## KAT Research Questions

/ Project Description / Research Objectives & Questions / Concepts / Literature Review /

## PROJECT DESCRIPTION: Knowing Mathematics for Teaching Algebra

Concerns about the quality of the mathematics
achievement of K-12 students in the

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.

# RESEARCH OBJECTIVES
& QUESTIONS

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**

- 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.) - To what extent can
distinct knowledge factors be identified?
- Is it possible to obtain
valid measures of knowledge by focusing on key content strands of the
algebra domain?

**2. Framework Validation**

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

**3. Status Study of Teacher Knowledge **

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