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This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a disciplinary discourse, and a pragmatic discourse., Comment: Encyclopedia of Mathematics Education, 2018

Rate-based processes comprise an important set of scientific phenomena, as well as an important part of the K12 science curricula. Electric current is one such phenomenon, which is taught in various forms from 4th - 12th grades. Research shows that students at all levels find electricity difficult to understand, and the difficulties persist even after classroom instruction. In this paper, we present a design-based research study and argue that interacting with multi-agent-based computational models based on the microscopic theory of electrical conduction, can enable 5th grade and 7th students to develop a deep understanding of electric current as an emergent process of flow in terms of its microscopic level entities and their attributes, by bootstrapping their repertoire of intuitive knowledge. We present a particular design strategy - representing electric current as a fictive and transient process of charge accumulation, without falling in previously reported traps of the "source sink" mental models - and show how this strategy was effectively implemented in the computational model as well as in the learning activities performed by the students. We identify the mental models that students developed through their interactions with the model, and show that after their interactions, students were able to provide correct, multi-level explanations of the behavior of electric current in a resistive circuit.

In this chapter, we argue for an epistemological shift from viewing coding and computational thinking as mastery over computational logic and symbolic forms, to viewing them as a more complex form of experience. Rather than viewing computing as regurgitation and production of a set of axiomatic computational abstractions, we argue that computing and computational thinking, should be viewed as discursive, perspectival, material and embodied experiences, among others. These experiences include, but are not subsumed by, the use and production of computational abstractions. We illustrate what this paradigmatic shift toward a more phenomenological account of computing can mean for teaching and learning STEM in K12 classrooms by presenting a critical review of the literature, as well as by presenting a review of several studies we have conducted in K12 educational settings grounded in this perspective. Our analysis reveals several phenomenological approaches that can be useful for framing computational thinking in K12 STEM classrooms., Comment: Computational Thinking in STEM Discipline: Foundations and Research Highlights, 2018

Contemporary debates on "open science" mostly focus on the pub- lic accessibility of the products of scientific and academic work. In contrast, this paper presents arguments for "opening" the ongoing work of science. That is, this paper is an invitation to rethink the university with an eye toward engaging the public in the dynamic, conceptual and representational work involved in creating scientific knowledge. To this end, we posit that public computing spaces, a genre of open- ended, public learning environment where visitors interact with open source computing platforms to directly access, modify and create complex and authentic scientific work, can serve as a possible model of "open science" in the university., Comment: This is a white paper commissioned by the NSF and NIH funded conference: http: //www.ncsa.illinois.edu/Conferences/ImagineU/

In this paper, we introduce 'public computation' as a genre of learning environments that can be used to radically broaden public participation in authentic, computation-enabled STEM disciplinary practices. Our paradigmatic approach utilizes open source software designed for professional scientists, engineers and digital artists, and situates them in an undiluted form, alongside live and archived expert support, in a public space. We present a case study of DigiPlay, a prototypical public computation space we designed at the University of Calgary, where users can interact directly with scientific simulations as well as the underlying open source code using an array of massive multi- touch screens. We argue that in such a space, public interactions with the code can be thought of as boundary work and play, through which public participation becomes legitimate scientific act, as the public engages in scientific creation through truly open-ended explorations with the code.

How can elementary grade teachers integrate programming and computational thinking with the science curriculum? To answer this question, we present results from a long-term, design-based, microgenetic study where 1) agent-based programming using ViMAP was integrated with existing elementary science curricula and 2) lessons were taught by the classroom teacher. We present an investigation of the co-development of children's computational thinking and scientific modeling and show that the integration of programming with scientific modeling can be supported by the development of sociomathematical norms for designing "mathematically good" computational models.

We extend the theory of disciplinary integration of games for science education beyond the virtual world of games, and identify two key themes of a practice-based theoretical commitment to science learning: (1) materiality in the classroom and (2) iterative design of multiple, complementary symbolic inscriptions (e.g., graphs and agent-based programs). We also identify the affordances of our proposed approach for facilitating student learning and teacher agency.

Studies of scientists building models show that the development of scientific models involves a great deal of subjectivity. However, science as experienced in school settings typically emphasizes an overly objective and rationalistic view. In this paper, we argue for focusing on the development of disciplined interpretation as an epistemic and representational practice that progressively deepens students' computational modeling in science by valuing, rather than deemphasizing, the subjective nature of the experience of modeling. We report results from a study in which fourth grade children engaged in computational modeling throughout the academic year. We present three salient themes that characterize the development of students' disciplined interpretations in terms of their development of computational modeling as a way of seeing and doing science., Comment: in Proceedings of the 12th International Conference of the Learning Sciences (ICLS 2016)

In this paper, we argue that a democratic approach to children's computing education in a science class must focus on the aesthetics of children's experience. In Democracy and Education, Dewey links "democracy" with a distinctive understanding of "experience". For Dewey, the value of educational experiences lies in "the unity or integrity of experience" (DE, 248). In Art as Experience, Dewey presents aesthetic experience as the fundamental form of human experience that undergirds all other forms of experiences, and can also bring together multiple forms of experiences, locating this form of experience in the work of artists. Particularly relevant to our current concern (computational literacy), Dewey calls the process through which a person transforms a material into an expressive medium an aesthetic experience (AE, 68-69). We argue here that the kind of experience that is appropriate for a democratic education in the context of children's computational science is essentially aesthetic in nature. Given that aesthetics has received relatively little attention in STEM education research, our purpose here is to highlight the power of Deweyan aesthetic experience in making computational thinking available to and attractive to all children, including those who are disinterested in computing, and especially those who are likely to be discounted by virtue of location, gender or race., Comment: to appear in the journal Educational Theory

We examine the process through which computational thinking develops in a perspectival fashion as two middle school students collaborate with each other in order to develop computational models of two graphs of motion. We present an interaction analysis of the students' discourse and computational modeling, and analyze how they came to a joint understanding of the goal of the modeling activity. We show that this process involves bringing about coherence between multiple perspectives: the object in motion, the computational agent, the other student, and graphs of motion.

We investigate how the integration of visual agent-based programming and computationally augmented physical structures can support curricular integration across STEM domains for elementary grade students. We introduce ViMAP-Tangible, a socio-technically distributed computational learning environment, which integrates ultrasonic sensors with the ViMAP visual programming language using a distributed computation infrastructure. In this paper, we report a study in which 3rd and 4th grade students used ViMAP-Tangible to engage in collaborative design-based activities in order to invent 'drawing machines' for generating geometric shapes. The curricular activities integrate engineering practices such as user-centered design, mathematical reasoning about multiplication, rates and fractions, and physical science concepts central to learning Newtonian mechanics. We identify the key affordances of the learning environment and our pedagogical approach in terms of the relationship between the structural elements of students' physical constructions and computational models, and their learning outcomes, both in terms of computational thinking, and the domain-specific, mathematical and scientific knowledge that they began developing., Comment: Proceedings of the Sixth International Conference on Computer Supported Education (CSEDU 2014) (In Press)

In this paper, we investigate the interactions among oligarchs, political parties, and voters using an agent-based modeling approach. We introduce the OLIGO model, which is based on the spatial model of democracy, where voters have positions in a policy space and vote for the party that appears closest to them, and parties move in policy space to seek more votes. We extend the existing literature on agent-based models of political economy in the following manner: (1) by introducing a new class of agents- oligarchs - that represent leaders of firms in a common industry who lobby for beneficial subsidies through campaign donations; and (2) by investigating the effects of ideological preferences of the oligarchs on legislative action. We test hypotheses from the literature in political economics on the behavior of oligarchs and political parties as they interact, under conditions of imperfect information and bounded rationality. Our key results indicate that (1) oligarchs tend to donate less to political campaigns when the parties are more resistant to changing their policies, or when voters are more informed; and (2) if Oligarchs donate to parties based on a combination of ideological and profit motivations, Oligarchs will tend to donate at a lower equilibrium level, due to the influence of lost profits. We validate these outcomes via comparisons to real world polling data on changes in party support over time., Comment: appears in Journal of Artificial Societies and Social Simulations, 2014

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 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). The main contribution of this paper is that 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.

The ${}^{11}$B NMR spectra in polycrystalline MgB$_2$ were measured for several magnetic fields (1.97 T and 3.15 T) as a function of temperature from 5 K to 40 K. The composite spectra in the superconducting state can be understood in terms of anisotropy of the upper critical field, $\gamma_{H}$, which is determined to be 5.4 at low temperature. Using Brandt's algorithm\cite{Brandt} the full spectrum, including satellites, was simulated for the temperature 8 K and a magnetic field of 1.97 T. The penetration depth $\lambda$ was determined to be $1,152\pm50$ {\AA}, and the anisotropy of the penetration depth, $\gamma_{\lambda}$, was estimated to be close to one at low temperature. Therefore, our findings establish that there are two different anisotropies for upper critical field and penetration depth at low temperatures., Comment: 10 pages, 7 figures