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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.

Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in mathematics education. In this study, we examined elementary students' solutions to a commonplace mathematics task to determine whether and how students moved among levels of abstraction as they solved the task. Furthermore, we analyzed student errors, categorizing them according to whether they related to moves among levels of abstraction or to purely mathematical steps. Our analysis showed: (1) students implicitly shift among levels of abstraction when solving "realworld" mathematics problems; (2) students make errors when making those implicit shifts in abstraction level; (3) the errors students make in abstraction outnumber the errors they make in purely mathematical skills. We discuss the implications for these findings, arguing they establish that there are opportunities for explicit instruction in abstraction in elementary mathematics, and that students' overall mathematics achievement and problem-solving skills have the potential to benefit from applying these computer-science ideas to mathematics instruction. [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]