# Remillard (2005)

Examining Key Concepts in Research on Teachers' Use of Mathematics Curricula

## Abstract

Studies of teachers' use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers' interactions with curriculum materials.

• Distinguishing Between the Intended and the Enacted Curricula
• The Significance of Mathematics
• Methods of Selection and Analysis
• Multiple Meanings of Curriculum Use
• Curriculum Use as Following or Subverting the Text
• Curriculum Use as Drawing on the Text
• Curriculum Use as Interpretation of Text
• Curriculum Use as Participation With the Text
• Implications for Studies of Curriculum Use
• Conceptions of Teaching with Respect to Curriculum
• Teaching as Multidimensional
• Remillard's Arenas of Curriculum Development
• Sherin and Drake's Models of Curriculum Use
• Individual Teacher Characteristics and Resources
• Conceptions of Curriculum Materials
• Texts as Subjective Schemes
• Texts as Objectively Given Structures
• The Teacher-Curriculum Relationship
• Framing Future Research
• The Teacher
• The Curriculum
• The Planned and Enacted Curriculum
• The Possibility of Teacher Learning Through Curriculum Use
• Implications for Policy and Practice

## Summary

Remillard begins her review by noting two trends: the availability of research-based curriculum based on the 1989 NCTM Standards and the tendency for districts to mandate a single curriculum in response to accountability pressures. The combination of these trends resulted in many teachers using new, unfamiliar texts as part of a reform strategy, something that may have doomed the prior reforms of the New Math era (Berman & McLaughlin, 1978; Sarason, 1982; Stake & Easley, 1978). Therefore, for new reforms to be successful, there is a need to better understand the relationship between teachers and the curriculum they use. Studies of this relationship tend to show great variability, with some teachers embracing new curriculum and being faithful to curriculum guides while other teachers reject new texts and avoid external curriculum guidance.

For Remillard, curriculum use refers to "how individual teachers interact with, draw on, refer to, and are influenced by material resources designed to guide instruction" (p. 212). By "curriculum" or "curriculum materials," Remillard means the "printed, often published resources designed for use by teachers and students during instruction" (p. 213), although she admits that "curriculum" can have other meanings. Some refer to the "formal curriculum," the goals and activities outlined by school policies or designed in textbooks, while letting "intended curriculum" refer to teachers' goals and the "enacted" or "experienced" curriculum represents what actually happens in the classroom (Gehrke, Knapp, & Sirotnik, 1992). Research of the enacted curriculum (Connelly & Clandinin, 1986; Cornbleth, 1988; Posner, 1988; Snyder, Bolin, & Zumwalt, 1992) generally acknowledges the interaction of teacher and curriculum and the role each plays in the process of enactment. Remillard uses "enacted curriculum" to refer to this view of curriculum that assumes the teacher is a designer of curriculum, not simply one who transmits or implements a lesson.

Remillard argues that mathematics education is a particularly rich and relevant subject for studying teachers' curriculum use, as traditionally mathematics has been more textbook-driven than literary-based subjects. Some mathematics teachers rely more heavily on their texts due to a lack of content knowledge; one study found that the same elementary teachers who enriched their language arts curriculum by adding to the text generally adhered closely to the exercises in their mathematics textbooks (Sosniak & Stodolsky, 2000). For her review, Remillard considered more than 70 studies spanning 25 years. The studies focused on teachers' interactions with curriculum and largely came either from peer-reviewed journals or, for recent work on Standards-based curriculum, dissertations and conference presentations. As the goal of this review was to provide the field with a theoretical foundation for research on curriculum use, Remillard chose to illustrate ideas with empirical examples instead of detailing the results of all relevant studies.

### Multiple Meanings of Curriculum Use

Remillard found that historical studies of curriculum use, such as those of the 1950s and 1960s, took a fixed view of curriculum and saw teachers simply as those who delivered that curriculum. Eventually, studies of teachers' adaptations and resistance to curriculum (e.g., Berman & McLaughlin, 1978; Sarason, 1982) challenged these views. Remillard found that some studies continue to see curriculum as fixed, "embodying discernible and complete images of practice" (p. 216), while others focus on classroom practice for curriculum analysis. These two are not mutually exclusive, Remillard cautions, as "fidelity with a curriculum guide is possible while examining the ways that a teacher uses the guide to construct her classroom practice" (p. 216). A third set of studies focused on teachers' interpretations of curriculum and do not assume that fidelity to textbooks is possible. This set is extended by a fourth group of studies that analyze the relationships teachers have with their curriculum resources, including factors that mediate that relationship. Fidelity-focused studies tend to be older while newer studies tend to take more nuanced views of teacher-curriculum relationships.

#### Curriculum Use as Following or Subverting the Text

Some studies take a perspective that the text is something to be followed with fidelity; in other words, that it is possible for the enacted curriculum to be equivalent to the written curriculum. These kinds of studies sometimes yield guidance for textbook authors who seek ways to help teachers follow the text more closely. For example, Remillard described a study by Stephens (1983) in which a failure by curriculum authors to understand traditions in schools as the reason a traditional group of teachers failed to follow a non-traditional text. Donovan (1983) made similar conclusions when he found teachers delegating responsibility for exploratory activities to classroom aides. When Komoski (1977) found differences between curriculum guides and the enacted curriculum, he faulted the district curriculum office for not providing more guidance. A study by Freeman & Porter (1989) acknowledged the role of teacher decision making, but proposed to reduce that decision making through more strict guidance in using textbooks, including potential sanctions for those failing to do so. Some studies of Standards-based curriculum also focused on fidelity of implementation, such as a 66-teacher, 2-year study by Manouchehri & Goodman (1998) that claimed a lack of teacher knowledge and curriculum support was the likely cause for differences between the written and enacted curriculum.

#### Curriculum Use as Drawing on the Text

Unlike the prior group of studies, which place the text first and then look at practice, Remillard includes in this group studies that put teacher practice first, and then look at how teachers use their curricular materials. The materials are seen as a resource or as tools, but the perspective stops short of seeing them as cultural artifacts (Cole, 1996; Wertsch, 1998) that act to shape human activity. The studies that Remillard found in this group included those in the Content Determinants Study (Floden, Porter, Schmidt, Freeman, & Schwille, 1981; Freeman & Porter, 1989; Kuhs & Freeman, 1979) which sought to find factors that determined mathematics content addressed in elementary classes, such as textbooks, parents, policies, and teacher factors. McCutcheon (1981) also looked at how textbooks combined with other influenced teacher reasoning and planning. Sosniak & Stodolsky (1993) found teachers used texts as a means to achieving larger curricular goals, although actual textbook use varied across teachers. A study of one teacher by Smith (2000) described how a Standards-based text and professional development combined both provide new ideas and conflict with previously held beliefs about learning.

#### Curriculum Use as Interpretation of Text

Studies in this category saw teachers as interpreters of their curriculum materials and assumes fidelity is impossible. Teachers use their knowledge and experience to give meaning to their materials (Ben-Peretz, 1990), and researchers with this perspective often apply the same logic to teachers' interpretation of policies and expected classroom practices. The Educational Policy and Practice Study (EPPS) examined how California teachers interpreted their materials and California's curriculum framework (e.g. Ball, 1990; Cohen, 1990; Heaton, 1992; Putnam, 1992; Weimers-Jennings, 1990; Wilson 1990, 2003). Teachers in these studies (known sometimes as the California Case Studies) frequently believed that their practice was aligned with reforms because they adhered to curricular materials that claimed to be aligned, yet their interpretations of the reforms, their texts, and their practice varied widely. Stake & Easley (1978) found similar results, where teachers claimed to be adhering to their text's goals of inquiry-based instruction, yet in practice lessons were generally teacher-led, step-by-step procedures. Collopy (2003) observed differences in how elementary teachers interpreted Standards-based texts, while Chavez (2003) studied 53 middle school teachers using Standards-based texts, also finding variations in practice.

#### Curriculum Use as Participation With the Text

These studies focus on the "teacher-text relationship," which Remillard describes as "collaboration with the materials" that "involves participation on the parts of both the teacher and the text" (p. 221). This overlaps with perspectives of text interpretation, but is distinguished by the focus on the activities of the teacher-text relationship, a relationship in which both the teacher and the text are seen as active participants. This perspective is rooted in Vygotsky's views of tool use and mediation (Cole, 1996; Vygotsky, 1978; Wertsch 1991; 1998) and studies taking this perspective often look at how teachers learn and change as they engage with curricular resources (e.g. Davenport, 2000; Remillard, 2000; Van Zoest & Bohl, 2002). Lloyd (1999) studied two high school teachers using Standards-based curriculum, focusing on how and why the teachers experienced success and difficulty using the materials for the first time. Remillard cites her own research (1996, 1999, 2000) of two fourth-grade teachers using a commercial publisher's reform-oriented textbook, where she found the teachers read different parts of the text and for different purposes, with one focused on assignments and the other on big ideas for planning. Sherin & Drake (2004) conducted a study with 10 elementary teachers and their use of a reform curriculum, trying to trace teachers' interactions with the text to classroom practices seen in enactment. Each teacher tended to follow a pattern of curriculum use, patterns that differed across teachers. In a science study, Brown (2002) found that depending on the situation, teachers either "offloaded" responsibility for curriculum design onto the materials, "adapted" the curriculum to differ from what was written, or "improvised" their own curriculum designs. These findings provided a theoretical foundation for the "Design Capacity for Enactment" framework which describes teacher actions as a result of the dynamic relationship between teachers and their materials.

## Also

APA
Remillard, J. T. (2005). Examining key concepts in research on teachers' use of mathematics curricula. Review of Educational Research, 75(2), 211–246. doi:10.3102/00346543075002211
BibTeX
@article{Remillard2005,
author = {Remillard, Janine T.},
doi = {10.3102/00346543075002211},
journal = {Review of Educational Research},
keywords = {curriculum materials,curriculum use,mathematics,teaching,textbooks},
number = {2},
pages = {211--246},
title = {{Examining key concepts in research on teachers' use of mathematics curricula}},
url = {http://rer.sagepub.com/cgi/doi/10.3102/00346543075002211},
volume = {75},
year = {2005}
}