Bringing Out the Algebraic Character of Arithmetic
NSF Grant #REC-9909591

Project Overview
We conduct classroom investigations of young students learning algebraic concepts and notation as an integral part of their learning of arithmetic. We followed 70 students in a school in Somerville, MA (four classrooms) as they progressed from second through fourth grade. We have produced and implemented lessons on addition, subtraction, multiplication, division, fractions, ratio, proportion, negative numbers, function tables, graphs, and equations, guided by the ideas that:

• Children's understanding of arithmetic provide a fruitful point of departure for algebra if arithmetic operations are treated as functions;
• Additive structures require that children develop an early awareness of negative numbers and quantities and of their representation in number lines;
• Children need to learn multiple representations for handling unknowns and variables -- including function tables, graphs, and algebraic notation -- as early as possible; and
• Over time children need to move from their spontaneous, quantities-based reasoning towards reasoning about the form and structure of mathematical representations.

Participants

• David Carraher, TERC, PI
• Analúcia D. Schliemann, Tufts University, Co-PI
• Bárbara M. Brizuela, Tufts University
• Darrell Earnest, TERC
• Susanna Lara-Roth, Tufts University
• Irit Peled, Haifa University, Visiting Professor at Tufts
• Anne Goodrow, Rhode Island College
• Jerry Karacz, Arlington Middle School and TERC

More information on the project, including publications and lesson plans, are available at the project's website.