Session Information
04 SES 04 B, Didactics
Paper Session
Contribution
This paper presents the findings of a study funded by the Esmée Fairbairn Foundation under the New Approaches to Learning strand, Grant Reference Number 08-3662.
The purpose of the research was to study the effects of developing a particular pedagogy in numeracy with mainstream primary teachers. The specific focus was on determining change in teachers’ knowledge and beliefs and the implications this had on practice in supporting all learners in learning mathematics. The programme developed was Cognitively Guided Instruction (CGI) (Carpenter et al., 1999), a research-based programme developed over twenty years at the University of Wisconsin-Madison (Carpenter et al., 2000). CGI is recognised as an emerging and effective pedagogy in the United States. This study represents the first time that CGI has been developed with a group mainstream primary teachers in the UK.
CGI is underpinned by a constructivist philosophy. It involves supporting teachers in building a deep knowledge of children’s mathematical thinking so that this knowledge can be applied to practice in order to support mathematical learning as a sense-making process for all children. In the classroom it involves children investigating mathematical problems, teachers then using their knowledge of children’s solution strategies to inform their teaching.
Inclusive pedagogy has been described as,
‘a collaborative approach to teaching based on the idea … that
participation in learning requires responses to individual differences
among learners that do not depend on ability labelling or grouping’
(McIntyre, 2009, p.603).
It has been argued that this response to individual difference does not imply a unique body of pedagogical knowledge required by teachers to support struggling learners (Florian & Rouse, 2009; Norwich & Kelly, 2005). This argument maintains that the interpretation of children’s understanding is a crucial element in developing inclusive practices, the application of this knowledge being more useful than the identification of learner deficits in themselves, a view that has been represented in the domain of literacy (Elliot & Gibbs, 2008). In mathematics education the proposition that knowledge of children’s mathematical thinking should inform instruction is well-established (Carpenter, et al. 1999; Franke & Kazemi, 2001; Yackel & Cobb, 1996). For children who struggle in their learning, a knowledgeable and informed response at the level of the individual is required (Stough & Palmer, 2003).
CGI provided a framework for the professional development of a group of Scottish primary school teachers. Following this professional development teachers were observed in practice and interviewed to determine any knowledge growth and changes in beliefs regarding their capacity to support all learners in their mathematical learning. This analysis was informed by the concept of pedagogical content knowledge (Shulman,1986) and Askew et als.’ (1997, p.24) framework that recognises the complex interplay between teachers’ beliefs, knowledge and classroom practices and pupils’ responses.
Aims of the study
- To introduce a group of mainstream primary teachers to the principles of Cognitively Guided Instruction.
- To determine the nature of teachers’ learning resulting from this professional development in terms of knowledge and beliefs and how these translate into practice in supporting all pupils.
Method
Expected Outcomes
References
Askew, M., Brown, M., Rhodes, V., Johnson, D. & Wiliam, D. (1997). Effective teachers of numeracy – Final report: report of a study carried out for the Teacher Training Agency1995-1996 by the School of Education, King’s College London. London: King’s College. Carpenter, T.P, Fenema, E., Franke, M.L., Levi, L. & Empson, S.B. (2000). Cognitively guided instruction- A research based teacher development program for elementary school mathematics, Report No. 003. National Center for Improving Student Learning and Achievement in Mathematics and Science. University of Wisconsin available at www.wcer.edu/ncisla Carpenter, T.P, Fenema, E., Franke, M. L., Levi, L. & Empson, S.B. (1999). Children’s mathematics – Cognitively guided instruction. Portsmouth, NH: Heinemann. Elliot, J.G. & Gibbs, S. (2008). Does dyslexia exist? Journal of Philosophy in Education, 42, (3-4),475-491. Florian, L. & Rouse, M. (2009). The inclusive practice project in Scotland: Teacher education for inclusive education. Teaching and teacher education, (25), 594-601. Franke, M. L. & Kazemi, E. (2001). Learning to teach mathematics: Focus on student thinking. Theory into Practice, 40, (2), 102-109. McIntyre, D. (2009). The difficulties of inclusive pedagogy for initial teacher education and some thoughts on the way forward. Teaching and Teacher Education, (25), 602-608. Norwich, B. & Kelly, N. (2005). Moderate learning difficulties and the future of inclusion. London: Routledge-Falmer. Ritchie ,J. & Lewis, J. (Eds.) Qualitative research practice- A guide for social science students and researchers. London: Sage. Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching, Harvard Educational Researcher, 15 (2), 4-14. Stough, L.M. & Palmer, D.J. (2003). Special thinking in special settings: A qualitative study of expert special educators. Journal of Special Education,36, (4), 206-222. Yackel, E. & Cobb, P. (1996) Socio-mathematical norms, argumentation and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.
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