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Managing to Collaborate with Secondary Mathematics Teachers at a Distance: Using Storyboards as a Virtual Place for Practice and Consideration of Realistic Classroom Contingencies
Abstract
OPEN ACCESS LINK: http://www.learntechlib.org/p/216903/
ABSTRACT: We describe how we further developed StoryCircles to support teacher learning online during COVID-19. In StoryCircles, a facilitator gathers teachers to collectively represent a lesson through iterative phases of scripting, visualizing, and arguing about alternatives. We share new innovations to the StoryCircles process that have helped us overcome common challenges, such as supporting teachers in anticipating elements of the lesson prior to implementation and intervening on teachers’ learning with instructional practices that may be novel for the group. Our work has implications for teacher educators across the world who are committed to supporting teachers to learn in, from, and for the complexities of actual classroom practice but are facing the very real challenges necessitated by times of extreme societal disruption—having to cancel field experiences or offer teacher education courses in blended contexts.
... Common to these implementations of StoryCircles is our intention to make progress toward realizing the vision of Hiebert and Morris (2012) for a PD system that not only facilitates groups of teachers in analyzing and evaluating their own teaching practices through collaborative development of lessons, but also broadens the knowledge base for mathematics teaching. While previous studies on StoryCircles have highlighted its potential to support teachers' professional growth, mathematical knowledge for teaching, and collaborative lesson development Milewski et al., 2018Milewski et al., , 2020 we have also documented challenges which prompted us to innovate (Brown et al., 2021). The intentional centering on teachers and their knowledge has some important implications for the role of the facilitator. ...
This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth.
To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, "How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers' knowledge and practices for teaching?" In this paper, we offer a model called the Dual Action Cycles of Approximations of Practice for identifying the pedagogical practices made available to pre-service teachers within various approximations of practice and describe its use to empirically investigate the potential of StoryCircles-a facilitated process of collaboratively representing a lesson using a multimedia storyboarding tool. We illustrate ways the model was used to make observations of pre-service teachers during StoryCircles. A key feature of the model is that it provides a bi-focal perspective on both the preactive and interactive phases of teaching, which help bring into focus the interdependent nature of these two phases. We close by suggesting that the development of new forms of approximation needs to be accompanied by research frameworks capable of investigating the potential of these various innovations.
In this conceptual chapter, we illustrate how a professional-development innovation called contingency cards can be used to elicit teachers’ subject-specific pedagogical decisions in an online learning environment. Contingency cards are representations of practice that can be used by facilitators to occasion conversations about realistic contingencies teachers might face in the context of their practice. Using the instructional situations of constructing a figure and doing proof drawn from the secondary geometry course in the USA (Herbst 2006), we illustrate how such contingency cards can be used to support teachers to interact about the subject-specific demands of teaching. Drawing on data from an online, practice-based professional development aimed to support teachers in learning to facilitate problem-based lessons, we demonstrate ways that geographically distant teachers can be supported in learning from both practice and one another through the use of contingency cards. More specifically, we illustrate various kinds of subject-specific decisions our teachers needed to grapple with when considering how to (1) elicit, (2) select, and (3) respond to students’ mathematical contributions. In particular, we share decisions that practicing teachers were asked to consider regarding how a whole class discussion about an open, novel task we call the Tangent Circle Problem could unfold. Finally, we share contingency card activities that could be used to elicit teachers' discussion about such decisions.KeywordsSubject-specific instructional practicesDiscursive movesPractical rationalitySecondary geometryProofConstructionNorms of instructionSecondary algebraContingency cardsProblem-based tasks
The transformation to reform mathematics teaching is a daunting task. It is often unclear to teachers what such a classroom would really look like, let alone how to get there. This article addresses this question: How does a teacher, along with her students, go about establishing the sort of classroom community that can enact reform mathematics practices? An intensive year-long case study of one teacher was undertaken in an urban elementary classroom with Latino children. Data analysis generated developmental trajectories for teacher and student learning that describe the building of a math-talk learning community-a community in which individuals assist one another's learning of mathematics by engaging in meaningful mathematical discourse. The developmental trajectories in the Math-Talk Learning Community framework are (a) questioning, (b) explaining mathematical thinking, (c) sources of mathematical ideas, and (d) responsibility for learning.
L'application des resultats de la recherche en education dans les ecoles a ete encouragee par les politiciens americains. Pourtant aucunes directives n'a ete donnee aux enseignants quant a la facon de les utiliser. Les AA. presentent un etat complet de la situation a l'aide d'une approche philosophique de la dichotomie theorie/pratique
Lesson study, a Japanese form of professional development that centers on collaborative study of live classroom lessons, has spread rapidly in the United States since 1999. Drawing on examples of Japanese and U.S. lesson study, we propose that three types of research are needed if lesson study is to avoid the fate of so many other once-promising reforms that were discarded before being fully understood or well implemented. The proposed research includes development of a descriptive knowledge base; explication of the innovation’s mechanism; and iterative cycles of improvement research. We identify six changes in the structure and norms of educational research that would enhance the field’s capacity to study emerging innovations such as lesson study. These changes include rethinking the routes from educational research to educational improvement and recognizing a “local proof route”; building research methods and norms that will better enable us to learn from innovation practitioners; and increasing our capacity to learn across cultural boundaries.
Novel tasks are valuable, yet discussions of novel tasks are often challenging to manage. In this paper, we describe a U.S. high school geometry lesson taught by two teachers in six different classes, in which students were assigned a novel task that the teacher framed as an instance of two familiar instructional situations — constructing a diagram and doing proofs — in order to support their students, while maintaining the cognitive demand of the task. We propose two ways of conceptualizing student work that help understand the teachers’ decisions: that student work might be seen as serviceable towards the learning objective of the lesson and that it could be seen as compliant with norms of those instructional situations.
Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching. © National Council of Teachers of Mathematics. All rights reserved.
There is growing interest in the field of education for leveraging emerging digital technologies to support teachers' learning in online or blended settings. This paper builds on Clarke and Hollingsworth's (2002) Interconnected Model of Professional Growth by investigating an alternative instantiation of professional experimentation. In particular, we examine the StoryCircles model of professional development (Herbst & Milewski, 2018), which ushers teachers into a simulated type of professional experimentation to support teacher growth through the design and improvement of lessons using storyboards. In that context, we investigate how StoryCircles enable teachers to experiment professionally in a virtual space. Focusing on the experiences of two secondary mathematics teachers, we illustrate how the StoryCircles processes of scripting and argumentation were associated with teacher growth. We discuss how the Clarke and Hollingsworth (2002) Interconnected Model of Professional Growth can be useful for the design and study of simulated professional experimentation.
The notion of practice-based teacher education has recently been offered to mitigate the long-standing tension between theory and practice in teacher education. In practice-based teacher education, preservice teachers study a core set of teaching practices by examining decompositions of practice and learn these practices through varied and multiple opportunities to approximate teaching. This chapter explores one way in which preservice teachers might engage in approximating practice through homework assignments. In particular, this chapter reports on a study comparing representations of practice produced in two media—via scripting classroom dialogue or representing them as storyboards. Over a one-semester secondary mathematics methods course, 13 preservice teachers created 412 representations of practice—182 in a text medium and 230 in a storyboard medium—to approximate five different mathematics teaching practices. This chapter discusses the results of the comparison between the content of these different representations and implications for mathematics teacher education. In particular, the storyboards included significantly more attention to the students in a classroom and to the mathematical representations as compared to the text medium. Yet, it was in the text medium where preservice teachers appeared to consider more alternative teaching moves. We also discuss the ways in which teacher education might maximize attention to these aspects by utilizing these features (student involvement and mathematical representations) in the prompts used to situate the work of storyboarding a response.
This chapter conceptualizes and illustrates StoryCircles, a form of professional education that builds on the knowledge of practitioners and engages them in collective, iterative scripting, visualization of, and argumentation about mathematics lessons using multimedia. The drive to invent and study new forms of professional education for mathematics teachers, such as StoryCircles, is predicated on the need to improve mathematics instruction. While many such efforts aim to support teachers to make broad sweeping changes, few take into account the actual predicaments of practice that make such changes difficult. StoryCircles aims to support teachers in making incremental improvements to practice by eliciting teachers’ practical wisdom and enabling participants to use each other’s knowledge and experience as resources for professional learning. In this chapter we outline critical characteristics of the StoryCircles interaction and illustrate how they are connected to seminal anchors in the professional development literature. We also illustrate those features with examples from various instantiations of StoryCircles. We close by providing some considerations for the affordances we see for the model both for the profession and for individual groups of teachers.
Teaching is complex and relational work that involves teacher???s interactions with individual or multiple students around the subject matter. It has been argued that observation experiences (e.g. field placement or watching video clips) are not sufficient to help prospective teachers to develop knowledge of teaching. This study aims to identify, examine, and illustrate the ways in which comics-based representations of teaching facilitate prospective teachers??? learning to teach. Specifically, the author explored how the use of a technology supported lesson-sketching tool, Depict, enabled prospective secondary mathematics teachers to attend to mathematical interactions between teacher and students in instruction when anticipating the development of a lesson.
Drawing resources from Systemic Functional Linguistics, the author examined the ways in which anticipations of classroom interaction about a planned lesson differ when the anticipation was done using the Depict tool as compared with talking through the written lesson plan. Using case study methodology, the study investigated the aspects of the teaching work prospective teachers attended to when engaged in depicting a lesson, and observed the ways in which prospective teachers employed the graphic resources to support their lesson depiction.
The results reveal that prospective teachers using Depict tool to create comics-based lesson slideshows immersed themselves in classroom settings and demonstrated their capacity to incorporate detailed teacher instructional actions, student reactions and mathematical tasks in their lessons. The prospective teachers unpacked their planned discrete class activities and attended to the relational nature among teacher, students and mathematics in instruction.
The study indicates that the anticipation of a lesson, through creation of comics-based lesson depiction, could be a learning opportunity that approximates the interactive nature of teaching practice. The study suggests that comics-based representations of teaching can be seen as semiotic resources that mediate prospective teachers??? generation of teacher-student moment-to-moment class interactions, and facilitate their attention to instructional issues they have not previously been aware of. The study also implies that in order to engage prospective teachers in learning to do the work of teaching, teacher educators should consider directing prospective teachers??? attention to issues of temporality, multimodality and multivocality in instruction.
Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is analyzed in two classes with an area problem designed to bring about and prove a conjecture about the relationship between the medians and area of a triangle. The article stresses that to understand the conditions of possibility to teach geometry with problems, questions of epistemological and instructional nature need to be asked not only whether and how certain ideas can be conceived by students as they work on a problem but also whether and how the kind of activity that will allow such conception can be summoned by customary ways of transacting work for knowledge.
[Link to the full version: http://www.citejournal.org/vol14/iss4/mathematics/article1.cfm] This paper builds on Grossman's notion of approximations of practice as scaled-down opportunities for preservice teachers to learn to teach by doing. The authors propose the use of media rich, collaborative web-authoring tools for preservice teachers to create, complete, or edit scenarios in which they practice particular activities of teaching, such as explaining a mathematics concept or reviewing students' work. The ways these environments can be used to fit the notion of approximations of practice are described, along with the authors’ experience using the web-based software Depict (in the LessonSketch platform) in the teaching of secondary mathematics methods. This use of multimedia scenarios combines the advantages of visual and video-based approaches to the study of practice with those approaches that ask the preservice teachers to create scenarios (e.g., lesson plays). The value of integrating this storyboarding web software in a larger environment where scenarios can be created collaboratively, annotated, and commented on in forums is presented.
To solve two enduring problems in education—unacceptably large variation in learning opportunities for students across classrooms and little continuing improvement in the quality of instruction—the authors propose a system that centers on the creation of shared instructional products that guide classroom teaching. By examining systems outside and inside education that build useful knowledge products for improving the performance of their members, the authors induce three features that support a work culture for creating such products: All members of the system share the same problems for which the products offer solutions; improvements to existing products are usually small and are assessed with just enough data; and the products are jointly constructed and continuously improved with contributions from everyone in the system.
In talk about teacher preparation and professional development, we often hear the word practice associated with what, how, or when the learning of teaching is supposed to happen. In this article, four different conceptions of practice are investigated, and their implications for how learning teaching might be organized are explored. Rather than a comprehensive review of the literature, what is presented here is a set of ideas that draw on both past and present efforts at reform. The purpose of this essay is to provoke clarification of what we mean when we talk about practice in relation to learning teaching. The author draws on her own research on the work of teaching from the perspective of practice to represent the nature of the work and to speculate from various perspectives on how that work might be learned.
The role of the critical friend in the development of teacher expertise
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Kroath, F. (1990). The role of the critical friend in the development of teacher expertise. Paper presented at an
International symposium on Research on Effective and Responsible Teaching, Université de Fribourg
Suisse, Fribourg, Switzerland, 3-7 September.