LEARNING COHERENT MATHEMATICS THROUGH SEQUENCES OF MICROTASKS: MAKING A DIFFERENCE FOR SECONDARY LEARNERS
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We report on the work of 3 schools which set out to make a difference for their previously low-attaining students. Through naturalistic enquiry over 3 years, we built a picture of their practices. Against a national trend, students reported positive attitudes to mathematics and, in 2 out of 3 schools, showed improvement in attainment, so we probe more deeply into the teaching. The lessons broadly conformed to an approach combining inclusive participation with complex and coherent development of mathematical ideas. To understand how the teachers orchestrated this, we developed lesson analysis techniques that focus on how thinking, repertoire and understanding are scaffolded by teachers through sequences of microtasks.
KEY WORDSimproving mathematics learning lesson analysis low-attaining students mathematical coherence scaffolding tasks
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- Askew, M., Hodgen, J., Hossain, S. & Bretscher, N. (2010). Values and variables: Mathematics education in high-performing countries. London: Nuffield Foundation.Google Scholar
- Beswick, K., Watson, A. & De Geest, E. (2010). Comparing theoretical perspectives for describing mathematics departments: Complexity and activity. Educational studies in mathematics, 75(2), 153–170.Google Scholar
- Biggs, J. & Collis, K. (1982). Evaluating the quality of learning: the SOLO taxonomy. New York: Academic Press.Google Scholar
- Boaler, J. & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th Annual meeting of the North American International Group for the Psychology of Mathematics Education (pp. 773–781). Toronto, Japan: University of Toronto.Google Scholar
- Brown, M., Brown, P. & Bibby, T. (2007). “I would rather die”: Attitudes of 16-year-olds towards their future participation in mathematics. Paper presented at annual conference of British Educational Research Association. Available from http://www.lancs.ac.uk/fass/events/mathematicalrelationships/comments/documents/Margaret%20BERA%202007.doc. Accessed 25 Nov 2009.
- Day, C., Sammons, P. & Kington, A. (2008). Effective classroom practice: A mixed method study of influences and outcomes: Full research report, ESRC End of Award Report, RES-000-23-1564. Swindon, UK: ESRC.Google Scholar
- Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Abingdon, UK: Routledge.Google Scholar
- Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study (NCES 2003–013). Washington, DC: U.S. Department of Education, National Center for Education Statistics.Google Scholar
- Leinhardt, G. (1988). Expertise in instructional lessons: An example from fractions. In D. Grouws, T. Cooney & D. Jones (Eds.), Perspectives on research on effective mathematics teaching (pp. 47–66). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Lincoln, Y. & Guba, E. (1985). Naturalistic inquiry. Thousand Oaks, CA: Sage.Google Scholar
- Marton, F. & Tsui, A. (2004). Classroom discourse and the space of learning. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Mason, J., Graham, A. & Johnston-Wilder, S. (2005). Developing thinking in algebra. London: Paul Chapman.Google Scholar
- Mullis, I., Martin, M. & Foy, P. (2008). TIMSS 2007 international mathematics report: Findings from IEA’s trends in International Mathematics and Science Study at the Fourth and Eighth Grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.Google Scholar
- Ofsted (2005). Mathematics in secondary schools 2003/4. Available from www.ofsted.gov.uk/publications/annualreport0304/subject_reports/secondary/maths.htm. Accessed 25 Nov 2009.
- Sturman, L., Ruddock, G., Burge, B., Styles, B., Lin, Y. & Vappula, H. (2008). England’s achievement in TIMSS 2007: National report for England. Slough, UK: NFER.Google Scholar
- Watson, A. (2007). The nature of participation afforded by tasks, questions and prompts in mathematics classrooms. Research in Mathematics Education 9 (111–126).Google Scholar
- Watson, A. & De Geest, E. (2005). Principled Teaching for Deep Progress: Improving Mathematical Learning Beyond Methods and Materials. Educational Studies in Mathematics, 58, 209–234.Google Scholar
- Watson, A. & Mason, J. (2005). Mathematics as a Constructive Activity: Learners Generating Examples, Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Wiliam, D., Brown, M. & Boaler, J. (1999). ‘We’ve still got to learn’: Low attainers’ experiences of setting. Equals, 5, 15–18.Google Scholar