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

A Reinforcement Learning Model of Precommitment in Decision Making

Addiction and many other disorders are linked to impulsivity, where a suboptimal choice is preferred when it is immediately available. One solution to impulsivity is precommitment: constraining one's future to avoid being offered a suboptimal choice. A form of impulsivity can be measured experimentally by offering a choice between a smaller reward delivered sooner and a larger reward delivered later. Impulsive subjects are more likely to select the smaller-sooner choice; however, when offered an option to precommit, even impulsive subjects can precommit to the larger-later choice. To precommit or not is a decision between two conditions: (A) the original choice (smaller-sooner vs. larger-later), and (B) a new condition with only larger-later available. It has been observed that precommitment appears as a consequence of the preference reversal inherent in non-exponential delay-discounting. Here we show that most models of hyperbolic discounting cannot precommit, but a distributed model of hyperbolic discounting does precommit. Using this model, we find (1) faster discounters may be more or less likely than slow discounters to precommit, depending on the precommitment delay, (2) for a constant smaller-sooner vs. larger-later preference, a higher ratio of larger reward to smaller reward increases the probability of precommitment, and (3) precommitment is highly sensitive to the shape of the discount curve. These predictions imply that manipulations that alter the discount curve, such as diet or context, may qualitatively affect precommitment

Expectancies in Decision Making, Reinforcement Learning, and Ventral Striatum

Decisions can arise in different ways, such as from a gut feeling, doing what worked last time, or planful deliberation. Different decision-making systems are dissociable behaviorally, map onto distinct brain systems, and have different computational demands. For instance, “model-free” decision strategies use prediction errors to estimate scalar action values from previous experience, while “model-based” strategies leverage internal forward models to generate and evaluate potentially rich outcome expectancies. Animal learning studies indicate that expectancies may arise from different sources, including not only forward models but also Pavlovian associations, and the flexibility with which such representations impact behavior may depend on how they are generated. In the light of these considerations, we review the results of van der Meer and Redish (2009a), who found that ventral striatal neurons that respond to reward delivery can also be activated at other points, notably at a decision point where hippocampal forward representations were also observed. These data suggest the possibility that ventral striatal reward representations contribute to model-based expectancies used in deliberative decision making

Low and High Gamma Oscillations in Rat Ventral Striatum have Distinct Relationships to Behavior, Reward, and Spiking Activity on a Learned Spatial Decision Task

Local field potential (LFP) oscillations in the brain reflect organization thought to be important for perception, attention, movement, and memory. In the basal ganglia, including dorsal striatum, dysfunctional LFP states are associated with Parkinson's disease, while in healthy subjects, dorsal striatal LFPs have been linked to decision-making processes. However, LFPs in ventral striatum have been less studied. We report that in rats running a spatial decision task, prominent gamma-50 (45–55 Hz) and gamma-80 (70–85 Hz) oscillations in ventral striatum had distinct relationships to behavior, task events, and spiking activity. Gamma-50 power increased sharply following reward delivery and before movement initiation, while in contrast, gamma-80 power ramped up gradually to reward locations. Gamma-50 power was low and contained little structure during early learning, but rapidly developed a stable pattern, while gamma-80 power was initially high before returning to a stable level within a similar timeframe. Putative fast-spiking interneurons (FSIs) showed phase, firing rate, and coherence relationships with gamma-50 and gamma-80, indicating that the observed LFP patterns are locally relevant. Furthermore, in a number of FSIs such relationships were specific to gamma-50 or gamma-80, suggesting that partially distinct FSI populations mediate the effects of gamma-50 and gamma-80

Covert Expectation-of-Reward in Rat Ventral Striatum at Decision Points

Flexible decision-making strategies (such as planning) are a key component of adaptive behavior, yet their neural mechanisms have remained resistant to experimental analysis. Theories of planning require prediction and evaluation of potential future rewards, suggesting that reward signals may covertly appear at decision points. To test this idea, we recorded ensembles of ventral striatal neurons on a spatial decision task, in which hippocampal ensembles are known to represent future possibilities at decision points. We found representations of reward which were not only activated at actual reward delivery sites, but also at a high-cost choice point and before error correction. This expectation-of-reward signal at decision points was apparent at both the single cell and the ensemble level, and vanished with behavioral automation. We conclude that ventral striatal representations of reward are more dynamic than suggested by previous reports of reward- and cue-responsive cells, and may provide the necessary signal for evaluation of internally generated possibilities considered during flexible decision-making

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

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

Emerging technologies in physics education

Three emerging technologies in physics education are evaluated from the interdisciplinary perspective of cognitive science and physics education research. The technologies - Physlet Physics, the Andes Intelligent Tutoring System (ITS), and Microcomputer-Based Laboratory (MBL) Tools - are assessed particularly in terms of their potential at promoting conceptual change, developing expert-like problem-solving skills, and achieving the goals of the traditional physics laboratory. Pedagogical methods to maximize the potential of each educational technology are suggested.Comment: Accepted for publication in the Journal of Science Education and Technology; 20 page

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