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  1. 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) frameworkmore »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.« less
  2. Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during their math and science lessons. Such information can support the creation of quality professional development experiences for teachers. We analyzed how eight elementary teachers created opportunities for their students to engage in four CT practices (abstraction, decomposition, debugging, and patterns) during unplugged mathematics and science activities. We identified threemore »strategies used by these teachers to create CT opportunities for their students: framing, prompting, and inviting reflection. Further, we grouped teachers into four profiles of implementation according to how they used these three strategies. We call the four profiles (1) presenting CT as general problem-solving strategies, (2) using CT to structure lessons, (3) highlighting CT through prompting, and (4) using CT to guide teacher planning. We discuss the implications of these results for professional development and student experiences.« less
  3. In this brief paper, we will share preliminary results of a study of how elementary-school teachers take up computational thinking (CT) ideas and incorporate them into their mathematics and science teaching. We describe the teachers’ school contexts, the professional development experiences in which they engaged, and our preliminary analyses of how they used computational thinking within their enacted lessons. In brief, the seven teachers in this study exhibited three patterns of implementation: (1) using computational thinking to guide their own planning and thinking; (2) using computational thinking to structure their lessons; and (3) presenting computational thinking concepts to students asmore »general problem solving strategies.« less
  4. In order to create professional development experiences, curriculum materials, and policies that support elementary school teachers to embed computational thinking (CT) in their teaching, researchers and teacher educators must under- stand ways teachers see CT as connecting to their classroom practices. Taking the viewpoint that teachers’ initial ideas about CT can serve as useful resources on which to build ed- ucational experiences, we interviewed 12 elementary school teachers to probe their understanding of six components of CT (abstraction, algorithmic thinking, automation, debug- ging, decomposition, and generalization) and how those com- ponents relate to their math and science teaching. Results suggestedmore »that teachers saw stronger connections between CT and their mathematics instruction than between CT and their science instruction. We also found that teachers draw upon their existing knowledge of CT-related terminology to make connections to their math and science instruction that could be leveraged in professional development. Teachers were, however, concerned about bringing CT into teaching due to limited class time and the difficulties of addressing high level CT in developmentally appropriate ways. We discuss these results and their implications future research and the design of professional development, sharing examples of how we used teachers’ initial ideas as the foundation of a workshop introducing them to computational thinking.« less
  5. 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 ormore »to purely mathematical steps. Our analysis showed: (1) students implicitly shift among levels of abstraction when solving “real- world” 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.« less
  6. Gresalfi, M. ; Horn, I. S. (Ed.)
    There is broad belief that preparing all students in preK-12 for a future in STEM involves integrating computing and computational thinking (CT) tools and practices. Through creating and examining rich “STEM+CT” learning environments that integrate STEM and CT, researchers are defining what CT means in STEM disciplinary settings. This interactive session brings together a diverse spectrum of leading STEM researchers to share how they operationalize CT, what integrated CT and STEM learning looks like in their curriculum, and how this learning is measured. It will serve as a rich opportunity for discussion to help advance the state of the fieldmore »of STEM and CT integration.« less
  7. Gresalfi, M. ; Horn, I. S. (Ed.)
    There is broad belief that preparing all students in preK-12 for a future in STEM involves integrating computing and computational thinking (CT) tools and practices. Through creating and examining rich “STEM+CT” learning environments that integrate STEM and CT, researchers are defining what CT means in STEM disciplinary settings. This interactive session brings together a diverse spectrum of leading STEM researchers to share how they operationalize CT, what integrated CT and STEM learning looks like in their curriculum, and how this learning is measured. It will serve as a rich opportunity for discussion to help advance the state of the fieldmore »of STEM and CT integration.« less