Attempts to identify the development of students' knowledge in science, mathematics, and other disciplines have included proposals concerning the development of naive theories or framework theories (Carey, 1999; Ioannides & Vosniadou, 2002), abstractions or abstract structures (Fuchs et al., 2003; Hershkowitz, Schwarz, & Dreyfus, 2001), and abstract rules or schemata (Gentner & Medina, 1998; Reed, 1993). While all these ideas represent different research methods and traditions as well as attempts to explain different aspects of learning and performance, I argue that all of them suggest assumptions about the abstract nature of students' naive and developing knowledge that deserve scrutiny. This notion of abstraction, while sometimes explicit, is often hidden in researchers' broad assertions that students make use of some single idea, meaning, theory, or knowledge structure across a wide span of situations with marked contextual differences. This paper calls on researchers across theses research agendas to make more careful distinctions between claims purporting to identify apparent consistency in students' performance and claims concerning that nature or structure of the knowledge that supports that performance.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education