Abstract
The authors present a new view of the relationship between learning fractions and learning algebra that (1) emphasizes the conceptual continuities between whole-number arithmetic and fractions; and (2) shows how the fundamental properties of operations and equality that form the foundations of algebra are used naturally by children in their strategies for problems involving operating on and with fractions. This view is grounded in empirical research on how algebraic structure emerges in young children’s reasoning. Specifically, the authors argue that there is a broad class of children’s strategies for fraction problems motivated by the same mathematical relationships that are essential to understanding high-school algebra and that these relationships cannot be presented to children as discrete skills or learned as isolated rules. The authors refer to the thinking that guides such strategies as Relational thinking.
The research summarized in this chapter was supported in part by a grant from the National Science Foundation (ESI-0119732) and a Faculty Research Assignment from the University of Texas. The opinions expressed in this chapter do not necessarily reflect the position, policy, or endorsement of the National Science Foundation or UT. The authors would like to thank Jeremy Roschelle, Walter Stroup, Scott Eberle, and Brian Katz, along with two anonymous reviewers, for very helpful reviews of this chapter as it was being written and Annie Keith and her students for helping us to understand the potential for developing algebraic thinking.
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Empson, S.B., Levi, L., Carpenter, T.P. (2011). The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School. In: Cai, J., Knuth, E. (eds) Early Algebraization. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_22
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