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In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni Journal of Computers in Mathematics and Science Teaching, 32(3), 265–284, 2013; Kramer Communications of the ACM, 50(4), 37–42, 2007; Wing Communications of the ACM, 49(3), 33–35, 2006). In this paper, we describe one way that attention to levels of abstraction could also support learning in mathematics. Specifically, we propose a framework for using abstraction in elementary mathematics based on Armoni's (2013) framework for teaching computational abstraction. We propose that such a framework could address an enduring challenge in mathematics for helping elementary students solve word problems with attention to context. In a discussion of implications, we propose that future research using the framework for instruction and teacher education could also explore ways that attention to levels of abstraction in elementary school mathematics may support later learning of mathematics and computer science. [ABSTRACT FROM AUTHOR]

A key debate in computer science education is whether and how computational thinking (CT) is used within disciplines other than computer science. Broad definitions provide many avenues for developing integrated instruction, as practices within existing activities can simply be reframed in terms of CT. But such general use of the term CT may confuse its meaning and dilute its power as a tool for bringing CS to all. In this paper, we take the viewpoint that mathematical thinking and computational thinking share common practices, such as using repetition to accomplish tasks, but these shared ideas may develop differently in mathematics and computer science. We use document analysis to analyze the K-5 Common Core State Standards for Mathematics for the presence of these common practices and describe the specific ways they develop in mathematics. We compare these elements of mathematical thinking to related elements of CT to identify synergies and differences between CT and mathematical thinking. We argue that these synergies and differences have implications for the development of integrated instruction designed to bring CS to all. [ABSTRACT FROM AUTHOR]

Content and discourse analysis of interviews with two elementary teachers revealed how they perceived features of their professional contexts as supports or constraints on their agency to create student-centered instruction as they planned from mathematics curriculum resources. Comparison of the cases suggested two cross-case themes: (1) Standards and assessments served as a particularly strong constraint on teachers' agency, and (2) Teachers often found or created space to consider students even when they felt constrained by context; occasionally, considerations of students even overpowered otherwise constraining effects of standards. Implications for supporting student-centered mathematics instruction are discussed. • Creating student-centered instruction from math curriculum resources requires teacher agency. • Grade-level standards served as a strong constraint on teacher agency. • Teachers created space to consider students even within constraints. • Student needs sometimes overpowered the effects of constraints. [ABSTRACT FROM AUTHOR]

Culturally responsive computing (CRC) frames the localized knowledges and practices of Black, Brown, and Indigenous communities as assets for working toward racial justice in science, technology, engineering, and mathematics (STEM). A key part of CRC is the role that local communities play in designing and/or implementing curricula and technologies. Yet, there is a dearth of research on collaborating with local knowledge experts and what they think about CRC. In response, this paper details a two-year long research project on the design and implementation of one CRC program called pH Empowered. pH Empowered uses computing to bridge Black hairstyling, chemistry, and entrepreneurship. Through a mixed-methods study of one pH Empowered professional development workshop, we show how cosmetologists, urban farmers, and librarians had diverse perspectives about how to be culturally responsive with STEM and the racial justice goal of broadening participation in STEM education. [ABSTRACT FROM AUTHOR]