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Developing pedagogical judgmentin novice teachers: mediated fieldexperience as a pedagogy for teachereducationIlana Seidel Horna & Sara Sunshine Campbellba Peabody College, Vanderbilt University, Wyatt Center 265,Nashville, TN 37203, USAb The Evergreen State College, 2700 Evergreen Parkway NW,Olympia, WA 98505, USAPublished online: 23 Mar 2015.

To cite this article: Ilana Seidel Horn & Sara Sunshine Campbell (2015) Developing pedagogicaljudgment in novice teachers: mediated field experience as a pedagogy for teacher education,Pedagogies: An International Journal, 10:2, 149-176, DOI: 10.1080/1554480X.2015.1021350

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Developing pedagogical judgment in novice teachers: mediated fieldexperience as a pedagogy for teacher education

Ilana Seidel Horna* and Sara Sunshine Campbellb

aPeabody College, Vanderbilt University, Wyatt Center 265, Nashville, TN 37203, USA; bTheEvergreen State College, 2700 Evergreen Parkway NW, Olympia, WA 98505, USA

(Received 16 April 2013; accepted 6 August 2014)

A common critique of teacher education centres on the gap between coursework andschools, with ample evidence that novice teachers seldom bring ambitious forms ofinstruction into classroom placements. We describe a 6-year design experiment con-ducted in a university teacher education program secondary mathematics methodscourse focused squarely on this issue. Using the framework of hybridity, or themerging of two contexts to make a third that has elements of the originals, wedeveloped a pedagogy we call the mediated field experience (MFE). We present ourdesign framework and describe the MFE cycle, where novices learned a concept incourse activities, followed by guided classroom observations and facilitated debriefswith partner teachers. We highlight how this pedagogy facilitated connections acrosscoursework and classrooms through narrative cases of novices’ learning. We argue thattheir learning provided the basis for a complex form of teacher thinking, pedagogicaljudgment. This article offers a proof-of-concept argument that teacher education cansupport novices’ learning in the service of ambitious practice.

Keywords: design research; field experience; mathematics education; teaching meth-ods; teacher education

1. Introduction: teacher education and the recontextualization problem

Increasingly in the United States, the value of pre-service teacher education has beencalled into question. In addition to academics expressing concerns about its contributionto the broader educational enterprise (Levine, 2006), the proliferation of alternativecertification pathways suggests that formal professional education may be superfluousto the work of teaching (Brantilinger & Smith, 2013; Zeichner, 2010a). These programshave garnered tremendous support from policy think-tanks (Gatlin, 2008), philanthropists(Rotherham, 2008), as well as the US Department of Education (Duncan, 2009; Paige,2003), reinforcing the general scepticism about the need for pre-service education.

While some critiques of traditional teacher education are certainly warranted, toscholars of teaching, the widespread devaluation of professional education reduces teach-ing from a professional to a technical activity. This perspective, often called the NewProfessionalism (Brantilinger & Smith, 2013; Zeichner, 2010a), diminishes the impor-tance of formal knowledge and training, such as the knowledge represented by theoreticalframeworks on student learning or guided practice in instruction through student teaching.

*Corresponding author. Email: [email protected]

Pedagogies: An International Journal, 2015Vol. 10, No. 2, 149–176, http://dx.doi.org/10.1080/1554480X.2015.1021350

© 2015 Taylor & Francis

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As teacher educators, we agree that teacher education needs to develop more effectivepedagogies. At the same time, we, along with many of our colleagues (Grossman,Hammerness, & McDonald, 2009; Lampert, Beasley, Ghousseini, Kazemi, & Franke,2010; Windschitl, Thompson, & Braaten, 2011) see that accomplished teaching can beginin pre-service education. In this article, we talk of our work engaging critiques oftraditional teacher education through a design experiment (Cobb, Confrey, diSessa,Lehrer, & Schauble, 2003) in the context of a university secondary mathematics teachingmethods class. This work aims to better foster novice teachers’ emergent competence.

Design experiments are an especially useful way to develop scholarship-in-practice(Singer-Gabella, 2012) since they entail both the engineering of particular forms oflearning and the systematic study of that learning within the contexts that support it.Through the testing and revision of learning environments, successive iterations ofdesigns provide variations that uncover the role of the environment in learning. Theoutcome of design experiments are theories of learning and instruction that can informothers working toward similar goals. In this spirit, we aim to contribute to a commonvocabulary for teacher education and support a more methodological investigation of thiswork (Ball & Forzani, 2009; Grossman & McDonald, 2008; National Academy ofEducation, 2009).

The present work grew out of a response to a familiar critique of teacher education,the limited uptake by novices of research-endorsed teaching practices in placementclassrooms and in full time teaching (Borko & Mayfield, 1995; Feiman-Nemser &Buchmann, 1985). Earlier work suggests that these practices often re-emerge later innovice teachers’ careers, provided they are supported by teachers’ conceptual under-standing of underlying goals (Grossman, Smagorinsky, & Valencia, 1999). In a studywe conducted as a part of a Teachers for a New Era (TNE) grant, we found novicesespecially struggled to maintain interactive teaching practices (Horn, Nolen, Ward, &Campbell, 2008; Nolen, Horn, & Ward, 2011; Ward, Nolen, & Horn, 2011).

This finding was alarming because our own secondary mathematics methods coursesfocused on highly interactive teaching practices, with the goal of making student learningmore equitable. Many of the well-articulated equitable teaching approaches, such asculturally responsive teaching (Gay, 2010), building off of children’s ideas (Newman,Grifin, & Cole, 1989), building off children’s funds of knowledge (Moll & Gonzalez,1994), or Complex Instruction (Cohen, 1994), are characterized by teachers’ responsive-ness to the particularities of their students, making them highly situated forms of instruc-tion. In other words, the methods we most valued were the most likely to bemisinterpreted or abandoned by the novices.

Often called ambitious teaching (Lampert & Graziani, 2009), practices that supportthe learning of children from all racial, ethnic, class and gender categories in under-standing key ideas in mathematics were the emphasis of our course. For example, wewanted our novices to learn how to engage students in solving rich problems. This isambitious practice when a broad range of students use this activity to sharpen theirmathematical thinking through the authentic mathematical discourse of justification andgeneralization, deepening their own understanding of important ideas (National Councilof Teachers of Mathematics, 2000). In the TNE study, we too often watched novices fromour program transform ambitious teaching practices into pedagogies-as-usual – problemsolving would turn into procedures – thus inspiring our redesign.

In our new course, we reworked our secondary mathematics methods course toaddress this problem through what we called a mediated field experience (MFE). A fullerdescription of the MFE follows, but the general idea was to structure the methods class so

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that the expertise of partner teachers and university instructors could jointly guide thenovices’ interpretations of teaching in those settings, supporting a deep and situatedunderstanding of how mathematics teaching looks when it strives to maintain disciplinaryintegrity while reaching more students. The first author began revamping the methodsclass to address this challenge, leveraging relationships with local classroom teachers toturn the course into a mediated field experience. The second author served as a consultantin the initial design, eventually taking over teaching the course, refining the design andstudying the novice teacher learning in the MFE as her dissertation work (Campbell,2012).

The article is organized as follows. First, we review literature on teacher education todig deeper into the challenges of uptake – what we refer to as recontextualization (vanoers, 1998) – and the relationship to well-known issues in pre-service education.Leveraging a framework that puts novice teachers’ learning at the centre, we then outlineour designed responses that focus squarely on shaping learning toward our desired aim, aform of situated teacher knowledge we call pedagogical judgment. Next, we explain howthis redesign came together as a pedagogy and practice for our methods course, describinghow we tracked our success and failures in reaching our learning goals with the noviceteachers. In our findings section, we illustrate the ways the mediated field experiencesupported novice teachers’ learning in ways we see as responsive to design. In the samesection, we discuss limitations and promises of our approach. We end with reflections onthe contribution of this study and its implications for studies of novice teacher learningand the design of teacher education.

2. Prior work: what gets in the way of recontextualizing teaching practice?

Our review of earlier research on novice teachers’ learning pointed to three main issues intraditional teacher education that contribute to the commonly identified difficulties inrecontextualizing instructional practices. First, in what we call the Learning OutcomeDilemma, it is not always clear whether teacher educators should prepare novices for theschools that are or the schools that should be. This ambiguity makes a fuzzy target forteacher educators as they design learning experiences in certification programs. Second,traditional teacher education typically uses an acquire–apply pedagogy. As we will furtherexplain, this pedagogy contributes to the recontextualization problem by treating theoryand practice as if they live in two different places, driving a wedge between what one saysand what one actually does as a teacher. Finally, traditional teacher education oftenmarginalizes experienced teachers’ knowledge and perspectives, setting up novices tohave negative judgments on the very people they are seeking to become. This arrange-ment creates a potential identity conflict, adding to the recontexualization burden byexacerbating the divide between universities and schools, theory and practice.

2.1. The learning outcome dilemma

Any good instruction should specify its goals for learners. In the case of teacher educa-tion, thoughtful program designers might ask what well-prepared novice teachers shouldlook like. However, the answer to this critical question is not straightforward, due, in part,to the endemic dilemma of teacher preparation we described above. That is, do we preparefuture teachers for the schools that are or the schools that should be? When the aim ishelping novices learn ambitious teaching practices, teacher education squarely sets itssights on the latter goal. While this may be laudable, it stands to intensify potential

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conflict within the learners, since teachers must function in the schools that are – even ifthey are working to transform them to the schools that should be.

The Learning Outcome Dilemma touches both teacher educators and novice teachers.By introducing novices to ambitious teaching practices, teacher educators risk eitherfalling short of preparing them for the institutions they will work in or expecting themto have the fortitude to work against the grain of well-established norms (Cochran-Smith,1991). This dilemma also stands to communicate mixed messages to novices about thevalue of school placements as sites for professional learning. Undoubtedly, classroomexperience is critical in learning to teach. Yet when teacher educators’ idealized version ofteaching is not well represented in classroom placements, we may unintentionally devaluethe learning potential of these settings – settings that, paradoxically, we are trainingnovices to work in.

Novices, then, are frequently set up to negotiate different value systems across theircoursework and field placements. The gap between coursework and fieldwork is perva-sive and frequently mentioned in the literature on pre-service education. It has beendescribed in many ways: the two-worlds pitfall (Feiman-Nemser & Buchmann, 1985),the university-school divide (Anagnostopoulos, Smith, & Basmadjian, 2007), and perhapsmost dramatically, the Achilles heel of teacher education (Darling-Hammond, 2009).

2.2. Acquire–apply pedagogy

Teacher education practice, like any institutionally rooted endeavour, is shaped by itssocial and cultural history. Thus, common models of teacher education are effectivelycultural practices, not wholly the result of deliberate design by teacher educators, withlearning goals explicitly stated and concerted deliberation on the contradictions inherent inthe Learning Outcome Dilemma we described in the previous section. Even whenindividual teacher educators are reflective and intentional, novices learn across multipleinstructors and contexts in teacher preparation programs, leaving them to encounter thecoursework/fieldwork gap in multiple forms and with some frequency.

As with any cultural practice, traditional approaches to teacher education reflect theirorigins (Clifford, 1990; Lortie, 1975). To point to one source for common structures inteacher education, we note that academia’s residue appears in many of the usual learningactivities for novice teachers. For instance, as with much post-secondary coursework,learning practices like reading articles and writing papers dominate instruction in teachereducation. The tacit assumption is that this coursework will help future teachers developunderstandings of teaching and then apply them to their classrooms. This acquire–applypedagogy presumes that effective performance in university coursework provides anadequate basis for novice teachers’ learning (Zeichner, 2010b).

However, the default acquire–apply pedagogy of teacher education contributes to thecoursework/fieldwork gap. In fact, as we said in the introduction of this article, researchon pre-service education frequently reports the difficulties novices have recontexualizingpractices from university coursework to the field (Britzman, 2003; Kennedy, 1999, 2005;Zeichner & Tabachnick, 1981). Acquire–apply pedagogies underestimate the inherentchallenge of moving across contexts, and in doing so, sidestep much of the complexityof what it means to learn to teach.

As we found in our own TNE study, implementation problems are particularly acutewith more interactive and student-centred teaching practices (Horn, 2008; Kennedy, 1999,2005). As a consequence, many novice teachers simply succumb to the dominant prac-tices of their particular schools or retreat to the practices they experienced as students


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(Borko et al., 2000; Brouwer & Korthagen, 2005; Lortie, 1975; Peressini, Borko,Romagnano, Knuth, & Willis, 2004; Zeichner & Tabachnick, 1981). In this way, theacquire–apply pedagogy of teacher education has greatly limited teachers’ – and teachereducators’ – ability to transform teaching practice, highlighting the consequential tensionof the Learning Outcome Dilemma.

Since the regression to traditional practice is such a common finding in teachereducation research, the acquire–apply pedagogy has already been a target for otherredesign efforts. Numerous teacher educators have worked to be mindful and movebeyond traditional university learning activities. For instance, novices often rehearsecomponents of teaching in what Grossman and her colleagues have called approximationsof practice (2009). These pedagogies have a long history in teacher education, frommicroteaching (Kallenbach & Gall, 1969) to the more recent content-specific rehearsals ofinstructional activities (Lampert & Graziani, 2009). Yet even when teacher educatorsbroaden their teaching tools to couple approximations with analytic decompositions(Grossman, Compton, et al., 2009), these approaches may remain inadequate for over-coming the gap.

Why is this? To begin with, enactments are not typically done in the complexenvironment of the classroom. While they may give novice teachers an embodiedexperience of, say, giving clear directions or explaining an idea, they omit the often-unpredictable responses of students, leaving critical aspects of the work unrepresented.Even when fellow novices are asked to play the role of students, they are likely to draw ontheir own (successful) experience in school, under-representing hard-to-reach students.Likewise, critiquing traditional schooling through decompositions may motivate novicesto learn new teaching practices, but it does not guarantee their effective implementation.

In sum, acquire–apply pedagogy not only exacerbates the coursework/fieldwork gap,it does so by underrepresenting the complexity of the classroom and limiting novices’ability to learn about responsive, ambitious teaching practices. Even when instructors tryto bring in complexity through richer representations of practice (Grossman, Compton,et al., 2009; Little, 2003), they are limited by the affordances of the traditional teachereducation setting. For this reason, this standard pedagogy was also a target for redesigntowards one that deeply considers maintaining the complexity of practice while making itvisible to novices.

2.3. Marginalizing experienced teacher knowledge

The limitations of acquire–apply pedagogy go beyond providing insufficient support forthe implementation of ambitious teaching practices. Returning to the endemic tension inpre-service education between what is and what should be, we note that a focus on thelatter glosses schools as contexts with their own norms and practices worth understanding.When university instructors view schools as settings in which novices should apply theideas and practices from coursework, they unintentionally de-value the extant norms andpractices in the field. Because not all field placements have norms and values worthemulating, the landscape for pre-service instruction grows complicated quickly, leadingsome pre-service educators to support partnerships with like-minded placements (Darling-Hammond, Bullmaster, & Cobb, 1995). Brouwer and Korthagen (2005) report that thisstrategy of deep university-field alignment provides better contexts for novices’ long termlearning, but we wonder whether the radical heterogeneity of US schools would affectwhat they found in the Netherlands; in the United States, more homogenous contexts forteacher learning may only delay the clash of teaching values until the novice finds a


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full-time position outside the university’s sphere of influence (Ward et al., 2011).Although more university-based teacher education programs are beginning to re-evaluatethe role of clinical experiences in their programs, the field of teacher education continuesto position schools as places to demonstrate learning rather than places in which to learn(Zeichner, 2010b).

Acquire–apply pedagogy also devalues experienced teachers’ knowledge. In particu-lar, this approach privileges the university’s view of good teaching practice and reducespractitioner knowledge as unimportant or irrelevant (Feiman-Nemser, 1998). This stanceon practitioner knowledge leads to attitudes such as a deficit view of teacher practice(Britzman, 2003), putting novices in the uneasy position of disdaining what they areworking to become.

However, because traditional forms of teaching continue their dominance in USclassrooms (Banilower, Smith, Weiss, & Pasley, 2006), much to the chagrin of thosewanting to promote ambitious instruction, this stance is easy to fall into. If we take a stepback to think about teaching more than teachers, we see a profession embedded inorganizations with certain resources, values and demands. We do not, for instance, haveeffective systems for ongoing teacher professional development. Even as teacher educa-tors, we do not typically help this issue: few teacher education programs have resources tosupport mentor teachers’ development, even though we know mentors trained in targetedforms of practice are more effective in supporting student teachers (Dever, Hager, &Klein, 2003; McIntyre & Killian, 1987). Such mentors are few and far between, perpe-tuating the gap and continuing the marginalization of practicing teachers’ knowledge andlimiting the value of their guidance for the new teachers. The problem for teachereducators then becomes finding ways to support practicing teachers and valuing theirparticular expertise, even if their practice does not reflect the ideals promoted in teachereducation.

Again, taking the larger view on the cultural context of teaching, we can reframe themisalignment between university methods and the field. Instead of positioning traditionalpractices as a deficit of the teachers themselves, we contextualize their ubiquity, in part, asa consequence of how schooling is organized. Additionally, we as teacher educators valuewhat practicing teachers do have to offer, even if their instructional methods do not alignto the ideal of ambitious practice. For instance, they often have deep knowledge of theirstudents, parents, community setting and time management on the job.

In this review of prior work on novice teachers’ learning in teacher education, wepoint to the typical and often problematic relationship between teacher education course-work and the field, highlighting the ways in which institutional arrangements contribute tothe Learning Outcomes Dilemma. In the next section, we discuss how we responded tothese issues in our re-design.

3. Theory and methods: designing to develop pedagogical judgment

In an effort to deliberately engage the Learning Outcome Dilemma, our redesign wasguided by the question: what would be a desirable learning outcome for novice teachers atthe end of teacher education? Following Kennedy’s (1999) analysis of pre-service educa-tion, we aimed our design at fostering novices’ “situated knowledge […], knowledge thatis understood through specific situations rather than, or in addition to, knowledge that isunderstood abstractly” (p. 71; emphasis in the original). In other words, rather than thetypically inert, propositional knowledge supported through acquire–apply pedagogy, we


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wanted to support the development of enacted, situated knowledge that, in Lampert’swords:

involves being fluent with routines in order to work efficiently and innovate when neces-sary, rethinking key ideas, practices, and values in order to respond to nonroutine inputs.(2010, p. 24).

We also wanted to extend other innovative pedagogies in teacher education that focus oninstructional activities to put more emphasis on the latter part of Lampert’s formulation:the need in teaching to respond to nonroutine inputs.

In our view, this is where the responsiveness of ambitious practice often fallsshort. Teachers need frameworks to work nimbly in the commonplace situation wherestudents do not respond to activities as expected. For this reason, our learning goalwas for novices to develop pedagogical judgment. Perennial puzzles of teaching –whom to call on, how much time to spend on a topic, whether to proceed with alesson as written or attend to an unanticipated student misunderstanding – often haveindeterminate answers and rely on teachers’ pedagogical judgment built on theirsituated knowledge of their particular teaching context. Pedagogical judgment is atthe very heart of ambitious teaching practices. By design, these practices aim to beresponsive to particularities of students and situations – the very thing our novicesstruggled with coming out of our earlier methods class. Our goal, then, was to help thenovices develop views on teaching that would sharpen their responsiveness to thesecritical moments of classroom life.

Based on earlier work on pedagogical reasoning (Horn, 2005, 2007; Horn & Little,2010), we noted that a hallmark of sophisticated pedagogical judgment is ecologicalthinking about the classroom. That is, teachers accomplished in ambitious instructionreason about situations in ways that keep in mind the interconnectedness among thingslike classroom climate, teaching moves, student participation, mathematical activitiesand student learning. For our design, we would view novices’ articulation of pedago-gical problems and tradeoffs in instructional choices as evidence of pedagogicaljudgment.

In the spirit of design research (Cobb et al., 2003), we set out to build off of thecritique of the acquire–apply pedagogy to reformulate our methods class, with an aimtoward cultivating novices’ pedagogical judgment. In design research, investigatorsleverage the empirical and theoretical findings of earlier scholars to re-imagine educa-tional situations. In this way, we worked to re-imagine the relationships among novices,practicing teachers, methods instructors, coursework and field placements using perspec-tives on learning that stood to cultivate this form of knowledge.

To support our work, we primarily drew on a situative perspective on learning. Greeno(2006) describes a situative approach as one that focuses on individual learners in activitysystems. In this view, information structures such as knowledge and beliefs are insuffi-cient in themselves for thinking about learning. Instead, analyses of learning need toencompass broader activities, including the activity systems of both coursework andschool placements. As we will explain in this section, three concepts from socioculturallearning theory organized our redesign framework. These are contradictions, identities,and hybridity, and they capture the interface between the individual learners’ and theactivity systems through which they learned.


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3.1. Contradictions

Learners make sense of new ideas through activity systems. To capture the nature oflearning through activities, we drew on Cultural Historical Activity Theory (CHAT). Likeother sociocultural perspectives, CHAT emphasizes that learning and development aresocially mediated activities (Edwards, 2005; Engeström, 1999; Roth & Lee, 2007). Thatis, people learn through participation in cultural contexts and through their use of culturalartefacts, or tools, which support their actions and help to interpret what is culturallyrelevant (Edwards, 2011). As people engage in situated practices, they interpret and actupon their world through their use of these conceptual and material tools. Their actionsand tools change their world so that learners continually shape and are shaped by theirenvironment (Edwards, 2005; Roth & Lee, 2007).

CHAT helped us frame coursework and field placement activities as two differentsystems that would reflect different values and knowledge that the novice teacher learnerswould need to negotiate. In the previous section, we made much of the contradictions andtensions between coursework and the field placements that novices had to navigate intraditional teacher education. CHAT takes such conflicts as a given by highlightingtensions between learning as an internal process and learning as a process of socialization(Engeström, 2001; Gutiérrez, Baquedano‐López, & Tejeda, 1999). Taking tensions asgiven and using this analytic framework, we conceptualized the coursework–fieldworkgap in teacher education as a result of contradictions between two learning-to-teachsettings, the university and field, and worked to imagine the ways these tensions can beproductive for learning. The central contradiction we sought to reconceptualize stemmedfrom the potential identity conflict in new teachers disdaining what they were working tobecome. By making practicing teachers’ practice and thinking available to novices, wesought structures that would uncover the connections and complexity to help reconcile theseeming incongruities. We focused on designing a new activity system that drew on eachof the original settings, what we called the Mediated Field Experience.

3.2. Identities

Early on in the original TNE study, we saw the value of looking at the relationshipbetween novice teachers’ identities and their learning during their pre-service education.The concept of identity provides a helpful link between sociocultural learning theory andlongstanding work on teacher development (e.g., Cochran-Smith, 1991, 2004). Identity, asan analytic construct, provides descriptive language capturing both individuals’ disposi-tions and the different environments they encounter; it helps us see the novices whoselearning we are trying to understand in context. For example, in our initial study, themultiple meanings of “good teacher” revealed one source of these contradictions. In theteacher preparation program, judgments of goodness highlighted fidelity to disciplinarythinking (in our case, mathematics) and inclusion of a broad range of students ininstructional activities. Judgments of goodness varied in the novices’ field placements,focusing on anything from dynamic instruction, positive relationships with students, goodclassroom management, or good test scores.

Identity, as a construct, helped us reconcile the contradictions described in theprevious section. Note, for instance, that in the images of “good teaching” we highlighted,the ideas emphasized in different settings are not mutually exclusive. In this way, theconcept of identity pressed us to design structures and activities that would createcoherence across these often-divergent settings to allow novices a strong identification


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with each place. In our ideal structure, the novice teachers could be both intellectual (aprimary value of university instructors) and authentic (a primary value of mentor tea-chers), not forced to choose one dimension of teaching identity over the other. Instead oftrying to eliminate the gap between coursework and field placements, we sought toreconceptualize it. The question then became one of making places for novice learningthat were intellectual and authentic, that valued multiple forms of pedagogicalcompetence.

3.3. Hybridity

The idea of hybridity helped us think carefully about the new learning environment wewould design with elements of the two activity systems that supported novices’ teachingidentities as intellectual and authentic. Hybrid learning spaces contain elements of theoriginal settings, including discourses and cultural patterns of interaction, but theseelements are themselves transformed through the interaction of multiple settings. Intheir research in elementary school classrooms, Gutiérrez and colleagues viewed hybridlearning environments as “polycontextual, multivoiced, and multiscripted” (1999, p. 286),another way of naturalizing contradictions across settings.

For our purposes, we sought to create a hybrid space between coursework and fieldplacements. In the resulting mediated field experience (MFE), activity was directedtoward novice teachers’ learning. Because the expertise novice teachers need in order tolearn how to teach is located in schools, colleges and universities, and communities, thepractices and activities of the MFE needed to strategically incorporate the knowledge ofboth the university and the field. In doing this, a reorganization of roles, division of labourand ways of participating created new activities and outcomes that could help to resolvethe contradictions between the two original activity settings.

Through the creation of the MFE, we recognize that simply moving a university-basedcourse into the field does not necessarily shift the ways in which novice teachers accessdifferent forms of knowledge. Rather, it is the inclusivity of the activities and structures,the privileging of knowledge often marginalized in more traditional forms of teachereducation, which help create such a hybrid space. In the next section, we provideprinciples, rooted in providing novice teachers access to multiple forms of knowledge,for the design of the MFE.

3.4. Design conjecture

To create a hybrid space that leveraged the strengths of both coursework and field settings,we redesigned our methods course to help the novice teachers develop the understandingsabout classroom life that would support them in doing this complex work.

Our principle conjecture wove our guiding concepts together: by attending to contra-dictions across settings and supporting positive teaching identities through the design ofhybrid settings that embraced the contradictions of coursework and school placements, wecould support novice teachers in developing a particular form of situated teacher knowl-edge, pedagogical judgment.

To specify this notion, we came up with six pedagogical principles for the MFE. Wehave labelled them as addressing contradictions (C), identities (I), or hybridity (H) to pointto the parts of our design conjecture that they responded to. They were the following:


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(1) Complexity. Providing novice teachers with a common object of classroominstruction that, unlike video and cases, is fully dimensional will help them seecomplexity in teaching. (C)

(2) Collegiality. Introducing novice teachers to collegial teaching where instructionand curriculum planning are public and open to discussion will support theexploration and reconciliation of any (desired) conflicts that arise and contributeto the development of pedagogical judgment. (C, I)

(3) Student Learning. Focusing novice teachers’ attention squarely on student learn-ing over time while making connections between student learning and teachingpractice will contribute to the development of pedagogical judgment. (C, H)

(4) Transparency. Instructors and partner teachers working collaboratively to supportnovice teachers as they observe and make sense of common aspects of classroomlife that are often invisible to the novice eye (e.g., norms, status, transitions) willhelp with the development of pedagogical judgment. (C, I, H)

Our labelling of each of these ideas is not meant to be exclusive, but highlights the wayswe attended to our interpretation of the literature in our redesign.

4. The redesigned methods course

In this section, we give an overview of the previous iteration of the course and the wayswe incorporated our pedagogical principles into the redesign.

4.1. Background: the original mathematics methods course

The original mathematics methods course was centred on four essential questions(Wiggins & McTighe, 2005) that guided the activities, readings and discussions through-out the quarter. These were the following:

● Why do some students struggle in math?● What does it mean to teach mathematics for understanding?● What is equitable mathematical learning?● What kind of classrooms, curricula and teaching practices optimally support

equitable mathematical learning?

Activities at the university were typical of a methods course. The novice teachers engagedin mathematics tasks meant for secondary students and explored the mathematical ideaswithin the task as a way of anticipating students’ responses. They would read papers oneffective teaching, watch video case studies, analyse mathematical tasks for cognitivedemand (Henningsen & Stein, 1997), rehearse high-press questioning (Kazemi & Stipek,2001), and put these practices together for an end-of-quarter microteaching assignment.

Complex instruction served as the primary ambitious pedagogy in both the originaland MFE versions of the course (Cohen, 1994; Horn, 2012). Concepts and practices suchas recognizing student status dynamics, creating multiple-ability mathematics tasks andeffectively using groupwork roles and norms were taught, rehearsed and discussedthroughout the quarter.

Before the MFE, the methods course spanned two quarters, meeting two days eachweek at the university. During weeks five and six of the first 10 week quarter, noviceteachers left the university coursework and had their first full time field experience. As is


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typical with field placements, they were placed in distinct classrooms and most often indifferent schools. The university instructors gave novice teachers assignments during thefield experience, but other than that had little connection to their school-based activities.At the conclusion of the two-week field component, the novice teachers would then returnto the university to complete their remaining coursework for the quarter.

In the revised version of the methods course which included the MFE structure, themethods course met once a week on campus for the 10-week period. For seven of the tenweeks, instructors, novice teachers and partner teachers met together a second day at thepartner school. The university activities remained more or less the same. The main (andsignificant) difference was that they were followed up by related, structured observationsin partner classrooms. The partner classrooms were selected based on a previouslyestablished partnership with an urban public school, Septima Clark High School.1 Wedetail the formation and structure of the partnership in the next section.

4.2. Mediated field experience redesign: partner classrooms

Our goal was to find partner classrooms where we could create hybrid-learning environ-ments for our novice teachers. Septima Clark was well suited for this since the mathe-matics teachers were actively working to improve their teaching practice and increasetheir students’ success. They had participated for the previous 5 years in a professionaldevelopment project led by the first author that used complex instruction as a vehicle forequitable mathematics teaching, the same ambitious pedagogy we built our methodscourse around.2 In this way, both groups of teachers were working on the same pedagogy.Important for our goals for both projects, the teachers were personally and emotionallyinvested in helping their students succeed in mathematics and were persistent in theirefforts to improve their instruction. This alignment of goals served to support our hybrid-learning environment (Wenger, 1998).

4.2.1. Contributions of partner teachers

Because we wanted to reduce identity conflict in our novices’ learning, we intentionallyfocused on the important resources the Septima Clark teachers brought to the partner-ship. First, they had developed collegial norms and conversational practices to supportpublic reflection and investigation into their practice (Bannister, in press). Second, theywere conversant in the target pedagogy of the methods class and familiar with theconcepts the instructors used in the course. They had trusting relationships with theinstructors, characterized by mutual respect and shared curiosity. Additionally, theytaught a diverse group of students, providing the methods instructors a means forteaching the novices how to have respectful curiosity about different children’s math-ematical engagement and thinking, something glaringly underrepresented in the originalmethods class. Finally, the meta-message of the partnership conveyed to the noviceteachers was that hybrid teacher identities exist: they need not choose between auniversity/intellectual and a classroom/authentic identity as teachers.3 They could, asthey say, have it all.

The MFE’s goals were to be mutually beneficial: to work in what Cochran-Smith(1991) has called collaborative resonance by offering learning opportunities for allinvolved. The MFE worked to link what novice teachers learn in their preparationprograms with what they learn in their field experience by providing them with boththe analytical skills they need to think critically about school practices and the resources


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to function as social agents. In addition to the resources the Septima Clark teachersoffered, our partnership supported the partner teachers through the novice teachers’targeted observations and our collective discussions. The partner teachers reported beingmore intentional on the days when the novices visited. Their continued participationwith the university over 6 years provided evidence that they found value in our sharedwork.

4.3. A hybrid-learning environment for novice teachers, teachers and instructors

Our goal was to create a productive hybrid-learning environment for the novices, partnerteachers and methods instructors, integrating and expanding university and practitionerknowledge. Using the principles of complexity, collegiality, student learning and transpar-ency (Figure 1), we structured learning activities as described in this section. First, noviceswere introduced to a concept or practice in a university activity. In the next class session,they participated in a guided observation in partner teachers’ classrooms. During theseobservations, interns were paired with students the partner teachers identified as strug-gling in mathematics. This structure allowed the interns to observe the classroom throughthese students. Immediately after the guided reflection, the interns would debrief with thepartner teachers and instructors. Finally, the novices submitted written reflections after thiscycle of activity.

Our weekly themes strongly resembled those of the original methods class, high-lighting important concepts or practices for effective ambitious mathematics teaching.Each week, at the first of our two class meetings, novice teachers and instructors gatheredat the university and participated in fairly standard course activities around topics such ashigh-press questioning, maintaining cognitive demand or status dynamics in the class-room. The second meeting of the week took place in our partner classrooms. This secondmeeting was a guided classroom observation attended by all novices and universityinstructors. This observation was considered a “shared text” and focused on the sametopic as the previous day’s work in the university.

Pairing of novices withstruggling students not

like them

Written

reflectionPartner

teacher

debriefGuided

observation

University

activity

Figure 1. Developing a concept through the hybrid activities of the MFE.


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4.3.1. Student-novice pairing

Our design needed to serve the goal of keeping student learning in the centre of thenovices’ emergent understandings of teaching. Before our first MFE visit to SeptimaClark High School, the partner teachers provided us with a list of students struggling intheir classrooms. We asked the partner teachers to specify the reasons the students werehaving difficulty. Novices were asked to select a student for focused observation who wasunlike them in some important way. For instance, highly organized novices were encour-aged to pair with a student with the messy backpack who always lost his homework;novices who had never been outside of the United States were prompted to pair withrecent immigrants.

The novices discretely observed their focal student during each guided observation.This structure supported our goal of broadening the novices’ pedagogical reasoning bydeveloping their sensitivity to the diversity of student experience, particularly experiencessignificantly departing from their own. Research shows that novice teachers often makethe narcissist error; that is, they often gravitate to structures and practices they liked asstudents (Hargreaves, 1994). Observing the same focal students across a 10-week periodaimed to broaden their pedagogical judgment by familiarizing them with students whoseexperience in math class differed from their own. We reasoned that this pairing wouldenable the novices to look more closely at the relationships between context and studentengagement in mathematics learning.

Critical to their role as observer, the novices sat in proximity to their focal studentswithout interacting with them beyond smiles and simple greetings. From the universityinstructors’ standpoint, the novices’ initial visits to the classroom provided opportunitiesto observe how students made sense of mathematical ideas and responded to differentactivities. From our partner teachers’ perspective, teacherly interactions would inhibit thestudents’ own burgeoning mathematical independence and the newly developed interde-pendence within their small groups. If the novices had interacted freely with the students,it would have inhibited the students’ interactions with each other. The students would nolonger look to their group members for help but would instead begin to look to the noviceteacher for explanations and assistance.

4.3.2. Structuring the visits

We structured our visits so there was mutual transparency about our partner teachers’goals and our own. With the assumption that inherent contradictions exist across oursettings, we nonetheless tried to support novices’ concept development by coordinatingour work. The partner teachers had copies of the syllabus and access to readings at thebeginning of our work together.

Before each observation, the university instructor and partner teachers communicatedover email. The instructor informed the partner teachers of the weekly theme. Whenavailable in advance, the partner teachers also received observation guides and anticipateddiscussion questions. In return, the partner teachers emailed the instructor the lesson theyintended to teach during the observation and sent any handouts they planned to use inclass.

The novices then received this information and were instructed to informally explorethe mathematics activity before the observation. In practice, this scheme did not alwayswork, as partner teachers made last minute adjustments to their plans based on studentlearning or unanticipated events at their school. When it worked, this supported the


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novices guided observations, since we prompted them to anticipate how their focalstudents might solve the problem and then see how students’ thinking actually unfoldedin class. When it did not, we could reflect with the novices on how teachers need to adjustthe pace of instruction for a variety of reasons, in line with the complex realities ofteaching.

4.3.2.1. Guided observation. During the classroom visits, novices used protocols toguide their observations, some of which were co-planned by the partner teachers andinstructors. For example, the second week’s theme centred on the question, “What keepsstudents from learning math?” Our goal was to focus the students on the social andemotional aspects of mathematics classrooms through the concept of equal status parti-cipation (Cohen, 1994; Horn, 2012). This is often a hard concept for novices to under-stand as it is dynamic: it refers to mathematical conversations that emphasize what isbeing said rather than who says it and in which every student feels entitled to participate.

During the guided observations, the novices were instructed to use an interactiontracker, noting verbal and nonverbal student participation in the small groups theyobserved. This activity not only allowed the novices to focus on student–student interac-tions but to notice how the interactions shifted in response to varying activity structuresand teacher interactions.

In this way, the guided observations moved novices past the abstract ideas of theconcept of equal status participation and introduced a level of complexity, focusing theirattention on often-imperceptible aspects of classroom life. The tool, as an artefact, lived ina productive hybrid space between the university and the classroom, representing bothinstructor and partner teacher goals: it pressed the novices to attend to aspects of practicedeemed central by both the university instructor through the essential questions of thecourse and the partner teachers through their teaching goals of increasing student parti-cipation. (In fact, the partner teachers asked if they could keep the filled out trackers as away to check on the students’ small group dynamics).

4.3.2.2. Debrief. The debrief was the heart of the MFE and where its design parts wayswith many models of traditional field experiences. Conceptually, it allowed us as instruc-tors to help the rubber of theory meet the road of practice, with all the varieties of frictionand smoothness this metaphor implies. Our leading concepts of complexity, collegiality,student learning and transparency all came together in a dialogic encounter with pedago-gical judgment.

Immediately following each observation, the novices, partner teachers and universityinstructors gathered in one classroom to debrief the observations. We had a routine fordebriefing sessions. First, the partner teachers detailed their goals for the day’s lesson,what they thought their students had learned, their evidence of student learning and whatmore they thought their students needed to learn. This allowed partner teachers to modeltheir pedagogical reasoning for the novices. This supported our principles of studentlearning and transparency, while giving novices’ access to more expert teachers’ pedago-gical judgment. Additionally, given the thoughtful way our partner teachers engaged inthe debrief sessions, it also supported a view of classroom complexity and modelled aform of collegiality.

On a few occasions, these conversations challenged partner teachers because thelessons did not succeed in ways they had hoped. However, leveraging the trust we hadestablished and in a great display of transparency, the partner teachers talked openly aboutwhy they thought the lessons did not go as they had planned, usually pointing to their


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assumptions about how students would respond to a lesson. For example, a worksheetthey had created in their collaborative planning period was deemed too challenging; thepartner teachers’ had overestimated the students’ prior understanding. These instancesalso modelled another kind of pedagogical reasoning: the post hoc analyses that stand toinform partner teachers’ next steps with their class, continuously refining and improvingtheir practice.

In the second part of the debrief routine, we invited the novice teachers to shareobservations or ask the partner teachers questions centred on the weekly focus. Typically,the questions and observations involved particular pedagogical decisions made by thepartner teachers or specific students and their histories as mathematics learners in thatclassroom. Again, this made experienced teachers’ pedagogical reasoning and judgmentavailable to the novices. The partner teachers valued these discussions since they gainedadditional insights into the focal students, precisely the children about whom they had themost concern.

The debriefing sessions lasted about one hour, with roughly half of that time allocatedto the first part of the routine and half allocated to the second. The instructors focused onfacilitation, letting the main dialogue go on between the novice teachers and partnerteachers, only occasionally offering their own perspectives to connect up to the universityactivities. This structure allowed for interpretive conflicts – novices might see a teachergiving a student more time to explain than others as “unfair”, which the partner teachersmight then reframe as important for the whole class’s learning – while revealing pedago-gical reasoning and modelling collegiality, supporting the goal of hybridity. All of thenovices were required to speak during the debrief through a go-around protocol (e.g., goaround and share one observation or ask a question about something).

4.3.2.3. Reflection. In the second iteration of the MFE, novices were required to submit ashort online reflection the same evening of the observation. This additional designelement was added because instructors wanted to better assess all of the novices’sensemaking and provide a place for them to air questions or thoughts that they mightnot want to share in front of the partner teachers out of a concern for being rude orpresumptuous. They were instructed to write their reflections based on the weekly theme,university activities, guided observations and debrief sessions. This reflection activityaimed to bring coherence to the novices’ learning by having them synthesize across theseexperiences to articulate their current understanding of a critical teaching concept orpractice. For the instructors, the reflections served as formative assessment, allowing usto identify what ideas the novices were struggling with and modify the focus of subse-quent activities in the university-based part of the course. For our research, the reflectionsserved as a rich data set for examining the ways in which novices made these connections.

5. Data collection and analysis

5.1. Research design and setting

Our work aims to explore novice teacher learning in the cross-contextual learningenvironment of the MFE. Our research sought proof-of-concept: can we redesign asecondary mathematics methods course in ways that attend to our leading concepts andsupport novices’ development of pedagogical reasoning? Given the situative nature ofdesign work, we have already provided a rich description of our research context. Inaddition to ourselves as instructors, we include our partner teachers from Septima Clark


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High School, whose experience ranged from 2 to 15 years. We note that we worked in arelatively small-sized teacher education program and had between 8 and 12 noviceteachers during each MFE cycle.

5.2. Researcher roles and data collection

Our data come from two design cycles with this work. The first author led the instruc-tional activities for the first cycle during the 2007–2008 academic year. The second authorparticipated by consulting on the design choices and collecting observational notes of theMFE. To better understand how novices’ pedagogical judgment developed, we followedfour of them into their student teaching, conducting interviews and observations.

The second design cycle, which included revisions based on what was learned throughthe first cycle and subsequent cycles, took place in 2008–2010. Another researcherinstructed the course, while the second author took on the role of collecting observationalrecords of the MFE for her dissertation (Campbell, 2012).

Data collection sought to capture novices’ learning across the settings of the MFE. Wecollected data for two cycles of the 10-week course. Primary data were records of thepost-observation debrief, audio recorded interviews with novice teachers and writtenreflections from novices in the second design cycle. In the first cycle, we have fieldnotesof the debriefs, while in the second, we have video recordings. Interviews and videos wereboth transcribed. Secondary data included artefacts of the MFE redesign (e.g., syllabus,planning notes, observation protocols, methods course observations) and informal con-versations with novices, which were memoed.

5.3. Data analysis

In looking at the effectiveness of the MFE, we sought evidence of novices’ developmentof pedagogical judgment. To identify pedagogical judgment, we looked for criticalincidents (Emerson, Fretz, & Shaw, 2011) that signalled synthetic learning on the partof the novices, precisely what our earlier methods course did not adequately support. Thatis, we wanted to see evidence of novice teachers’ ecological thinking about teachingthrough their identification of interrelationships among teaching practices, student learn-ing and mathematics content.

For the first cycle, notes of the debrief sessions were read in an open coding manner(Miles & Huberman, 1994), looking for evidence of novices’ learning. For the secondcycle, we added the written reflection element to the MFE with an aim of getting more ofthe novices to make the kind of connections that some of the novices did in the first cycle,ones that would support the development of pedagogical judgment. We analysed thesecond cycle data in a similar open coding manner, looking for evidence of learningacross debrief transcripts, interviews and novices’ written reflections.

Using these critical learning incidents, we constructed narratives to show the uniquelearning opportunities the hybrid learning environment of the MFE, with an emphasis onthe MFE resources they drew on that supported their critical insights. We argue that theMFE structure, on the whole, afforded novices opportunities to develop situated under-standings of teaching practices to support their emerging pedagogical judgment.


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6. Looking at the development of pedagogical judgment through hybrid learningenvironments

In this section, we present three narratives of novice teacher learning using criticallearning incidents of Luke, Hannah and Suzanne. Suzanne’s case came from the firstMFE cycle (2007–2008 academic year), while Luke and Hannah came from thesecond (2008–2009 academic year). We make two claims about these critical learningincidents, which we identified through their talk in the debriefs, written reflections andinterviews. First, the hybrid-learning environment of the MFE uniquely fostered thislearning. Second, the learning supported the development of pedagogical judgment.

We present each case of learning by providing an overview of the teaching knowl-edge the novices developed and its relation to ambitious teaching. We then describe thecritical learning incidents, explaining how the MFE uniquely supported it. Finally, weexplore how this understanding might support the learning outcome of pedagogicaljudgment.

6.1. Luke: the need for classroom norms to cohere across activities

6.1.1. What was learned

Luke learned about the interplay of norms across classroom activities. Typically, noviceteachers are focused on getting through their lesson plan and do not attend to thepotentially contradictory messages about valued participation across, say, a classroomcompetition and a cooperative group. Indeed, we saw this exact contradiction and sub-sequent student shutdown in our earlier study of the original methods course (Horn,2008). Sophisticated teachers recognize the need to align norms across activities to givestudents coherent messages. Norms are consequential for student learning: they commu-nicate important messages about what mathematics is, how to participate and whose ideasare valued in a classroom (Yackel & Cobb, 1996).

6.1.2. How Luke’s learning was supported by the MFE

The weekly concept was on the importance of fostering positive interdependence amongstudents in collaborative learning. Positive interdependence – where students rely on andvalue each other’s thinking – supports the creative and respectful exchange of ideas andwell-distributed participation. The goal is to minimize the common problems of dom-inance or non-participation in collaborative learning (Horn, 2012). The guided observa-tion question was, “How are teachers facilitating the lesson so that students are makingconnections across each other’s ideas?”

During the lesson, one of the partner teachers, Wendy Meyer, explicitly told herstudents that she wanted them to use each other’s thinking. Afterwards, in the debriefingsession, one of the novices, Luke, noticed how Wendy had extended this expectation ofher students beyond the groupwork setting into a student presentation during a wholeclass discussion. In this way, Wendy unwittingly modelled how to connect norms acrossboth situations.

As Luke recounted during the debrief, Wendy had asked a student, Marisol, to cometo the front and present a solution to a problem. Marisol struggled to communicate herthinking. Luke went on to describe the interaction:


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Marisol, she was unprepared but she went up to the board […] and Asheed said, “She messedup, huh, Ms. Meyer?” and Wendy said, “You’re in her group! Why aren’t you – you shouldbe keeping track of this and helping out!” So really putting the responsibility back on thestudents and making sure they are focused on their groups. (4.23.2010, MFE debrief)

Luke’s final sentence summarized the significance of Wendy’s reminder to Asheed that hewas to help Marisol’s thinking, not just correct it. Luke linked the interaction to the themeof positive interdependence: in the whole class setting, Wendy “[put] the responsibilityback on the students” to support each other, in and out of their groups.

Luke’s astute connection about how the norm for positive interdependence could besupported across activity structures was uniquely afforded by the MFE, an observationthat could not be as clearly communicated in either the university or the field alone. It is achallenging idea for teacher educators to highlight for novices, who might understand it inthe abstract but have trouble coordinating it with all the other issues competing for theirattention during instruction. From our own observations of her classroom, we think theseinstructional moves were deeply intrinsic to Ms. Meyer’s practice.

6.1.3. How this understanding might contribute to pedagogical judgment

Pedagogical judgment is characterized by the ecological thinking captured in Lampert’snotion of needing to “respond to nonroutine inputs” (2010, p. 24). That is, teachers whoare effective with ambitious pedagogies must respond to students while keeping their eyeson issues of classroom climate, content, pacing and broader learning goals. By recogniz-ing the relationship of norms across settings, Luke was better prepared to take on thepotential conflicts in expectations in different activities in the classroom.

When Wendy asked Marisol to present and she really struggled, this became apedagogical problem. Decisions had to be made: should Wendy let her sit down? Whatwould that communicate to Marisol about the value of her rough draft thinking? Wereonly correct and complete answers worth discussing? Should she have chastised Marisolfor not knowing since her group was ostensibly finished? Should she have helped heralong through leading questions that might lessen the intellectual work? As Luke noticed,Wendy leveraged the norms developed in the small groups and demonstrated how thatsame norm can apply to the presentations. Luke picked up on this as a judgment Wendymade. It was not solely Marisol’s responsibility to be prepared for the presentation – theresponsibility continued to fall on her entire group. This interaction, within the context ofthe classroom dynamics and history, revealed to Luke the relationship between reinforcinggroup interdependence and its consequences for other aspects of Wendy’s classroomculture.

6.2. Hannah: rethinking “on-task” versus “engagement”


Hannah learned important differences between on-task and engaged student behaviour. Indiscussion-centred mathematics classrooms, teachers often struggle to make this judg-ment. Most novices’ images of on-task behaviour come from traditional instruction, whereinteractions are strongly teacher directed and students are limited to primarily academictalk. Teachers working in discussion-centred classrooms need to reconceptualize whatstudent engagement looks like in this different setting. For instance, if students are given amodelling problem to calculate which fast food chains’ French fries are a better deal, they


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will most likely talk about French fries, fast food chains and other related topics inaddition to linear equations if they are engaged in the problem. When we broaden theterrain of student learning and give students opportunities for sensemaking, the scope oftheir talk will change accordingly, leading to different images of “engagement”.

Critical learning event: In the following excerpt from her reflection, Hannah com-mented on her observation of three boys who “had lots of energy and (were) verytalkative”:

I noticed that the students talked almost non-stop during the groupwork session. Theirdiscourse switched seamlessly and rapidly between math talk and social talk – even somequiet singing/chanting. I was using the task, social/personal, and behavior identifiers wediscussed in our Adolescent Development class to track interactions. After a few minutes, Inoticed that the boys continued to make steady progress on their worksheet even as theybantered back and forth. Math talk seemed to break out whenever one of the students had aquestion or was stuck on the problem. Then other group members would explain theirsolution or offer suggestions. Just as quickly, the conversation returned to non-math relatedtopics. This pattern repeated continuously. At the end of the hour, the group had stayedtogether and completed the front of the worksheet. During the Teacher Checkout [a class-room routine], each boy was able to successfully explain his reasoning in problem #3. Thismade me wonder about the way I code student discourse. I was reminded of Boaler’s (2002)remarks about off-task talk in Phoenix Park classrooms and Gay’s (2010) discussion ofculturally appropriate norms. I wonder if I need to adjust my interpretation of on-task, off-task discourse for this group of students. I wonder if my biases about “appropriate” studentbehavior limit my ability to recognize all the times when students are doing math. (Hannah,Reflection #6, 5.2010)

In this reflection, Hannah noted that the interwoven social and academic talk did notdetract from the students’ learning, as was evidenced by their performance with theTeacher Checkout. By linking it to readings from her teacher education program,Hannah made two important connections. First, by linking her observation to the Boaler(2002) reading, Hannah invoked the distinction between compliance and learning, atheme in that study. Second, Gay’s (2002) writing challenges teachers to understandthat the white middle class norms of school may not reflect children’s home cultures,but these differences should not be seen as deficits. Hannah saw that the partner teacher,by making a place for the boys’ less schoolish talk, made a place for their learning. As aEuropean American woman observing a classroom of mostly African American students,Hannah commented on her own “bias” and reimagined the ways that she would respondto “on-task” and “off-task” student talk in her future classrooms.

6.2.2. How the MFE supported this learning

The hybrid learning space of the MFE supported Hannah’s synthesis of ideas frommultiple courses in her university teacher education program. Watching the boys work –more closely than she would be able to had she been conducting the class as a studentteacher or watching the lesson on video – Hannah made critical links between readings inher Math Methods (Boaler), Adolescent Development (task, social/personal scheme), andMulticultural Education (Gay) courses. Ultimately, the work of teaching requires this kindof synoptic analysis, making these linkages critical to Hannah’s development. The pushfor synthesis modelled in the MFE activity structure, as well as the ways this wasmodelled through the debrief conversations, invited such extensions of the MFE.


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6.2.3. How this learning contributes to pedagogical judgment

Teachers constantly make choices during instruction about speaking rights in the class-room (Cazden, 2001). Because Hannah could sit and observe the group interaction overthe entire class period, she was able to see the ways students got their work done. Thisobservation pushed against her previous conceptions about what “on task” looks like.Sensitizing her to cultural differences and the ways social and academic talk can worktogether, Hannah understood better that she needed to pay closer attention to whatstudents were actually doing when working small groups instead of just assuming thatsocial talk necessarily happened to the exclusion of learning. In her future work as ateacher, this stood to inform her judgment about when students are engaged and how todirect their discourse.

6.3. Suzanne: recognizing hidden competence


In our original methods class, we often emphasized the importance of getting to knowyour students. It is a human truth that we are more willing to take risks when we trust thatour effort will be received with kindness and understanding. Making positive connectionsto students engenders this trust and increases students’ willingness to think aloud andcontribute mathematically.

6.3.2. Critical learning event

To understand the significance of Suzanne’s learning, we must start with a bit of herbiography. Suzanne was highly sceptical of the teaching approach promoted in ourmethods course. Teaching was Suzanne’s second career, and, given her own experiences,she was sceptical about our emphasis on developing conceptual understanding in mathe-matics. Her own children had attended private schools where instruction stronglyresembled her own experiences as a student: mastery of procedures with limited applica-tions in word problems. In an interview, Suzanne described herself as being “a 4.0student, over-achieving and competitive with myself and others. I am a perfectionist”.

Suzanne’s critical learning event came over time, from an unexpected relationship shebuilt with her focal student Daniel. According to the partner teacher, Daniel struggledbecause he was often absent and did not turn his homework in – the ideal classroom tourguide for organized and diligent Suzanne.

As Suzanne observed Daniel every week, she found herself bothered by his lack ofstudent skills. Soon, challenging circumstances in Daniel’s life led to a two-week absence.When Daniel returned to school, the partner teacher asked Suzanne to work with himindividually to get him caught up. (This spontaneous tutoring, incidentally, was anexample of our presence serving as a resource to the partner teachers.)

Although we did not design for Suzanne to have individual time with Daniel, theexperience profoundly shifted Suzanne’s understanding of struggling students. InSuzanne’s words:

Daniel was sharp but too cool to do any work. He didn’t want anyone to know. [When Iworked with him] he was really successful. I learned how to not give up and let kids off thehook.


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Suzanne was surprised to find that disorganized Daniel had so much mathematicalaptitude. The experience she had with him drove a conceptual wedge for her betweenbeing a good student and being good at math – more powerfully, we add, than any of ourdeclarations that these were in fact different qualities.

Daniel became an important archetype for Suzanne as she entered her first year ofteaching. At her first full time position, she described a young man who reminded her ofDaniel and how she used what she learned from him to persist in working with this newstudent:

Now I have a kid and he came into class as Mr. Macho. He came in not wanting to doanything. He had a total attitude but I can tell he is really smart. One day I told him “You areso smart, why don’t you do this stuff?” Over the last several weeks, he really had a come-back. He participates from his seat. Now, I’m going to work on getting him to come up to theboard and present. I didn’t just write him off and I wouldn’t let him sit in the back and donothing. My nagging was part of believing in him. One time I wrote on his paper: “This isreally good – why don’t you let other people know how smart you are?” (Suzanne, Interview5A, 2007)

6.3.3. How the MFE supported this learning

Suzanne was able to reflect on what she learned about Daniel, distinguishing student skills(organization, homework, compliance) with mathematical ability. Daniel’s example car-ried forth from the hybrid setting of the methods class into her own teaching, providingher a way of interpreting the behaviour of this bright-but-macho student, reluctant toparticipate, as well as a vision for a possible future that went against his own. HadSuzanne not had the experience working with Daniel during the MFE, she may havemisunderstood this new student’s struggles in math, falling back on deficit-based narra-tives, and given up on him.

We believe that university coursework alone would not have sufficed in teaching anovice like Suzanne, who was highly invested in traditional modes of instruction, theimportant distinction between student competence and mathematical competence. TheMFE, with her poignant experience with Daniel, shifted Suzanne’s thinking in a way thatendured into her first years of teaching. In interviews, Suzanne reported always being onthe lookout for “more Daniels” in her classes.

6.3.4. How it contributes to pedagogical judgment

When teachers make decisions, they use what they know about students. The power ofexpectations is a well-documented instructional phenomenon (Steele, 1997; Weinstein,2002). Similar to Hannah, Suzanne recognized that she needed to stay open about studentsand their engagement and ability in class. Hannah’s observations challenged her assump-tions about classroom talk, while Suzanne’s relationship with Daniel challenged herassumptions that seemingly disengaged students are not smart. As a result of her experi-ence, she reported a shift in stance to stay alert to students’ potential. She deepened herpedagogical repertoire and took up the practices we worked on with our novices aroundstudent status, working to broaden students’ understanding of what it means to be good atmath so they, too, can find their place in the mathematics classroom.


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7. Discussion

We have presented three instances of novice teachers’ learning that, in our estimation,arose out of the hybrid-learning environment of the MFE. By attending to contradictionsand giving novices opportunities to engage their identities, we saw powerful learninghappen. The understandings developed by Luke, Hannah and Suzanne would not havecome as readily through the university or the field alone. The hybrid learning environ-ment, with its multiple discourses of academia and authentic practice, provided uniqueopportunities for the novice teachers’ learning, providing them frameworks through whichto notice important aspects of classroom practice and complex settings in which todevelop their pedagogical judgment.

We summarize the cases of Luke, Hannah and Suzanne in Figure 2. We note that whateach novice learned involved aspects of teaching that, from our experience as teachereducators, are difficult to communicate without live examples of practice. We also claimthat the MFE pedagogy supported the second part of ambitious practice – the inclusion ofall students – in ways that instructional activity pedagogies might not by supportingnovices in developing their ability to notice aspects of the classroom ecology that areconsequential for student participation and learning (van Es & Sherin, 2008).

These three examples built off of observations in the MFE spanning different amountsof time and addressing different issues in teaching. Luke linked the way interactionsreinforce norms across activity structures in a single class period. Hannah made importantconnections about student engagement, synthesizing ideas from multiple theoreticalperspectives through a single instance of classroom interaction. Suzanne learned todistinguish doing school from learning mathematics by observing and developing arelationship with Daniel over time. All of these are important concepts for novice teachersto bring into their classrooms to support ambitious teaching practice, and the uniquelyhybrid structure of the MFE helped the novice teachers build these connections that willsupport their future pedagogical judgment. These examples stand up to more carefulscrutiny of the data. In her analysis of the larger corpus of novice teachers’ learning inthe MFE, Campbell (2012) found that novice teachers learned to notice differentlythrough the hybrid learning environment before they were responsible for designing andmaintaining the activities in the classroom.

Novice What was learned Critical learningevent

MFE contribution Pedagogicaljudgment

Luke Maintaining normsacross activities

Seeing a student heldto the sameexpectations in twoactivity settings

Guidedobservation,debrief with partner teacher

Leveraging normsin one activity tosupport productivestudent behavior in another.

Hannah On task and engagedare not the same

Watching boysswitch seamlesslybetween social andmathematical talk

Guidedobservation,written reflection

Listen carefully tostudents talkbefore makingjudgments aboutwhether learning isgoing on.

Suzanne Making distinctionsbetween doing schooland doing math

Working with astudent who wasgood at doing mathbut struggled withdoing school

Guidedobservation,debrief with partner teacher

Students may becapable of morethan meets the eye.

Figure 2. A summary of the cases of learning in the MFE and their contribution to pedagogicaljudgment.


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As Figure 3 represents, going through MFE routine repeatedly provided us as instruc-tors to build concepts over time. The routine of university activity, guided observation,debrief and reflections got repeated, giving instructors more opportunities to interweavepractice and theory. The class developed shared examples of practice from the guidedobservations that become referents in university activities. Likewise, we revisited conceptsdeveloped in earlier weeks as they emerged in subsequent observations. Future work canbetter address the affordances of learning in the MFE over time, as novices build on andrevisit different concepts and episodes of teaching.

8. Limitations and promises of our approach

Like all complex and context-sensitive teaching approaches, the MFE has its challenges.First, this teacher preparation pedagogy requires a particular type of relationship betweenpartner teachers and university instructors. In order for a teacher to agree to allow 10 to 20novice teachers to observe their lesson on a weekly basis, the partner teacher must trustthat the university instructor will simultaneously protect the partner teacher’s needs,represent the partner teacher’s practice respectfully in the university class and willstructure the debrief sessions in ways that benefit the partner teachers as well as thenovice teachers. In addition, the partner teachers and university instructors must take onjoint responsibility for communication about upcoming math activities, observation pro-tocols and, most importantly, what they notice about how the novice teachers are makingsense of their experiences in the MFE.

Second, the university instructor needs facilitation skills that are different from theskills needed to teach a typical methods course. This structure presses instructors to figureout what is essential for novice teachers to learn. When the first author redesigned hermethods class to include the MFE, she had to significantly reduce her syllabus readingsand activities. As a consequence, the instructor needed to trust that the MFE could be an

Partner

teacher

debriefGuided

observation

University

activity

Partner

teacher

debriefGuided

observation

University

activity

Written

reflectionPartner

teacher

debriefGuided

observation

University

activity

Written

reflection

Written

reflection

Figure 3. Representing multiple iterations of the MFE.


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alternative, and significantly more nuanced, way to go about teacher preparation. Ratherthan staying within the safe and protected space of the university classroom where mostactivities and events can be planned in advance, the instructor is required to be flexibleand responsive to the often unpredictable events in the classroom observations, as theyguide the content of the debrief conversation. This requires the instructor to hold onto thecritical focus of the observation, look for the student and teacher interactions during thelesson that demonstrate the focus, while still being spontaneous. We have numerousexamples of this from our own instruction, but here it was illustrated by Suzanne’scase. By letting her work one-on-one with Daniel instead of doing the observation asplanned, Suzanne had access to significant learning about teaching. Although this learningopportunity was unique to her, she shared her experience with her classmates, who,knowing Suzanne’s initial position on interactive teaching methods, took note of theshifts in her thinking. This approach to teacher education takes both additional planningand coordination while simultaneously heightening uncertainty.

Third, enacting the MFE requires teachers to take on an additional responsibility.Although the teachers in our MFEs were compensated for their time, committing toparticipate as a partner teacher in the MFE is a significant personal and professionalundertaking. It requires them to talk openly about their lessons, their students and theirschool context. Not all MFE debrief sessions were lighthearted. At times, the lesson didnot go as the partner teacher had planned, and these days were filled with strong emotions.With very little time for personal reflection, the partner teacher then had to reveal how andwhy their lesson did not take its intended path. These were difficult conversations but alsocritical in the learning process for novice teachers, as the partner teachers modelled copingwith the disappointing lesson.

Given these challenges, it is significant that the MFE continued over the last 6 yearswith a number of Septima Clark High School math teachers participating as partnerteachers. It is obvious that they value this relationship and find it rewarding. In fact, oneof the partner teachers stated that she continued to participate in the MFE because she is:

willing to share my ideas and experiences. I am by no means saying, “This is how you solvethis problem” [of teaching]. But I am willing to talk about it. I am proud of being part of adepartment that talks about this (4.2010).

She recognized expertise in teaching as a work in progress. Teachers improve in talkingabout and analysing problems, but new issues arise constantly that respond to students’understandings and experiences.

In order for the partner teachers and university instructors to continue the MFE, bothgroups of participants must fundamentally benefit in some way and believe that their workalso benefits the future teaching practices of the novice teachers who observe in theclassrooms. To date, this has been the experience of the novice teachers, instructors andpartner teachers in the MFE.

The second author has managed to continue developing her MFE pedagogy in anelementary math methods class. The instructor, novices and partner teacher have found itto be a positive experience: the novices reported it to be one of the most meaningfulexperiences in their Masters in Teaching program and the partner teacher wanted to getmore involved in the co-planning. Given the potential to address the perennial course-work–fieldwork gap and the possibility of contributing to practicing teachers, we hopeothers can benefit from what we have learned through this 6-year teaching experiment.


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AcknowledgementsThe authors thank Susan Nolen and Chris Ward for their collaboration in the study that inspired thiswork. We are grateful to Elizabeth Self for providing helpful feedback on earlier versions of this article.

Disclosure statementNo potential conflict of interest was reported by the authors.

FundingThis research was supported by a grant from the Carnegie Foundation’s Teachers for a New Eraproject.

Notes1. This, along with all proper nouns, is a pseudonym to protect participants’ identities.2. For more on The Adaptive Professional Development Project, please see Bannister (in press).3. We state these dichotomies not to characterize the social position and related associations of

university and classroom settings, not to ennoble scholars or disparage teachers.

Notes on contributorsIlana Seidel Horn is Associate Professor of Mathematics Education at Vanderbilt UniversityPeabody College. Her research uses sociolinguistic methods to study secondary mathematicsteachers’ learning, with the aim to improve education for students and supports for teachers,particularly in urban schools. Her current research projects investigate instructional improvementat scale and mathematics teachers’ use of student performance data.

Sara Sunshine Campbell is a faculty member at The Evergreen State College and teaches in theMaster in Teaching Program. Much of her work centres on supporting pre-service and in-serviceteachers to implement teaching practices that support rich and equitable mathematics learning. She isparticularly interested in how to draw stronger connections between teacher education courseworkand classroom practice by leveraging practitioner knowledge.

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