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This study investigated the seeds of algebraic thinking that Kindergarten students use when engaging with function tables and graphs. Through interviews with three Kindergarteners, we explored how they reasoned about functional relationships. Our results illustrate how the Kindergarteners used seeds of algebraic thinking when using function tables and graphs to represent and reason about functional relationships. Building on the seeds of algebraic thinking and Knowledge in Pieces frameworks, we categorized these seeds as either strategies (classify, pair, and compare) or ideas (seeds of covariation). Strategy seeds were goal-oriented, and seeds of covariation were elicited without any goal and reflected a broader understanding of change between quantities. 

Energy is a central, cross-cutting concept in science, but its abstract nature poses challenges for learners. Metaphor has been recognized as a productive resource used by students, teachers, and scientists to understand and communicate about energy. While much research has focused on metaphors about energy expressed in learners’ speech, we know less about the range of ways learners use gesture to evoke metaphors about energy. In particular, the metaphor energy as substance has been found to be useful for conceptualizing various features of energy. Using a microethnographic approach, we demonstrate how students in an introductory algebra- based university physics course use gesture in three different ways to evoke substance-like metaphors that offer valuable affordances for sensemaking about energy: These include (1) container metaphor gestures, (2) stimulus metaphor gestures, and (3) accounting metaphor gestures. Implications for learning and teaching about energy are discussed. 

Computational modeling of scientific systems is a powerful approach for fostering science and computational thinking (CT) proficiencies. However, the role of programming activities for this synergistic learning remains unclear. This paper examines alternative ways to engage with computational models (CM) beyond programming. Students participated in an integrated Science, Engineering, and Computational Modeling unit through one of three distinct instructional versions: Construct a CM, Interpret-and-Evaluate a CM, and Explore-and-Evaluate a simulation. Analyzing 188 student responses to a science+CT embedded assessment task, we investigate how science proficiency and instructional versions related to pseudocode interpretation and debugging performances. We found that students in the Explore-and-Evaluate a simulation outperformed students in the programming-based versions on the CT assessment items. Additionally, science proficiency strongly predicted students’ CT performance, unlike prior programming experience. These results highlight the promise of diverse approaches for fostering CT practices with implications for STEM+C instruction and assessment design. 

Not AvailableEngaging with computational models is central to both scientific and computational learning. A promising approach to “lower the floor” and make computational modeling more accessible is the development of domain-specific and block-based environments, which reduce programming complexity while leveraging students’ intuitions about scientific ideas. To balance usability and expressiveness in these environments, we develop the feature of “unpacking” blocks, allowing users to open and modify high-level blocks into the simpler constituent elements that define them. In this study, we analyze high school students’ models, screen recordings, and artifact-based interviews to investigate their motivation for modifying domain-specific blocks for eutrophication in aquatic ecosystems. We found that unpacking and modifying blocks supported students in both exploring scientific ideas and addressing specific goals of computational modeling, providing insights on how unpacking domain-specific blocks can support both computing and science learning. 

Not AvailableAn emerging body of work in the learning sciences has examined how computational models can support teachers in responding to students' prompts, inquiry, and ideas. This work has highlighted how teachers make discursive moves in relation to computational models to support classroom discussion. In this paper, we focus on a complementary phenomenon: teachers' design of code reflections, or curricular modifications that deepen students' engagement with one another's code for scientific and computational sensemaking. We highlight how these code reflections advanced student discourse and how both the code reflections and discourse became more sophisticated over time, shifting towards making connections across code, behaviors, simulation outcomes, data and the scientific process being represented. We reflect on how this progression was driven by shifts in the teachers’ comfort with code and computational modeling and the resources designers can offer to educators to support the development of code reflections.