The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks
 Jeffrey Choppin
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This study explores the extent to which a teacher elicited students’ mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher’s knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher’s reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students’ ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.
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 Title
 The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks
 Journal

Mathematics Education Research Journal
Volume 23, Issue 1 , pp 525
 Cover Date
 20110301
 DOI
 10.1007/s1339401100018
 Print ISSN
 10332170
 Online ISSN
 2211050X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Curriculum
 Local theory
 Challenging tasks
 Teacher knowledge
 Instructional practices
 Authors

 Jeffrey Choppin ^{(1)}
 Author Affiliations

 1. Department of Teaching and Curriculum, The University of Rochester, Dewey Hall 1160K, Box 270425, Rochester, NY, 14627, USA