Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers pp 291-318 | Cite as

# Developing a Structural Perspective and Its Role in Connecting School Algebra and Abstract Algebra: A Factorization Example

## Abstract

One goal of school algebra is the development of students’ facility with algebraic structures. Essential to that development is a *structural perspective*, which we consider as having three interrelated components—(1) ability to recognize and look for elements of a given type, (2) awareness of structure, and (3) tendency to attend to and look for structure. We suggest the adoption of a structural perspective as a central theme in both school algebra and abstract algebra, and argue that focusing instruction in an abstract algebra course on developing a structural perspective could help teachers teach school algebra as a coherent whole (rather than a set of loosely related procedures). We illustrate our argument with a description of algebraically parallel structures between the set of integers and the set of polynomials, and articulate how these structures can be understood coherently through an abstract algebra lens (integral domain) and the concept of factorization. We also describe how undergraduate mathematics students engage in mathematical tasks involving factorization of integers and polynomials and make structural sense of the relationship between the set of integers and the set of polynomials in the context of factorization. Using a new categorical framework of EDUS, we propose how teacher educators can engage prospective teachers in building toward a structural perspective in the context of factorization.

## Keywords

Structural perspective Structural/operational understanding Factorization Integral domain## References

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