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The development of teachers’ expertise through their analysis of good practice in the mathematics classroom

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Abstract

This paper describes a study into the development of teachers’ expertise, conceptualised as enhanced understanding of practice. This enhancement is detected through various indicators of the teachers’ awareness of the complexity of the learning–teaching process, including purposes, beliefs, subject content, and connections between theory and practice. The study is guided by the search for evidence that discussion of what constitutes good teaching leads to a more complex understanding of practice. It starts with a description of the collaborative analysis of a mathematics lesson by a group of teachers, guided by exploring notions of good practice. From this analysis, the researchers extract evidence of improvements in understanding practice on the part of the teachers, in terms of the above indicators. We conclude that the process of characterising good practice in relation to actual samples of teaching can promote the development of teaching expertise. We also note that, in order to analyse practice, teachers require accessible theoretical tools, which allow reflection to go beyond the specifics of a particular lesson.

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Notes

  1. Spanish ‘Proyecto de Investigación Colaborativo’: Collaborative Research Project.

  2. Nevertheless, we would claim an improvement in teachers’ knowledge. A different issue is how this knowledge is acquired or built. Perspectives suggesting that better knowledge implies better understanding (and vice versa) of the situation are overly simplistic. However, the importance of teachers’ knowledge and the need to improve it has been recently emphasised, in particular, in respect of mathematics knowledge for teaching (Ball et al., 2008). The development of teacher’s expertise must include the improvement of this knowledge. For example, understanding situations about learning difficulties on the concept of polygon has its impact on Ball et al.’s sub-domain of knowledge of mathematics and students, but, at the same time, this knowledge helps understand those situations. This perspective resonates with one of the modes highlighted for teacher’s expertise by Russ et al. (2011), that of the mathematics teacher as diagnostician.

  3. In Spain, a nursery teacher gives classes to children aged from 3 to 5 years. These teachers follow the same university training courses as primary teachers, with appropriate specialisations, and likewise go through the same selection process to enter the state system. All the primary schools offer these educational levels. The old kindergartens do not offer these levels any more.

  4. In Muñoz-Catalán et al. (2010) we deal with the role of interactions between the PIC members.

  5. Contributions by the researchers are labelled R1 and R2 (the novice researcher was unable to attend these PIC sessions); those of the teachers are labelled A, B, C (for Carmen) and so on.

  6. Given that teacher reflection on practice is an inherent feature of the PIC sessions, we have chosen not to highlight the corresponding indicator 8 (The teacher reflects on their classroom performance).

  7. See the indicators of improvement in understanding of practice in Sect. 2.

Abbreviations

PIC:

Proyecto de Investigación Colaborativa (Collaborative Research Project)

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Acknowledgments

This research is financially supported by the research Projects SEJ2007-6011/EDUC (Multiculturality and Mathematics: towards the inclusion of minor cultural groups), and EDU2009-09789EDUC (Mathematics knowledge for teaching with respect to problem solving and reasoning).

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Authors and Affiliations

  1. Department of Science Education, University of Huelva, Campus El Carmen, Avda. 3 de Marzo, s/n, 21007, Huelva, Spain

    José Carrillo & Nuria Climent

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  1. José Carrillo
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  2. Nuria Climent
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Correspondence to José Carrillo.

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Carrillo, J., Climent, N. The development of teachers’ expertise through their analysis of good practice in the mathematics classroom. ZDM Mathematics Education 43, 915–926 (2011). https://doi.org/10.1007/s11858-011-0363-0

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