The Knowledge Building Approach to Science Education: A Problem-Solving Perspective

University of Minnesota Ph.D. dissertation. September 2019. Major: Education, Curriculum and Instruction. Advisor: Gillian Roehrig. 1 computer file (PDF); xii, 191 pages.Science education is reasonably constructed around a vision of authentic scientific practices. Yet, this vision of science is clearly a construct as seen when viewing its changes throughout the last 120 years, as well as viewing it through different theoretical perspectives. While there are diverse descriptions of science and its enactment, going back to Dewey and Peirce, the mission of science is commonly considered to be about the advancement of theory through inquiry where problems serve a central function. Beyond the challenge of constructing an understanding of scientific inquiry as theory development where the diversity in perspectives of scientists is seen as essential, there is the challenge of devising pedagogy and approaches that effectively promote this vision. There are a rich mix of approaches working at solving different parts of this complex problem. One such approach is called, "knowledge building" (Scardamalia and Bereiter, 2006). This approach seeks to scaffold classroom communities such that they develop and grow into a complex community where progressive science-theory improvement emerges. It is considered that these sorts of communities where innovation is the norm have relevance beyond the fields of science and STEM: innovation and knowledge creation is becoming the essential practice of the knowledge age. The knowledge building approach is designed to support the growth of classroom communities that embody the essential nature of progressive scientific inquiry. To effectively support this kind of classroom community development, the unique assets and needs presented by the ever-increasing diversity of thinking and knowing that are emergents of the students' cultures, developmental levels, neurological diversities and iv networks of communities. Overall, this research sought to support and augment classrooms as they strive to grow into classroom communities of scientific inquiry. The research occurred in two stages. It first used philosophical methods to generate a simple, high-level model of problem-solving made possible by Popper's World-3 conception. This conception is a keystone in some epistemologies developed to support approaches aimed at helping students grow in knowledge-innovation practices. The visual problem-solving model that was developed seeks to provide students and teachers with a very simple yet flexible model allowing them to describe, analyze and reflect on the state of their community's knowledge improvement and through this understanding adaptively and effectively respond. The second stage of research utilized hybrid philosophical-empirical methods to develop a framework that describes science in terms of its mission to progressively improve theory through the iterative solving of and subsequent unfolding of new knowledge-problems. These research methods involved an iterative process where promising theories are tested on their ability to describe students' actual online knowledge-building discourse in a satisfying way. In this iterative process, empirical classroom data informed and yet also constrain the theory generation which was informed by diverse theoretical perspectives. These theoretical perspectives included for example, ideas of scientific practices, theories of design such as design thinking and understandings of classroom diversity as represented in the Next Generation Science Standards (NGSS Lead States, 2013) which were intentionally founded upon theories of v culturally responsive pedagogy. The developed framework seeks to scaffold teachers as they design and enact lessons aimed at growing communities of diverse scientists. Taken together, the products of this research seek to provide conceptual structures to aid the students and teachers in classroom communities as they seek to grow into complex communities of scientists

Language, chaos and entropy: a physical take on biolinguistics

In this paper we will try to provide arguments for the thesis that language is a physical system aiming at justificative adequacy: what architectural properties license the occurrence of certain emergent phenomena. We will claim that the derivational dynamics that can be found in language (and other systems of the mind) should be analyzed from the perspective of complex non-linear systems, as an open dynamic system. We will propose an oscillatory engine for linguistic computations, which yields cycles as a natural emergent property given mutually incompatible tendencies between output conditions: global semantic effects and local linearization requirements. This architecture, in which structure building is conditioned by irreconciliable conditions, con�figures a kind of dynamical system well known in physics: a dynamical frustration. We will attempt to show that interesting effects arise when we consider that there is a dynamical frustration at the core of cognitive dynamics

The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations

We introduce a 'uniform tension-reduction' (UTR) model, which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the UTR-model can be further generalized into a 'general tension-reduction' (GTR) model, describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this ampler framework, particularly suitable to describe experiments in cognitive science, we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article.Comment: 50 pages, 10 figure

Possible Paths Forward for a Practice-Based Teacher Education Centered on Justice

This dissertation seeks to address limitations of Practice-Based Teacher Education (PBTE) in relation to (1) narrow conceptions of practice and teacher learning, and (2) peripheralization of equity and justice. After aiming to understand the landscape of limitations in PBTE, this study situates itself within specific manifestations of these limitations that exist in common conceptualizations of teacher learning and practice-based pedagogies. To (re)emphasize the situated nature of practice and center equity and justice in PBTE, I theorize an expanded notion of teacher learning, develop design features for contextually situated pedagogies of practice (Grossman et al., 2009), and implement the design with a group of three mathematics teacher candidates. This dissertation, as three manuscripts, represents, through theory and practice, a possible version of PBTE that attends to “issues of voice, power, context, and subjectivity” (Peercy et al., 2019, p. 1175). Within the first manuscript, I pursue questions related to understanding the conversations of critique around PBTE – specifically as it relates to the use of undertheorized notions of ‘practice’ and the peripheralization of equity and justice. Within this manuscript, through an integrative review of literature (Torraco, 2016), I synthesize the critiques and re-envisioned aspects of PBTE in order to generate possible paths forward for research and practice in the field. The second manuscript highlights work that consequently pursues one of the possible paths, theorizing an expanded framework for teacher learning that spans justice and practice-based notions. Using case-study methodology (Merriam, 2009), I investigate what is made visible and possible to understand about teacher resources by using the Critical Framework for Teacher Learning (Karr, 2021) as a lens for analysis. The final manuscript aims to answer a call to emphasize the situatedness of teaching by articulating design features for pedagogies of practice (Grossman et al., 2009) that provide “opportunities to experience the complexities of power that permeate learning of teaching practices” (Dutro & Cartun, 2016, p. 119). I then show how these pedagogies assist in making visible TCs’ resources for responding to injustices. Findings from this study highlight how PBTE might develop deep interrogative stances on subjectivities, envision pedagogies of practice centered on enactment toward justice, and leverage robust conceptual frameworks for teacher learning to include justice-based dimensions. It also illustrates how, when leveraging robust notions of teacher learning, we can view teaching practice as a contextually complex construction, which moves PBTE away from viewing practice and practices as static, universal, or ‘best.’ Furthermore, in presenting design features for practice-based pedagogies, I show that features oriented toward the contextualization of teaching help to elicit teaching practice that is contingent and responds to injustice

Learnability, representation, and language : a Bayesian approach

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 225-243).Within the metaphor of the "mind as a computation device" that dominates cognitive science, understanding human cognition means understanding learnability not only what (and how) the brain learns, but also what data is available to it from the world. Ideal learnability arguments seek to characterize what knowledge is in theory possible for an ideal reasoner to acquire, which illuminates the path towards understanding what human reasoners actually do acquire. The goal of this thesis is to exploit recent advances in machine learning to revisit three common learnability arguments in language acquisition. By formalizing them in Bayesian terms and evaluating them given realistic, real-world datasets, we achieve insight about what must be assumed about a child's representational capacity, learning mechanism, and cognitive biases. Exploring learnability in the context of an ideal learner but realistic (rather than ideal) datasets enables us to investigate what could be learned in practice rather than noting what is impossible in theory. Understanding how higher-order inductive constraints can themselves be learned permits us to reconsider inferences about innate inductive constraints in a new light. And realizing how a learner who evaluates theories based on a simplicity/goodness-of-fit tradeoff can handle sparse evidence may lead to a new perspective on how humans reason based on the noisy and impoverished data in the world. The learnability arguments I consider all ultimately stem from the impoverishment of the input either because it lacks negative evidence, it lacks a certain essential kind of positive evidence, or it lacks suffcient quantity of evidence necessary for choosing from an infinite set of possible generalizations.(cont.) I focus on these learnability arguments in the context of three major topics in language acquisition: the acquisition of abstract linguistic knowledge about hierarchical phrase structure, the acquisition of verb argument structures, and the acquisition of word leaning biases.by Amy Perfors.Ph.D

Stochastic Mathematical Systems

We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves {stochastic mathematical systems} (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a ``calibration'' relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an ``oracle'' SMS that can be interpreted as deciding whether the question-answer pairs of the reasoner SMS are valid. To ground thinking, we understand the answers to questions given by this oracle to be the answers that would be given by an SMS representing the entire mathematical community in the infinite long run of the process of asking and answering questions. We then introduce a slight extension of SMSs to allow us to model both the physical universe and human reasoning about the physical universe. We then define a slightly different calibration relation appropriate for the case of scientific reasoning. In this case the first SMS represents a human scientist predicting the outcome of future experiments, while the second SMS represents the physical universe in which the scientist is embedded, with the question-answer pairs of that SMS being specifications of the experiments that will occur and the outcome of those experiments, respectively. Next we derive conditions justifying two important patterns of inference in both mathematical and scientific reasoning: i) the practice of increasing one's degree of belief in a claim as one observes increasingly many lines of evidence for that claim, and ii) abduction, the practice of inferring a claim's probability of being correct from its explanatory power with respect to some other claim that is already taken to hold for independent reasons.Comment: 43 pages of text, 6 pages of references, 11 pages of appendice

Syntax inside the grammar

This volume collects novel contributions to comparative generative linguistics that “rethink” existing approaches to an extensive range of phenomena, domains, and architectural questions in linguistic theory. At the heart of the contributions is the tension between descriptive and explanatory adequacy which has long animated generative linguistics and which continues to grow thanks to the increasing amount and diversity of data available to us. The chapters address research questions on the relation of syntax to other aspects of grammar and linguistics more generally, including studies on language acquisition, variation and change, and syntactic interfaces. Many of these contributions show the influence of research by Ian Roberts and collaborators and give the reader a sense of the lively nature of current discussion of topics in synchronic and diachronic comparative syntax ranging from the core verbal domain to higher, propositional domains

Understanding the Elements of Executable Architectures Through a Multi-Dimensional Analysis Framework

The objective of this dissertation study is to conduct a holistic investigation into the elements of executable architectures. Current research in the field of Executable Architectures has provided valuable solution-specific demonstrations and has also shown the value derived from such an endeavor. However, a common theory underlying their applications has been missing. This dissertation develops and explores a method for holistically developing an Executable Architecture Specification (EAS), i.e., a meta-model containing both semantic and syntactic information, using a conceptual framework for guiding data coding, analysis, and validation. Utilization of this method resulted in the description of the elements of executable architecture in terms of a set of nine information interrogatives: an executable architecture information ontology. Once the detail-rich EAS was constructed with this ontology, it became possible to define the potential elements of executable architecture through an intermediate level meta-model. The intermediate level meta-model was further refined into an interrogative level meta-model using only the nine information interrogatives, at a very high level of abstraction