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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. Driven by the need for students to be prepared for a world driven by computation, a number of recent educational reforms in science and mathematics have called for computational thinking concepts to be integrated into these content areas. However, in order for computational thinking (CT) to permeate K-12 education, we need to educate teachers about what CT ideas are and how they relate to what happens in their classroom on a day-to-day basis. This paper presents a toolkit to scaffold elementary teachers’ understanding of computational thinking ideas and how to integrate them into their lesson plans.
  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
  8. Free, publicly-accessible full text available June 1, 2023
  9. Abstract The multiplicity dependence of jet production in pp collisions at the centre-of-mass energy of $$\sqrt{s} = 13\ {\mathrm {TeV}}$$ s = 13 TeV is studied for the first time. Jets are reconstructed from charged particles using the anti- $$k_\mathrm {T}$$ k T algorithm with resolution parameters R varying from 0.2 to 0.7. The jets are measured in the pseudorapidity range $$|\eta _{\mathrm{jet}}|< 0.9-R$$ | η jet | < 0.9 - R and in the transverse momentum range $$5more »by the ALICE forward detector V0. The $$p_{\mathrm T}$$ p T differential cross section of charged-particle jets are compared to leading order (LO) and next-to-leading order (NLO) perturbative quantum chromodynamics (pQCD) calculations. It is found that the data are better described by the NLO calculation, although the NLO prediction overestimates the jet cross section below $$20\ {\mathrm {GeV}}/c$$ 20 GeV / c . The cross section ratios for different R are also measured and compared to model calculations. These measurements provide insights into the angular dependence of jet fragmentation. The jet yield increases with increasing self-normalised charged-particle multiplicity. This increase shows only a weak dependence on jet transverse momentum and resolution parameter at the highest multiplicity. While such behaviour is qualitatively described by the present version of PYTHIA, quantitative description may require implementing new mechanisms for multi-particle production in hadronic collisions.« less
    Free, publicly-accessible full text available June 1, 2023