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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.

UW-Madison education professor Sharon Derry and colleagues are studying middle grade students' transition from arithmetic into algebraic reasoning. They seek to develop and evaluate proper educational approaches to improve the learning and teaching of increasingly complex mathematics.

Derry and colleagues address three interrelated areas of study, or tiers:

• Student learning and development
• Teacher beliefs, knowledge and practice
• Professional development

The team's approach emphasizes the parallel structures and processes among these tiers, as distinct but inseparable aspects of a unified system.

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. In the teaching tier, the team examines the effects of instructional interventions on students and teachers and tests a promising pedagogical approach called Bridging Instruction, which is designed to facilitate students' transition to more complex mathematics. The team also explores teachers' affective and cognitive views regarding student knowledge and learning, as well as how they perceive their own practices.

In the professional development tier, the team designs, implements, and evaluates a "proof-of-concept" teacher professional development program, building on the team's cumulative insights in the other tiers. This prototype implementation extends an existing technology-based approach and enables the team to evaluate and perfect a scalable model of teacher professional development designed to impact teacher practice on a broad scale, moving the results of this research into middle school, classrooms.

Derry and colleagues also 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.

For more information : Sharon Derry, sharond@wcer.wisc.edu