Algebraic Thinking in Adult Education


M. Manly
L. Ginsburg
Publication Year
Resource Type
Informational Material
Number of Pages
Product Type

This resource explores the reasons that algebraic thinking is necessary for adults to enable them to meet the demands of the workplace of the future.  It further explores the reasons that algebraic reasoning needs to be integrated early into all levels of arithmetic instruction.

The authors use the term algebraic thinking "to mean thinking that involves

  • looking for structure (patterns and regularities) to make sense of situations
  • generalizing beyond the specific by using symbols for variable quantities
  • representing relationships systematically with tables, graphs, and equations
  • reasoning logically to address/solve new problems"

This resource includes sections on why algebra should be included in adult education, what recent scholarship says about algebra, current adult education mathematics instruction, revising mathematics instruction in adult education, supporting classroom practice, & what research would contribute to this discussion.

"This paper recommends two significant and necessary changes in our concept of algebra and the ways we approach it in education: a shift from thinking of algebra as one course to thinking of it as a content strand integrated into arithmetic instruction and a shift from thinking of algebra as merely manipulation skills to thinking of it as a means of representing and analyzing real situations."

What the experts say

The most significant impact that this resource has to offer to the field of adult education is that the way we teach algebraic thinking needs to change from one that is procedural to one that is conceptual, and that we should be introducing algebraic concepts in all levels of mathematics. For the administrators or other leaders in adult education, this resource serves as a reminder of the lack of knowledgeable Adult Math Educators that exist.  Furthermore, the need for good professional development to assist non-algebraic instructors to become confident in their understanding is critical in assisting learners to advance to the next level within the workplace or at college. 

This well-written article is an essential tool for those in the field of adult education: instructors, professional development specialists, and administrators.  The authors provide compelling reasons for revising mathematics instructions for adults, and they provide concrete suggestions (with examples) for doing so.  The authors make a good case for introducing algebraic reasoning early in adult learning of arithmetic, as well as for thinking of algebra as a means of representing real situations. Both authors are extremely well qualified to provide such reasoning, in terms of their experience in teaching, assessment, and research.

The authors provide examples to “illustrate the use of—and need for—algebra in everyday situations, formal education, and the workplace. “ These examples include personal finance and decision-making, academic requirements, entrance-to-employment requirements, and on-the-job requirements.

Most readers of this article will recognize the authors’ descriptions of current numeracy instruction, the problems that adult learners face, and the limitations in instructors’ ability to teach mathematics adequately and with confidence.  The authors are very aware of factors in adults learning math: student persistence, English-language learning, and issues of learning differences/disabilities.

If this is not enough to convince readers of the importance of this article, they should take notice of changes ahead.  The authors describe the content specifications for the GED 2012 Math Test: 

“The cognitive specifications for the 2012 version of the test require that only 20 percent of the items will be procedural in nature, while 30 percent will be conceptually based and 50 percent will reflect applications, modeling, and problem solving. Examinees will be allowed to use a calculator for the entire test. In terms of content, 30 percent of the items will come from the area of “Algebra, Functions, and Patterns,” where benchmarks focus on concepts emphasized in the modeling approach to algebra.”

Some of the Resources Cited in the article:

Kaput, J.J. 2007. What is algebra? What is algebraic reasoning? In D.W. Carraher, J.J. Kaput, and M.L. Blanton (eds.), Algebra in the early grades. New York: Routledge.

Carpenter, T.P., and M.L. Franke. 2001. Developing algebraic reasoning in the elementary school: Generalization and proof. In H. Chick, K. Stacey, J. Vincent, and J. Vincent (eds.), The future of the teaching and learning of algebra: Proceedings of the 12th ICMI study conference (vol. 1), 155–162. Melbourne, Australia: University of Melbourne.

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