Abstract
This chapter explores how elementary teachers can use functional thinking to build algebraic reasoning into curriculum and instruction. In particular, we examine how children think about functions and how instructional materials and school activities can be extended to support students’ functional thinking. Data are taken from a five-year research and professional development project conducted in an urban school district and from a graduate course for elementary teachers taught by the first author. We propose that elementary grades mathematics should, from the start of formal schooling, extend beyond the fairly common focus on recursive patterning to include curriculum and instruction that deliberately attends to how two or more quantities vary in relation to each other. We discuss how teachers can transform and extend their current resources so that arithmetic content can provide opportunities for pattern building, conjecturing, generalizing, and justifying mathematical relationships between quantities, and we examine how teachers might embed this mathematics within the kinds of socio-mathematical norms that help children build mathematical generality.
The research reported here was supported in part by a grant from the U.S. Department of Education, Office of Educational Research and Improvement to the National Center for Improving Student Learning and Achievement in Mathematics and Science (R305A600007-98). The opinions expressed herein do not necessarily reflect the position, policy, or endorsement of supporting agencies. This chapter is a revised version of an article published in ZDM—International Reviews on Mathematical Education, 37(1), 34–42. DOI 10.1007/BF02655895.
J.J. Kaput is deceased.
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Blanton, M.L., Kaput, J.J. (2011). Functional Thinking as a Route Into Algebra in the Elementary Grades. 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_2
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