This working session explores tools for and approaches to measuring teaching practice in connection to curriculum material use. The goals of the session are to generate interaction about teaching practice and the relationship between written and enacted curricula and to examine and critique tools developed to measure this relationship.

Conceptual Perspectives

This session focuses on the overarching question: How can teaching practice be measured to investigate the kinds of teacher capacities needed for effective curriculum use? This question emerges from our ongoing explorations of the relationship between written and enacted curricula. 

Published curriculum programs, past and present, are relied upon heavily to improve instruction and increase student learning. This reliance is based on the assumptions that curricular programs are designed with a set of intentions, and that teachers will use curriculum programs in ways that are aligned with those intentions. Yet, there is substantial variation in how teachers use mathematics curriculum materials. These variations are functions of teachers’ personal characteristics, such as knowledge and dispositions, as well as their pedagogical choices and interactions with students during curricular enactment (Stein, Remillard, & Smith, 2007). Curriculum materials designed to foster ambitious math instruction place even greater demands on teachers than conventional materials (Stein & Kim, 2009) and require different kinds of capacity to use them. Brown (2009) used the term “pedagogical design capacity” to refer to “an individual teacher’s ability to perceive and mobilize curricular resources in order to design instruction” (p. 29). This capacity is at the heart of how teachers use and enact the written curriculum.

Examining teaching practice, then, is critical in our investigation of kinds of teacher capacities that are needed for teachers to transform written to enacted curricula. Existing instruments for analyzing classroom practices focus on normative criteria related to the quality of the mathematical task (e.g., academic rigor or mathematical quality) or assess fidelity to the curriculum. Drawing on some ideas in these existing ones, the two research projects represented in this proposal are developing new tools to measure teaching practice as it relates to the curriculum being used and the role that teacher capacity plays; one focuses on the elementary level and the other on the secondary level. Our aim is to develop measures of curriculum use that are tied to central ideas in the curriculum being used and that capture the complex work of curriculum enactment in the classroom. During the session, the participants will have an opportunity to work with and critique tools developed by both project teams.  

Project 1 (elementary): This project investigates teachers’ curriculum use and the capacities and supports critical to it. After undertaking analyses of five elementary curriculum programs, ranging from reform-oriented to commercially-developed, researchers collected data on how teachers used the teacher’s guides to plan lessons and then video recorded enacted lessons. Analysis of video data focuses on design moments, which refer to instances during a lesson when the teacher makes decisions that are not specified in the book or her plans. Examples of design moments include instances where the teacher makes choices about who to call on, how to respond to student errors or questions, and even when to move on. Our aim is to develop a coding scheme for analyzing teacher moves in these design moments that can be used with any curriculum programs and can be used to access teacher capacity.

Project 2 (secondary): This project explores teachers’ use of a coherent high school mathematics curriculum organized around mathematical habits of mind, or ways of thinking central to the discipline of mathematics. The substantive focus on habits of mind mirrors the focus on mathematical practices in the Common Core State Standards, where standards for practice are as important as standards for mathematics content to be taught. The habits of mind focus in the curriculum and professional development are intended by be educative for teachers on two levels: in supporting their instruction and in providing opportunities to learn mathematics practices and content. To test this theory, researchers have developed and adapted instruments to examine the role the curriculum plays in the design, selection, and modification of mathematical tasks and in particular, the ways in which teachers make use of the mathematical habits of mind approach in their classroom. Our goal is to refine a set of instruments that can be used in future large-scale research studying the relationships between use of a principled curriculum and teacher learning, teaching practice, and student achievement in high school mathematics.

Organization of the Session

Following a brief introduction, the session will consist of two 15-minute presentations about each study, including main aspects that are focused on in the analysis of teaching practice and preliminary tools developed to measure those aspects. Then, the participants will be asked to analyze two classroom video clips (one elementary and one secondary) using the tools shared in the presentations and then engage in critique of these two approaches. Finally, the participants and organizers will discuss the issues related to measuring teaching practice using the following guiding questions:

1. What does it mean to measure teaching practice, especially, in relation to curriculum use?
2. What is the relationship between curriculum fidelity and high capacity curriculum enactment?
3. To what extent do the tools presented measure aspects of teaching that the studies intend to capture? What elements are missing?
4. Are the elements of the tools clearly described in order to produce consistent results? In what ways can they be improved?
5. What are the limitations of the tools? What additional tools can be used with them?

Educational and Scientific Importance 

The work presented in this session, which seeks to examine the relationship between written and enacted curriculum, represents an important area of research that is currently underdeveloped in the literature. The session will contribute to this research by engaging participants in exploring conceptual and methodological issues related curriculum use and teacher capacity.  

References

Brown, M. W. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J.T. Remillard, B.A. Herbel-Eisenmann, & G.M. Lloyd (Eds.), Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction, (pp. 17-36). New York: Routledge.

Stein, M.K., & Kim, G. (2009). The Role of Mathematics Curriculum Materials in Large-Scale Urban Reform: An Analysis of Demands and Opportunities for Teacher Learning. In J.T. Remillard, B.A. Herbel-Eisenmann, & G.M. Lloyd (Eds.), Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction, (pp. 37-55). New York: Routledge.

Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). New York: Macmillan.