The STAAR Project: Supporting the Transition from Arithmetic to Algebraic Reasoning
Technical Summary of the STAAR Project
This page corresponds to Section B of the original grant proposal to the IERI.
This project seeks to understand middle grade students' transition from arithmetic into algebraic reasoning, and to develop and evaluate proper educational approaches to improve the learning and teaching of increasingly complex mathematics. Acknowledging the complexity of this area of study, we have designed a comprehensive, systemic research and development program to address three inter-related areas of study, or tiers: Student learning and development; teacher beliefs, knowledge and practice; and professional development. Our approach emphasizes the parallel structures and processes among these tiers, as distinct but inseparable aspects of a unified system. Our specific research activities reflect this multi-tiered and dynamic framework, as an attempt to move beyond piecemeal, disconnected insights to reach a deeper appreciation of the learning process we set out to study, and to develop a coherent program of instruction and professional development.
We argue that the improvement of algebra education must be grounded in sound theory of how students develop algebraic reasoning and acquire domain knowledge and skills; and the beliefs and existing practices of teachers. The theory informs curriculum design, assessment, teaching practices, and professional development efforts. Specifically, the student tier is designed to allow the construction of a detailed developmental model of students' evolving algebraic reasoning and skill acquisition, paying close attention to the transition from intuitive, verbally-grounded reasoning and concrete problem-solving strategies to comprehension and mastery of the formal, abstract, symbolic methods of algebraic reasoning. Based on this model, we propose to construct a diagnostic assessment system, embedded in classroom activities, that will guide instruction designed to move learners toward the use of more effective, higher-level strategies. In the teaching tier, we examine the effects of instructional interventions on students and teachers and test a promising pedagogical approach—Bridging Instruction—designed to facilitate students' transition to more complex mathematics; we also explore teachers' affective and cognitive views regarding student knowledge and learning, as well as how the perceive their own practices; and finally, we investigate the role of reform-based curricula on teacher beliefs, practice and change. In the professional development tier, we design, implement and evaluate a "proof-of-concept" teacher professional development (TPD) program, building on our cumulative insights in the other tiers. This prototype implementation extends an existing technology-based approach and enable us to evaluate and perfect a scalable model of TPD designed to impact teacher practice on a broad scale, moving the results of this research into middle school classrooms.
Our methodological approach is both naturalistic and experimental. From a naturalistic viewpoint, we study the situated learning and teaching experiences of students and teachers to construct a detailed developmental model, and to document and understand how initial conceptions and participation patterns influence performance and development. From an experimental view, questions center on how theoretically motivated interventions in complex classroom settings can lead to measurable and sustainable improvements in algebraic reasoning and instruction, above and beyond conditions that do not reflect the interventions. Extensive comparative studies address this question.
Technology is a central aspect of this project. We examine ways in which computer, telecommunications, and video case-based technologies support student learning and the development of professional communities of middle school mathematics teachers. We implement our findings into a coherent educational program for students and teachers using Algebra Cognitive Tutors, and the STEP Web teacher professional development environments.
This project is designed, conducted, and interpreted by an interdisciplinary team of investigators from mathematics and mathematics education, developmental psychology, educational psychology, technology and learning environment design, teaching and teacher education, research methods and program evaluation. The investigative team represents three often disparate research traditions: psychometrics, cognitive science, and situativity. We take a multi-disciplinary approach to wrestle with a plurality of perspectives, to identify theoretical and empirical synergies, as well as conflicting predictions and explanations, and to expand the theoretical and methodological knowledge of the members of the investigative team and the educational research community.