Differentiation from an Advanced Standpoint: Outcomes of Mathematics Teachers’ Action Research Studies Aimed at Raising Attainment
Keywords:differentiation from an advanced standpoint, mathematics teacher-research, low prior attainment, action research, enactivism
In this article we propose the notion of differentiation from an advanced standpoint as a teaching strategy, particularly valuable for working with students with low prior attainment. The notion arose from an enactivist analysis of the work of three teachers, engaged in action research in their own classrooms. All three teachers chose to teach their students (who were aged 15-16) topics that are usually only offered to those with relatively high prior attainment in mathematics. No intermediate or bridging topics were offered, instead, these teachers found ways to differentiate work for their classes, from this advanced standpoint. There is tentative evidence of students experiencing their relationship to mathematics in new ways, recognising they were doing “A-grade” work, and of gains in their attainment. There is also evidence of the teachers’ own surprise at what their students could achieve.
Altrichter, H., Posch, P., & Somekh, B. (1993). Teachers investigate their work: An introduction to the methods of action research. Routledge.
Barclay, N. (2021). Valid and valuable: Lower attaining pupils’ contributions to mixed attainment mathematics in primary schools. Research in Mathematics Education. https://doi.org/10.1080/14794802.2021.1897035
Bateson, G. (2000). Steps to an ecology of mind. University of Chicago Press.
Bateson, G. (2002). Mind and nature: A necessary unity. Hampton Press.
Boaler, J. (2002) Open and closed mathematics approaches. In L. Haggarty (Ed.), Teaching mathematics in secondary schools (pp. 99–112). Routledge.
Brown, L. (2015). Researching as an enactivist mathematics education researcher. ZDM Mathematics Education, 47(2), 185–196. https://doi.org/10.1007/s11858-015-0686-3
Brown, L., & Coles, A. (2011). Developing expertise: How enactivism re-frames mathematics teacher development. ZDM Mathematics Education 43, 861–873. https://doi.org/10.1007/s11858-011-0343-4
Brown, L., & Dobson, A. (1996). Using dissonance: Finding the grit in the oyster. In T. Atkinson, G. Claxton, M. Osborn, & M. Wallace, (Eds), Liberating the learner: Lessons for professional development in education (pp. 212–227). Routledge.
Brown, L., & Waddingham, J. (1982). An addendum to Cockcroft. Resources for Learning Development Unit (RLDU). https://www.stem.org.uk/resources/elibrary/resource/31296/addendum-cockcroft
Cockcroft, W.H. (1982). Mathematics counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the Chairmanship of Dr W.H. Cockcroft. HMSO, http://www.educationengland.org.uk/documents/cockcroft/cockcroft1982.html
Coles, A. (2015). On enactivism and language: Towards a methodology for studying talk in mathematics classrooms. ZDM Mathematics Education 47(2), 235–246. https://doi.org/ 10.1007/s11858-014-0630-y
Department for Education (2013). Mathematics programmes of study: Key stages 1 and 2. Crown Copyright, https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
Department of Education and Science (1985). Mathematics from 5 to 16: HMI Series: Curriculum Matters 3. Her Majesty’s Stationery Office, http://www.educationengland.org.uk/documents/cockcroft/cockcroft1982.html
Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics, 12, 133-150.
Krainer, K. (2011). Teachers as stakeholders in mathematics education research. In B. Ubuz (Ed.), Proceedings of the thirty-fifth conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 47–62). PME 35.
Maturana, H., & Varela, F. (1987). The tree of knowledge: The biological roots of human understanding. Shambhala.
Rittle-Johnson, B., Siegler, S., & Alibali, M. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93(2), 346–362.
Sullivan, P., Bobis, J., Downton, A., Livy, S., Hughes, S., McCormick, M., & Russo, J. (2020). Ways that relentless consistency and task variation contribute to teacher and student mathematics learning. For the Learning of Mathematics Monograph 1, 32–37.
Sutherland, R. (2014). Education and social justice in a digital age. Policy Press.
Taylor, B., Francis, B., Archer, L., Hodgen, J., Pepper, D., Tereshchenko, A., & Travers, M.C. (2017). Factors deterring schools from mixed attainment teaching practice. Pedagogy, Culture & Society, 25(3), 327–345. https://doi.org/10.1080/14681366. 2016.1256908
Taylor, B., Hodgen, J., Tereshchenko, A., & Gutierrez, G. (2020). Attainment grouping in English secondary schools: A national survey of current practices, Research Papers in Education. https://doi.org/10.1080/02671522.2020.1836517
von Bertalanffy, L. (2015). General system theory: Foundations, development, applications. George Braziller.
Walkerdine, V. (2011). Neoliberalism, working class subjects and higher education. Contemporary Social Science 6(2), 255–271.
Watson, A. (2008). Adolescent learning and secondary mathematics. In P. Liljedahl, S. Oesterle, & C. Bernoche (Eds.), Proceedings of the 2008 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 21-29). Universite de Sherbrooke.