Reinventing College Physics for Biologists: Explicating an epistemological curriculum

The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department's large service courses, serving primarily life-science majors. After consultation with biologists, we re-focused the class on helping the students learn to think scientifically -- to build coherence, think in terms of mechanism, and to follow the implications of assumptions. We designed the course to tap into students' productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials, including Peer Instruction, Interactive Lecture Demonstrations, and Tutorials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations, and we administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material

Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

Epistemic Complexity and the Journeyman-Expert Transition

Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work the authors have demonstrated that some of these difficulties may be epistemological. Students may limit the kinds of knowledge that they use. For example, they may use formal manipulations and ignore physical sense making or vice versa. Both beginning (novice) and intermediate (journeymen) students demonstrate these difficulties. Learning both to switch one's epistemological lens on a problem and to integrate different kinds of knowledge is a critical component of learning to solve problems in physics effectively. In this paper, we present two case studies in which journeyman students (upper-division physics majors) demonstrate switching between epistemological resources in approaching a complex problem. We conjecture that mastering these epistemological skills is an essential component of learning complex problem solving in physics.Comment: 12 page

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

Learning physics in context: a study of student learning about electricity and magnetism

This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel university class in electricity and magnetism are analyzed to demonstrate the central and inextricable role of context in student learning. This work sits within a broader effort to create and analyze environments which support student learning in the sciencesComment: 36 pages, 4 Figure

Analyzing Problem Solving Using Math in Physics: Epistemological Framing via Warrants

Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical processing, computation, blending ancillary information with the math, and reading out physical implications from the math and vice versa. From videotaped observations of intermediate level students solving problems in groups, we note that students often "get stuck" using a limited group of skills or reasoning and fail to notice that a different set of tools (which they possess and know how to use effectively) could quickly and easily solve their problem. We refer to a student's perception/judgment of the kind of knowledge that is appropriate to bring to bear in a particular situation as epistemological framing. Although epistemological framing is often unstated (and even unconscious), in group problem solving situations students sometimes get into disagreements about how to progress. During these disagreements, they bring forth explicit reasons or warrants in support of their point of view. For the context of mathematics use in physics problem solving, we present a system for classifying physics students' warrants. This warrant analysis offers tangible evidence of their epistemological framing.Comment: 23 page

Bandit Models of Human Behavior: Reward Processing in Mental Disorders

Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for multi-armed bandit problem, which extends the standard Thompson Sampling approach to incorporate reward processing biases associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. We demonstrate empirically that the proposed parametric approach can often outperform the baseline Thompson Sampling on a variety of datasets. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions.Comment: Conference on Artificial General Intelligence, AGI-1

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Can dual processing theory explain physics students' performance on the Force Concept Inventory?

According to dual processing theory there are two types, or modes, of thinking: system 1, which involves intuitive and nonreflective thinking, and system 2, which is more deliberate and requires conscious effort and thought. The Cognitive Reflection Test (CRT) is a widely used and robust three item instrument that measures the tendency to override system 1 thinking and to engage in reflective, system 2 thinking. Each item on the CRT has an intuitive (but wrong) answer that must be rejected in order to answer the item correctly. We therefore hypothesized that performance on the CRT may give useful insights into the cognitive processes involved in learning physics, where success involves rejecting the common, intuitive ideas about the world (often called misconceptions) and instead carefully applying physical concepts. This paper presents initial results from an ongoing study examining the relationship between students’ CRT scores and their performance on the Force Concept Inventory (FCI), which tests students’ understanding of Newtonian mechanics. We find that a higher CRT score predicts a higher FCI score for both precourse and postcourse tests. However, we also find that the FCI normalized gain is independent of CRT score. The implications of these results are discussed

Integrating Early Results on Ventral Striatal Gamma Oscillations in the Rat

A vast literature implicates the ventral striatum in the processing of reward-related information and in mediating the impact of such information on behavior. It is characterized by heterogeneity at the local circuit, connectivity, and functional levels. A tool for dissecting this complex structure that has received relatively little attention until recently is the analysis of ventral striatal local field potential oscillations, which are more prominent in the gamma band compared to the dorsal striatum. Here we review recent results on gamma oscillations recorded from freely moving rats. Ventral striatal gamma separates into distinct frequency bands (gamma-50 and gamma-80) with distinct behavioral correlates, relationships to different inputs, and separate populations of phase-locked putative fast-spiking interneurons. Fast switching between gamma-50 and gamma-80 occurs spontaneously but is influenced by reward delivery as well as the application of dopaminergic drugs. These results provide novel insights into ventral striatal processing and highlight the importance of considering fast-timescale dynamics of ventral striatal activity