Taxes & Accounting


Accountability conversations: mathematics teachers’ learning through challenge and solidarity

Teacher learning through professional development is a complex process and is not yet well understood. Some features of professional development programs are known to be important, such as a focus on learner needs, design of and reflection on
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  Accountability conversations: mathematics teachers’learning through challenge and solidarity Karin Brodie  • Yael Shalem   Springer Science+Business Media B.V. 2011 Abstract  Teacher learning through professional development is a complex process and isnot yet well understood. Some features of professional development programs are knownto be important, such as a focus on learner needs, design of and reflection on classroomartefacts, and the creation and sustaining of communities of support for teacher profes-sional learning. In this paper, we describe the workings of such communities in a teacherprofessional development program, which focused on learner errors in a well-researchedmathematical topic—the equal sign. Drawing on data from program sessions whereteachers discussed their lesson designs and reflections on their teaching with each other, wedevelop the notions of challenge and solidarity as important in developing accountabilityconversations among teachers. We show how our program supported teachers to challengeeach other and to build solidarity with each other and in so doing to develop accountabilityto each other and the profession, for their practices and their learning. Keywords  Professional development    Professional learning communities   Accountability Introduction: teacher professional development Teacher learning through professional development is a complex process and is not yetwell understood (Borko 2004; Llinares and Krainer 2006). The difficulties of under- standing teacher learning arise from the complexity of teachers’ practice and the conditionsthat support teacher learning. Teachers’ engagement with the practice of teaching isinfluenced by a range of factors: their own personal resources; the resources made avail-able by their schools and departments; the organizational and institutional constraints intheir school situations; and systemic issues such as standardized testing and curriculum K. Brodie ( & )    Y. ShalemSchool of Education, University of the Witwatersrand, PO Wits, Johannesburg, 2050, South Africae-mail: Shaleme-mail:  1 3 J Math Teacher EducDOI 10.1007/s10857-011-9178-8  developments (Hargreaves 2005). Borko argues that ‘‘meaningful learning is a slow anduncertain process for teachers, just as it is for students’’ (2004, p. 6). The challenge forresearch on teacher development is to develop models of teacher learning that apply acrossprograms and contexts and that map teachers’ growth in teacher development programs.Zawojewski et al. (2008) argue that.research methodologies are needed for professional development experiences whereparticipants are not expected to converge toward a particular standard, yet teachersgrow and improve as a result of participating in the professional developmentexperience (p. 219)Given the complexities of teacher learning, there is extensive agreement on importantprinciples for professional development programs. First, short-term, fragmented seminarsand workshops do not work (Borko 2004; Elmore and Burney 1997). Long-term, devel- opmental programs are necessary. The second is that teacher development should have a‘‘clear and defensible focus’’ (Katz et al. 2009, p. 23). In the field of mathematics edu-cation, researchers argue that teacher development programs should focus on teachers’practices and the knowledge required for these practices (Ball et al. 2008; Bannan-Ritland2008; Borko 2004; Cohen and Ball 2001; Llinares and Krainer 2006). The use of actual school and classroom data has been found to be critical in developing teachers’ judgment,through developing personal meaning about their learners’ 1 needs, and in turn their ownlearning needs (Katz et al. 2005, 2009). A third principle for professional development programs is that both design of educational objects (Bannan-Ritland 2008; Zawojewskiet al. 2008) and opportunities for systematic reflection (Llinares and Krainer 2006) are important aspects of teacher learning. When teachers are involved in designing educationalobjects, Zawojewski et al. (2008) argue, they make their working theories explicit ‘‘bydescribing and explaining their principles (e.g., how the educational object worked, underwhat conditions, and why)’’ (p. 223). Katz et al. (2009) argue that a key aspect of reflectionis for teachers to make their tacit knowledge explicit so that they and others become awareof the principles that guide their practice—of how they teach and how their learners learn.Such awareness is a necessary first step in the process of significantly improving practice.A fourth principle is that support networks are crucial for teacher learning. The liter-ature shows that communities 2 that afford deep and sustainable learning experiencesrequire ongoing and supportive, yet rigorous and critical discussion, where genuine inquiryinto the objects and practices of teaching are sustained and where ownership andengagement among teachers is fostered (Borko 2004; Earl and Katz 2006; Katz et al. 2009). Borko (2004) argues that to create successful learning communities, we need to create norms of interaction which support teachers to take risks in talking with each other.These norms include keeping channels of communication open; building trust among thegroup; keeping the group on track; and helping the group get to the heart of the activity.Katz et al. (2009) argue that honesty, critique, and challenge are important characteristicsof professional leaning communities and that moderate professional conflict is necessary tosupport focused professional learning. These features help teachers to suspend the familiarand open themselves up to a new sense of ‘‘camaraderie and common purpose’’ (Supovits 1 In South Africa the word learner is used instead of student or pupil. We use these words interchangeablyas appropriate in context. 2 The literature refers variously to such support networks as communities of practice (Llinares and Krainer2006), professional learning communities (Borko 2004) or networked learning communities (Katz et al. 2009). We use the term professional learning communities.K. Brodie, Y. Shalem  1 3  2006, in Katz et al. 2009, p. 17). Such communities are difficult to create and sustain, andtherefore, good facilitation is key for the success of professional learning communities(Katz et al. 2009).In this paper, we focus on professional learning communities that were created within aprofessional development program in mathematics education. The project—the Data-Informed Practice Improvement Project (DIPIP)—is a 3-year project based at a highereducation institution in Johannesburg, South Africa. A set of structured activities weredesigned to support professional learning communities among mathematics teachers acrossgrades 3–9. In different ways, each activity required the teachers to make their tacitknowledge explicit through articulating what counts for them in relation to mathematicsteaching and learning. Our analysis examines the ways in which the professional learningcommunities became vehicles to support teacher externalization and reflection of theirthinking about their practice and about their learners’ thinking. We use the notions of ‘‘challenge’’, ‘‘solidarity’’, and ‘‘accountability’’ to describe how the teachers engaged inongoing long-term conversations about their practice and reflected on their learners’learning. We argue that these constructs successfully describe the form of learning thatprofessional learning communities can support. The analysis shows that by creating con-ducive conditions for ‘‘accountability conversations’’ (Earl and Katz 2005), teachers beginto imagine new possibilities and, in turn, develop new professional knowledge andaccountability to that knowledge. In the process, their own criteria become objects forconversation and reflection for themselves and others, thus opening up new conditions of possibility for action.Our analysis is divided into four parts. We begin by explaining the notion of accountability and its link to the idea of teaching as a practice. We proceed to describe theteacher development program from which the data for our analysis were derived. In thethird section, we examine the mathematical concept that provided the content for designand reflection for the teachers—the equal sign. In the last section, we present our analysisof the teachers’ ‘‘accountability conversations’’, using ‘‘challenge’’ and ‘‘solidarity’’ toframe the process by which teachers accounted for what counts  for   them in their practice. Accountability in practice Practices involve patterned, coordinated regularities of action directed toward particulargoals (MacIntyre 1981; Scribner and Cole 1981). Practices are simultaneously practical and more than practical as they involve particular forms of knowledge, skills, and tech-nologies to achieve the goals of the practice (Cochran-Smith and Lytle 1999; Scribner andCole 1981). Practices are always located in historical and social contexts that give structureand meaning to the practice and situate the goals and technologies of the practice. Thus,‘‘practice is always social practice’’ (Wenger 1998, p. 47), and practices involve social and power relations among people and interests (Kemmis 2005). For McIntyre, a practice is ameans whereby goods and standards of excellence internal to the practice are realised and‘‘human powers to achieve excellence  …  are systematically extended’’ (MacIntyre 1981,p. 175). Thus, learning is central to a practice, because as social goods and goals shift, sodo the means to achieve them. According to Wenger (1998), practice entails community, meaning, and learning; practices learn and grow, and people learn and grow in practice.There are two key elements in any practice: the criteria for what counts as appropriateacts within that practice and how the community that constitutes the practice defines whatcounts in the practice and holds people to account to the criteria of the practice. As Ford Accountability conversations  1 3  and Forman argue (2006), ‘‘in any academic discipline, the aim of the practice is to buildknowledge, in other words, to decide what claims ‘‘count’’ as knowledge, distinguishingthem from those that do not’’ (p. 3). The same holds for professional practices such asteaching, which rests on a knowledge base and which is concerned with the enculturationof learners into knowledge-saturated practices (Darling-Hammond 1989; Shulman 1987). So practices always have content and are always socially situated. Explicitly articulatingwhat counts as knowledge means that boundaries are delineated (Bernstein 2000), within which people can learn to act and hence begin to gain access to the practice. By com-municating to each other what counts as that practice, members discursively constitute thepractice in an ongoing way and hold each other to account for participation in the practice.The criteria of a practice are never fixed and unchanging, rather a key characteristic of apractice is that criteria change and develop as the practice learns and grows. Soaccountability is as much about the shifting nature of a practice as it is about the currentcriteria of the practice.Both mathematics and mathematics teaching constitute practices in relation to the aboveunderstandings. The goals of mathematics are to produce new mathematical knowledge,shaped by communities of mathematicians, while the goals of mathematics teaching are toproduce new generations of mathematicians and ‘‘doers’’ of mathematics in other fields(Ball 2003), as well as to produce mathematically literate citizens. The social context of mathematics teaching as a practice is shaped by a range of institutions and the agentswithin them, including schools, the education system and policies, and teacher educationproviders. The two practices of mathematics and mathematics teaching intersect throughthe use of the knowledge and technologies of mathematics, which include symbolising,generalising, solving problems, justifying, explaining, and communicating mathematicalideas and concepts (Ball 2003). The knowledge, artefacts, and technologies of the practiceof mathematics teaching further include the mathematics curriculum; understandings of learning mathematics and learners; mathematics teaching approaches; and assessmentstrategies. 3 A key task for teachers is to work across these two practices to give access tothe practice of mathematics to their learners (Ball and Bass 2003; Brown et al. 1989). Teacher learning in professional communities can also be seen as a practice, which bringsthe practices of mathematics and mathematics teaching together. This view has importantimplications for teachers’ learning: first, that successful teacher learning requires sustained,coordinated patterns of activity focused on the knowledge, artefacts, and technologies of mathematics and mathematics teaching; second, that teacher learning is strongly connectedto the goals of the practices of mathematics and mathematics teaching and to what countsfor these practices; and third, that teacher learning is constructed as a situated dialoguebetween teachers, who are situated within specific contexts, and more knowledgeablepractitioners, who represent principles that go beyond specific contexts.A further distinction that is important for our work needs to be made here. Earl and Katz(2005) draw a distinction between ‘‘accounting’’, which is the gathering and organising of data, often for monitoring and benchmarking purposes, and ‘‘accountability’’, which refersto educational conversations about what the information means and how it can informteaching and learning. For Earl and Katz, internal accountability 4 is where teachers are‘‘constantly engaged in careful analysis of their beliefs and their practices, to help them do 3 This can be seen as a more situated version of Shulman’s (1986, 1987) distinctions between subject matter knowledge and pedagogical content knowledge. 4 When we use the terms ‘‘account’’ and ‘‘accounting’’ we use it as the verb of this form of accountability.K. Brodie, Y. Shalem  1 3  things that they do not yet know how to do’’ (2005, p. 63). This notion of accountability issimilar to Darling-Hammond’s (1989) distinction between bureaucratic and professionalaccountability, is consistent with our notion of accountability in practice as discussedabove, and illuminates the function of accountability in teacher development programs.Accountability takes teacher reflection a step further, constituting it as a shared process,which requires that teachers in professional learning communities hold themselves andeach other ‘‘to account’’, that is, require that they account for their ideas and actions interms of their experiences and their professional knowledge. Accountability conversationscan give participants imaginations for possibilities that they do not yet see and can help tomake tacit knowledge explicit and shared, thus creating new professional knowledge andexpanding the practice. In our project, which we will describe below, a set of structuredactivities and artefacts support teachers to talk in and across differences in their taken-for-granted criteria, articulating what counts for them in relation to mathematics teaching andlearning. In the process, their own criteria become objects for conversation and reflectionfor themselves and others, thus opening up new conditions of possibility for action. The DIPIP project The Data-Informed Practice Improvement Project (DIPIP) is a professional developmentprogram that works with teachers to both design and reflect on lessons, tasks, andinstructional practices, and builds professional learning communities. The project focuseson building teachers’ understandings of learner errors, both more generally and in par-ticular topics. A focus on errors as evidence of reasonable and interesting mathematicalthinking on the part of learners provides a mechanism for teachers to learn to think morecarefully about learner thinking (Borasi 1994; Nesher 1987; Smith et al. 1993). The project set up the following activities:1. Analyses of learner result on an international standardized, multiple-choice test, with aparticular focus on the reasoned errors implied by the distractors for each test item;2. Mapping of the test in relation to the South African mathematics curriculum;3. Reading and discussions of texts in relation to learner errors on a mathematicalconcept;4. Drawing on the above three analyses, developing lesson plans for between three andfive lessons, which aim to engage with learner errors and misconceptions in relation tothe concept; and5. Reflections on videotaped lessons of some teachers teaching from the lesson plans.Prediger (2009) suggests four constituents of a focus on learner thinking: interest in learners’ thinking; an orientation to interpreting from the learners’ perspectives; generalknowledge about learning; and knowledge about specific mathematical concepts. In theDIPIP project, the general knowledge about learning is presented in the form of discussionsabout errors and misconceptions and what these might mean. The specific knowledge aboutmathematical concepts comes from particular mathematical topics that we ask the teachersto work on, with a focus on learner errors in these topics. The first two activities—testanalysis and curriculum mapping 5 —aimed to develop teacher interest in learners’ thinkingand knowledge about and sensitivity to learner errors in relation to the curriculum. Thesetwo activities formed the basis of the program and were carried through to two cycles of  5 See Brodie et al. (2010) for a discussion of the second activity.Accountability conversations  1 3
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