’t have a clue: The persistence of fixed-ability thinking and practices in primary mathematics in English schools. Forum, 55(1), 31-44. https://doi.org/10.2304/forum.2013.55.1.31
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. https://doi.org/10.1080/14926156.2013.784830
Mills, M., Keddie, A., Renshaw P., & Monk, S. (2017). The politics of differentiation in schools. Routledge.
Maulana, R., Smale-Jacobse, A., Helms-Lorenz, M., Chun, S., & Lee, O. (2020). Measuring differentiated instruction in The Netherlands and South Korea: Factor structure equivalence, correlates, and complexity level. European Journal of Psychology of Education, 35(4), 881-909. https://doi.org/10.1007/s10212-019-00446-4
Prescott, A. (2011). Are we singing from the same songbook? In S.
Schuck & P. Pereira (Eds.), What counts in teaching mathematics: Self study of teaching and teacher education practices (Vol. 11, pp. 161 – 176). https://doi.org/10.1007/978-94-007-0461-9_6
Reeve, J., & Halusic, M. (2009). How K-12 teachers can put self-determination theory principles into practice. Theory and Research in Education, 7(2), 145 –154. https://doi.org/10.1177/1477878509104319
Roche, A., Clarke, D. M., Clarke, D. J., & Chan, M. C. E. (2016). Learning from lessons: Teachers’ insights about intended actions arising from their learning about student thinking. In B. White, M. Chinnapan, & S. Trenholm (Eds.), Opening up mathematics education research: Proceedings of the 39th annual conference in Mathematics Education Research Group of Australasia (pp. 560–567). MERGA. https://files.eric.ed.gov/fulltext/ED572349.pdf
Ross V., & Chan, E. (2016). Personal practical knowledge of teacher educators. In J. Loughran, & M. L. Hamilton (Eds.), International handbook of teacher education, (Vol. 2, pp. 3 – 34). Springer. https://doi.org/10.1007/978-981-10-0369-1
Samaras, A. (2011). Self-study teacher research: improving your practice through collaborative inquiry. SAGE.
Smith, M. S., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematical discussions (2nd ed.). National Council of Teacher of Mathematics.
Shulman, L. S. (1987). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 – 14. https://doi.org/10.3102/0013189X015002004
Sullivan, P. (2011). Australian Education Review: Teaching mathematics: Using research informed strategies. ACER Press.
Sullivan, P. (2015). Maximising opportunities in mathematics for all students: Addressing within- school and within-class differences. In A. Bishop, H. Tan, & T.N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 239-254). https://doi.org/10.1007/978-3-319-05978-5_14
Sullivan, P. (2020). Leading improvement in mathematics teaching and learning. ACER Press.
Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18, 123–140. https://doi.org/10.1007/s10857-014-9279-2
Sullivan, P., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Russo, J. (2020). Ways that relentless consistency and task variation contribute to teacher and student mathematics learning. In A. Coles (Ed.), For the Learning of Mathematics: Proceedings of a symposium of learning in honour of Laurinda Brown: Monograph 1 (1st ed., pp. 32-37). FLM Publishing Association.
Sullivan, P., & Mornane, A. (2014). Exploring teachers’ use of, and students’ reactions to challenging mathematics tasks. Mathematics Education Research Journal, 26, 193 – 213. https://doi.org/10.1007/s13394-013-0089-0
Sullivan, P., Mousley, J., & Jorgensen, R. (2009). Tasks and pedagogies that facilitate mathematical problem solving. In B. Kaur, Y. B. Har, & M. Kapur (Eds.), Mathematical problem solving (pp. 17-42). World Scientific Publishing. https://doi.org/10.1142/9789814277228_0002
Tomlinson, C. A. (1999). The differentiated classroom: Responding to the needs of all learners. Association for Supervision and Curriculum Development.
Tomlinson, C. A., & Imbeau, M. B. (2010). Leading and managing a differentiated classroom. ASCD.
van der Lans, R. M., van de Grift, W. J. C. M., & van Veen, K. (2018). Developing an instrument for teacher feedback: Using the Rasch model to explore teachers' development of effective teaching strategies and behaviors. The Journal of Experimental Education, 86(2), 247-264. https://doi.org/10.1080/00220973.2016.1268086
van Geel, M., Keuning, K., Frèrejean, J., Dolmans, D., van Merriënboer, J., & Visscher, A.J. (2019) Capturing the complexity of differentiated instruction, School Effectiveness and School Improvement, 30(1), 51-67. https://doi.org/10.1080/09243453.2018.1539013
Warshauer, H. K. (2015) Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18, 375-400. https://doi.org/10.1007/s10857-014-9286-3