Understanding how students reason with logical implication is essential for supporting students’ construction of increasingly powerful ways of reasoning in proofs-based mathematics courses. We report on the results of an NSF-funded case study with a mathematics major enrolled in an introductory proofs course. We investigate the epistemological obstacles that she experienced and how they might relate to her treatment of logical implications as actions. Evidence shows that an action conception may pose challenges when students transform or quantify implications and may contribute to erroneous assumptions of biconditionality. Our report on available ways of operating with logical implications as actions is a first step in designing instructional tasks that leverage students’ existing reasoning skills to support their continued development.
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Secondary Mathematics Teachers’ Anticipations of Student Responses to Cognitively Demanding Tasks
This study examines secondary mathematics teachers’ anticipations of student responses related to a series of cognitively demanding mathematics tasks from multiple mathematical domains presented in the context of voluntary and asynchronous online professional development modules. We analyze 283 anticipations made by 127 teachers to 17 mathematics tasks and present four distinct foci of teachers’ anticipations. Teachers focused on actions students might take, ways they might think about the task, how they might react emotionally, and what actions they might take in advance or in response to their anticipations. We conclude with a discussion of ways our results can inform efforts to support improvements in mathematics teachers’ practice of anticipating.
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- Award ID(s):
- 2100903
- PAR ID:
- 10517918
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Investigations in Mathematics Learning
- Volume:
- 16
- Issue:
- 2
- ISSN:
- 1947-7503
- Page Range / eLocation ID:
- 65 to 82
- Subject(s) / Keyword(s):
- Secondary mathematics teachers Anticipating Instructional practices Professional development
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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