Conceptual and procedural knowledge in mathematical cognition

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When faced with a mathematical problem involving fractions, do children think about the problem conceptually, or do they instead work through a procedure to generate the "right answer"? Results from research to date suggest varying answers to this question. Different researchers have suggested that children learn concepts first, that they learn procedures first, and that they learn concepts and procedures in tandem. This project builds upon a different finding that suggests that all of these might be true; these contradictory claims could be the result of individual differences in children's use of conceptual and procedural knowledge. In other words, some children may rely more on conceptual understanding, some might rely more on procedural understanding, and others might equally rely on both. Building on this previous result, this research project will delve deeper into individual differences in children's conceptual and procedural knowledge in three main ways. First, longitudinal and intervention studies will look at the progression of individual differences over time and how training in conceptual or procedural understanding can affect children with different conceptual and procedural profiles. Second, additional studies will investigate whether the individual differences evident in fractions understanding will also be present in children's understanding of more complicated mathematical topics like algebra. Third, this project will probe whether fraction's understanding can be helped or hindered by what other researchers have called people's "number sense". All of these studies are meant to better understand how different young people think about fractions, and more complicated mathematical topics, and may result in better ways to focus teaching for these different kinds of learners.