ABSTRACT
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews, P. (2007). Mathematics teacher typologies or nationally located patterns of behaviour? International Journal of Educational Research, 46, 306–318.
Askew, M., Hodgen, J., Hossain, S. & Bretscher, N. (2010). Values and variables: Mathematics education in high-performing countries. London: Nuffield Foundation.
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.
Biggs, J. & Collis, K. (1982). Evaluating the quality of learning: the SOLO taxonomy. New York: Academic Press.
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.
Boaler, J., Wiliam, D. & Brown, M. (2000). Students’ experiences of ability grouping—disaffection, polarisation and the construction of failure. British Educational Research Journal, 26, 631–648.
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.
Dorman, J., Adams, J. & Ferguson, J. (2002). Psychosocial environment and student self-handicapping in secondary school mathematics classes: A cross-national study. Educational Psychology, 22, 499–511.
Greeno, J. (1994). Gibson’s affordances. Psychological Review, 101, 336–342.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Abingdon, UK: Routledge.
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.
Ireson, J., Hallam, S. & Plewis, I. (2001). Ability grouping in secondary schools: Effects on pupils’ self-concepts. British Journal of Educational Psychology, 71, 315–326.
Krainer, K. (2005). What is ‘good’ mathematics teaching, and how can research inform practice and policy? Journal of Mathematics Teacher Education, 8, 75–81.
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.
Lincoln, Y. & Guba, E. (1985). Naturalistic inquiry. Thousand Oaks, CA: Sage.
Marton, F. & Tsui, A. (2004). Classroom discourse and the space of learning. Mahwah, NJ: Lawrence Erlbaum Associates.
Mason, J., Graham, A. & Johnston-Wilder, S. (2005). Developing thinking in algebra. London: Paul Chapman.
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.
Nardi, E. & Steward, S. (2003). Is mathematics T.I.R.E.D.? A profile of quiet disaffection in the secondary mathematics classroom. British Educational Research Journal, 29, 345–367.
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.
Pietch, J., Walker, R. & Chapman, E. (2003). The relationship among self-concept, self-efficacy, and performance in mathematics during secondary school. Journal of Educational Psychology, 95, 589–603.
Sternberg, R. (1986). Toward a unified theory of human reasoning. Intelligence, 10, 281–314.
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.
Watson, A. (2007). The nature of participation afforded by tasks, questions and prompts in mathematics classrooms. Research in Mathematics Education 9 (111–126).
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.
Watson, A. & Mason, J. (2005). Mathematics as a Constructive Activity: Learners Generating Examples, Mahwah, NJ: Lawrence Erlbaum Associates.
Wiliam, D., Brown, M. & Boaler, J. (1999). ‘We’ve still got to learn’: Low attainers’ experiences of setting. Equals, 5, 15–18.
Wilson, P., Cooney, T. & Stinson, D. (2005). What constitutes good mathematics teaching and how it develops: Nine high school teachers’ perspectives. Journal of Mathematics Teacher Education, 8, 83–111.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Watson, A., De Geest, E. LEARNING COHERENT MATHEMATICS THROUGH SEQUENCES OF MICROTASKS: MAKING A DIFFERENCE FOR SECONDARY LEARNERS. Int J of Sci and Math Educ 10, 213–235 (2012). https://doi.org/10.1007/s10763-011-9290-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10763-011-9290-3