Structuring teacher candidate learning about differentiated instruction through coursework

Teaching and Teacher Education 69 (2018) 62e74

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Research paper

Structuring teacher candidate learning about differentiated instruction through coursework Hilary Dack Assistant Professor of Middle Grades Education, Department of Middle, Secondary, & K-12 Education, University of North Carolina at Charlotte, Cato College of Education, 9201 University City Blvd., Charlotte, NC 28223, United States

h i g h l i g h t s
Varied activities supported appropriation of DI's conceptual & practical tools.
Participants' appropriation processes were markedly individualized.
Modeling of DI's practical tools was mostly unrecognized without explicit dialog.
All participants' prior beliefs about teaching aligned with DI's conceptual tools.
New knowledge of DI's conceptual & practical tools expanded participants' beliefs.

a r t i c l e i n f o Article history: Received 20 March 2017 Received in revised form 29 August 2017 Accepted 26 September 2017

1. Introduction Teacher education is charged with preparing teachers for the complexities of the classroom and is held responsible when candidates are insufficiently prepared to respond to its daily demands (Goodlad, 1990; Korthagen, Loughran, & Russell, 2006). In the last two decades, one aspect of the complexities of the contemporary classroom upon which teacher preparation has focused involves responding to increasing diversity among learners at all grade levels (e.g., Kober, 2012). The movement to differentiate instruction in the general education classroom in response to such diversity has gained increasing momentum both in the United States and internationally, with Tomlinson's (1999, 2014) model of differentiated instruction, or differentiation, being the most widely cited and visible approach. As a result, calls have been issued for teacher education programs to improve the quality of the preparation teacher candidates receive on instruction that responds to academic diversity effectively through Tomlinson's model and related approaches (Holloway, 2000; Tomlinson, 1999).

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Although support for differentiation is widespread, this philosophical approach to teaching and learning has not been implemented with fidelity in most K-12 settings, where one-size-fits-all instruction remains common (Brighton, Hertberg, Moon, Tomlinson, & Callahan, 2005; Callahan, Moon, & Oh, 2017; Tomlinson, 2016). Sherman (2009) offers one explanation of this lack of implementation, arguing that when teachers implement differentiation as a standardized recipe rather than a theory to be applied in situationally-specific contexts and improved outcomes are not immediately observed, teachers may abandon differentiation for other approaches perceived to be less labor-intensive quick fixes. Critical distinctions exist between a superficial, formulaic understanding of differentiation and a deep, meaningful understanding that lends itself to resourceful application and persistent fine-tuning. For prospective teachers to develop the latter form of understanding e one that would support the implementation of differentiation with fidelity over time in future practice e they must participate in thoughtfully crafted experiences in teacher education coursework designed to meet this goal. Through such strategic learning experiences, candidates may develop an accurate and robust vision of a differentiated classroom in which the needs of diverse learners are respected and proactively addressed. While several studies have examined the development of candidate knowledge of and attitudes toward Tomlinson's model of differentiation when enrolled in a teacher education course focused on the approach (Goodnough, 2010; Wan, 2016; West & West, 2016), they did not directly explore how specific learning experiences in coursework may be related to the development of candidate knowledge of and attitudes toward the model. Although this small body of research begins to suggest what candidates may come to know or feel about differentiation as they study it in depth,

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extant empirical work has not yet examined how specific, intentionally designed course learning experiences, or in-class activities, discussions, readings, and out-of-class assignments, should support teacher candidate learning about responding effectively to academic diversity. Further examination of how coursework focused on differentiation should be structured to support learning is therefore needed to clarify and illustrate how teacher educators can best instruct candidates in the model. This paper reports findings from a larger study on how teacher candidates made meaning of Tomlinson's model of differentiation in a course taught by Tomlinson1 focused solely on this model of teaching and learning (Dack, under review). The findings reported here respond to three research questions: (a) How were learning experiences in Tomlinson's course structured to support candidate appropriation of pedagogical tools related to differentiation?, (b) How did instructor modeling of differentiation support candidate appropriation of pedagogical tools related to differentiation?, and (c) How did candidates' prior beliefs about teaching and learning affect their appropriation of pedagogical tools related to differentiation? Study findings, which center upon participants' individualized responses to the course, suggest specific implications for teacher education programs that prepare candidates to respond to academic diversity and more general implications for programs that prepare candidates to enact forms of ambitious instruction.

2. Literature review 2.1. Differentiated instruction Differentiation presents an instructional approach in which a teacher proactively anticipates and responds to diverse learner needs (Tomlinson, 2014). It reflects a philosophy of teaching and learning grounded in the beliefs that academic diversity is both inevitable and positive, every learner should have equitable access to excellence in teaching, and the central purpose of teaching is to maximize each learner's capacity (Tomlinson & Imbeau, 2010). Academic diversity (Tomlinson, 2017) is defined as differences among students that may affect learning, including their (a) readiness, or current level of proficiency with knowledge or skill; (b) interests in particular topics; and (c) learning profile composed of preferences for approaching learning in ways that are most efficient, which may be influenced by traits related to culture (Gay, 2013; Ladson-Billings, 1995), intelligence preference (e.g., Sternberg, 1985), or other factors. A teacher in a differentiated classroom recognizes that students enter learning experiences at different starting points and with different backgrounds; thus, they will benefit from multiple options to access information, an array of ways to process information, a variety of outlets to demonstrate learning, and a range of supports. While a number of specific strategies for modifying instruction are common in differentiated classrooms, Tomlinson's model presents a way of thinking about teaching and learning rather than a set formula or recipe (Tomlinson, 2001). Researchers have documented positive effects on achievement and higher-order thinking skills among diverse K-12 student populations in classrooms where multiple elements of Tomlinson's model have been implemented with fidelity (Geisler, Hessler, Gardner, & Lovelace, 2009; Marulanda, Giraldo, & Lopez, 2006; Rasmussen, 2006). Likewise, increases in achievement across

1 IRB approval and participant permission to identify course instructor and research site were obtained. Because teacher educators' presentations of Tomlinson's model often reflect misconceptions about differentiation's principles and practices (Sands & Barker, 2004; Santangelo & Tomlinson, 2012), establishing that participants in this study learned about it with accuracy and fidelity was critical.

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content areas, grade levels, and diverse demographic groups have been reported in instances where Tomlinson's model has been adopted schoolwide (Beecher & Sweeny, 2008; Burris & Garrity, 2008; Tomlinson, Brimijoin, & Narvaez, 2008). 2.2. Teacher educator modeling In the context of teacher education, modeling effective pedagogy, including responsive instruction, assumes a unique role because teacher educators are in the business of teaching how to teach. The likelihood that candidates will effectively translate course content into their future practice increases when teacher educators model practices and beliefs (Grossman et al., 2000). However, modeling must be implemented effectively for future transfer to occur. “Congruent teaching” refers to the instructional approach in teacher education of both intentionally modeling a key strategy for candidates and offering “meta-commentary” on instructional decision-making and related theory (Swennen, Lunenberg, & Korthagen, 2008). This approach goes a step beyond “implicit modeling,” in which the instructor demonstrates a practice for candidates as they participate in the learning experience, but there is no discussion of instructor reasoning underlying instructional choices (Bullock, 2009). Although implicit modeling gives candidates opportunities to view a strategy in action, intended learning may not occur if candidates do not recognize or fully appreciate what was modeled (Lunenberg, Korthagen, & Swennen, 2007). In contrast, congruent teaching involves the second component of meta-commentary, which Lunenberg et al. (2007) suggested is necessary for candidates to ultimately translate modeled strategies in their own practice. Effective meta-commentary involves explicitly explaining why the instructor made particular decisions surrounding the modeled behavior (Lunenberg et al., 2007) and then connecting those decisions to relevant theory (Swennen, Korthagen, & Lunenberg, 2004). Ruys, Defruyt, Rots, and Aelterman (2013) proposed congruent teaching as a way to better prepare candidates to differentiate instruction, citing difficulties early career teachers often experience when attempting implementation (Humphrey et al., 2006; Wertheim, 2002). In their study of an instructor in a Flemish teacher training institute, researchers noted that, although the instructor modeled differentiation, she rarely explained her instructional decision-making, and only once connected it to theory. In turn, candidates appeared not to recognize the instructor's implementation of differentiation (Ruys et al., 2013). The researchers concluded “modeling is not enough” (Ruys et al., 2013, p. 104) when teaching candidates how to differentiate instruction by demonstrating its practices. The use of meta-commentary surrounding the modeling of differentiation can be especially important because, when accomplished with fidelity, seamless integration of the approach into teaching practice often passes unnoticed by students who experience it. Modeling differentiation not only offers opportunities for candidates to see Tomlinson's model in action and deconstruct its use by the instructor. It also allows instructors to better meet the needs of diverse candidates enrolled in teacher education programs. A growing body of research indicates that differentiating instruction in education coursework may yield improved academic outcomes for diverse adult learners (An, Tillman, Zhang, Robertson, & Tinajero, 2016; Chamberlin & Powers, 2010; Dosch & Zidon, 2014; Tulbure, 2011). 2.3. Candidates’ prior beliefs Teacher candidates often enter teacher education programs

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with firmly rooted beliefs, attitudes, and assumptions about teaching and learning (Borko & Putnam, 1996; Feiman-Nemser, 2001; Pajares, 1992; Wideen, Mayer-Smith, & Moon, 1998). Images of teaching formed in elementary and secondary school during the long “apprenticeship of observation” (Lortie, 1975, p. 61) provide an initial lens through which candidates may interpret ideas encountered in teacher preparation. Established beliefs may shape what candidates are able to learn from their programs (FeimanNemser, 2001), as well as pedagogical decision-making in the classroom (Chant, Heafner, & Bennett, 2004; Levin & He, 2008; Pham & Hamid, 2013). Pre-existing beliefs about teaching and learning arising from individual K-12 experiences often conflict with philosophical frameworks of teaching and learning advocated by teacher edu
, 2007; cation programs (Bryan, 2003; Leavy, McSorley, & Bote Stuart & Thurlow, 2000). Initial beliefs may become filters through which candidates sift and discard incompatible ideas encountered in teacher preparation, including instructional approaches with which they are unfamiliar (Bryan, 2003; Levin & He, 2008; Richardson, 2003). These beliefs often function as obstacles to change by narrowing the range of ideas candidates are willing to entertain (Feiman-Nemser, 2001). While prior beliefs about teaching and learning can be entrenched and inflexible (Bryan, 2003; Leavy et al., 2007; Richardson, 2003; Weinstein, 1990), candidates are more likely to change their views of teaching and learning in contexts in which they are continually prompted to probe and evaluate their own beliefs (Feiman-Nemser & Buchmann, 1986). 2.4. Conceptual framework Study design and implementation were grounded in cultural historical activity theory (CHAT). Viewed through this theoretical lens, learning is seen as an activity in a specific setting that occurs €m, 1999; Wenger, through collective social interaction (Engestro 1998). The learning setting reflects a particular activity system, or group of subjects who share the goal of transforming an object using available tools while conforming to rules that govern tool use € m, 1999; Wenger, 1998). and subject interactions (Engestro Applied to the process of learning to teach, especially through ambitious instruction, CHAT effectively frames the examination of novice teacher conceptions of teaching and learning and the available tools and common social interactions in settings of learning (Grossman, Smagorinsky, & Valencia, 1999; Grossman et al., 2000). Grossman et al. (1999) explained, “activity theory has the potential to illuminate how teachers' progression through a series of contexts can mediate their beliefs about teaching and learning” and thus can “help account for changes in teachers' thinking and practice” (p. 4). The key question CHAT frames is: “Under what circumstances do particular kinds of changes take place?” (Grossman et al., 1999, p. 4). Each teacher education course serves as an activity setting with its own “specific motive, structural features, sets of relationships, and resources for learning to teach” (Grossman et al., 1999, p. 11). In each course, candidates are taught particular conceptual tools, or broad principles that guide decisions about instruction, and practical tools, or specific classroom practices and strategies (Grossman et al., 1999). Extent of appropriation of these pedagogical tools depends on the congruence between the candidate's prior beliefs and the goals of the instructor presenting the tools (Grossman et al., 1999). CHAT offers an appropriate framework for empirical examination of (a) changes in candidates' prior beliefs about teaching and learning and (b) candidate appropriation of conceptual and practical tools presented in particular activity settings, including individual teacher education courses. This study focused on how learning experiences and

instructor modeling in a course on differentiation were structured to support candidate appropriation of key conceptual and practical tools, and how candidates' beliefs shaped their appropriation of those tools (see Fig. 1). 3. Method A qualitative research design is appropriate when an issue warrants exploration to develop a complex, detailed understanding, and when the voices of individuals involved with the issue will illuminate that understanding (Creswell, 2013). An exploratory qualitative paradigm presents unique strengths for research when its purpose is to understand the impetus behind the phenomenon of study and to identify factors associated with the phenomenon (Marshall & Rossman, 2011). The aims of the present study - to develop from the voices of participants a complex, detailed understanding of how factors such as course learning experiences, instructor modeling, and beliefs about teaching and learning may be related to candidate appropriation of differentiation's pedagogical tools - were therefore best met through an exploratory qualitative design. Interpretive qualitative approaches (Coffey & Atkinson, 1996; Erickson, 1986; Marshall & Rossman, 2011) to data analysis were used to explore participant meaning-making perspectives. The conceptual framework grounded in CHAT applied to the process of learning to teach informed the research design, including development of research questions focused on appropriation and selection of data sources that would best reveal activity setting outcomes. A graduate-level course on differentiation taught by Tomlinson in spring 2014 at a mid-sized public university in the United States served as the research site. The instructor is a Caucasian female who was a public school teacher for over 20 years and a university instructor for over 40 years. All 24 students enrolled in the course were invited to participate in the study, and 20 consented. Eighteen of those who consented were teacher candidates seeking initial licensure. This report reflects data only from the 18 teacher candidate participants, who were assigned pseudonyms (see Table 1). In spring 2014, 17 participants had completed student teaching and were in their final semester of coursework. 3.1. Differentiating instruction course Fourteen class meetings lasting two and a half hours were held throughout the spring semester (see Appendix A). Course content focused directly on conceptual tools of differentiation, or critical principles forming the model's philosophical foundation, and its practical tools, or specific classroom practices informed by those principles (see Appendix B; Tomlinson, 2014; Tomlinson & Imbeau, 2010). Content was presented through a variety of approaches including whole-group and small-group discussion and workshop sessions on specific instructional strategies. Candidates were often shown video clips of K-12 teachers responding to academic diversity or implementing specific differentiation strategies and prompted to consider the overt practical tools and underlying conceptual tools they reflected. Ten major course assessments involved candidates: (a) writing five reflections to periodically consider their evolving understanding of differentiation (see Appendix C); (b) developing three differentiated lesson plans that modified instruction based on readiness, interest, or learning profile; (c) writing a synthesis of the key principles of differentiation reflecting the content of three texts on Tomlinon's model; and (d) developing a final product of their choice. All participants read two required texts (Tomlinson & Imbeau, 2010; Tomlinson, 1999), a third self-selected text about Tomlinson's model, and numerous

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Fig. 1. Illustration of the study's conceptual framework grounded in CHAT, based on the work of Grossman et al. (1999, 2000). While tool appropriation by the end of the course was the primary desired outcome of the activity setting, potential changes in subjects' beliefs related to differentiation were also possible outcomes of experiences in the mediating context. Desired outcomes may not have occurred in a linear fashion at the course conclusion; rather, tool appropriation and changes in beliefs may have occurred in an iterative fashion throughout the course while participants engaged in interactions in the activity setting.

Table 1 Participant information. Participant

Program

Age

Gender

Race

Licensure Endorsement Sought

Allie Cora Courtney Haley James

B/MT B/MT B/MT B/MT B/MT

22 23 23 22 22

Female Female Female Female Male

Elementary Education, preK-6 History & Social Sciences, 6-12 Elementary Education, preK-6 & Special Education, K-12 English Education, 6-12 History & Social Sciences, 6e12 & Special Education, K-12

John Karen Leila Lindsey Marisa Martin Matt Michelle

B/MT PG/MT B/MT B/MT PG/MT PG/MT PG/MT B/MT

22 24 23 23 25 26 23 23

Male Female Female Female Female Male Male Female

Nicole Rachel Sarah Simone Stacy

B/MT B/MT PG/MT B/MT B/MT

23 23 26 23 23

Female Female Female Female Female

Caucasian Caucasian Caucasian Caucasian AfricanAmerican Caucasian Caucasian Caucasian Caucasian Caucasian Caucasian Caucasian AfricanAmerican Caucasian Caucasian Caucasian Caucasian Caucasian

History & Social Sciences, 6-12 Elementary Education, preK-6 & Gifted Education, K-12 History & Social Sciences, 6-12 Elementary Education, preK-6 & Special Education, K-12 English Education, 6-12 Mathematics, 6e12 Gifted Education, K-12 History & Social Sciences, 6-12 Elementary Education, preK-6 & Special Education, K-12 Elementary Education, preK-6 History & Social Sciences, 6-12 Elementary Education, preK-6 Elementary Education, preK-6 & Special Education, K-12 Elementary Education, preK-6

Note. Participants were enrolled in five-year bachelor/master of teaching (B/MT) or two-year postgraduate master of teaching (PG/MT) programs. Information included in the table was self-reported during initial interviews in January 2014. All participants but Haley were in their final semester of coursework in spring 2014 and graduated from their programs in May 2014. Haley completed her program in May 2015.

practitioner-oriented articles about differentiation. Tomlinson intentionally modeled key practices of differentiation throughout the course (Santangelo & Tomlinson, 2012). Many workshops and small-group activities were differentiated in response to diversity in student readiness, interest (often in particular content areas), or preferences for working configurations. The researcher assisted Tomlinson with the course. This assistance focused on administrative aspects of the course rather than leading instruction or grading assessments.

3.2. Data collection Interviews, informal in-class observations, and course assignments served as data sources. One-on-one interviews with participants were conducted at regular intervals throughout the course. Eleven participants identified as potential cases for longitudinal study were interviewed four times throughout the semester, while seven participants were interviewed twice at the beginning and end of the course. Interviews averaged approximately 40 min long.

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Interview questions were designed to illuminate participants' developing conceptions of differentiation, with a particular focus on potential appropriation of differentiation's pedagogical tools. Conducting interviews throughout the course, including at its start and conclusion, allowed potential changes in participant beliefs about teaching and learning related to differentiation, such as beliefs about the importance or feasibility of responding to academic diversity through instruction, to be examined. All interviews were conducted using semi-structured protocols, audio-recorded, and transcribed verbatim. The researcher attended all class meetings, engaging in informal participant-observation. Participants were observed during wholegroup discussions and while working with classmates in workshops or discussions. Questions participants raised during wholeclass discussions, as well as comments to classmates, were recorded verbatim. The ten written assignments each participant completed served as the third data source. These assignments were generated by participants using word processing software and submitted electronically to a course website. 3.3. Data analysis Participant meaning-making perspectives were examined through interpretive qualitative approaches (Coffey & Atkinson, 1996; Erickson, 1986; Marshall & Rossman, 2011) to data analysis. NVivo qualitative analysis software was used to organize data, code data, and compose analytic memos. Each participant served as one unit of analysis or case. Data were initially organized by case such that all data sources for each participant e two or four interviews, ten assignments, and any observation field notes recording their statements or actions - were coded together in the order in which the data were created.2 This was done to ensure each data source would be used in a balanced way to paint a representative portrait of the findings. This also allowed changes over time in participant tool appropriation and beliefs to be seen at the beginning, middle, and end of the course. The first stage of the coding process involved deductive provi~ a, 2014) using sional coding of all data (Miles, Huberman, & Saldan start codes grounded in the literature, such as codes reflecting key conceptual and practical tools enumerated in the differentiation literature (e.g., Tomlinson, 2014). The code list was then revised, refining the meanings of some codes and adding new ones, and a second round of inductive coding of all data was completed (Miles et al., 2014). For example, following deductive coding, new codes were added to reflect participants’ varied perceptions of instructor modeling of differentiation for subsequent inductive coding: perceived significant modeling, perceived limited modeling, or perceived modeling lacking. Following these two rounds of coding, analysis shifted from within-case examination of individual participant data sets to cross-case examination across all data sources based on tentative categories identified from recurring patterns. These categories were repeatedly tested and refined through analytic memoing (Charmaz, 2006). Ultimately, well-developed categories with the richest descriptions across data sources were identified as key themes reflected in the findings. For instance, following deductive and inductive coding rounds, a tentative category was identified surrounding participants' varied responses to the issue of which course learning experiences best supported their appropriation of

2 While the researcher's reflexive journal was not formally coded as a data source, the journal was referenced throughout the coding and analysis process to highlight context and background for events referenced in the data and support reflexivity.

differentiation's pedagogical tools. While coding made evident each participant could point to specific learning experiences as particularly supportive of their learning, subsequent cross-case analysis across all data sources based on this tentative category yielded the theme that participant conclusions regarding which learning experiences were the most beneficial were often decidedly individualized. This emerging theme was tested and refined through analytic memoing. While all data sources were given equal weight during early stages of the analysis process, interviews and written reflection assignments consistently yielded the richest data in response to the research questions, as their prompts were intentionally designed to illuminate how course learning experiences, instructor modeling, or beliefs about teaching or learning and the appropriation of differentiation's pedagogical tools may be related. However, to ensure data sources were drawn upon in a balanced way and findings would appropriately represent the data, other data sources including the five other assignments and observation field notes were consulted regularly to support triangulation and negative case analysis. Maxwell's (2013) framework for optimizing descriptive, interpretive, and theoretical validity was used. To support validity optimization, the project was structured to include: intensive, longterm interaction with participants; keeping a reflexive journal in which researcher-as-instrument issues were examined; using rich descriptions in detailing findings; creating and maintaining an organized audit trail; devoting attention to searching for negative cases and discrepant evidence; and engaging in data source triangulation (Maxwell, 2013). However, several study limitations and researcher-as-instrument issues should be considered when interpreting findings. A learner's thinking one day may be significantly different the next as new knowledge is encountered. Developing an understanding of a complex philosophy is a constantly evolving process, while primary study data sources were reflections and interviews completed at set time points. Eliciting data from participants at specific moments in time cannot guarantee a holistic understanding of a complex sense-making process. Throughout the study, researcher background, interests, and potential biases, and the effects those may have had on perceptions and interpretations of data, were also repeatedly considered. The researcher is a Caucasian female who worked extensively with Tomlinson's model as a middle grades teacher and graduate student. Through a constant focus on reflexivity, the researcher worked to ensure that personal beliefs about the potential efficacy of differentiation did not cloud what was perceived or recorded. An open environment for honest dialog with participants that communicated a non-evaluative stance was maintained. All interviews were conducted in private spaces that protected confidentiality and used carefully structured questions to avoid evaluative phrasing. 4. Findings Findings indicated Tomlinson intentionally structured course learning experiences that strongly supported teacher candidate appropriation of differentiation's pedagogical tools, including whole-class discussions, readings, analyzing sample differentiated lessons, writing differentiated lesson plans, and receiving individualized feedback, and Tomlinson frequently modeled differentiation through her own instruction with varied outcomes. Additionally, candidates' existing beliefs about teaching and learning appeared to be related to the appropriation of differentiation's pedagogical tools. While some commonalities existed among participant experiences with appropriating the pedagogical tools of differentiation, different learning experiences often

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supported appropriation for different students in unique ways.

4.1. Structuring course learning experiences to support appropriation of practical and conceptual tools During the course, all participants recognized their conceptions of differentiation were changing over time. As the course progressed, the evolution of every participant's conceptions included all of the following: deepening holistic understandings of the model as they gained knowledge of its structure and function, resolving misconceptions, refining conceptions of specific model components, and anticipating a role for differentiation in future practice in light of beliefs about its efficacy (See Dack, under review, for additional discussion of how participants made meaning of Tomlinson's model.). All participants attributed the evolution of their understanding of differentiation to specific learning experiences encountered in Tomlinson's course that supported appropriation of the model's pedagogical tools (see Table 2). In particular, five of these were identified by more than half of participants as playing a key role in supporting their learning about differentiation: (a) writing differentiated lesson plans, including descriptions of modifying instruction using data from assessments aligned to clear learning objectives; (b) receiving specific, individualized feedback on drafts of differentiated lesson plans; (c) reading assigned texts; (d) analyzing high quality differentiated lessons through video clips of differentiated classrooms or sample lesson plans; and (e) engaging in whole-class discussions led by Tomlinson about key principles and practices of differentiation. Participants who identified these five learning experiences as critical all indicated that the experiences supported appropriation of numerous practical tools of differentiation because they built accurate and specific knowledge of what each strategy is, how it works, and when to use it. Examples of these practical tools included tiering, Sternberg's triarchic theory of intelligence, RAFTs, and learning contracts (Tomlinson, 1999, 2014). When describing the effects of writing differentiated lesson plans, receiving feedback on lesson plan drafts, and analyzing differentiated lessons through video clips or sample lesson plans, participants reached similar conclusions about which key conceptual tools related to differentiation they made deeper meaning of as a result. These included principles focused on clear learning goals, flexible grouping, curricular alignment, “respectful tasks,” “teaching up,” the interdependence of model components, building community, and modifying instruction (Tomlinson, 1999, 2014). Participants who identified these three learning experiences as critical indicated the experiences supported appropriation of these conceptual tools because they offered opportunities to think through why the principles benefit student outcomes and to

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envision both how teachers act upon those principles in the classroom and how they themselves might act upon those principles in future practice. When it came to the effects of key course readings and other learning experiences, however, participant conclusions were markedly individualized. While 16 participants referenced a particular required reading as having a significant effect on their evolving understanding of differentiation, no more than three participants mentioned the same reading as supporting appropriation of pedagogical tools. Thus, participant conclusions about which readings were the most supportive of their learning in the course varied greatly, with no discernible patterns based on participant certification areas, content areas, backgrounds, or prior experiences being apparent. The degree to which students referenced highly specific statements Tomlinson made during whole-class discussions as influencing their appropriation of conceptual tools stood out within the data corpus. Comments such as “I remember Dr. Tomlinson talking about how …” appeared repeatedly throughout participant interviews and written reflections. Fourteen participants identified at least one particular statement Tomlinson made during a class meeting as critical to their deepening beliefs in the importance of differentiation's guiding principles, with five participants making four separate references to different comments she made during class meetings when describing ways in which their understanding of the principles had changed. The notable effect of instructor statements on appropriation of conceptual tools may have been heightened by participant awareness of Tomlinson's status as an expert on differentiation. Significantly, almost all of the statements participants referenced were different. Some participants pointed to specific analogies Tomlinson used that impacted their thinking, others highlighted colorful classroom anecdotes she shared, and many recounted straightforward yet powerful explanations of key concepts she offered in response to questions. Such statements, spread throughout every class meeting, all served to clarify and illuminate the complex guiding principles of the model, but which statements stood out in participants' minds as particularly compelling was highly varied. Notably, a number of participants pointed to a particular course learning experience that played a critical role in their developing understanding of differentiation which no other participant identified as important. For example, Allie was the only student who felt small group discussions were crucial to her learning, saying, “In small group discussion, we really get to touch on how we are feeling about the way we will incorporate differentiation into our teaching practice, what stands out to us in terms of words that relate to differentiation, strategies, and techniques we would use in our own classrooms.” James was the only participant who pointed

Table 2 Numbers of participants who identified course learning experiences as critical to appropriation of conceptual and/or practical tools of differentiation. Course Learning Experience

Number Identifying as Critical (n ¼ 18)

Participating in Whole-Class Discussions Completing Assigned Course Readings Hearing Tomlinson's Statements in Discussions Writing Differentiated Lesson Plans Analyzing Sample Differentiated Lessons Receiving Feedback on Differentiated Lesson Plans Participating in Workshop on Writing Learning Goals Synthesizing Three Texts on Differentiation Developing Final Course Product Receiving Handout on Writing Clear Learning Goals Writing Reflections Participating in Small-Group Discussions Analysis of Hrabowski Leadership Vision

17 16 14 14 11 10 5 3 2 1 1 1 1

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to an activity in which students analyzed University of Maryland, Baltimore County President Freeman Hrabowski's leadership vision as indispensable to his own understanding of building a supportive classroom leaning environment, saying, “the Hrabowski video … had a huge impact on my philosophy. I actually went home and changed … my online electronic [job application] portfolio because of it.” Again, no discernible patterns based on participant certification areas, content areas, backgrounds, or prior experiences were apparent in these conclusions. These findings point to the fact that, although there were commonalities among participant perceptions of which learning experiences best supported appropriation of differentiation's pedagogical tools, many participants also reached unique conclusions as to which additional learning experiences molded their thinking. 4.2. Modeling differentiation to support appropriation of practical tools Throughout the course, Tomlinson modeled differentiation in her own teaching practice with fidelity through the use of modified instruction based on readiness, interest, and preferences for working configurations; the establishment of a supportive learning environment; the use of ongoing formative assessment to inform instruction; and other methods. Practical tools of differentiation were demonstrated for candidates through learning experiences in which they directly participated, with the goal that they would recognize the strategy and consider how it was implemented. For some, the implicit modeling (Bullock, 2009) of differentiation did support appropriation of practical tools by providing an example of strategy execution. However, for most participants, the use of modeling did not fully achieve the desired outcome. While multiple elements of a differentiated classroom were modeled for candidates in all class meetings, the modeled practical tools were not explicitly discussed, and study participants varied in the degree to which they recognized they were experiencing elements of differentiation as learners. Participants fell into three categories: those who felt modeling of practical tools was lacking, those who recognized differentiation was modeled in significant ways, and those in between who saw differentiation modeled in limited ways. When asked about the presence of differentiation in course instruction, Matt was the only participant who reported seeing no examples of its practical tools modeled. John reported seeing it only in the final course product, which was differentiated based on interest, and in the instructor's building connections with students as a classroom community, while Stacy saw it only in how students were grouped. Both John and Stacy saw the course as “lacking” modeling of differentiation. John explained: There's such an opportunity to - why not differentiate this class about differentiation? I was kind of waiting for that, and it never really happened … I just feel like it would have made it easier to understand than just hypothetical or looking at a classroom, but actually differentiating the differentiation class … actual applications within the class itself. John suggested that a workshop on writing learning objectives held during one class meeting could have been differentiated based on readiness, saying, “We turned in drafts of [learning objectives before the workshop], so maybe break it up by readiness to work on it or edit them with other people.” In fact, Tomlinson had differentiated the learning objectives workshop based on readiness by placing students into different groups to complete different tasks after reviewing previous drafts of student work. In contrast to John's perceptions, Haley identified this workshop as the strongest

example of differentiation Tomlinson modeled. She was the only participant who identified the workshop as differentiated. The second group of participants perceived that Tomlinson modeled differentiation “a lot.” When asked to do so, Karen quickly identified five examples of how Tomlinson modeled it and commented that she felt this amount of modeling was helpful, saying, “I feel like they were good examples to the extent it could be modeled in our [higher education] class.” Simone likewise identified three accurate, in-depth examples of how differentiation was modeled in the course. Karen and Simone identified more specific examples of modeled differentiation than any other participants. The majority of participants identified only one or two examples. The most common example cited was flexible grouping used frequently in the course. Several participants noted they were unaware of the reasoning behind different groupings, as it was not explained and therefore seemed random. Thus, differentiation was implicitly modeled in numerous ways that participants generally did not recognize. When these practical tools of differentiation were not explicitly identified and the reasoning behind them was not discussed, their presence often passed unnoticed by the learners experiencing them. At other times, participants seemed to sense differentiation was occurring but lacked clarity about its purpose and structure. Lindsey explained, “I assume a lot of times when we split off into groups it was differentiated. I don't really know how or why or what the logic was there, but I just kind of assumed because it was a differentiated class.” Without explicit conversations, many participants appeared challenged in recognizing their own participation in learning experiences as reflections of the practices of differentiation. As a result, structuring the course to model practical tools of differentiation appeared not to support appropriation to the degree it might have if explicit discussion of modeled practices had been included. 4.3. Effects of prior beliefs on appropriation of practical and conceptual tools Because CHAT posits that the extent of a teacher candidate's appropriation of pedagogical tools depends on the congruence between candidate beliefs and the goals of the instructor presenting the tools (Grossman et al., 1999), this study also examined participants’ prior beliefs about teaching and learning. As candidates were exposed to new conceptual tools of differentiation throughout the course, they were repeatedly asked to evaluate the alignment between the beliefs underlying those principles of differentiation and their current beliefs about teaching and learning. Four of the written reflections called upon participants to examine this issue explicitly. For instance, two reflections at different points in the semester prompted them to explain which of the principles recently encountered in the course (see Appendix B) resonated most with their own beliefs about teaching and learning, surprised them most in light of their existing beliefs, and created the most challenge when attempting to align the principle with their beliefs (see Appendix C). Reflection prompts were posed at strategically timed points, including the beginning and end of the course, to illuminate participants' pre-existing beliefs about teaching and learning related to differentiation and potential changes over time. Participant responses to such prompts revealed complex internal processes through which they appropriated elements of conceptual tools of differentiation. Significantly, every participant recognized strong connections between the philosophy and principles of differentiation taught in the course and beliefs about teaching and learning with which they entered the course. No participant identified any areas in which their pre-existing beliefs conflicted with the tenants of

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differentiation. Marisa's comment was typical of participant responses to this issue: “I feel like pretty much everything we talked about in class or we studied … seemed right to me.” 4.3.1. Common pre-existing beliefs Participants identified a number of specific beliefs integral to their personal teaching philosophy as aligned with the conceptual tools of differentiation presented in the course. Most commonly referenced were the beliefs that: teachers should focus on student growth and improvement, all students can learn, children are unique individuals with varied needs, teachers should support varied learners differently, and high quality teaching is studentcentered. Each of these beliefs was identified by around half of all participants as critical to both differentiation and their pre-existing ideas about good teaching. Haley described a common participant reaction to examining differentiation's conceptual tools: I really like the idea that differentiation is rooted in deep respect for all students and in the belief that all students have a lot to contribute. Thus, our job is to figure out how to help them tap into their potential and excel, no matter where they are starting from. This fits nicely with my own beliefs about the importance of empowering all students and … harness everyone's talents. All participants appeared to recognize this “fit” between personal beliefs held at the beginning of the semester and conceptual tools underlying Tomlinson's model, using similar language such as “seeing connections,” “struck home,” “resonated,” and “alignment.” Five participants also discussed ways in which the course provided opportunities to clarify their pre-existing beliefs and acquire new verbiage with which to describe them. At the conclusion of the semester, Haley described being able to “say” her beliefs “better” after the course required her to “think through it more systematically,” and being able to describe why she had always wanted to be responsive to students. Nicole noted that the course “helped me put words to what all those things I was thinking meant,” such as beliefs related to mindset (Dweck, 2007). She explained, “I'd say they were ideas that had been forming and … we've talked about those two things for the majority of the semester, so thinking through that and being in the material and teasing it out through class have helped it crystalize.” Karen and Sarah experienced a similar type of clarification process that had the effect of confirming their beliefs as they examined them in conjunction with the philosophy of differentiation. Karen commented, “The course helped me define those beliefs [about teaching] and then reaffirmed what I had been thinking.” Similarly, Sarah identified a number of beliefs about teaching and learning reflected in the conceptual tools of Tomlinson's model which she had possessed before taking the course and re-committed to maintaining as part of her teaching philosophy after completing key course learning experiences. 4.3.2. Changes related to beliefs During the course, half of participants perceived a change related to their beliefs as a result of ideas to which they were exposed in class. Some reported a change in their beliefs about teaching and learning, while others reported a change in how they thought about their future practice in light of their beliefs. Those who reported a change in their beliefs about teaching and learning explained their beliefs had “grown” or “expanded.” This expansion of beliefs in some participants was the result of having, as Simone explained it, “incorporated more of the aspects of differentiation” into their philosophy of teaching and learning. For Sarah, this involved a “shift” through which beliefs she already held about challenging every student and focusing on student growth increased in importance, while Stacy perceived a “subtle” change in

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her teaching philosophy reflecting a deepened belief in the teacher's role as facilitator of learning who offers “different ways for you to learn that match what you need.” Other participants recognized changes in their ideas about how they would put their beliefs into practice when leading their own classrooms. Rachel's comment reflected their perceptions: The main core of what I believed, I don't think it changed, but I think that it’s kind of enhanced with differentiation, ‘cause … when I stand in front of a classroom, I think differently about how I would go about it …. My philosophy is still the same, but I might go about teaching them differently …. I have more tools. I have more ideas about how I would reach them and get them to their goal. Similarly, Karen commented that, although she had always believed in the importance of responding to student needs, “differentiation gives you a how to do thatda specific how … a more systematic way of doing that.” She went on to describe that knowing the “how” would allow her to put her philosophy into practice. Participant comments reflected that those who perceived a change in beliefs about teaching and learning appeared to appropriate the conceptual tools of differentiation by integrating those tools into their existing philosophy of teaching and learning without difficulty, while some viewed the practical tools of differentiation as specific methods of putting their individual philosophy into action. 4.3.3. Connections to pre-existing beliefs developed through teacher education A third of participants specifically pointed to the alignment among their personal beliefs about teaching and learning, the philosophy of teaching and learning emphasized in prior teacher education coursework, and conceptual tools reflected in Tomlinson's model. The importance of knowing your students as individuals was participants' primary example of this alignment. For example, Matt described the development of his beliefs about student-centered teaching as occurring in three phases. While he initially entered the teacher education program with existing beliefs about teaching and learning, such as the importance of a teacher's having a growth mindset (Dweck, 2007) toward students, his belief in the importance of “student-first” teaching deepened as he progressed through coursework emphasizing this approach. He characterized this as thinking about student needs in the “aggregate” and explained that, during the course, he took “the next step” with this belief as he began “seeing those individual students and being responsive to individual students and putting those individual interests first.” While Matt learned that “students collectively are first” from previous teacher education coursework, during the differentiation course, his belief evolved to become “deeper than that” to reflect the idea that “individual students come first. And once you make that leap, then differentiation becomes very much … what you're trying to do in the classroom.” Of the 18 participants, 16 took the course as an elective, while two were required to enroll for a gifted education endorsement. Because all participants entered the course with basic understandings of differentiation based on prior coursework, it is possible the 16 participants who took the course as an elective selfselected into it because they recognized their beliefs about teaching and learning aligned with the philosophy of Tomlinson's model. Sarah explained: I was very intentional in taking this course because … from what I had heard about it, I felt that it really resonated with me, and I liked what I had heard so far, and I know that it was something

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that I wanted to really incorporate as a part of my teaching, so I deliberately took the course because I wanted to shape myself as a teacher in this model. The fact that every participant perceived that the conceptual tools of differentiation aligned with their existing beliefs about teaching and learning is noteworthy. Participants did not experience major changes in beliefs about effective teaching and learning during the course. Instead, their existing beliefs were affirmed and expanded in learning about the model's conceptual tools. Participant focus was uniformly on developing a deeper understanding of the conceptual tools of differentiation and gaining new knowledge of its practical tools, rather than on addressing conflicts between the model's conceptual tools and their personal beliefs. Under these circumstances, participants' prior beliefs powerfully supported appropriation of the conceptual and practical tools of Tomlinson's model. 5. Discussion & implications The present study examined how learning experiences and instructor modeling in Tomlinson's course were structured to support candidate appropriation of conceptual and practical tools related to differentiation and how candidates' prior beliefs about teaching and learning affected appropriation of those tools. The present findings corroborate previous research and extend the extant literature by illustrating how variety in teacher education pedagogical experiences supported appropriation of targeted pedagogical tools of differentiation in different candidates. 5.1. Course learning experiences All participants connected specific learning experiences in Tomlinson's course to changes in their understanding of pedagogical tools comprising the model. While several learning experiences were identified by the majority of participants as playing a key role in supporting their developing understanding of Tomlinson's model, participants often pointed to different statements made by Tomlinson, course readings, or in-class learning activities when describing which experiences had the most influence on appropriation. No patterns based on participant background were discernible in these conclusions, underscoring the individualized nature of candidate meaning-making processes. This study offers an example of the power of a differentiated approach to teacher education in supporting the appropriation of targeted pedagogical tools. Because the course offered variety in activities, teaching strategies, resources, and assessments, and featured numerous differentiated learning experiences rather than a one-size-fits-all-candidates approach, wide variety existed in which aspects of the course participants identified as enhancing their developing understanding of the model. These findings align with recent research indicating differentiation in education coursework can yield improved outcomes for diverse learners (An et al., 2016; Chamberlin & Powers, 2010; Dosch & Zidon, 2014; Tulbure, 2011). 5.2. Instructor modeling Although practical tools of differentiation were modeled for candidates with fidelity in dynamic and diverse ways in every class meeting, participants varied in the degree to which they recognized them. Most participants were only able to identify one or two examples from Tomlinson's instruction, and the largest number of examples any participant was able to give totaled five. It should be

noted that participants enrolled in the course because they were motivated to acquire new knowledge of differentiation, and multiple participants' comments indicated that many were actively analyzing Tomlinson's instruction for examples of differentiation. Yet participants were unable to identify almost all of the ways in which Tomlinson modeled differentiation when the modeled practical tools and related conceptual tools were not explicitly identified and unpacked, or when implicit modeling (Bullock, 2009) was employed instead of congruent teaching featuring meta-commentary (Swennen et al., 2008). These findings directly echo those of Ruys et al. (2013), who found that candidates seemed not to recognize implementation of differentiation when the instructor's instructional decision-making was not explained or connected to theory. 5.3. Beliefs about teaching and learning The course continually prompted candidates to examine the degree of alignment between their prior beliefs about teaching and learning and the principles of Tomlinson's model. Every participant noted strong alignment between the two, and none reported any areas of disconnect. This may be related to the fact that almost all participants enrolled in the course as an elective, perhaps based on initial recognition of this alignment. Thus, no participants' preexisting beliefs served as filters through which they discarded incompatible ideas (e.g., Levin & He, 2008) or served to narrow the range of new ideas they were willing to entertain (Feiman-Nemser, 2001). Half of participants reported that a change related to their beliefs resulted from course learning experiences. Some reported that newly acquired knowledge of the conceptual tools of differentiation expanded their beliefs related to student growth, while others reported that knowledge of the practical tools of differentiation clarified how to put their beliefs into practice. While this study cannot establish that these changes resulted from participants' repeated reflection on their beliefs prompted by written assignments and in-class discussions, previous research (FeimanNemser & Buchmann, 1986) has suggested candidates are more likely to change ideas about teaching and learning when they are repeatedly prompted to examine and evaluate their own beliefs. 5.4. Implications The findings suggest implications for teacher education programs that prepare candidates to respond to academic diversity, as well as more general implications for programs that prepare candidates to enact forms of ambitious instruction. These implications center upon: (a) differentiating course experiences to support appropriation of practical and conceptual tools; (b) enacting congruent teaching to demonstrate the implementation of practical tools; and (c) prompting candidates to repeatedly examine their beliefs about teaching and learning in conjunction with conceptual tools gained through coursework. 5.4.1. Differentiate course experiences To differentiate effectively, teacher candidates must acquire both conceptual and practical tools of differentiation, drawing a distinction between the strategies of differentiation and its underlying principles. This distinction should be strongly emphasized in teacher education coursework. As Sherman (2009) explains: Teacher candidates are usually eager to learn the ‘how to’ in methods classes … But a rapid jump to the “how to” may sacrifice attention to the “why,” which provides a rationale for selecting particular teaching techniques and may better support progressive educational practice for the long-term. (p. 51)

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Making the “why” of differentiation a primary focus of teacher education coursework in addition to the “how” is therefore necessary. To support the development of robust understandings of the conceptual and practical tools of differentiation, course activities should be structured in ways that allow candidates to construct meaning of principles of differentiation for themselves and to experience practical tools from the learner perspective. A teacher educator may model differentiated strategies in her own instruction and offer candidates high quality examples to analyze through videoed lessons or lesson plans. In these instances, having candidates deconstruct both the “how” and “why” of differentiated elements of the lesson is critical. For example, an instructor might play a video of a teacher presenting a lesson differentiated based on student readiness. The instructor might prompt candidates to consider practical tools reflected in the video by analyzing distinctions between the groups’ tasks, whether both tasks were “respectful” (Tomlinson & Moon, 2013), and how the teacher used formative assessment data to group students and develop tasks. Candidates could also be prompted to consider the conceptual tools underlying the lesson by analyzing how teacher statements or other aspects of the learning environment reflected specific conceptual tools related to readiness or mindset (Dweck, 2007). Most importantly, study findings reinforce the assertion that teacher educators’ instruction should be differentiated and should incorporate a variety of resources and teaching strategies. Deeper levels of appropriation (Grossman et al., 1999) may be supported by offering strategically designed variety in course components of: content, or inputs of learning such as reading materials; process, or sense-making activities and assignments; and products, or openended summative assessments such as writing curricular units (Tomlinson, 2017). Implementing differentiation in teacher preparation coursework, rather than a one-size-fits-all curriculum, can better support the varied learning needs of teacher candidates as candidate pools reflect increasing diversity, while simultaneously modeling effective methods of teaching academically diverse students in robust ways; as Santangelo and Tomlinson (2012) aptly note: The former is necessary to ensure a pool of teachers that aligns with the range of cultures and backgrounds in society and the schools that serve society. The latter is necessary to prepare that candidate pool for the realities of increasingly heterogeneous classrooms. (p. 323)

5.4.2. Enact congruent teaching Teacher educators should provide unambiguous models of the practices of differentiation in action. In addition to demonstrating a repertoire of strategies candidates can use across content areas (Taylor, 2015), modeling should demonstrate fidelity to the full model of differentiation (Santangelo & Tomlinson, 2012). Instructors should devote significant time to pointing out varied aspects of modeled practical tools with candidates, rather than assuming each instance of modeling has been recognized, and connecting applicable conceptual tools to modeled practical tools. Specifically, Ruys et al. (2013) propose congruent teaching, which includes post-modeling discussion of instructional decisionmaking and connections between those decisions and related theory (Lunenberg et al., 2007; Swennen et al., 2004), as a way to prepare candidates to differentiate. When using congruent teaching, teacher educators must ensure that they (a) model practical tools effectively, clearly, and with fidelity to related conceptual tools; (b) build in opportunities for meta-commentary; and (c)

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possess sufficiently deep knowledge of theory related to the modeled strategy such that meta-commentary is accurate and valuable (Ruys et al., 2013). The use of congruent teaching is especially critical when modeling teaching approaches such as differentiation that can be implemented in ways that are largely invisible to students or under circumstances in which a teacher would otherwise strive to downplay differences among tasks, such as tiered tasks in readiness-based differentiation (Tomlinson & Imbeau, 2010). 5.4.3. Facilitate examination of beliefs Teacher education programs should incorporate repeated, thought-provoking opportunities for candidates to examine their current beliefs about teaching and learning in a variety of contexts throughout their course of study. Candidates must be provided with safe spaces in which they can make such repeated, candid assessments. According to Borko and Putnam (1996), teacher education programs: must help prospective teachers make their implicit beliefs explicit and create opportunities for them to confront the potential inadequacy of those beliefs. They should also provide opportunities for prospective teachers to examine, elaborate, and integrate new information into their existing systems of knowledge and belief. (p. 701) Throughout coursework, candidates must continually answer questions such as: What specific new knowledge of the guiding principles of teaching and learning am I gaining? How does it align or conflict with knowledge I already possess? How will I integrate this new knowledge into the system of what I already know? What do I believe about effective and ineffective teaching? What do I believe about what students need in order to learn? What is the relationship between my new knowledge and what I believe about teaching and learning? Do I need to reconsider my beliefs based on what I am learning? For teacher education programs in which responding to the needs of diverse learners is a key component of the conceptual tools taught in coursework, to support appropriation, candidates must be given repeated opportunities to integrate new knowledge of this topic into their existing belief system. In particular, candidates must be prompted to honestly examine their deeply-held beliefs about diverse learners (Stodolsky & Grossman, 2000; Tomlinson et al., 1995). They must actively consider connections among those beliefs and their knowledge, skills, and dispositions surrounding approaches to identifying and responding to student needs (Goodnough, 2010). It is unlikely that practical tools of differentiation will be put into effect in the classroom of a teacher who does not possess conceptual tools grounded in the beliefs that all students have the capacity to grow beyond where they began and that educators should be committed to meeting the needs of all learners. Candidates should be asked to explicitly consider differentiation's potential role in the ethics of teaching diverse students. In sum, findings of the present study suggest implications for teacher education programs seeking to prepare candidates to differentiate or enact forms of ambitious instruction that envision both teacher educators and candidates as reflective practitioners. Teacher educators who strive to prepare candidates to teach responsively to varied learner needs must be intentional in structuring differentiated course experiences that support individualized appropriation of the practical and conceptual tools candidates must possess; in using congruent teaching to help candidates build connections among modeled practical tools, instructor reasoning, and relevant educational theory; and in designing ongoing opportunities for candidates to reflect deeply on beliefs that may affect

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their appropriation of conceptual tools related to responsive teaching. In turn, candidates learning to differentiate must adopt a thoughtfully reflective mindset in considering the nuanced and complex relationships between beliefs about teaching and learning brought into teacher education programs and new understandings of the practical and conceptual tools of responsive instruction gained from coursework. At a time when candidates bring increasingly diverse backgrounds and experiences to preparation programs, further studies that examine how differentiating coursework may not only offer a powerful model of responsive instruction but also better support varied candidate learning needs are critical. Further research is needed on how learning experiences and instructor modeling in teacher education coursework can support the appropriation of differentiation's pedagogical tools and how candidates' evolving beliefs about teaching and learning related to academic diversity can affect appropriation. Additionally, research that employs a mixed-methods design in which empirical pre and post methods are used to examine changes in the appropriation of differentiation's pedagogical tools and teachers' beliefs about teaching and learning related to differentiation may further illuminate how these are related to desired teacher preparation outcomes. Last, further research is needed on the use of congruent teaching e and particularly on the use of meta-commentary e in preparing candidates to enact differentiation or forms of ambitious instruction.

Acknowledgements The author gratefully acknowledges Peter Youngs and the reviewers for their comments on previous versions of this manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Appendix A

Topics Discussed in Spring 2014 Differentiating Instruction Course Meetings WEEK

TOPICS DISCUSSED

Week 1








Week 2 Week 3

Week 4

Week 5

Week 6

Week 7 Week 8 Week 9 Week 10 Week 11

Week 12

Introduction to the course Differentiation's audience (who we teach) Defining differentiation Learning environment (where we teach) Learning environment (where we teach) (cont.) ◦ Role of mindset in differentiation
Low-preparation differentiation strategies
Effective curriculum as differentiation's starting point (what we teach) ◦ Teaching up and respectful tasks
Low-preparation differentiation strategies (cont.)
Effective curriculum as differentiation's starting point (what we teach) (cont.) ◦ Writing KUDs
Effective curriculum as differentiation's starting point (what we teach) (cont.)
Modification of instruction by readiness
Modification of instruction by readiness (cont.)
Modification of instruction by learning profile
Ongoing assessment Spring Recess e NO CLASS
Modification of instruction by learning profile (cont.)
Modification of instruction
Strategies for modifying instruction: RAFTs, learning contracts
Modification of instruction by interest

(continued ) WEEK

TOPICS DISCUSSED

Week 13 Week 14 Week 15







Ongoing assessment (cont.) Leading and managing a differentiated classroom Leading and managing a differentiated classroom Grading in a differentiated classroom

Appendix B Differentiating Instruction Course Learning Objectives [Written in the format of what students should know, understand, and be able to do as a result of the course, based on the approach developed by Wiggins and McTighe (2005).] At the end of this course, students should: UNDERSTAND THAT (Us)
Differentiation is a philosophy of responsive teaching designed to maximize the capacity of each learner.
Differentiation professionalizes teachers and is respectful of students, individually and as a group.
Defensible differentiation reflects five non-negotiable, interdependent elements which address environment, curriculum, assessment, instruction, and management. ◦ Creating an environment that actively supports students in the work of learning through a growth mindset, connections among the teacher and students, and a strong classroom community encourages intellectual risk-taking and growth. ◦ Absolute clarity about a powerful learning destination and teaching up to help students reach that destination promote student engagement and understanding. ◦ Continuously knowing where students are in relation to the learning destination through ongoing assessment informs instruction and provides students with meaningful feedback on their performance. ◦ Modifying instruction in response to student readiness, interest, and learning profile helps ensure that each student arrives at the learning destination, and moves beyond it when possible. ◦ Effective leadership and management allow different students to work on different tasks at different times efficiently and independently within a flexible classroom.

KNOW (Ks)
key terminology of differentiation, including: ◦ mindset ◦ on-going assessment (pre-, formative, summative) ◦ flexible grouping ◦ respectful tasks ◦ readiness, interest, learning profile ◦ teaching up ◦ Know-Understand-Do (KUD) learning goals.
key instructional strategies for differentiation.

BE ABLE TO (Ds)
Develop clear KUDs.

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Align KUDs, assessments, and learning activities.
Design lessons using key instructional strategies which modify content, process, or products based on student readiness, interest, or learning profile.
Analyze and evaluate differentiated tasks using the nonnegotiables and key terminology.
Reflect on plans for leading and managing a differentiated classroom.
Reflect on personal philosophy and practice in relation to the non-negotiables and key terminology.
Synthesize critical ideas from selected resources on differentiation.
Create a product for an external audience which extends understanding and insight regarding the principles and practices of differentiation. Appendix C Sample Differentiating Instruction Course Reflection Prompts REFLECTION 3eDue Week 6 (February 16, 2014) At this point of the semester, you've already completed onethird of the course. Consider how your ideas about the course content have developed over the past five weeks, and answer the following questions in a Microsoft Word document:
Consider the “ah ha” or “hang on a sec” moments you've experienced so far in the course through class discussions, readings, workshops, and your own reflection. ◦ Out of all the new ideas you've encountered, which one resonated the most with your own beliefs or teaching practices? Why? ◦ What's been the most surprising thing you've learned about differentiation? Why was it such a surprise? ◦ Out of all the new ideas you've encountered, which one created the most dissonance, challenge, confusion, or conflict in you? Why?
Consider the class discussions, readings, and workshop on high quality curriculum we've done in the last few weeks. ◦ Out of the elements of planning for engagement, focusing on understanding, teaching up, and writing clear KUDs, which one or two would present the greatest challenge for you in your own teaching practice? Why? What might you do to overcome that challenge? (If you choose writing clear KUDs, make sure your response goes beyond saying: I’m not good at writing them yet/I need more practice.)
What's the biggest question you still have about the principles or practices of differentiation (other than wanting to learn more concrete strategies and see more specific examples of differentiation in action)?

REFLECTION 5eDue Week 13 (April 6, 2014) Review the KUDs for the course listed on pages 2e3 of the syllabus. [Course learning objectives related to what candidates should know, understand, and be able to do as a result of the course appear above as Appendix B.] 1. Us:
For which U has your own depth of understanding developed the most this semester? (Please type out the full U in your response.) ◦ Describe your growth in understanding that U. ◦ How would you describe your thinking about the ideas in that U before the course began?

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◦ How did your ideas change over time? ◦ Was there a particular turning point or “aha!” moment at which you experienced significant growth in this U, or was it so gradual you can't point to a particular moment? Why do you think that is? ◦ Which whole class or small group discussions, individual reflections, readings, or assignments contributed the most to your growth in this U? ◦ How will your understanding of this U contribute to your future practice as an educator?
For which U do you feel you still have the most growth to do in deepening your understanding? (Please type out the full U in your response.) ◦ How did your understanding of this U develop throughout the course (even though it hasn't developed quite as deeply as you'd like yet)? ◦ What is it about this U that causes it to be the one you still need to grow in the most? ◦ What will you do in your future practice as an educator to support your continued growth in this U? 2. Ks: Think about how you would have defined these Ks on the first day of the course and how you would define them now. Choose the K for which you think your definition has changed the most.
Describe how you would have defined it on the first day (or explain that you wouldn't have known enough to give a definition at all), and give your current definition in your own words.
Describe your growth in coming to know or better appreciate this K: ◦ Was there a particular turning point or “aha!” moment at which your knowledge of this term expanded significantly, or was it so gradual you can't point to a particular moment? Why do you think that is? ◦ Which whole class or small group discussions, individual reflections, readings, or assignments contributed the most to your growth with this K?
Explain how your knowledge of this term will play a role in your future practice as an educator. 3. Ds:
For which D has your proficiency developed the most this semester? (Please type out the full D in your response.)
Describe your growth in being able to do the skill. ◦ How would you describe your proficiency with the skill before the course began? ◦ How did your proficiency change over time in the course? ◦ Was there a particular turning point or “aha!” moment at which you experienced significant growth in this skill, or was it so gradual you can't point to a particular moment? Why do you think that is? ◦ Which whole class or small group discussions, individual reflections, readings, or assignments contributed the most to your growth in this skill?
How will your proficiency with this skill contribute to your future practice as an educator? References An, S. A., Tillman, D. A., Zhang, M., Robertson, W., & Tinajero, J. (2016). Hispanic preservice teachers' peer evaluations of interdisciplinary curriculum development: A self-referenced comparison between monolingual generalists and bilingual generalists. Journal of Hispanic Higher Education, 15(4), 291e309. Beecher, M., & Sweeny, S. M. (2008). Closing the achievement gap with curriculum

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