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Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations— their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction. We analyzed a collection of 173 thinking-as-a-resource orientations inferred from scenario-based interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation’s relationship to three frameworks related to recognizing and leveraging high-potential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinking-as-a-resource orientations could support or hinder a teacher’s development of the practice of building on student thinking. The work contributes to the field’s understanding of why particular orientations might have more or less potential to support teachers’ development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers’ specific needs.
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Reconfiguring the Challenge of Biological Complexity as a Resource for Biodesign
ABSTRACT Biological complexity is widely seen as the central, intractable challenge of engineering biology. Yet this challenge has been constructed through the field’s dominant metaphors. Alternative ways of thinking—latent in progressive experimental approaches, but rarely articulated as such—could instead position complexity as engineering biology’s greatest resource. We outline how assumptions about engineered microorganisms have been built into the field, carried by entrenched metaphors, even as contemporary methods move beyond them. We suggest that alternative metaphors would better align engineering biology’s conceptual infrastructure with the field’s move away from conventionally engineering-inspired methods toward biology-centric ones. Innovating new conceptual frameworks would also enable better aligning scientific work with higher-level conversations about that work. Such innovation—thinking about how engineering microbes might be more like user-centered design than like programming a computer or building a car—could highlight complexity as a resource to leverage, not a problem to erase or negate.
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- Award ID(s):
- 2114750
- PAR ID:
- 10435726
- Editor(s):
- Tringe, Susannah Green
- Date Published:
- Journal Name:
- mSphere
- Volume:
- 7
- Issue:
- 6
- ISSN:
- 2379-5042
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1128/msphere.00547-22
