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Teaching and Learning Patterns in School Mathematics pp 183–197Cite as

Patterns and Graded Algebraic Thinking

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Abstract

In this concluding chapter, we discuss ways in which algebra can be grounded in patterning activity. As a consequence, the development of algebraic generalization is also graded from nonsymbolic, to pre-symbolic, and finally to symbolic, reflective of the conceptual changes that occurred in the history of the subject. Over the course of four sections, we clarify the following points: (1) the different contexts of patterning activity and the kinds of algebraic generalizations they generate; (2) the relationship between arithmetical thinking and context-based structural thinking; (3) the grounding of algebra, functions, and models in nonsymbolic and pre-symbolic algebraic contexts; and (4) the graded vs. transitional nature of pattern generalization.

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Authors and Affiliations

  1. Department of Mathematics, San Jose State University, San Jose, CA, USA

    Ferdinand Rivera

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  1. Ferdinand Rivera
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Rivera, F. (2013). Patterns and Graded Algebraic Thinking. In: Teaching and Learning Patterns in School Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2712-0_7

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