Walter Stroup, The University of Texas at Austin, firstname.lastname@example.org
Algebra, Function-based algebra, Modeling, Technology, Curricular reform
To date, the multiple-strands based approach to curricula promoted by the National Council of Teachers of Mathematics (1989, 2000) has not displaced the single-strand Algebra I course as gatekeeper in the educational system of the United States and elsewhere around the world. If anything, in the US the standard, "stand-alone", Algebra I course is now even more central at many levels, including in state curricula (e.g., minimum course requirements and exit exams) and in nationally administered tests. In other countries many of the same topics, although sometimes in courses with varied names, are increasingly important in school-aged mathematics curricula. As a result, improving student outcomes related to content in a traditional Algebra I curriculum is among the most strongly felt needs in secondary mathematics education.
Against this backdrop of ever-increasing expectations regarding the teaching and learning of algebra we look to directly address the following question: Are there ways of systematically improving on expected student outcomes that move well beyond the current over-reliance on repetition, remediation or the rote rehearsal of what are often tricks, or simple mnemonics, for getting a "right" answers? A much more proactive strategy is needed that both targets the core of current algebra curricula and is likely to improve outcomes for ever-expanding numbers of students. Toward this end, we look to revisit issues surrounding how a function-based approach to algebra can begin to move us beyond the current state of the art in school-based practices. For this effort to be effective, however, we believe the current understanding of what is a function-based approach must expand beyond simply emphasizing multiple representations (e.g., tables, graphs, and expressions) and modeling co-variant relationships (e.g., instances of modeling constant rates of change).
Traditional algebra, as taught in schools, can be seen to center on three core ideas: equivalence, equals (as one kind of comparison of functions), and key aspects of linear functions. Function-based approaches to learning algebra can help students better understand all three of these core elements, as well as other many other topics typically found in most school-based mathematics curricula around the world. In addition, low cost computing has made the wide-scale adoption of a function-based approach possible. This adoption, we argue, is contingent on the mathematics education community doing a much better job of clarifying the ways in which a function-based approach addresses the core of the school-based algebra teaching and learning.