KAT Research Questions

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PROJECT DESCRIPTION: Knowing Mathematics for Teaching Algebra

Concerns about the quality of the mathematics achievement of K-12 students in the United States continue to dominate national dialogue in the academic and popular press. Students’ performance in algebra is particularly worrisome (Blume & Heckman, 2000; RAND Mathematics Study Panel, 2003). Today’s accountability-oriented policy environment produces pressure both for the improvement of students’ performance in mathematics, and for intensified efforts to explain variation in their performance.

The role of research in clarifying the complex array of factors that bear upon student performance in classrooms is central. Indeed, a variety of national and international efforts, such as the studies relating curriculum and student achievement that have been reported by Senk and Thompson (2003) and Valverde, Bianchi, Wolfe, Schmidt and Houang (2002) have made important contributions to better understanding these factors. The picture of how teachers’ knowledge relates to the effectiveness of their practice and to student performance is far less clear. The RAND Mathematics Study Panel (2003) has identified teachers’ mathematical knowledge and its development and use in teaching as one of three focal research areas for the nation. Studying this area will require clarification of the knowledge demands of teaching, tools for assessing mathematical knowledge for teaching across grade levels and mathematical domains, and deeper understanding of the ways in which prospective and practicing teachers have opportunities to acquire this kind of knowledge.

This project builds directly on the work undertaken in the NSF ROLE-funded project, A Study of Algebra Knowledge for Teaching at the Secondary Level (Joan Ferrini-Mundy, PI; Sharon Senk and Daniel Chazan, Co-PIs). That project produced a theoretically based provisional framework that describes the construct of algebra knowledge for teaching and is gathering empirical evidence for some of the aspects within this construct. To begin to validate the framework we are also producing draft assessment items to measure teachers’ knowledge of expressions, equations, and linear functions for teaching.


We are developing items and test forms, elaborating and validating a framework for knowledge for teaching algebra at the secondary school level, and exploring how knowledge for teaching algebra varies across preservice and in-service teachers. The research has three main objectives:

1. Instrument Design

  1. What set of categories should comprise knowledge of algebra for teaching for measurement  purposes? (Possibilities include: knowledge of school algebra content, knowledge of abstract and linear algebra content, understanding of students’ algebra misconceptions, curricular knowledge in algebra, and algebra knowledge for teaching.)
  2. To what extent can distinct knowledge factors be identified?
  3. Is it possible to obtain valid measures of knowledge by focusing on key content strands of the algebra domain?

2. Framework Validation

  1. What are the factors within knowledge of algebra for teaching ?
  2. If distinct factors can be identified, how can they be characterized?

3. Status Study of Teacher Knowledge

  1. How does knowlege of preservice teachers compare with that of experienced teachers?
  2. What is the status of knowledge among preservice teachers in different mathematics and mathematics education course settings?
  3. What is the status of knowledge among secondary school mathematics teachers who have participated in various algebra-related professional development experiences?



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