Discourse Analysis: A Catalyst for Reflective Inquiry in Mathematics Classrooms

The objectives of this project are to examine: the nature of mathematical discourse in middle school mathematics classrooms; the ways in which middle school mathematics teacher's beliefs impact the discourse when working to enact reform-oriented instruction; and how this information can be used to incorporate practitioner research using
concepts and tools of discourse analysis to improve mathematics instruction. The significance of this work comes in understanding how classroom discourse can affect the learning environment and engage students in learning mathematics in the ways proposed by the Standards. The focus of those documents has been to promote conceptual understanding and sense making instead of the procedural emphasis that often takes precedence in more traditional
mathematics teaching. The Standards vision can only be achieved if some of the discourse patterns in current mathematics instruction are changed from a transmission model of communication to one that supports inquiry.

The project is conducting case studies of the discourse in middle school mathematics classrooms. These case studies highlight classroom discourse patterns -the form, function, and meaning. In addition, we capture the process of teachers engaging in practitioner research projects in which they choose an aspect of their discourse to change and
study the affects of that change on the classroom learning environment. The project also examines how the combination of tools and concepts from discourse analysis and practitioner research projects affect teacher beliefs. Having teachers choose their focus of inquiry helps them invest and own the research process and enables them to understand, change and test out new ideas. It also allows them to gather evidence that can potentially change their beliefs.

The educational goal of this project is to design a long-term professional development program that will continue beyond this funding with other cohorts of teachers. The research case studies and other data are used to write case studies for both undergraduate methods courses and to as part of a long-term professional development program. In addition, these cases are made available to other teacher educators. The university-researchers and teacher researchers are collaboratively developing the courses and workshops that comprise the professional
development program.

This work offers a different approach to professional development (i.e., practitioner research) and different theoretical perspectives (i.e., tools and concepts of discourse analysis) for improving mathematics teaching and learning. focuses on teachers who would like to examine their instructional practice (or "enacted beliefs") at a fine-grained level. The research and educational activities make use of current advances in the study of and development of mathematics teaching and teachers. In addition, these activities offer a new perspective to be brought to the mathematics classroom - that of discourse tools and concepts as a mechanism of inquiry.

As discussed above, the intellectual merits lie in its ability to: a) offer insight into changes in teacher beliefs and classroom practices, b) provide frameworks and methodologies for studying classroom discourse, and c) uncover ways of helping teachers focus more centrally on the role of mathematics in classroom discourse. The broader impacts include: a) graduate students and teacher researchers will do research in a collaborative environment, disseminate findings to broad audiences, and be involved in planning the professional development program and coursework; b) case studies will be written and made available to other mathematics teacher educators; c) a long-term professional development program will continue with other cohorts of mathematics teachers; and d) similar case studies and activities will be used in undergraduate methods courses.

Project Publications and Presentations:

Herbel-Eisenmann, B. & Schleppegrell, M. (2008). 'What question would I be asking myself in my head?' Helping all students reason mathematically. Mathematics for all: Instructional strategies for diverse classrooms, Grades 6-8.

Males, L., Otten, S, & Herbel-Eisenmann, B. (2010).Challenges of critical colleagueship: Examining and reflecting on study group interactions. Journal of Mathematics Teacher Education, v. 13 (6), 459-471.

Herbel-Eisenmann, B.; Wagner, D & Cortes, V (2010). Lexical bundle analysis in mathematics classroom discourse: The significance of stance. Educational Studies in Mathematics, v. 75 (1), 23-42.

Otten, S.; Herbel-Eisenmann, B. & Males, L.M. (2010). Proof in algebra: An example of reasoning beyond examples. Mathematics Teacher, v.103 (7), 514-518.