The STAAR Project: Supporting the Transition from Arithmetic to Algebraic Reasoning

  • The STAAR Project
  • About the Project
  • Technical Summary
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  • This material is based upon work supported by the National Science Foundation under Grant No. 0115609. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

The CU Professional Development Component

As part of the Interagency Education Research Initiative (IERI) grant "Supporting the Transition from Arithmetic to Algebraic Reasoning", our research team at the University of Colorado–Boulder spent three years developing and implementing a new professional development model for mathematics teachers: the "Problem-Solving Cycle". Its core goals are to help teachers expand their professional knowledge and improve the quality of their teaching.

The Problem-Solving Cycle

We based this model on the theory that teachers' own classrooms can be used together with supportive peer communities to create powerful tools for their continued learning. It consists of a series of three interconnected professional development workshops in which teachers share a common learning, planning and teaching experience, organized around a rich mathematical task.

During Workshop 1, teachers collaboratively solve the mathematical task and develop plans for teaching it to their own students. The goals of this workshop are to help teachers develop deeper knowledge of the subject matter and strong planning skills.

After the first workshop, teachers take the problem to their own students. Their classroom lessons are videotaped, and facilitators carefully select clips which highlight key moments in the instruction and students' thinking about the problem.

Workshops 2 and 3 focus on the teachers' classroom experiences and rely on video clips from their lessons. The goals of these workshops are to help teachers learn more about the mathematical concepts and skills entailed in the problem, to explore a variety of instructional strategies for teaching the problem, and to learn how to build on student thinking. The major focus of Workshop 2 is on exploring the role played by the teacher in implementing the problem, including ways they introduced the task or questions they posed as students worked on the task. Activities in Workshop 3 center on a critical examination of students' mathematical reasoning, such as unusual or unexpected methods they used to solve the task, or interesting conversations they had with one another in small problem-solving groups.

We conducted three iterations of the Problem-Solving Cycle with a group of middle school mathematics teachers. We used a design experiment research approach to study and refine this model. We collected and analyzed a large amount of data on the processes involved in developing and carrying it out, and its effect on the participating teachers' professional knowledge and teaching practices.

Facilitator's Guide

One important product from our initial development work is a facilitator's guide, which is intended for use by individuals (such as math coaches) who are interested in understanding and carrying out the Problem-Solving Cycle with teachers. This guide offers facilitators a description of and rationale for the types of activities involved in the Problem-Solving Cycle, along with examples from the STAAR project.

This model is intended to be relatively flexible, and open to many variations depending on the specific needs and interests of the facilitators and teacher participants. The facilitator's guide is written to help facilitators understand what components of the Problem-Solving Cycle are most central to its successful implementation, based on the goals and theoretical perspective of the research development team.

Click here to download a draft version of the Facilitator’s Guide. You may need to download and install the free Adobe Acrobat Reader if you do not already have a way to view PDFs.


For a more detailed statement of the recent work of the CU professional Development component, read Preparing Teachers to Foster Algebraic Thinking: A STAAR Professional Development Program, a presentation made at the 2005 IERI conference.