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In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic exercise. This paper recommends two significant and necessary changes in the concept of algebra and the ways the authors 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. This fresh look at algebra and mathematics can result in instruction that appeals to mature students by addressing their needs in pursuit of a career and in their daily life by actively involving them in solving meaningful problems.