From ‘Algorithmic Mode’ to ‘Conceptual Gestalt’ in Understanding the Behavior of Gases: an epistemological perspective

Abstract

The experimental work of Boyle, Charles and Gay‐Lussac dealt with observable properties of gases, and the Ideal Gas Law is based entirely on empirical evidence (inductive process). According to Hanson a law might have been arrived at empirically (enumerating particulars); it could then be built into a hypothetico‐deductive (H‐D) system as a higher order proposition. From an epistemological perspective, resolution of gas problems based on the Ideal Gas Law, derived by the inductive process, primarily requires manipulation (i.e. enumeration of particulars; of the different variables, and thus can be characterized by the ‘algorithmic mode’. On the other hand, resolution of gas problems based on the Ideal Gas Law, which derives its meaning from the Kinetic‐Molecular Theory of Maxwell‐Boltzmann (an H‐D system), requires the understanding of a pattern within which data appear intelligible, i.e. a sort of ‘conceptual gestalt’. One of the main objectives of this study is to compare performance of students on gas problems that require two distinct approaches, i.e. the ‘algorithmic mode’ and ‘conceptual gestalt’. Results obtained show that student performance on problems requiring the two approaches is quite different. It is concluded that one should not expect training or experience with algorithmic problems to develop the understanding required to solve conceptual problems.