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Research about modeling emphasizes the importance of heterogeneity in science learning. At the same time, a growing body of scholarship seeks curricular pathways for epistemic and representational convergence. In response to this tension, we propose two constructs: heterogeneity-seeking curricula and commitments. Heterogeneity-seeking curricula emphasize generating and valuing multiple representations of phenomena, offering an image of science that foregrounds messy, nonlinear aspects of learning. Commitments parallel epistemic cognition research by focusing on values that shape students' modeling; however, rather than looking for disciplinary practices in students' modeling, commitments take students' values as a starting point, mapping them to disciplinary resources not typically foregrounded in science education. Using a lens of commitments, we analyze six implementations of a heterogeneity-seeking 6th grade modeling curriculum, and we compare the lens of commitments to the lens of epistemic ideals. Then, we show that, in this context, commitments functioned like epistemic ideals by acting as evaluative resources during modeling. However, commitments also extended beyond this role by helping students ask and explore questions that were not anticipated by the curriculum, problematizing a view of phenomena as objective and external to students' modeling work and showing them instead to be a production of the classroom's multidimensional modeling discourse.

In recent years, the field of education has challenged researchers and practitioners to incorporate computing as an essential focus of K-12 STEM education. Integrating computing within K-12 STEM supports learners of all ages in codeveloping and using computational thinking in existing curricular contexts alongside practices essential for developing mathematical and scientific expertise. In this paper, we present findings from a design-based, microgenetic study in which an agent-based programming and computational modeling platform--ViMAP--was integrated with existing elementary science and math curricula through lessons co-designed and taught by the classroom teacher across a period of seven months. We present a dialogical re-positioning of coding, where disciplinarily grounded meanings of code emerge through the construction of computational utterances--i.e., computer models as well as complementary conversations and physical models that serve as mathematical and scientific explanations--through the use of socio-mathematical norms.

This paper situates a critical review of studies that we have conducted within the broader research literature to analyze the affordances of integrating modeling within disciplinarily-integrated games from computational thinking and science as practice perspectives. Across the studies, the analyses pursue two themes: (a) the role of agent-based modeling as a synergistic local practice around which we can integrate computational thinking and scientific modeling within digital games and (b) the role of collaboration in leveraging those synergies. We then present a design of a disciplinarily-integrated game that integrates these themes to demonstrate one such possible instantiation of the themes. Finally, we discuss the implications for design and praxis with a particular focus on learning in classrooms across the curriculum. Specifically, we first explore the implications in terms of connecting to teachers' views of practice by framing computational modeling and computational thinking as mathematization. We then explore the implications of shifting from a focus on single players to communities of practice in terms of computational participation as science as practice. We close by exploring the pragmatic and pedagogical affordances of shifting from stand-alone single-topic games to flexible agent-based environments in terms of student development across the curriculum.

Studies of scientific practice demonstrate that the development of scientific models is an enactive and emergent process (e.g., Pickering 1995; Chandrasekharan and Nersessian 2017). Scientists make meaning through processes such as perspective taking, finding patterns, and following intuitions. In this paper, we focus on how a group of fourth grade learners and their teacher engaged in interpretation in ways that align with core ideas and practices in kinematics and computing. Cycles of measuring and modeling--including computer programming--helped to support classroom interactions that highlighted the interpretive nature of modeling and participation in model construction as a knowledge-building process. We draw on literature from the history and philosophy of science in order to analyze the students' interpretive actions as forms of epistemic and representational agency, constituting a construct we term "disciplined interpretation." We demonstrate how students' disciplined interpretative moves help to position them as owners of their own design decisions and their rights to interpret the phenomena they were modeling, data collected from those phenomena, and the scientific and computational models themselves. We present four extended episodes that characterize the nature of activity in the classroom and the development of students' disciplined interpretations in terms of learning to recognize scientific patterns amid complex perceptual fields, and to represent them in ways that support sensemaking.

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects or actors that obey simple rules assigned or controlled by the user. It is the interactions between these agents that give rise to emergent, aggregate-level behaviors in complex systems. While several researchers have argued for the effectiveness of ABMs for learning about complex systems, the design of classroom activity systems using ABMs, especially for elementary students, has received relatively less attention. In this paper, we report on a 2-week long proof-of-concept study conducted in a third-grade classroom of 15 students in which students began with an embodied modeling activity of foraging behavior, followed with the generation of mathematical inscriptions based on their embodied actions, and finally, conducted further inquiry of interdependence in an ecosystem using two separate ABMs. Furthermore, we show that the lens of mechanistic reasoning can be productively used to identify the process of students' conceptual development of interdependence in an ecosystem as they engage in the modeling activities.

Computational thinking (CT) parallels the core practices of science, technology, engineering, and mathematics (STEM) education and is believed to effectively support students' learning of science and math concepts. However, despite the synergies between CT and STEM education, integrating the two to support synergistic learning remains an important challenge. Relatively, little is known about how a student's conceptual understanding develops in such learning environments and the difficulties they face when learning with such integrated curricula. In this paper, we present a research study with CTSiM (Computational Thinking in Simulation and Modeling)--computational thinking-based learning environment for K-12 science, where students build and simulate computational models to study and gain an understanding of science processes. We investigate a set of core challenges (both computational and science domain related) that middle school students face when working with CTSiM, how these challenges evolve across different modeling activities, and the kinds of support provided by human observers that help students overcome these challenges. We identify four broad categories and 14 subcategories of challenges and show that the human-provided scaffolds help reduce the number of challenges students face over time. Finally, we discuss our plans to modify the CTSiM interfaces and embed scaffolding tools into CTSiM to help students overcome their various programming, modeling, and science-related challenges and thus gain a deeper understanding of the science concepts.

Environments in which learning involves coordinating multiple external representations (MERs) can productively support learners in making sense of complex models and relationships. Educational digital games provide an increasing popular medium for engaging students in manipulating and exploring such models and relationships. This article applies cognitive science research on MERs to a range of popular educational and recreational games that focus on the interpretation and manipulation of models. We leverage the literatures on embodied cognition, adaptive scaffolding, science education, and dynamic visualizations to address the challenges, trade-offs, and questions highlighted by the research. We apply these research-derived design considerations to analyze (a) the extent and forms through which the design considerations are reflected in the design of the games, (b) the implications for designing effective model-based games for learning, and (c) the implications for future research on MERs.

In this paper, we investigate how elementary school students develop multi-level explanations of population dynamics in a simple predator-prey ecosystem, through scaffolded interactions with a multi-agent-based computational model (MABM). The term "agent" in an MABM indicates individual computational objects or actors (e.g., cars), and these agents obey simple rules assigned or manipulated by the user (e.g., speeding up, slowing down, etc.). It is the interactions between these agents, based on the rules assigned by the user, that give rise to "emergent", aggregate-level behavior (e.g., formation and movement of the traffic jam). Natural selection is such an emergent phenomenon, which has been shown to be challenging for novices (K16 students) to understand. Whereas prior research on learning evolutionary phenomena with MABMs has typically focused on high school students and beyond, we investigate how elementary students (4th graders) develop multi-level explanations of some introductory aspects of natural selection--species differentiation and population change--through scaffolded interactions with an MABM that simulates predator-prey dynamics in a simple birds-butterflies ecosystem. We conducted a semi-clinical interview based study with ten participants, in which we focused on the following: a) identifying the nature of learners' initial interpretations of salient events or elements of the represented phenomena, b) identifying the roles these interpretations play in the development of their multi-level explanations, and c) how attending to different levels of the relevant phenomena can make explicit different mechanisms to the learners. In addition, our analysis also shows that although there were differences between high- and low-performing students (in terms of being able to explain population-level behaviors) in the pre-test, these differences disappeared in the post-test.

Novice learners find motion as a continuous process of change challenging to understand. In this paper, we present a pedagogical approach based on agent-based, visual programming to address this issue. Integrating agent-based programming, in particular, Logo programming, with curricular science has been shown to be challenging in previous research on educational computing. We present a new Logo-based visual programming language--ViMAP--and, a sequence of learning activities involving programming and modeling, designed specifically to support seamless integration between programming and learning kinematics. We describe relevant affordances of the ViMAP environment that supports such seamless integration. We then present ViMAP-MoMo, a curricular unit designed in ViMAP for modeling kinematics, for a wide range of students (elementary-high school). Finally, we describe in detail a sequence of learning activities in three phases, discuss the underlying rationale for each phase, and where relevant, report results in the form of observational data from two studies.