Characterizing perfect recall using next-step temporal operators in S5 and sub-S5 Epistemic Temporal Logic

We review the notion of perfect recall in the literature on interpreted systems, game theory, and epistemic logic. In the context of Epistemic Temporal Logic (ETL), we give a (to our knowledge) novel frame condition for perfect recall, which is local and can straightforwardly be translated to a defining formula in a language that only has next-step temporal operators. This frame condition also gives rise to a complete axiomatization for S5 ETL frames with perfect recall. We then consider how to extend and consolidate the notion of perfect recall in sub-S5 settings, where the various notions discussed are no longer equivalent

Students’ Use of Symmetry with Gauss’s Law

To study introductory student difficulties with electrostatics, we compared student techniques when finding the electric field for spherically symmetric and non-spherically symmetric charged conductors. We used short interviews to design a free-response and multiple-choice-multiple-response survey that was administered to students in introductory calculus-based courses. We present the survey results and discuss them in light of Singh\u27s results for Gauss\u27s Law, Collins and Ferguson\u27s epistemic forms and games, and Tuminaro\u27s extension of games and frames

Assessing context-based learning: Not only rigorous but also relevant

Economic factors are driving significant change in higher education. There is increasing responsiveness to market demand for vocational courses and a growing appreciation of the importance of procedural (tacit) knowledge to service the needs of the Knowledge Economy; the skills in demand are information analysis, collaborative working and 'just-in-time learning'. New pedagogical methods go some way to accommodate these skills, situating learning in context and employing information and communications technology to present realistic simulations and facilitate collaborative exchange. However, what have so far proved resistant to change are the practices of assessment. This paper endorses the case for a scholarship of assessment and proposes the development of technology-supported tools and techniques to assess context-based learning. It also recommends a fundamental rethink of the norm-referenced and summative assessment of propositional knowledge as the principal criterion for student success in universities

Inquisitive bisimulation

Inquisitive modal logic InqML is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states. We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. These results crucially require non-classical methods in studying bisimulation and first-order expressiveness over non-elementary classes of structures, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory

Reinventing discovery learning: a field-wide research program

© 2017, Springer Science+Business Media B.V., part of Springer Nature. Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based pedagogical philosophy, citing an inherent structural challenge of students constructing historically achieved conceptual structures from their ingenuous notions. This special issue presents six educational research projects that, while adhering to principles of discovery-based learning, are motivated by complementary philosophical stances and theoretical constructs. The editorial introduction frames the set of projects as collectively exemplifying the viability and breadth of discovery-based learning, even as these projects: (a) put to work a span of design heuristics, such as productive failure, surfacing implicit know-how, playing epistemic games, problem posing, or participatory simulation activities; (b) vary in their target content and skills, including building electric circuits, solving algebra problems, driving safely in traffic jams, and performing martial-arts maneuvers; and (c) employ different media, such as interactive computer-based modules for constructing models of scientific phenomena or mathematical problem situations, networked classroom collective “video games,” and intercorporeal master–student training practices. The authors of these papers consider the potential generativity of their design heuristics across domains and contexts

Epistemic Strategies for Solving Two-Dimensional Physics Problems

An epistemic strategy is one in which a person takes a piece of knowledge and uses it to create new knowledge. Students in algebra and calculus based physics courses use epistemic strategies to solve physics problems. It is important to map how students use these epistemic strategies to solve physics problems in order to provide insight into the problem solving process. In this thesis three questions were addressed: (1) What epistemic strategies do students use when solving two-dimensional physics problems that require vector algebra? (2) Do vector preconceptions in kinematics and Newtonian mechanics hinder a student\u27s ability to apply the correct mathematical tools when solving a problem? and, (3) What patterns emerge with students of similar vector algebra skill in their problem solving abilities? Literature discussing epistemic games and frames was reviewed as well as literature discussing qualitative research, quantitative research, and think-aloud protocols. Students were given various problems in two-dimensional kinematics, statics and dynamics. They were asked to solve the problems using think-aloud protocol. After the student solved the problem he was asked to recall what he remembered about the solution process. This procedure gave more insight into the thought process of the student during the time he solved the problems. In addition to the interviews, a vector pre-assessment survey was administered to students at the beginning of the term. The vector pre-assessment survey provided data about the vector knowledge students brought into the physics course. Students scoring lower than fifty percent on the vector pre-assessment survey did not solve any problems correctly. These data and the results of a grounded theory study provided information about the problem solving strategies of the students interviewed in this study. Seven epistemic strategies were observed. These seven epistemic strategies fell into three frames: the qualitative sense making frame, the quantitative sense making frame, and the rote problem solving frame. The epistemic strategies identification of frames gave a detailed overview of how students solve physics problems involving vector algebra. Incomplete pieces of epistemic strategies, called strands, were also observed. Students would move between strategies without completing all the steps for a specific strategy. Strands were observed for most students. Advanced problem solvers or those students with more experience solving physics problems, moved from the qualitative sense making frame into the quantitative sense making frame to solve the problems. Students solving the problems correctly consistently moved into the quantitative sense making frame. However, if a student had access to an example that showed the exact solution, that student could end the problem with a correct solution in the rote problem solving frame. If no solutions or examples similar to the problem were available, the student was always unsuccessful solving the problem unless he/she moved into the quantitative sense making frame. Misconceptions about motion and forces were identified. Vector preconceptions were difficult to identify in this project, but difficulties with vector algebra were observed

EPISTEMIC FOUNDATIONS OF SOLUTION CONCEPTS IN GAME THEORY: AN INTRODUCTION

We give an introduction to the literature on the epistemic foundations of solution concepts in game theory. Only normal-form games are considered. The solution concepts analyzed are rationalizability, strong rationalizability, correlated equilibrium and Nash equilibrium. The analysis is carried out locally in terms of properties of the belief hierarchies. Several examples are used throughout to illustrate definitions and concepts.