Stein, Remillard, & Smith (2007)

Handbook chapter from the Second handbook of research on mathematics teaching and learning by Mary Kay Stein, Janine Remillard, and Margaret Smith.

Detailed Chapter Summary

Stein, Remillard, and Smith open their chapter with comments on the growth of research in the area of curriculum use. The 1992 NCTM Handbook did not include a chapter on this topic, but the emergence of new curricula following the 1989 NCTM Standards spurred a greater research interest in curricula and how they influence student learning. Also, the No Child Left Behind requirement that federal funds only be spent on effective curricular materials drove curriculum developers to prove their materials had a positive effect on student learning.

Conceptual Issues, Definitions, and Boundaries

Multiple Meanings of Curriculum

Stein, Remillard, and Smith define curriculum as "the substance or content of teaching and learning (as distinguished from the 'how' of teaching)" (p. 321). They recognize, however, that curriculum is frequently used to describe a prescribed set of materials or content expectations described by policy documents or frameworks.

Within curriculum research, care is typically taken to describe differences in curriculum:

• Written (Remillard, 1999; Stein, Grover, & Henningsen, 1996) curriculum refers to curriculum as it exists on the printed page, or the goals and activities described by textbooks and policy documents. This is also known as the formal (Doyle, 1992), planned (Gehrke, Knapp, & Sirotnik, 1992), institutional, or intended curriculum.
• Intended (Remillard, 1999; Stein, Grover, & Henningsen, 1996) curriculum refers to the teachers' plans for instruction, which may differ from the written curriculum.
• Enacted (Gehrke, Knapp, & Sirotnik, 1992; Remillard, 1999; Stein, Grover, & Henningsen, 1996) curriculum refers to the curriculum implemented in classrooms.
• Experienced (Gehrke, Knapp, & Sirotnik, 1992) or attained (Valverde, Bianchi, Wolfe, Schmidt, & Houang, 2002) curriculum describes the impact the enacted curriculum has on students. Stein, Remillard, & Smith simply refer to this as student learning.

Opportunities for research exist both within and bewtween each of these stages of curriculum. For example, teachers' beliefs and goals transform a written curriculum into an intended curriculum, and within the enacted curriculum exists all the complexities of classrooms full of students that shape the implementation of a lesson. Furthermore, the enacted curriculum and student learning will shape teachers' future indended curriculum. Stein, Remillard, and Smith summarize the following list of factors that mediate curriculum:

• Teacher beliefs (Cohen, 1990; Jennings, 1996; Putnam, 1992; Remillard, 1992; Spillane, 1999; Spillane & Jennings, 1997) and knowledge (Brophy, 1991, 2001; Stein, Baxter, & Leinhardt, 1990)
• Teachers' orientations toward curriculum
• Teachers' professional identity (Remillard & Bryans, 2004)
• Teacher professional communities (Cobb, McClain, de Silva Lamberg & Dean, 2003; Little & McLaughlin, 1993; Louis, Marks, & Kruse, 1996; Stein, Silver, & Smith, 1998)
• Organizational and policy contexts (Berends, Kirby, Naftel, & McKelvey, 2001; Bodilly, 1998; Datnow, Hubbard, & Mehan, 2002; Fullan, 1991; Kirby, Behrends, & Naftel, 2001)
• Classroom structures and norms (Doyle, 1983)

Frequently the written curriculum is improperly judged to have a direct causal relationship on student learning. When all factors are considered, "it points to the fallacy of assuming that the materials themselves are the primary agent in shaping opportunities for student learning and instead uncovers the important role played by the interpretive and interactive influences of teachers and students" (p. 323).

Curriculum Materials: An Evolving Concept

Like many people, Stein, Remillard, and Smith use the terms curriculum materials and textbook somewhat interchangeably, intending to refer to "printed or electronic, often published, materials designed for use by teachers and students before, during, and after mathematics instruction" (p. 323). To distinguish the two, the authors pose textbooks as a classroom resource traditionally seen as the provider of practice exercises while curriculum includes instructional guides that emphasize both pedagogy and mathematical content. Interestingly,

To many, the term curriculum materials was used to connote something akin to an "anti-textbook" because these resources offered programs of instruction that rejected the notion that learning mathematics involved completing decontextualized exercises in a book. In contrast to textbooks, which were developed and marketed by commercial publishing companies, curriculum materials tended to be designed by mathematics experts and mathematics education researchers and, prior to the late 1990s, were sold independently to a fairly small market. For most standards-based curriculum materials, students' work during instruction involves investigative projects instead of exercises found on the pages of a "student textbook." Student textbooks are replaced by thin, often consumable, student workbooks that are designed to support students investigative work. The centerpiece of most lessons is the thinking that is required to grapple with the investigative task; student work books are designed to support that thinking by providing a basis for recording, summarizing or reflecting on one’s actions and thinking." (p. 323)

In contrast to curricula of the past, like the New Math materials, modern standards-based curricula typically include pedagogical guidance. In this way they are targeted at teacher learning and not meant to be used by students directly and independent of the teacher, an approach Remillard (2000) refers to as speaking to rather than speaking through the teacher. Standards-based curriculua are typically published by a commercial publisher alongside other materials, a process that can create compromises in the author's approach and blur the lines between standards-based and tradtional materials.

Some believe that the written and enacted curriculum should differ as little as possible, with teachers implementing the written text precisely as intended by the author or publisher. Others believe a text and other materials are merely a resource for teachers to use in their lessons. This belief typically views fidelity of implementation as impossible as both teachers and students will construct their own vision of the curriculum (Remillard, 2005).

Summary and Conclusions

The Success of Standards-Based Curricula is Influenced by Multiple Factors

END

Metadata

APA

Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369). Charlotte, NC: Information Age.

BibTeX

@incollection{Stein2007,
address = {Charlotte, NC},
author = {Stein, Mary Kay and Remillard, Janine T. and Smith, Margaret Schwan},
booktitle = {Second handbook of research on mathematics teaching and learning},
chapter = {8},
editor = {Lester, Frank K.},
pages = {319--369},
publisher = {Information Age},
title = {{How curriculum influences student learning}},
year = {2007}
}