An International Perspective on the Role of Algebra in Elementary School Mathematics

University Of Massachusetts, Dartmouth, North Dartmouth MA

Investigators

Abstract

The Algebra Problem: US Mathematics Education has an increasingly difficult in Algebra Problems to solve. The standard indicators of student achievements international comparisons, NAEP and other national measures, as well as state test results all point in the direction of lower achievement as grade levels increase. Well-known TIMSS analyses of US curricula point in the direction of repetition of elementary skill building and superficiality of topic coverage as important contributors to the problem, combined with tell-and-drill pedagogy that puts students in overly passive position as learners. And, of course, high failure rates in first year algebra courses contribute to alienation on the part of students and low morale among teachers. Responses involve a wide variety, but largely ineffective tactics involving middle and early high school curricula: pre-algebra courses of various kinds, screening and diagnostic tests, district and state mandates that all students take Algebra I, lengthened courses, modifying the definition of if algebra, creating different versions of if algebra, end-of-course exams, among others. Each adjustment produces small improvements, although, since the tactics tend to be ad hoc and implemented independently, improvements do not accumulate or multiply. NCTM recommendations for integrating the development of algebraic reasoning across K-12 are implemented only in a few of the standards-based curricula, and these mainly at the middle school level. Research Towards Solutions: Several research teams studying the development of algebraic reasoning in the early (K-5) grades, who are represented in this proposal, have formed an informal research collaborative, renewing a prior collaboration funded by the US DoE OERI in the early/mid 1990. These researchers share broad hypotheses regarding the large positive potential of building algebraic reasoning in the context of elementary mathematics, the need to exploit untapped student learning capacities among younger students, the powerful role of generalization and formalization in deepening students experience and understanding of elementary mathematics especially arithmetic and the potential for using changes in the curricular relationships between algebra and elementary mathematics as a catalyst and vehicle for faculty development of elementary teachers. These researchers are engaged in several complementary lines of work focusing on different aspects of the challenges student learning, classroom practice, curriculum development, professional development, capacity building, and so on. Proposed Combination of Travel, Conferences and Monograph: The collaborating researchers have all been invited to present papers to an important conference to be held December 8-15, 2001, in Melbourne, Australia on The Future of the Teaching and Learning of Algebra which is being sponsored by the International Commission on Mathematics Instruction. Professor Kaput has been designated to Co-Chair the Early Algebra Group at the conference. We request funds to exploit, in 3 ways, this unique opportunity to bring an intensely international perspective to bear upon our active research program: (1) To support travel to the international conference. (2) To hold two meetings in the US, one prior to and one following the Melbourne conference, involving a slightly larger group of mathematics educators working in this area. (3) To write and publish a monograph expressing our findings in order to inform policy makers, curriculum developers and assessment builders of the latest developments in this rapidly changing field. Hence we also request a small amount of funding for editorial work to pull together and publicize the monograph, which in turn will point to additional web resources illustrating relevant research.