Modeling and Representing Conceptual Change in the Learning of Successive Theories

Abstract

Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive theories is steadily increasing, thus opening new areas of interest to discipline-based education research, e.g., quantum logic, quantum information, and communication. Here, we present an initial proposal for modeling the transition from the understanding of a theory to the understanding of its successor and explore its generative potential by applying it to a concrete case—the classical-quantum transition in physics. In pursue of such task, we make coordinated use of contributions from research not only on conceptual change in education, but also on the history and philosophy of science, on the teaching and learning of quantum mechanics, and on mathematics education. By means of analytical instruments developed for characterizing conceptual trajectories at different representational levels, we review empirical literature in the search for the connections between theory change and cognitive demands. The analysis shows a rich landscape of changes and new challenges that are absent in the traditionally considered cases of conceptual change. In order to fully disclose the educational potential of the analysis, we visualize categorical changes by means of dynamic frames, identifying recognizable patterns that answer to students’ need of comparability between the older and the new paradigm. Finally, we show how the frame representation can be used to suggest pattern-dependent strategies to promote the understanding of the new content, and may work as a guide to curricular design.

Promoting the transition to quantum thinking: development of a secondary school course for addressing knowledge revision, organization, and epistemological challenges

“…The design of the course was informed by the description of educationally relevant changes in individual notions, which, according to tools used by researchers on conceptual change, were displayed in comparison tables (see, e.g., Vosniadou, 2008, table 1.1 [7]). Zuccarini and Malgieri [32] converted these tables into dynamic frames, an instrument used by philosophers of science to visualize aspects of the categorical structure of a concept in a scientific theory, and therefore to analyze its dynamics in theory change [35]. The traditional format of a single frame was subsequently adapted to the direct description of change, not only in concepts (ontological change) but also in constructs (representational change).…”

“…• Knowledge revision activity: relying on the representation of the conceptual trajectory of a classical notion [32] with the aim to promote a consistent interpretation of its quantum counterpart (often structured in terms of interpretive tasks);…”

“…Then, we move on to discuss its new feature, active and stochastic (when the initial property is not an outcome-property) as a form of generalization of the first case. The main characteristics of strategies related to this pattern are described in the work of Zuccarini and Malgieri [32].…”

“…In Unit 3, we focused on the remaining features of superposition, where the pattern of value disjunction (see Section II.1.1) occurs in two out of three cases. This patterns suggests a different strategy to address the revision process: starting from the development of an understanding of the new features of the construct, and then to contrast them with those of its classical counterparts, in order to identify which of the familiar features lead to unproductive reasoning in a quantum context [32]. Prior intuition is used as a contrast at the end of the instructional sequence on the topic.…”

“…In particular, we show how it is possible to convert epistemic practices of the theoretical physicist such as thought experiments and mathematical modelling into active learning strategies that engage students in a theoretical form of inquiry. Our analysis inspired the development of a model of the transition from the understanding of a theory to the understanding of its successor presented by Zuccarini and Malgieri [32]. It is an initial proposal, including an exploration of the impact of theory change on various factors of learning, its application to the case of QM, and the identification of strategies for promoting the understanding of the new content.…”