Explicit and Implicit States of Model Mixing in Conceptual Development

Researchers in science education have demonstrated that students can hold several different understandings of a single concept and apply them inconsistently to tasks related to the concept. Many studies have been conducted to investigate how these coexisting and competing understandings of concepts affect the process of conceptual development. Based on the context dependence of learning, we developed Model Analysis as a theoretical and measurement framework to capture the process of how different types of understandings of a concept evolve and develop in learning and to quantitatively assess the existences and changes of these different understandings. In Model Analysis, we use the term models to represent the layer of functional mental constructs and describe the uses of different constructs with model states. A model state gives the distribution of probabilities for a student to apply different types of models in given contexts. When a student holds multiple models and applies them inconsistently across contexts, the student is described with a mixed model state. With this method, students’ changes of their understandings can be represented quantitatively with the structures (in terms of probability distributions) of their model states. This paper reports a new progress in Model Analysis, which identifies two different mixed model states: explicit state and implicit state. The author will discuss the theoretical basis, empirical evidence, and a mathematical representation developed to use with quantitative instruments such as multiple-choice questions. Examples of research applications are also discussed.