Abstract
While development of a teacher’s expertise includes continuous incorporation of innovations throughout his/her career, teachers are often reluctant to adopt and implement new practices when challenged by innovative teaching approaches. This paper presents an analysis of the development of teachers’ expertise in relation to the implementation of novel (for them) instructional material. The study examines the ways in which teachers implement multiple-solution tasks (MSTs) (as an example of instructional tools new to the teacher) in their classes, following a professional development course in which they participated. The analysis focuses on the nature of MSTs implemented by the teachers and of the subsequent class discussion. The nature of MSTs is analyzed focusing on the goals with which MSTs were implemented, mathematical connections embedded in the MSTs, scaffolding provided to the learners and the learning settings. This analysis has led to the identification of four main implementation styles: straightforward, simple, adaptive and inventive. Concluding discussions are examined with respect to elevating and framing elements. Two lessons by mathematics teachers are described in the paper to explain how lessons were analyzed, and to exemplify adaptive and inventive implementation styles.
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Notes
Proof is a concrete type of a problem solution when the problem requires proving (see Fig. 1).
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Acknowledgments
This research was made possible by Grant #891/03 from the Israel Science Foundation. I wish to thank Irena Gurevich for her assistance in data collection and Anat Levav-Waynberg for her meaningful contribution to the data analysis. I am indebted to the teachers who participated in the study for their collaboration and goodwill.
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Leikin, R. Multiple-solution tasks: from a teacher education course to teacher practice. ZDM Mathematics Education 43, 993–1006 (2011). https://doi.org/10.1007/s11858-011-0342-5
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DOI: https://doi.org/10.1007/s11858-011-0342-5