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

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The Algebra Problem: US Mathematics Education has an increasingly difficult in AlgebraProblems to solve. The standard indicators of student achievements international comparisons, NAEPand other national measures, as well as state test results all point in the direction of lower achievementas grade levels increase. Well-known TIMSS analyses of US curricula point in the direction of repetitionof 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, ofcourse, high failure rates in first year algebra courses contribute to alienation on the part of students andlow morale among teachers. Responses involve a wide variety, but largely ineffective tactics involvingmiddle and early high school curricula: pre-algebra courses of various kinds, screening and diagnostictests, district and state mandates that all students take Algebra I, lengthened courses, modifying thedefinition 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 andimplemented independently, improvements do not accumulate or multiply. NCTM recommendations forintegrating the development of algebraic reasoning across K-12 are implemented only in a few of thestandards-based curricula, and these mainly at the middle school level.Research Towards Solutions: Several research teams studying the development of algebraicreasoning in the early (K-5) grades, who are represented in this proposal, have formed an informalresearch collaborative, renewing a prior collaboration funded by the US DoE OERI in the early/mid1990. These researchers share broad hypotheses regarding the large positive potential of buildingalgebraic reasoning in the context of elementary mathematics, the need to exploit untapped studentlearning capacities among younger students, the powerful role of generalization and formalization indeepening students experience and understanding of elementary mathematics especially arithmeticand the potential for using changes in the curricular relationships between algebra and elementarymathematics as a catalyst and vehicle for faculty development of elementary teachers. These researchersare engaged in several complementary lines of work focusing on different aspects of the challengesstudent learning, classroom practice, curriculum development, professional development, capacitybuilding, and so on.Proposed Combination of Travel, Conferences and Monograph: The collaborating researchershave all been invited to present papers to an important conference to be held December 8-15, 2001, inMelbourne, Australia on The Future of the Teaching and Learning of Algebra which is being sponsoredby the International Commission on Mathematics Instruction. Professor Kaput has been designated toCo-Chair the Early Algebra Group at the conference. We request funds to exploit, in 3 ways, this uniqueopportunity 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 andone following the Melbourne conference, involving a slightly larger group of mathematics educatorsworking in this area. (3) To write and publish a monograph expressing our findings in order to informpolicy makers, curriculum developers and assessment builders of the latest developments in this rapidlychanging field. Hence we also request a small amount of funding for editorial work to pull together andpublicize the monograph, which in turn will point to additional web resources illustrating relevantresearch.