Difference between pages "Stein, Remillard, & Smith (2007)" and "Brown (2009)"

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The chapter ''How Curriculum Influences Student Learning'' was written by [[Mary Kay Stein]], [[Janine Remillard]], and [[Margaret Smith]] and published in the [[Second Handbook of Research on Mathematics Teaching and Learning]].
{{Title|The Teacher-Tool Relationship: Theorizing the Design and Use of Curriculum Materials}}


== Detailed Summary of ''How Curriculum Influences Student Learning'' ==
* Author: [[Matthew Brown]]
* Book: ''[[Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction]]''
* Year: 2009
* Source: http://www.routledge.com/books/details/9780415990103/


Stein, Remillard, and Smith open their chapter with comments on the growth of research in the area of curriculum use. The [[Handbook of research on mathematics teaching and learning|1992 NCTM ''Handbook'']] did not include a chapter on this topic, but the emergence of new curricula following the [[Curriculum and Evaluation Standards for School Mathematics|1989 NCTM ''Standards'']] spurred a greater research interest in curricula and how they influence student learning. Also, the [https://en.wikipedia.org/wiki/No_Child_Left_Behind_Act 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 ===
== Outline of Headings ==


==== Multiple Meanings of Curriculum ====
* 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
* Types of Curriculum Use: Offloading, Adapting, and Improvising
* 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


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.
== Summary ==


Within curriculum research, care is typically taken to describe differences in curriculum:
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 ({{Cite|Ball & Cohen|1996}}; [[Cohen (1988) Tech|Cohen, 1988]]; Cuban [[Cuban (1992)|1992]], [[Cuban (1993)|1993]]; {{Cite|Snyder, Bolin, & Zumwalt|1992}}), the reasons of which have been attributed to practitioners ({{Cite|Cohen|1990}}; {{Cite|Spillane|1999}}), policies ({{Cite|Spillane|1998}}), and professional development ({{Cite|Putnam & Borko|2000}}; {{Cite|Wilson & Berne|1999}}). Other studies have focused on how teachers interpret curriculum materials ({{Cite|Ben-Peretz|1990}}; {{Cite|Brown|2002}}; {{Cite|Brown & Edelson|2003}}; {{Cite|Lloyd|1999}}; Remillard [[Remillard (2000)|2000]], [[Remillard (2005)|2005]]; {{Cite|Wiley|2001}}) and how curriculum materials might be better designed to meet the need of teachers ({{Cite|Brown|2002}}; {{Cite|Brown & Edelson|2003}}; {{Cite|Davis & Krajcik|2005}}; {{Cite|Davis & Varma|2008}}; {{Cite|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 ({{Cite|Gibson|1977}}; {{Cite|Hutchins|1996}}; Norman [[Norman, (1988)|1988]], [[Norman (1991)|1991]]; {{Cite|Pea|1993}}; Wertsch, [[Wertsch (1991)|1991]], [[Wertsch (1998)|1998]]), which Brown uses to highlight three key points:


* ''Written'' ([[Remillard (1999)|Remillard, 1999]]; [[Stein, Grover, & Henningsen (1996)|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)|Doyle, 1992]]), ''planned'' ([[Gehrke, Knapp, & Sirotnik (1992)|Gehrke, Knapp, & Sirotnik, 1992]]), ''institutional'', or ''intended'' curriculum.
# Curriculum materials play an important role in affording and constraining teachers' actions.
* ''Intended'' ([[Remillard (1999)|Remillard, 1999]]; [[Stein, Grover, & Henningsen (1996)|Stein, Grover, & Henningsen, 1996]]) curriculum refers to the teachers' plans for instruction, which may differ from the written curriculum.
# Teachers notice and use such artifacts differently given their experience, intentions, and abilities.
* ''Enacted'' ([[Gehrke et al. (1992)|Gehrke, Knapp, & Sirotnik, 1992]]; [[Remillard (1999)|Remillard, 1999]]; [[Stein, Grover, & Henningsen (1996)|Stein, Grover, & Henningsen, 1996]]) curriculum refers to the curriculum as implemented in classrooms.
# "Teaching by design" is not so much a conscious choice as an inevitable reality (p. 19).
* ''Experienced'' ([[Gehrke et al. (1992)|Gehrke, Knapp, & Sirotnik, 1992]]) or ''attained'' ([[Valverde, Bianchi, Wolfe, Schmidt, & Houang (2002)|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 between 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:
[[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 ({{Cite|Wertsch|1998}}). Artifacts mediate human activity ({{Cite|Vygotsky|1978}}; Wertsch, [[Wertsch (1991)|1991]], [[Wertsch (1998)|1998]]) in ways shaped by the artifact's affordances and constraints. Affordances might be attributed to the functional properties of the artifact ({{Cite|Gibson|1977}}) or perceptual cues that suggest how they might be used ({{Cite|Norman|1988}}). Constraints of artifacts restrict the ways in which we act and what we see as possible ({{Cite|Burke|1966}}; {{Cite|Wertsch|1998}}).


* Teacher beliefs ([[Cohen, 1990|Cohen, 1990]]; [[Jennings (1996)|Jennings, 1996]]; [[Putnam (1992)|Putnam, 1992]]; [[Remillard (1992)|Remillard, 1992]]; [[Spillane (1999)|Spillane, 1999]]; [[Spillane & Jennings (1997)|Spillane & Jennings, 1997]]) and knowledge ([[Brophy (1991)|Brophy, 1991]], [[Brophy (2001)|2001]]; [[Stein, Baxter, & Leinhardt (1990)|Stein, Baxter, & Leinhardt, 1990]])
[[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 ({{Cite|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:
* Teachers' orientations toward curriculum
* Teachers' professional identity ([[Remillard & Bryans (2004)|Remillard & Bryans, 2004]])
* Teacher professional communities ([[Cobb, McClain, de Silva Lamberg & Dean (2003)|Cobb, McClain, de Silva Lamberg & Dean, 2003]]; [[Little & McLaughlin (1993)|Little & McLaughlin, 1993]]; [[Louis, Marks, & Kruse (1996)|Louis, Marks, & Kruse, 1996]]; [[Stein, Silver, & Smith (1998)|Stein, Silver, & Smith, 1998]])
* Organizational and policy contexts ([[Berends, Kirby, Naftel, & McKelvey (2001)|Berends, Kirby, Naftel, & McKelvey, 2001]]; [[Bodilly (1998)|Bodilly, 1998]]; [[Datnow, Hubbard, & Mehan (2002)|Datnow, Hubbard, & Mehan, 2002]]; [[Fullan (1991)|Fullan, 1991]]; [[Kirby, Behrends, & Naftel (2001)|Kirby, Behrends, & Naftel, 2001]])
* Classroom structures and norms ([[Doyle (1983)|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).
# They are static representations of abstract concepts and dynamic activities — a means for transmitting and producing activity, not the activity itself.
# They are intended to convey rich ideas and dynamic practices, yet they do so through succinct shorthand that relies heavily on interpretation.
# 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.
# They may reflect common or existing practices and at the same time aim to shape innovative or new practices.
# They represent an interface between the knowledge, goals, and values of the author and the user.
# They require craft in their use; they are inert objects that come alive only through interpretation and use by a practitioner (pp. 21-22).


==== Curriculum Materials: An Evolving Concept ====
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 ({{Cite|Barab & Luehmann|2003}}; {{Cite|Brown|2002}}; {{Cite|Davis & Krajcik|2005}}; {{Cite|Matese|2005}}; {{Cite|Remillard|2005}}). Even when curriculum materials are provided, teachers still ''select'' materials according to their beliefs, skills, knowledge, and goals ({{Cite|Freeman & Porter|1989}}; {{Cite|Tarr, Reys, Reys, Chavez, Shih, & Osterlind|2008}}) or resist scripted or otherwise inflexible materials ({{Cite|Cohen|1990}}; {{Cite|Remillard|1992}}; {{Cite|Wilson|1990}}) based on their goals and beliefs (Cohen, [[Cohen (1988) Practice|1988]], [[Cohen (1990)|1990]]; {{Cite|Lloyd|1999}}; {{Cite|Lloyd & Wilson|1998}}; {{Cite|Wilson & Goldenberg|1998}}). Next, teachers ''interpret'' materials in planning and instruction ({{Cite|Ben-Peretz|1990}}; {{Cite|Stein, Remillard, & Smith|2007}}). Then teachers ''reconcile'' those interpretations with their instructional goals ({{Cite|Ben-Peretz|1990}}; {{Cite|Remillard|2005}}), and ''accommodate'' the needs of their students, making continual adjustments and providing feedback ({{Cite|Stein|1996}}; {{Cite|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 ({{Cite|Remillard|1992}}; {{Cite|Tarr, Reys, Reys, Chávez, Shih, & Osterlind|2008}}).


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,
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).


<blockquote>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)</blockquote>
=== Types of Curriculum Use: Offloading, Adapting, and Improvising ===


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 curricula 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.
From his dissertation work ([[Brown (2002)|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.


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)|Remillard, 2005]]).
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,


==== Literature Selection and Boundaries of this Review ====
<blockquote>
"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).
</blockquote>


For this chapter, Stein, Remillard, and Smith reviewed peer-reviewed research related to the effects of textbooks on both students and teachers. Most of the research stemmed from the NSF-funded curriculum development following the publication of the [[Curriculum and Evaluation Standards for School Mathematics|1989 NCTM ''Standards'']]. As an NSF requirement, curriculum developers were required to do evaluations of their work and many of the developers were researchers with the appropriate skills and methods for determining the effectiveness of curriculum. In contrast, research by commercial publishers often focuses on marketability instead of student learning. Stein, Remillard, & Smith provide a table (p. 325) listing common curricula by grade level, funder, and if they judge it to be standards-based or conventional. The authors did not consider policy documents or curriculum frameworks, although they acknowledge the influence of such documents.
=== Facets of the Teacher&ndash;Tool Relationship: The Design Capacity for Enactment Framework ===


=== Section One: Research on Curriculum Materials and Student Learning ===
Brown's ''Design Capacity for Enactment'' (DCE) framework ([[Brown (2002)|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.


Stein, Remillard, and Smith associate the growth in curriculum research on the math wars of the 1990s. While the [[1989 NCTM Standards]] were broad enough to garner wide appeal, the standards-based curriculum that followed had to be more specific and brought more scrutiny. Critics wanted "proof" that the texts were effective, even though "conventional textbooks used at the time had little or no evidence of their effectiveness" (p. 326). Most of the studies that followed assumed that curriculum materials mattered and caused differences in what students learned, ignoring details associated with the intended and enacted curriculum.
Brown identified three teacher resources in the DCE. The first, subject matter knowledge, consists of knowledge about the domain ({{Cite|Ball|1991}}; {{Cite|Stodolsky & Grossman|1995}}), while pedagogical content knowledge ({{Cite|Shulman|1986}}) combines general knowledge about teaching with domain-specific teaching knowledge. Lastly, teachers' goals and beliefs ({{Cite|Ball & Cohen|1999}}) describe teachers' motivations to teach particular content in particular ways. Sometimes goals and beliefs conflict with instructional approaches ({{Cite|Spillane|1999}}; {{Cite|Wilson|1990}}) and can be a barrier to the implementation of reforms (Cohen, [[Cohen (1988) Tech|1988]], [[Cohen (1988) Practice|1988]]).


==== Research on Content of Curriculum Materials ====
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 ({{Cite|Herbel-Eisenmann|2007}}), contextual factors ({{Cite|Grossman|1990}}), cultural teaching norms ({{Cite|Stigler & Hiebert|1998}}), professional identity ({{Cite|McClain, Zhao, Visnovska, & Bowen|2009}}; {{Cite|Smith|1996}}), or teachers' orientation toward curriculum materials ({{Cite|Remillard & Bryans|2004}}).


Most teachers rely on curriculum materials as a primary teaching tool ([[Grouws, Smith, & Sztajn (2004)|Grouws, Smith, & Sztajn, 2004]]) and the research clearly indicates that content coverage is important; students must be exposed to a mathematical topic to learn it ([[Hiebert & Grouws (2007)|Hiebert & Grouws, 2007]]). Yet, many factors affect how well content is learned, and some curriculum materials attempt to be educative for teachers ([[Davis & Krajcik (2005)|Davis & Krajcik, 2005]]) as well as students.
=== Pedagogical Design Capacity ===


===== What Content is Covered? =====
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 ({{Cite|Ball & Cohen|1999}}). Clarifying, Brown adds:


Content analyses compare curriculum materials to standards, frameworks, curriculum from other countries, or other external criteria, depending on the values of the researcher doing the comparison. The [[National Research Council (2004)]] found poor reliability in ratings depending on the rater and the various criteria available. Therefore, it is important to align one's goals and values for curriculum with the goals and values of the curriculum analysis.
<blockquote>
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)
</blockquote>


Stein, Remillard, and Smith summarize the three most prominent content analyses of the decade before their chapter was written:
In his dissertation, Brown ([[Brown (2002)|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.


* '''Project 2061''', a project of the [http://www.project2061.org/publications/textbook/default.htm American Association for the Advancement of Science], reviewed in the late 1990s 13 middle school textbooks and only found 4 to be satisfactory. The best of these four were ''Connected Mathematics'', followed by ''Mathematics in Context'', ''MathScape'', and ''Middle Grades Math Thematics''. No conventional texts were rated satisfactory.
=== Implications ===
* The <b>U.S. Department of Education</b> in 1999 used 8 criteria to find the following texts to be "exemplary:" ''Connected Mathematics Project'' (CMP), the ''Middle School Mathematics through Applications Project'' (MMAP), ''Cognitive Tutor'', ''College Prepatory Mathematics'' (CPM), ''Contemporary Mathematics in Context'' (Core-Plus), and the ''Interactive Mathematics Program'' (IMP). Judged as "promising" were ''Everyday Mathematics'', ''MathLand'', ''Number Power'', and the ''University of Chicago School Mathematics Program'''s (UCSMP) ''Integrated Mathematics 7-12''. These ratings came under attack by mathematicians opposed to the [[1989 NCTM Standards|NCTM ''Standards'']].
* The organization and website [http://mathematicallycorrect.com '''Mathematically Correct'''], known for its opposition to the [[1989 NCTM Standards|''Standards'']], reviewed a number of textbooks across several grade levels. Conventional textbooks were judged superior to standards-based curricula; ''Everyday Mathematics'' was the highest-rated standards-based text with a grade of "C", with all others getting a "D" or "F." Nearly all conventional curricula were given grades of "A" or "B."


The lessons learned from these reviews may say more about the reviewing methods themselves than the reviewed curriculum. [[Hiebert (1999)]] recommended that consumers determine what they value and then seek out the review whose methods most reflect those values.
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. ([[Brown, Pellegrino, Goldman, Nacu, Julian, Tarnoff, et al. (2004)|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" ({{Cite|Wiley|2001}}) has also explored such modular resources, which contrasts with research of scripted and inflexible curriculum resisted by teachers (e.g., {{Cite|Ben-Peretz|1990}}).


===== How is Content Presented? =====
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 ({{Cite|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.


In this section, Stein, Remillard, and Smith get at the "pedagogical intent" (p. 330) of curricular materials, and concede that just as values and judgement play a part in content coverage, "the criteria that researchers have used to make judgments about the pedagogical intent of various curricula are necessarily related to personally held views regarding the nature of mathematics and how students learn it" (p. 330). Curricular materials might influence teachers' practice with the inclusion of features like pre-tests, formative assessments, differentiation strategies, group activities, and group discussion prompts. Stein, Remillard, and Smith identify three overarching features of how curriculum is presented:
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.


* '''Order and manner of presentation'''. Materials vary in how they are sequenced and how explicit they are about new ideas; some texts strategically build to higher-order thinking, while others engage students in introductory activities designed to bring out student thinking.
== Corrolary ==
* '''Balance'''. Texts vary in their use of competing curricular elements, such as concepts vs. procedures, calculators vs. by-hand calculation, and balance of mathematical representations. For example, [[Clopton, McKeown, McKeown, & Clopton (1998)]] from Mathematically Correct discouraged calculator use, while many reformers endorse calculator use.
* '''Organizational style'''. Some textbooks use sequenced chapters and lessons, many of which ''spiral'' ([[Stein & Kim (2009)|Stein & Kim, 2009]]) to integrate previous topics into new content with increased expectations for mastery. [[Stein & Kim (2009)]] refer to these as ''integral'' curriculum because they must be taught in sequence over time to have the intended effect. Others curricula take a ''modular'' approach ([[Stein & Kim (2009)|Stein & Kim, 2009]]), often structured around thematic units, that allows subcomponents of the curriculum to be separated and recombined in different configurations. Many standards-based curriculum are modular, but research has said little about the effectiveness of this approach.
 
Both [http://www.project2061.org/publications/textbook/default.htm Project 2061] and [http://mathematicallycorrect.com Mathematically Correct] have reviewed how content is presented. Project 2061 used 24 instructional criteria in 7 categories, and rated highly ''Connected Mathematics'', ''Mathematics in Context'', ''MathScape'', and ''Middle Grades Math Thematics''. All conventional texts were rated unsatisfactory in the criteria of instructional support. Mathematically Correct's review focused on "quality of presentation" and "quality of student work." ''Connected Mathematics'' and ''Math Thematics'' received the lowest scores, while conventional texts (and ''Saxon'' texts in particular) rated highly.
 
===== The Support of Teacher Learning =====
 
Stein, Remillard, and Smith find that because standards-based curriculum focuses on students "doing mathematics" instead of the explicit instruction of skills, teachers need to provide the right classroom environment for the curriculum to have the intended effect. Often standards-based curricula is designed to help teachers with both the subject matter and how to teach it ([[Ball & Cohen (1996)|Ball & Cohen, 1996]]; [[Davis & Krajcik (2005)|Davis & Krajcik, 2005]]). This kind of ''educative curricula'' seeks to meet these five high-level criteria ([[Davis & Krajcik (2005)|Davis & Krajcik, 2005]], pp. 5-6):
 
# Educative curricula could help teachers learn how to anticipate and interpret what learners may think about or do in response to instructional activities.
# Educative curricula could support teachers’ learning of subject matter.
# Educative curricula could help teachers consider ways to relate units during the year.
# Educative curricula could make visible curriculum developers’ pedagogical judgments.
# Educative curricula could promote teachers’ pedagogical design capacities or their ability to use personal resources and the supports embedded in the materials to adapt curriculum to achieve productive instructional ends (as opposed to performing “lethal mutations”) ([[Brown & Campione (1996)|Brown & Campione, 1996]], p. 291).
 
[[Stein & Kim (2009)]] evaluated ''Everyday Mathematics'' and ''Investigations'' to determine how each communicated the text developers' rationale and reasoning (which Stein and Kim called ''transparency'') and how the textbooks helped teachers predict student strategies on tasks. Stein and Kim found that ''Investigations'' was more transparent and therefore more easily implemented with fidelity, whereas tasks in ''Everyday Mathematics'' had rationales that were less clear ([[Stein, Kim, & Seeley (2006)|Stein, Kim, & Seeley, 2006]]).
 
[[Brown (2009)]] organizes curricula into resource-centric or procedure-centric. Resource-centric attempts to communicate to teachers the main ideas and curricular features to teachers, but leaves details of implementation to the teachers. Procedure-centric focuses on actions for executing lessons. [[Stein & Kim (2009)]] judged ''Everyday Mathematics'' to be procedure-centric while ''Investigations'' was resource-centric. Stein, Remillard, and Smith judge that neither resource- or procedure-centric materials are always superior, as the needs of teachers vary with experience, the nature of the adopted curricula, and the instructional skills of the teachers.
 
==== Examination of Student Learning from Mathematics Curriculum Materials ====
 
Because the NSF-supported curriculum projects required formative and summative evaluations, much data was collected about their influence on student learning. Many of the summative evaluations are reported in ''[[Standards-Based Mathematics Curricula: What Are They? What Do Students Learn?]]'', a 2003 book edited by [[Sharon Senk]] and [[Denisse Thompson]]. Findings for the new curriculum were promising: students using the new curricula commonly equaled their traditionally-taught peers on traditional measures of mathematics ability, such as computation, and exceeded the performance of their peers on tasks focused on conceptual understanding and problem solving ([[Putnam (2003)|Putnam, 2003]]; [[Chappell (2003)|Chappell, 2003]]; [[Swafford (2003)|Swafford, 2003]]). However, some caution about these results is warranted due to differences in methodology, selection strategies for comparison groups, and possible researcher bias, as in some cases the curriculum creators personally trained the teachers in the study and/or performed the evaluations. Even so, many of the studies used standardized test data to make their comparisons, instead of creating assessments that might have favored their particular curriculum ([[Kilpatrick (2003)|Kilpatrick, 2003]]).
 
===== Comparative Studies Conducted by External Researchers =====
 
Stein, Remillard, and Smith point out that determining if one curriculum is better than another is more difficult than it might seem. The validity of such a study depends on having credible well-tested outcome measures with known psychometric properties. Also, it becomes difficult to compare two curricula with widely differing goals; does an evaluator only consider the goals the curricula have in common, the combined goals of both, or favor some goals over others? Also, how are comparison groups of students, classrooms, and teachers created in contexts where random assignment is not possible? Lastly, how does an evaluator account for variability in curriculum enactment? It is well-established that even teachers using the same task will vary in their approach ([[Stein, Grover, & Henningsen (1996)|Stein, Grover, & Henningsen, 1996]]; [[Tarr, Chávez, Reys, & Reys (2006)|Tarr, Chávez, Reys, & Reys, 2006]]). Observing these differences for a large number of teachers is resource-intensive and self-reporting from teachers is unreliable ([[Ball & Rowan (2004)|Ball & Rowan, 2004]]). These and other difficulties led the [[National Resource Council (2004)]] to state that the "studies as a whole across 19 programs studied does not permit one to determine the effectiveness of individual programs with a high degree of certainty" (p. 3). Stein, Remillard, and Smith remind readers that inconclusive evidence does not necessarily mean the curricula are ineffective, but only that the NRC panel was unable to make confident judgments about effectiveness.
 
The [http://ies.ed.gov/ncee/wwc/ What Works Clearinghouse] produced a report on middle school mathematics curriculum summarizing four randomized controlled studies. One study revealed significant effects for ''Cognitive Tutor Algebra 1'' ([[Morgan & Ritter (2002)|Morgan & Ritter, 2002]]) while another showed significant effects for ''I CAN Learn'' ([[Kirby (2004)|Kirby, 2004]]). Both curricula are standards-based and incorporate technology. The other two studies, involving the standards-based ''Expert Mathematician/UCSMP'' and the traditional ''Saxon'' curricula failed to find significant effects.
 
Non-randomized studies do reveal a pattern of higher student conceptual understanding and problem solving when using standards-based curricula (e.g. [[Boaler (1997)|Boaler, 1997]]; [[Huntley, Rasmussen, Villarubi, Sangtong, & Fey (2000)|Huntley, Rasmussen, Villarubi, Sangtong, & Fey, 2000]]; [[Thompson & Senk (2001)|Thompson & Senk, 2001]]). On skill-based and procedural tasks, students using standards-based curricula frequently scored the same as peers using more conventional curricula (e.g., [[Riordan & Noyce (2001)|Riordan & Noyce, 2001]]; [[Thompson & Senk (2001)|Thompson & Senk, 2001]]). There were exceptions to this, however, as in a study by [[Huntley, Rasmussen, Villarubi, Sangtong, & Fey (2000)]] where students using the standards-based Core-Plus Mathematics scored lower than conventionally-taught peers on skill-based Algebra problems when calculators were not allowed.
 
The general agreement between various studies has led some (e.g., [[Schoenfeld (2002)|Schoenfeld, 2002]]) to declare that standards-based curricula as effective. However, Stein, Remillard, and Smith remind us that goals and expected outcomes matter, as students will perform best on tests that resemble the content and approach of their textbooks. Also, the measures that claim students in one curricula outperform those using another might not apply to students of all abilities, or might not have much practical significance. Implementation also plays a larger role than many of these studies reveal. In [[Boaler & Staples (2008)]], teachers using the same curriculum reported scores that differed significantly according to their teaching approach, findings similar to [[Huntley, Rasmussen, Villarubi, Sangtong, & Fey (2000)]]. [[Balfanz, Mac Iver, & Byrnes (2006)]], in a non-observational study, found that higher levels of implementation were associated to higher student achievement. Therefore, one should be cautious about making causal statements between curriculum and student achievement, as few studies reveal ''how'' the curriculum takes affect and is influenced by other variables in instruction. A study by [[Tarr, Reys, Reys, Chávez, Shih, & Osterlind (2008)]] is one of a few studies that attempt to describe these interaction, defining what they termed a "standards-based learning environment" (SBLE). The authors found that using standards-based curriculum led to higher SBLE, and students in high-SBLE classrooms outperformed those in lower-SBLE classrooms using the same standards-based curriculum, similar to results seen by [[Boaler & Staples (2008)]].
 
=== Section Two: How Teachers Engage With and Interpret Curricular Materials ===
 
==== Framing of the Relationship between Written and Intended Curriculum ====
 
===== Content Coverage =====
 
===== Components of the Curriculum =====
 
===== Program Philosophy =====
 
==== Conceptualizations of Curriculum Use ====
 
===== Curriculum Use as Following or Subverting =====
 
===== Curriculum Use as Interpretation =====
 
===== Curriculum Use as Participating With =====
 
=== Section Three: The Enactment of Curricula in Classrooms ===
 
==== Ways in Which Curriculum Enactment Has Been Studied ====
 
==== The Source and Nature of Mathematical Tasks ====
 
==== Setting Up and Implementing Mathematical Tasks ====
 
==== Investigating Processes Involved in Task Implementation ====
 
=== Section Four: Explaining Transformations Within and Between Different Phases of Curriculum Use ===
 
==== The Teacher Matters ====
 
===== Beliefs and Knowledge =====
 
===== Orientation =====
 
===== Professional Identity =====
 
==== Students Matter ====
 
==== The Context Matters ====
 
===== Time =====
 
===== Local Cultures =====
 
===== Teacher Support =====
 
==== The Curriculum Matters ====
 
===== Conventional versus Standards-based Curricula =====
 
==== Curriculum Features ====
 
==== Educative Curriculum ====
 
=== Section Five: How the Enacted Curriculum Influences Student Learning ===
 
=== Summary and Conclusions ===
 
==== Curricula Differ in Significant Ways ====
 
==== These Differences Impact Student Learning ====
 
==== No Curriculum is Self-Enacting ====
 
==== Standards-Based Curricula are Challenging to Enact as Well ====
 
==== The Success of Standards-Based Curricula is Influenced by Multiple Factors ====
 
END
 
== About ==
 
=== APA ===
 
Stein, M. K., Remillard, J. T., & 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). Charlotte, NC: Information Age.
 
=== BibTeX ===


;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
<pre>
<pre>
@incollection{Stein2007,
@incollection{Brown2009,
address = {Charlotte, NC},
address = {New York, NY},
author = {Stein, Mary Kay and Remillard, Janine T. and Smith, Margaret Schwan},
author = {Brown, Matthew W.},
booktitle = {Second handbook of research on mathematics teaching and learning},
booktitle = {Mathematics teachers at work: Connecting curriculum materials and classroom instruction},
chapter = {8},
chapter = {2},
editor = {Lester, Frank K., Jr.},
editor = {Remillard, Janine T. and Herbel-Eisenmann, Beth A. and Lloyd, Gwendolyn M.},
pages = {319--369},
pages = {17--36},
publisher = {Information Age},
publisher = {Routledge},
title = {{How curriculum influences student learning}},
title = {{The teacher-tool relationship: Theorizing the design and use of curriculum materials}},
year = {2007}
year = {2009}
}
}
</pre>
</pre>


[[Category:Summaries]]
[[Category:Book Chapters]]
[[Category:2009]]
[[Category:Curriculum Use]]
[[Category:Curriculum Use]]
[[Category:Book Chapters]]
[[Category:Teacher Knowledge]]

Revision as of 14:50, 17 August 2014

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


Outline of Headings

  • 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
  • Types of Curriculum Use: Offloading, Adapting, and Improvising
  • 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, Chavez, 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).

Types of Curriculum Use: Offloading, Adapting, and Improvising

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,
address = {New York, NY},
author = {Brown, Matthew W.},
booktitle = {Mathematics teachers at work: Connecting curriculum materials and classroom instruction},
chapter = {2},
editor = {Remillard, Janine T. and Herbel-Eisenmann, Beth A. and Lloyd, Gwendolyn M.},
pages = {17--36},
publisher = {Routledge},
title = {{The teacher-tool relationship: Theorizing the design and use of curriculum materials}},
year = {2009}
}