# Brown (2009)

The Teacher-Tool Relationship: Theorizing the Design and Use of Curriculum Materials

• Teaching as Design
• Theoretical Background
• Artifacts can Extend Human Capacities
• Curriculum Materials as Artifacts
• How Curriculum Artifacts Influence Instruction
• How Teachers Interpret and Use Curriculum Artifacts
• How Teaching is Design
• Analyzing Teacher Use of Curriculum Artifacts
• Facets of the Teacher-Tool Relationship: The Design Capacity for Enactment Framework
• Applying the Design Capacity Enactment Framework
• Pedagogical Design Capacity
• Design Implications
• The Design of Materials
• Multiple Points of Access
• Resource-Centric Material Design
• Creating Reusable Resources and Supporting Customization
• The Design of Professional Development

## Summary

Brown begins this chapter comparing the relationship between teachers and curriculum materials to those of musicians and their music; just as the same song played by different musicians takes on its own character, teachers interpret and adapt curriculum materials in ways that make their practice unique, even if there are similarities across classrooms. Curriculum materials are often used to promote educational reforms and the results of such efforts have been mixed (Ball & Cohen, 1996; Cohen, 1988; Cuban 1992, 1993; Snyder, Bolin, & Zumwalt, 1992), the reasons of which have been attributed to practitioners (Cohen, 1990; Spillane, 1999), policies (Spillane, 1998), and professional development (Putnam & Borko, 2000; Wilson & Berne, 1999). Other studies have focused on how teachers interpret curriculum materials (Ben-Peretz, 1990; Brown, 2002; Brown & Edelson, 2003; Lloyd, 1999; Remillard 2000, 2005; Wiley, 2001) and how curriculum materials might be better designed to meet the need of teachers (Brown, 2002; Brown & Edelson, 2003; Davis & Krajcik, 2005; Davis & Varma, 2008; Schneider & Krajcik, 2002). Brown's purpose in writing this chapter is to describe a theoretical framework for the relationship between curriculum materials and teacher practice. In doing so, Brown conceives of teaching as a design activity in which teachers evaluate their resources and make decisions in an effort to achieve instructional goals. Tensions between teachers (the agent) and their curriculum materials (the tool) build on a well-established body of learning theory (Gibson, 1977; Hutchins, 1996; Norman 1988, 1991; Pea, 1993; Wertsch, 1991, 1998), which Brown uses to highlight three key points:

1. Curriculum materials play an important role in affording and constraining teachers' actions.
2. Teachers notice and use such artifacts differently given their experience, intentions, and abilities.
3. "Teaching by design" is not so much a conscious choice as an inevitable reality (p. 19).

Wartofsky (1973) theorized artifacts as human-created tools that play a prominent role in our survival. Artifacts can be transmitted or preserved across place and time and our progress is inseparable from the artifacts we use (Wertsch, 1998). Artifacts mediate human activity (Vygotsky, 1978; Wertsch, 1991, 1998) in ways shaped by the artifact's affordances and constraints. Affordances might be attributed to the functional properties of the artifact (Gibson, 1977) or perceptual cues that suggest how they might be used (Norman, 1988). Constraints of artifacts restrict the ways in which we act and what we see as possible (Burke, 1966; Wertsch, 1998).

Norman (1988) suggested that humans often design artifacts to afford and constrain human activities in particular ways. In the case of curriculum, materials are designed to promote certain instructional, assessment, and student practices while discouraging the use of others. Often, curriculum materials allow teachers to engage in practices they could not have done alone, thus representing a shared capacity across teachers and their materials. Artifacts are also not limited to physical materials (Wartofsky, 1973); our cultural and historical ideas and practices also act to shape our activity. Brown enumerates six characteristics of curriculum materials that influence instruction:

1. They are static representations of abstract concepts and dynamic activities — a means for transmitting and producing activity, not the activity itself.
2. They are intended to convey rich ideas and dynamic practices, yet they do so through succinct shorthand that relies heavily on interpretation.
3. They observe a number of culturally shared notational rules, norms, and conventions in their representations — although fewer consistently and conventions in their representations — although fewer consistently used conventions exist for curriculum materials than for sheet music.
4. They may reflect common or existing practices and at the same time aim to shape innovative or new practices.
5. They represent an interface between the knowledge, goals, and values of the author and the user.
6. They require craft in their use; they are inert objects that come alive only through interpretation and use by a practitioner (pp. 21-22).

In addition to the influence of curriculum materials on teachers, Brown notes the importance of understanding the "dynamic and constructive ways" (p. 22) teachers interpret and use curriculum materials (Barab & Luehmann, 2003; Brown, 2002; Davis & Krajcik, 2005; Matese, 2005; Remillard, 2005). Even when curriculum materials are provided, teachers still select materials according to their beliefs, skills, knowledge, and goals (Freeman & Porter, 1989; Tarr, Reys, Reys, Chávez, Shih, & Osterlind, 2008) or resist scripted or otherwise inflexible materials (Cohen, 1990; Remillard, 1992; Wilson, 1990) based on their goals and beliefs (Cohen, 1988, 1990; Lloyd, 1999; Lloyd & Wilson, 1998; Wilson & Goldenberg, 1998). Next, teachers interpret materials in planning and instruction (Ben-Peretz, 1990; Stein, Remillard, & Smith, 2007). Then teachers reconcile those interpretations with their instructional goals (Ben-Peretz, 1990; Remillard, 2005), and accommodate the needs of their students, making continual adjustments and providing feedback (Stein, 1996; Wilson & Lloyd, 2000). Depending on the perceived success of the plan, teachers may add, modify, or omit parts of the curriculum, either due to interest or ability (Remillard, 1992; Tarr, Reys, Reys, Chávez, Shih, & Osterlind, 2008).

This perspective on teachers' curriculum use leads Brown to conclude that teaching is a form of design, a process that "is about crafting something in order to solve a human problem, to change the state of a particular situation from a current condition to a desired one, and to accomplish a goal" (p. 23). Understanding teaching as design highlights the dynamic between teachers and their materials, and Brown provides three constructs for understanding this relationship. The first contrasts offloading, adapting, and improvising and gives us a way to think about the degree to which teachers appropriate instructional materials. Second, Brown describes a framework for examining interactions between teachers and features of their materials. Lastly, he describes pedagogical design capacity, described as a teacher's "ability to perceive and mobilize existing resources in order to craft instructional contexts" (p. 24).

From his dissertation work (2002), Brown identified three ways teachers appropriate their materials as they design instruction. Offloading occurs when teachers follow curriculum materials closely, giving agency to the materials for guiding instruction. On the other end of the scale is improvising, when teachers craft instruction spontaneously and/or without specific guidance from their materials, thus shifting agency to themselves. In between, adapting occurs when teachers modify their materials to support instructional goals, thus sharing the agency between themselves and the materials.

Brown emphasizes that this scale does not necessarily correlate to teacher expertise and is not intended to measure the fidelity with which materials are used. It is designed to describe the nature of teachers' interactions with resources, not the outcomes of those interactions. Each position on the scale can serve a strategic purpose and be used with varying degrees of effectiveness. Brown explains,

"Just as a novice teacher might offload instructional responsibility to a scripted lesson due to limited understanding of the subject matter, so might an expert teacher offload instructional responsibility to a worksheet that supports her goals, freeing her to roam the room and respond to student needs as they arise" (p. 25).

### Facets of the Teacher–Tool Relationship: The Design Capacity for Enactment Framework

Brown's Design Capacity for Enactment (DCE) framework (2002) attempts to describe the aspects of both curriculum resources and teachers that influence why teachers interact with curriculum materials in different ways. The DCE framework includes three basic aspects of curriculum: physical objects, representations of tasks (procedures), and representations of concepts (domain representations). Physical objects include the material nature of the curriculum materials, including supplementary and recommended materials. Representations of tasks refers to the instructions and procedures given to teachers and students in using the materials, such as lesson guides or recommended homework problem sets. Domain representations consist of the ways materials organize concepts using diagrams, models, analogies, and the sequencing of topics.

Brown identified three teacher resources in the DCE. The first, subject matter knowledge, consists of knowledge about the domain (Ball, 1991; Stodolsky & Grossman, 1995), while pedagogical content knowledge (Shulman, 1986) combines general knowledge about teaching with domain-specific teaching knowledge. Lastly, teachers' goals and beliefs (Ball & Cohen, 1999) describe teachers' motivations to teach particular content in particular ways. Sometimes goals and beliefs conflict with instructional approaches (Spillane, 1999; Wilson, 1990) and can be a barrier to the implementation of reforms (Cohen, 1988, 1988).

Together, the three curriculum factors and three teacher factors provide a basis for understanding teachers' offloading, adapting, or improvising with curriculum resources. The factors are not all-inclusive, as other researchers have studied characteristics such as the "voice" of curriculum (Herbel-Eisenmann, 2007), contextual factors (Grossman, 1990), cultural teaching norms (Stigler & Hiebert, 1998), professional identity (McClain, Zhao, Visnovska, & Bowen, 2009; Smith, 1996), or teachers' orientation toward curriculum materials (Remillard & Bryans, 2004).

### Pedagogical Design Capacity

Brown describes pedagogical design capacity (PDC) as a teacher's "skill in perceiving the affordances of the materials and making decisions about how to use them to craft instructional episodes that achieve her goals" (p. 29) and more succinctly defines it as "a teacher's capacity to perceive and mobilize existing resources in order to craft instructional episodes" (p. 29). Whereas the DCE framework referred mostly to the resources, which Brown refers to as the nouns of the interaction between teachers and their materials, PDC applies to the verbs of the interaction and teachers' ability to accomplish new things with their knowledge (Ball & Cohen, 1999). Clarifying, Brown adds:

PDC represents a teacher's skill in perceiving affordances, making decisions, and following through on plans. Whether such design decisions manifest as offloads, adaptations, or improvisations is a separate matter. It is the skill in weaving various modes of use together and in arranging the various pieces of the classroom setting that is the mark of a teacher with high PDC, not whether they happen to be offloading, adapting, or improvising at any given moment. Rather, PDC describes the manner and degree to which teachers create deliberate, productive designs that help accomplish their instructional goals. (p. 29)

In his dissertation, Brown (2002) used PDC to describe how two teachers with similar resources described by the DCE framework nonetheless differed in the enactment of their curricula. Likewise, PDC was also used to describe teachers with similar enactment despite different resources described by the DCE framework. While Brown had evidence that PDC may emerge in teachers over time as they become more familiar with resources, more research is needed to understand how PDC is developed. There is also a need to develop measures for PDC and better understand its role in achieving outcomes.

### Implications

Better understanding of PDC would have implications for teacher preparation, curriculum design, and research methods. If curriculum materials were PDC-aware, they could offer support for different kinds of use which would be backed by aligned professional development. There is a natural tension between flexible, open-ended instructional designs and maintenance of coherence intended by curriculum authors. Brown et al. (2004) developed an online system called AIM (Adaptive Instructional Materials) that integrated a database of resources with a capability to adapt those resources into lesson and course plans. Similar research on "learning objects" (Wiley, 2001) has also explored such modular resources, which contrasts with research of scripted and inflexible curriculum resisted by teachers (e.g., Ben-Peretz, 1990).

The approach used for AIM by Brown et al. applied three key principles. First, a range of teacher expertise with content and instruction was supported with multiple ways of accessing the resources. Experts could browse or search for resources to assemble into plans or use pre-authored lessons. For teachers with less expertise, pre-authored materials annotated by developers to highlight affordances and constraints supported teacher learning and decision-making. Second, materials were designed to be resource-centric; that is, materials were organized around concepts, encouraging use in different contexts and avoiding a procedure-focused approach to organization. When materials were used in pre-authored lessons, designers attempted to be transparent (Davis & Krajcik, 2005) in their annotations by explaining the decisions made to use the materials in the chosen way. Lastly, to encourage reuse of resources and to support customization, designers attempted to balance the need to have materials dependent on context yet sufficiently generalized to be useful in different parts of the curriculum. This was done with descriptions of pedagogical affordances that avoided limiting teachers to the use of single strategies for implementation.

PDC's implications for professional development indicate a need to support teachers' decision-making about the resources they choose and how they use them. Brown suggests teachers receive help in evaluating features and affordances of materials and necessary modifications to align materials with instructional goals. This kind of professional development would have the added benefit of providing a context in which teachers could improve their understanding of instruction and student learning.

## Corrolary

APA
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, NY: Routledge.
BibTeX
@incollection{Brown2009,