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Approximating the Practice of Mathematics Teaching: What Learning Can Web-based, Multimedia Storyboarding Software Enable?
Abstract
[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.
... But those PT who visually depicted lessons attended to more instructional details and better specified teacher actions (e.g., crafting exactly what the teacher would say and the representations they would show) compared to those PT who simply talked through a lesson plan (and alluded to what they would say and show without being explicit). Depicting lessons led to more specific considerations of teacher actions, student individuality, and instructional nuances, suggesting its potential to enhance teacher preparation beyond traditional lesson planning methods (see also Herbst et al., 2014). In her study, Chen (2012) documented how the storyboard medium not only enabled expressing what PT planned to do but also examining the flow of the scripted events and engaging in discussions among the pairs of PT that led to revisions of the storyboard. ...
... Beginning in 2011, the first author started to use storyboards as a scripting multimodality with his methods class, on account that storyboards afforded resources to better represent the co-occurrence of verbal and nonverbal actions (e.g., speaking about a diagram on the board). Herbst et al. (2014) argued that engaging PT in storyboarding is a form of approximation of practice, because, like print-based scripting, storyboarding leaves a trace that, when read, creates a milieu that provides feedback to the authors. Because print scripts and storyboards continue to exist after they have been composed, authors and others can peruse them (e.g., in reenactments or read alouds) to visualize the lesson and can rely on their experience in such perusals to decide whether details are missing or whether something needs to be corrected. ...
... Through the continuous design of StoryCircles, the goal is to delineate the roles that multimodal scripting, visualization, and argumentation about a lesson play in the elicitation and improvement of professional discourse and to identify the technologies and resources that best support such work. As in earlier uses with PT (e.g., Chen, 2012;Herbst et al., 2014;Rougée & Herbst, 2018), the key hypothesis is that the visualization of a lesson through a storyboard perusal serves as a feedback mechanism on the actions considered while scripting . As in Chen's (2012) design, the collaborative nature of the visualization seeks to support the sharing of claims of what the lesson needs and the argumentation for or against those claims. ...
Addressing the need for practice-based teacher education to attend to context, we describe anticipations of a lesson as a case of approximations of practice that may anchor practice to its disciplinary context. After providing a general framework for how to think about anchoring practice in context we consider the StoryCircles process as an approximation of practice and illustrate the variability in anticipations of a lesson that can be generated by different StoryCircles. We use this variability to propose a conceptualization of lesson which is of particular value to practice-based teacher education.
... Similarly, Güngör and Güngör (2019) pointed to the benefit of a model involving research, rehearsal and reflection to support prospective teachers, through experiences that approximate practice. Initial findings around technology as a tool to approximate practice (e.g., Grossman et al., 2009;Herbst et al., 2014) show promise for continued use in teacher preparation. Additional data are needed to fully understand how prospective teachers perceive the use of technology to practise teaching, including their rationale for how the technology is useful to help them learn to teach. ...
... In addition to studies focused on LessonSketch as a tool for teacher educators to use, some studies have engaged prospective teachers in creating the depictions; a subset of these studies have also made a specific connection to Grossman et al.'s (2009) approximations of practice. Specifically, Herbst et al. (2014) wrote a paper promoting media-rich environments, such as LessonSketch, as web-based tools that support prospective teachers in practising the profession. These authors made a specific claim that prospective teacher-authored depictions are a means for approximating practice. ...
... These authors made a specific claim that prospective teacher-authored depictions are a means for approximating practice. Following this, Ghousseini and Herbst (2016) analysed prospective teacher use of LessonSketch as an approximation of practice to support understanding about managing classroom discussions, and Herbst et al. (2014) argued for the use of LessonSketch as an important tool for practice-based mathematics teacher education. These studies support the availability to use LessonSketch as a tool to approximate practice. ...
The use of technology affords opportunities for prospective teachers to engage in actions that are proximal to the work of teaching. The authors designed a task in which prospective teachers (n = 95) at four institutions created an animation or depiction of a classroom scenario using one of two technology platforms: GoAnimate or LessonSketch. They used a convergent mixed-methods design in which qualitative findings were quantitised and then examined statistically to determine what technological aspects prospective teachers used to create their approximations of practice, as well as how they perceived platform use. Findings indicate that the perception of being fun, having a learning curve and being difficult to use statistically affected evaluation. Two technological aspects also had a significant effect on perception: mathematical representation and altered visual field. Findings imply that prospective teachers’ experiences with technology use, coupled with how they use the tools, impact their appraisal of the platform.
... we capitalized on the technological affordances of the rich-media online environment LessonSketch. It houses a variety of digital tools that teacher educators can use to create interactive rich-media experiences involving activities such as: analyzing a video or cartoon representation of a classroom scenario; examining student work; participating in discussion forums around specific instructional episodes; and creating one's own representation of teaching which can be shared, evaluated and discussed with others (Herbst et al. 2014). ...
... 598). Herbst et al. (2014) maintain that "LessonSketch cartoon-based artifacts and tools play a crucial role, as 'mediators of cognition,' to help teacher users externalize their thoughts and ideas about instructional practice" (p. 4). ...
... Such representation allowed PSTs to envision themselves as teachers called on to manage the depicted classroom interactions, but in conditions of reduced complexity. We used the Plan tool of LessonSketch (Herbst et al. 2014) to create a virtual learning experience for PSTs comprised of sequences of representations, accompanied by questions and prompts to support the study of specific components of teaching practice. ...
There is a consensus among mathematics educators that in order to provide students with rich learning opportunities to engage with reasoning and proving, prospective teachers must develop a strong knowledge base of mathematics, pedagogy and student epistemology. In this chapter we report on the design of a technology-based task “What can you infer from this example?” that addressed the content and pedagogical knowledge of the status of examples in proving of pre-service teachers (PSTs). The task, originally designed and implemented with high-school students, was modified for PSTs and expanded to involve multiple components, including scenarios of non-descript cartoon characters to represent student data. The task was administered through LessonSketch, an online interactive digital platform, to 4 cohorts of PSTs in Israel and the US, across 4 semesters. In this chapter we focus on theoretical and empirical considerations that guided our task design to provide rich learning opportunities for PSTs to enhance their content and pedagogical knowledge of the interplay between examples and proving, and address some of the challenges involved in the task implementation. We discuss the crucial role of technology in supporting PST learning and provide an emergent framework for developing instructional tasks that foster PSTs’ engagement with proving.
... Approximations of practice allow novice teachers to attempt making specific decisions within moments of a scenario that models a particular component of a real classroom (Grossman et al., 2009). Many approximations intentionally limit the scope of what novice teachers can rehearse, such as only responding to an individual student's mathematical thinking (Shaughnessy et al., 2019;Herbst et al., 2014) or facilitating a small group discussion (Cohen et al., 2020;Kavanagh et al., 2020). Further, some simulations present moments where a teacher has to have a difficult follow-up conversation with a student, such as when they feel their teacher calls them out for talking because of their race while ignoring their peers doing the same thing (Self & Stengel, 2020). ...
... Such tailored feedback allows novices to either reflect on why they made those choices if that reasoning and choice led to the intended experience for young people and to take that together as an opportunity to attempt that moment again within a similar approximation (Dotger et al., 2010;Grossman et al., 2009). While the method of delivery differs (e.g., video annotating, talking with a professor, written journaling), providing feedback has enhanced novice teachers' confidence in responding across these different scenarios to prepare them in the classroom (Herbst et al., 2011;Herbst et al., 2014). But with such situated complexity that exists between students, mathematical content, mathematical pedagogy, schools, and larger structural systems, it is challenging for MTEs to try to design, facilitate, and debrief approximations that attend to all of this. ...
The chapter posits that the conceptualization of the in-between can be used in the design, debrief, and analysis of digital clinical simulations with novices to (re)imagine how approximations can be used to support the development of novice teachers' ambitious and equitable pedagogies. Decisions made within the design and debrief of approximations are illustrated and broken down in terms of how tensions that arrive within the in-between can be used to build a novice teachers' awareness of if and how their choices align with tenets of ambitious and equitable mathematics teaching. Further, these perspectives create an opportunity for mathematics teacher educators (MTEs) to make sense of novice teachers' experience within digital clinical simulations in terms of how they develop an iterative awareness, or navigation, of their choices in moments of tension.
... Chen found that when storyboarded, lesson anticipation contained significantly more attention to critical aspects of the lesson enactment (e.g., students' conceptions and misconceptions were spelled out, potential interactions were sketched, task details were provided) than when PSTs simply narrated the lesson. Consistent with other research regarding the use of the storyboard medium with PSTs (Herbst et al., 2014;Rougée & Herbst, 2018), Chen's findings suggest storyboarding provides stimulus for anticipating more details than merely planning and discussing lessons. More research, however, is needed to explore the learning process afforded by using storyboards to simulate and rehearse teaching practice for PSTs. ...
... We suggest that the virtual representation of storyboards as embedded in the StoryCircles process provides feedback to participants from which they might learn, both from the representation itself as well as from participants interacting with the same representation. Drawing on constructionist notions of learning, Herbst et al. (2014) argued that the material artefacts of storyboards provide opportunities for self-regulating feedback from the environment-like one might receive in microworld environments such as LOGO or Minecraft (e.g., Papert, 1980Papert, , 1993Short, 2012;Spiliotopoulos et al., 2019). Building on that argument, we suggest the collaborative and public construction of storyboard artefacts embedded in the StoryCircles process adds a second kind of feedback for participants-namely the sharing of knowledge amongst individuals (see also Tettegah, 2005). ...
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.
... Howell and colleagues (2019) listed "role of feedback" as one possible dimension that contributes to varying authenticity. Peer and instructor feedback has been used to inform PSTs' actions in simulated teaching environments (formative feedback); thus, feedback plays a role of scaffolding during approximations (Herbst et al., 2014). Approximations wherein PSTs have options to select and engage with the full practice are considered loosely constrained approximations . ...
... PSTs created classroom scenes by selecting characters, regulating movement, and constructing conversations to generate playable animations to enact plans. For instance, in Herbst et al. (2014), PSTs approximated planning and enacting lessons by rehearsing classroom actions using technological mediation and online interaction. The online discussion was also used as a platform to exchange feedback after enacting lessons. ...
Approximations of practice are opportunities for preservice teachers (PSTs) to engage in components of teaching. However, how the varying levels of complexity or authenticity of teaching create different learning opportunities for PSTs is underexplored. Forty-one studies related to approximations of mathematics teaching were reviewed to explore how approximations are embedded in PST education, how authenticity represents itself in approximations, and how mathematics teacher educators report approximations facilitating PSTs’ learning. The review identified eight types of approximations used, indicating that PSTs developed aspects of specific practices such as professional noticing, conducting a meaningful mathematics discussion, as well as generic lesson planning and implementation. We propose teacher education programs consider a continuum of authenticity to capture the complexity of approximations of practice as well as the recomposition of decomposed practices. We discuss how varying levels of authenticity in approximations of practice creates different opportunities for PSTs.
... The created flowchart is then used as a guide for designing storyboards, resulting in a planning design that is in accordance with the media structure (see Figure 4). The storyboard is a rough outline of the display of the learning media that will be created, including the media's content, layout, and the majority of the elements that will be included (Jones, 2008;Herbst et al., 2014;Webel and Conner, 2017). The story-board is then used as a guide in creating the interface design. ...
... Flowcharts are created to provide a high-level over-view of the flow or course of learning media from one slide to the next. The story-board is used to describe each slide, which includes an image display, conversation bubbles, and other pertinent information (Jones, 2008;Herbst et al., 2014;Webel and Conner, 2017). The results of this stage are displayed in the interface. ...
Using ICT-based interactive learning media is a learning method that strongly supports the teaching and learning process for students and teachers during the COVID-19 pandemic. This ICT-based learning media must be easily accessible to teachers and students, and one of the interactive media that is easily accessible is android-based learning media. This development research aims to design android-based learning media on valid trigonometric material and improve students’ mathematical critical thinking skills. This development research using the ADDIE model took 121 Ipeople consisting of expert validators, user (teacher), and students. The expert validators consisted of one mathematics education material expert and one ICT expert. Meanwhile, user represented by one mathematics teacher were involved in validating the use of the media design. In addition, there were participants from among students, which included 118 class X high school students throughout the Province of West Java, Indonesia, who took part in a limited trial phase of 20 people, an extensive trial of 50 people, and a product trial of 48 people. A sample of 118 students came from high school in the medium cluster. So, the reason for taking the sample represents the condition of students both on the island of Java and in Indonesia. The results showed that the developed android-based learning media was valid and could be used without revision with a combined percentage of 87.33%, with details of material experts at 84%, media experts at 92%, and validation by mathematics teachers at 86%. The results of the practicality test on students of 81% showed that the Android-based learning media design had a strong response, so the learning media made were very practical to use. The product test results show that the achievement of mathematical critical thinking skills of students who learn to use android-based learning media is better than those who learn not to use android-based learning media.
... To enhance the responsive teaching skills of preservice teachers (PSTs), researchers suggested decomposing complex teaching practices into discrete and manageable components, then providing opportunities to practice and reflect on each component of the teaching practice within less complex environments, known as approximations of practice (Grossman et al., 2009;Grossman & McDonald, 2008). Several technology-enhanced approximated approaches have been explored to help PSTs develop their competency in teaching practices, such as analyzing teaching practices in video-recorded lessons (e.g., Sun & Van Es, 2015), generating classroom scenes with animations (e.g., De Araujo et al., 2015), and engaging in specific practices through storyboarding software (e.g., Herbst et al., 2014). These supports can enhance novice teachers' skills and develop their responsiveness before actual classroom experiences (Ayalon & Wilkie, 2020;Codreanu et al., 2020). ...
... Digital teaching simulations have been used as a means of integrating practice-based learning into teacher education (e.g., Lee, 2021) to enhance PTSs' professional skills, identify important connections between teacher education coursework and field experiences (e.g., Carrington et al., 2009), and understand various aspects of classroom teachers' tasks through clinical experience (e.g., Dotger, 2013). For example, LessonSketch has been used to provide approximating teaching practices such as making professional decisions, generating teacher-student interactions (Herbst et al., 2011(Herbst et al., , 2014, suggesting feedback (Lee & Lim, 2020), and questioning in response to student thinking (Webel & Conner, 2017). Theelen et al. (2019) argued that computer-based classroom simulations had positive associations with PSTs' classroom management and teaching skills and bridged the gap between teacher education programs and field placement. ...
Responsive teaching promotes students' mathematical reasoning and positive attitudes toward mathematics. Due to the complexity of the work of teaching, preservice teachers (PST) have been provided with approximated opportunities to practice responsive teaching skills in teacher education programs. Although increasing demand for adaptive learning reinforces the need for research on artificial intelligence (AI) in education, there have been few approaches that engaged learners in meaningful interactions. Our goal was to develop an AI-based chatbot that engaged PSTs in an authentic, meaningful, and open-ended teaching situation to enhance PSTs' responsive teaching skills, specifically questioning skills through approximations of practice. The chatbot was designed to act as a virtual student who displayed misconceptions on the topic of fractions. By employing design-based research, we examined 1) design features and structure of the chatbot, 2) coverage of users' input, 3) PSTs' questioning patterns, and 4) users' experiences. Two iterations of design, implementation and evaluation took place in an elementary mathematics education methods course. To build the chatbot we qualitatively analyzed the training data, categorized them into the smallest meaningful intents of users, and prepared corresponding responses to each intent. At the final iteration, the refined chatbot adequately covered PSTs’ questions and provided realistic responses. We found a pattern of PSTs asking similar questions repeatedly in the conversation data. Through multiple iterations, certain design features could lead to improved questioning patterns and user perceptions, including sequential responses, informing responses, and personification. Implications, design features, and limitations are discussed.
... For example, in Sherin and van Es's (2005) study, teachers used a software program, Video Analysis Support Tool, to analyze video excerpts from their mathematics classes. Besides videos, researchers have investigated the use of other technologies such as animation and Les-sonSketch (Amador, Weston, Estapa, Kosko, & de Araujo, 2016;Herbst, Chazan, Chen, Chieu, & Weiss, 2011;Herbst, Chieu, & Rougee, 2014;Lee, 2020;Lee & Lim, 2020). For instance, Amador et al. (2016) examined the use of animation technology for representing teacher noticing and found that PSTs could communicate their noticing of classroom settings, connections between teachers and students and among students, and other aspects in more detail via animation technology than in written accounts. ...
... LessonSketch (Chazan & Herbst, 2012;Herbst et al., 2011) is a web-based online platform, which, according to Herbst et al. (2014), can be used to "construct, visualize, annotate, share, and discuss representations of teaching" (p. 360). ...
This study investigated effects of employing the Three-point framework (Key Point, Difficult Point, Critical Point) and three technology-aided interventions (online discussions, clinical interviews, and graphic lesson plan construction) on developing preservice teachers’ noticing skills in elementary mathematics pedagogy courses. Pre- and post-intervention assessments revealed significant improvement in the treatment group’s scores, and two case studies illustrated how the interventions can help preservice teachers develop noticing skills. These findings suggest that combining the framework with technology support provides an accessible model for guiding preservice teachers to use evidence from task-based interactions with learners to support instructional decisions.
... Accordingly, I investigated the use of LessonSketch, a free web-based online platform, as a tool to depict follow-up lessons after analyzing a student's mathematical solution involving some errors. Herbst, Chieu and Rougee (2014) have described Lesson-Sketch as a program that can be used to "construct, visualize, annotate, share, and discuss representations of teaching" (p. 360), pointing out that the Depict tool enables students to create comics format storyboards in which they manipulate people and objects to create a narrative in sequential still frames with speech bubbles. ...
... LessonSketch has been used to develop scenarios for various teaching practices, such as questioning and providing feedback on students' written work (Herbst, Chazan, Chen, Chieu, and Weiss 2011;Herbst et al. 2014;Lee and Lim 2020;Walkoe and Levin 2018). Lee and Lim (2020) used LessonSketch in a learning module in which PSTs practiced giving feedback to students on a mathematics examination by creating comics-based scenarios. ...
The purpose of this study was to investigate the affordances and constraints of a technological tool to foster pre-service teachers’ (PSTs) noticing skills including attending to, interpreting, and responding to students’ mathematical work. Participants were 99 junior or senior PSTs in a mathematics pedagogy course at a large university. Using LessonSketch, a web-based online platform, participants manipulated comics-based teaching scenarios to demonstrate what they attended to in a student’s mathematical written work and their related instructional decisions. Data comprised PSTs’ LessonSketch representations, their responses to prompts related to noticing skills, their reflections on the use of technology, and a focal group interview transcript. Inductive content analyses were applied to these data. The findings show that LessonSketch helped PSTs focus on how to ask questions, predict students’ answers, and respond in ways that supported students’ learning. The PSTs attended well to the student’s mistakes, but many did not clearly interpret her mathematical difficulties. Also, their pedagogical suggestions tended to be teacher-centered and procedural rather than supportive of conceptual learning. PSTs found LessonSketch helpful for locating themselves in the classroom situation and merging into the teaching moment. Despite the limitation of using only one written task, the study supports the critical role of technology in providing preliminary rehearsal of teaching practices and improving PSTs’ noticing skills, warranting further examination of the use of technology to support professional noticing.
... Lampert et al. (2013) share that envisioning practice through rehearsal is one way in which preservice teachers are able to approximate practice. Herbst et al. (2014) argue that creating classroom representations that include scripting can provide valuable learning experiences for preservice teachers. Scripting enables preservice teachers to produce teaching artifacts that could allow for "visual, collaborative, and relatively fast authoring of representations of teaching by teachers" (Herbst et al., 2014, p. 361). ...
... The rehearsal or artifact mentioned in the previous studies on scripting can then be discussed collaboratively in a class, or one on one with an instructor, and anno-tated and improved. Feedback by the instructor or classmates can provide others' perspectives on the representation-perhaps things that the author (preservice teacher) did not see, which can be valuable as preservice teachers learn to understand the power of discourse in the classroom (Herbst et al., 2014). Zazkis and Zazkis (2014) point out another potential benefit to scripting. ...
This chapter discusses the application of a scripting tool in teacher education and how scripting can support preservice teacher learning. Two preservice teachers participated in an intervention using a media-based scripting tool. The study examined changes in the preservice teachers’ scripting. Findings indicate that common characteristics can be clustered, and we attempted to organize those clusters into a set of scripting trajectories. We argue that preservice teachers can develop skills for generating dynamic classroom discourse into their scripts through a cycle of feedback and revision with scripting exercises, and that there is a strong need for curricula in teacher preparation programs reflecting appropriate learning pathways at the preservice teacher level to support preservice teachers’ development of effective discursive skills.
... In doing this, Helen was setting up an online environment for the PSTs which she hoped would enable their participation in an ''approximation of teaching practice'' (Herbst et al. 2014, citing work by Grossman and colleagues). In attempting to create such a simulation, it is important to identify how accurate an approximation of teaching practice is being implemented, especially in the online space. ...
... For example, when developing the activity-which was designed by building on experience, pre-existing knowledge, and intuition-she felt it would act as an ''approximation of practice''. She did not, however, have deep knowledge of the theoretical underpinnings of constructionism and the building of artifacts (such as public conversations about a student's work) as explicated in the ideas from the literature review of Herbst et al. (2014). ...
The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.
... As previously mentioned, current research has examined approximations of practice in multiple forms, including through technological mediums and other avenues (e.g. Herbst et al., 2014;lampert et al., 2013). in fact, Herbst et al. (2014) focused on media-rich, web-authoring tools for preservice teachers to create scenarios as an approximation of practice. We argue that our use of animation provides similar opportunities for approximating teaching as does their platform, lessonSketch. ...
... As previously mentioned, current research has examined approximations of practice in multiple forms, including through technological mediums and other avenues (e.g. Herbst et al., 2014;lampert et al., 2013). in fact, Herbst et al. (2014) focused on media-rich, web-authoring tools for preservice teachers to create scenarios as an approximation of practice. We argue that our use of animation provides similar opportunities for approximating teaching as does their platform, lessonSketch. ...
This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n=126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data analysis focused on the extent to which preservice teachers were specific or general with respect to mathematics in written and animated accounts of noticing. Findings illuminate preservice teachers’ degrees of specificity, with most preservice teachers being more specific about mathematics in their animations, showing promise for animation as a tool for communicating what is noticed. Further, preservice teachers perceived the use of animations a transformational experience, meaning the technological medium provided learning and access beyond what could have been accomplished without the technological support.
... In particular, in a study of the discourse employed by teachers discussing them, animations performed just as well as video in eliciting participants' statements about norms of professional practice, as measured by participants use of the modality resources of language; but animations were better than videos in eliciting modal statements of the normativity type (e.g. should; Herbst and Kosko 2014). At the same time that we examined the data from focus groups, we also started developing the infrastructure to take this research approach to the internet – exploring whether and how the animations could elicit similar kinds of noticing and reflection when delivered online (Chieu, Herbst, and Weiss 2011). ...
... The platform combines facilities found in media authoring and archiving software, media playing and annotating software, questionnaire editing, delivering, and reporting software, and learning content management systems. Its facilities can be used not only by researchers but also by professional developers and by professionals themselves (see Herbst, Aaron, and Chieu 2013; Herbst, Chieu, and Rougée 2014) though in this paper we are only discussing the methods and technology developed for research on teaching knowledge elicited from practicing teachers. 2 While creators of multimedia online experiences could rely on found videos or on our suite of animations as they author multimedia online experiences, Depict allows them to create their own scenarios very easily. ...
We describe how multimedia scenarios delivered online can be used in instruments for the study of professional knowledge. Based on our work in the study of the knowledge and rationality involved in mathematics teaching, we describe how the study of professional knowledge writ large can benefit from the capacity to represent know-how using multimedia representations of practice and alternatives to it. These instruments can be used to study what professionals notice and decide to do in practice in ways that improve upon earlier uses of written representations of professional scenarios or videorecorded episodes. In particular, storyboards and animations of nondescript cartoon characters can be used to explore professional knowledge variables systematically while the multimodal representation of human activity in context ensures the face validity of questions.
... Specifically, digital teaching simulations have been used to enhance PSTs' responsive teaching skills. For example, the LessonSketch tool has been used to provide approximations of teaching practices, such as making professional decisions while reviewing student work (Herbst et al., 2011;Herbst et al., 2014), helping PSTs notice students' reasoning and errors in a mathematical problem (Lee & Lim, 2020), and questions in response to student thinking (Webel & Conner, 2017). Theelen et al. (2019) found that computer-based classroom simulations had positive associations with PSTs' classroom management and teaching skills and bridged the common gap between teacher education programmes and field placements. ...
Background
Artificial Intelligence (AI) technologies offer unique capabilities for preservice teachers (PSTs) to engage in authentic and real‐time interactions using natural language. However, the impact of AI technology on PSTs' responsive teaching skills remains uncertain.
Objectives
The primary objective of this study is to examine whether interaction with a responsive AI‐based chatbot that acts as a virtual student improves pre‐service teachers' noticing abilities. The second objective is to compare how the presence or absence of chatbot responses affects changes in PSTs' questioning practices. Finally, the third objective is to investigate how the experience of interacting with the responsive virtual student affects PSTs' perceptions of the effectiveness of their questioning, their satisfaction with the interactions, and their confidence about interacting with a real student compared to the non‐responsive chatbot.
Methods
A randomised controlled pre‐ and post‐test design was used with 50 PSTs. PSTs' noticing, interaction with the chatbot, and post‐survey data were collected, and a t‐test was conducted to examine significant differences by group.
Results and Conclusion
In the experimental group, the virtual student responded to PSTs' questions, while in the control group, she did not. Notable differences were observed in their questioning practices.
Takeaways
Overall, AI‐based chatbots hold promise for enhancing PSTs' responsive teaching skills. Future research is needed to examine the long‐term impact of responsive chatbot use on PSTs' noticing skills.
... We would argue that similar to other types of skills, professional skills require that learners be engaged in both sorts of activities: consuming and composing (consider for example the sorts of critical connections between reading and writing). The act of composing a professional scenario requires an individual to anticipate several aspects of the scenario, such as clients' emotions; and for this reason we argue that the act of composing scenarios can add to the training of professionals (see Brown et al., 2021;Herbst et al., 2014;Milewski et al., 2018Milewski et al., , 2020. ...
Technology-mediated simulations of teaching are used increasingly to represent practice in the context of professional development interventions and assessment. Some such simulations represent students as cartoon characters. An important question in this context is whether simplified cartoon representations of students can convey similar meanings as real facial expressions do. Here, we share results from an implementation and replication study designed to observe whether and how (1) cartoon-based representations of emotion using graphical facial expressions can be interpreted at similar levels of accuracy as photo representations of emotions using actors and (2) the inclusion of markers of student emotions in storyboard-based scenarios of secondary mathematics teaching affects teachers’ appropriateness rating of the actions taken by a teacher represented in the storyboard. We show graphical representations of emotions can evoke particular intended emotions and that markers of student emotions in representations of practice could cue mathematics teachers into particular judgments of action.
The Impact Sheet to this article can be accessed at 10.6084/m9.figshare.24219964
... Building on prior research exploring the effectiveness of lesson visualizations in aiding individual pre-service teachers' lesson design and learning (Chen, 2012), our team hypothesized that visualization-the engagement of teachers with storyboards to represent their expectations for how a lesson may unfold-could serve as a robust form of feedback to facilitate teacher collaboration. To conceptualize this process, Herbst et al. (2014) drew on Papert's constructionism, which views learning as the construction of artifacts (Papert & Harel, 1991), and Brousseau's (1997) notion of the milieu. Brousseau's theory posits that the milieu presents itself to learners as a space free of didactic intentions and thus, excludes the teacher's feedback-which, in PD alludes to the facilitator's feedback. ...
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.
... These two activities were also done in the study conducted by Hidayat et al. (2023) and the study revealed that the preparation of content outline and flowchart of an Android-based learning media by considering the characteristics of learners can provide an overview of the flow or course of learning media at each stage. In addition, through the outline and flowchart display, the application developer can be easier in developing the next stages (Herbst et al., 2014;Jones, 2008;Webel & Conner, 2017). ...
Equations are often used in mathematics and other subjects, which means that a media can teach students how to solve equations, particularly linear equations of two variables, or Sistem Persamaan Linear Dua Variabel (SPLDV) as it is called in Indonesian, is needed. However, most teachers are still focused on developing the learning process and teaching materials rather than developing an application technology-based learning media. As we know that technology-based learning is currently the focus of teaching and learning activities in the digital era, especially learning after the pandemic. This study aimed to develop an application that can be a reference for teaching media in learning activities to improve students' mathematical understanding and ability. The developed application is named, Integrated and Convenient Android-based Simulation or Simulasi Android Terpadu dan Nyaman, abbreviated as SANTUY. This development study with Analysis, Design, Development, Implementation, and Evaluation (ADDIE) model, explained in detail in the paper, took seventy-five subjects consisting of six expert validators, nine users, and sixty students. The expert validators comprised three media experts and three material experts. The evaluation stage involved students from two groups, each consisting of thirty students. The results showed that the average percentage of the feasibility of the SANTUY SPLDV solution simulation-assisted application with differential learning nuance was 79.62%, which means the application is adequate. The level of usefulness of the SANTUY SPLDV solution simulation-assisted application with differential learning nuance was 86.11%, which is categorized as "excellent". In addition, using the SANTUY SPLDV application had a direct positive influence on improving students' mathematical understanding and ability.
... Others used teaching simulations with a hypothetical student profile (i.e., a person whose actions and statements are guided by artificial reasoning and responding, including scripted responses) [4]. In recent years, teaching simulations via digital platforms also have become more popular [30]. ...
This study presents an analysis of 95 lesson play scripts—hypothetical dialogues between the teacher and a student—written by 32 preservice teachers (PSTs). Writing lesson scripts was part of the assessment design activities to elicit and respond to students’ thinking. The findings present the types and frequencies of teacher talks/moves in fraction-related tasks during a stage of lesson plays, such as launch, active elicitation, and closure. Our analysis indicates a wide range in the number of turns taken by the PSTs, while there is little correlation between the number of turns and effectiveness at eliciting and responding to student thinking. The study also confirmed that some unproductive talk moves were still present in the lesson play context, although the PSTs had plenty of time to craft a script. This study drew implications of PSTs’ prior perceptions, experiences, knowledge, and needs in mathematics teacher education regarding the ways to create learning opportunities for them to elicit and respond to student thinking.
... The LessonSketch digital platform allowed us to create classroom scenes depicting particular aspects of mathematics instruction that we wanted to make visible for the PTs and that teachers might encounter in their work: small groups, whole groups, written work, and/or transcribed speech bubbles (Herbst et al. 2011(Herbst et al. , 2014(Herbst et al. , 2016. We designed the Noticing and Naming Students' Mathematical Strengths (NNSMS) LessonSketch experience as an assignment for PTs in our mathematics methods courses in order to provide a simulated classroom scenario in which to explore and rehearse the noticing and naming students' mathematical strengths. ...
Deficit discourse and framing of multilingual students and their academic potential is a persistent challenge in mathematics education research and practice. It is a challenge for teachers of all experience levels to learn how to use asset-based language when working with students who are learning mathematics in a non-dominant language. This article reports on a study that explored how prospective teachers (PTs) position multilingual students and their primary language when learning mathematics. The participants are elementary and secondary PTs who were introduced to and had the opportunity to practice asset-based discourse to describe students’ mathematical strengths. Findings illustrate that after these learning opportunities PTs’ positioning of multilingual students shifted from using deficit and uncommitted discourse to asset-based. A closer look, however, showed no explicit mention of the value of the student’s primary language for learning mathematics. Only a few PTs did so implicitly. This study shows it is possible for PTs to shift deficit language, but that more explicit support is needed to help them communicate the value of language/linguistic diversity in the learning of mathematics.
... StoryCircles engages teachers in collaboratively designing and improving a lesson by creating storyboards that represent possible implementations of the lesson.While the StoryCircles process draws crucial inspiration from other practice-based, lesson-centered approaches such as Japanese lesson study 2 (Lewis, Perry, & Murata, 2006), the StoryCircles lesson revision process does not solely depend on classroom implementation. The storyboard medium-central to the StoryCircles process-acts as a critical source of feedback, informing lesson revisions (like virtual microworlds such as MineCraft enables users to both see and assess their work, see Chen, 2012;Herbst, Chieu, & Rougée, 2014;Rougée & Herbst, 2018). The storyboard medium has also enabled us to ensure participants are confronted with realistic lesson contingencies-in spite of their absence from regular classroom practice. ...
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.
... NNSMS used an existing design called Making Bags of Apples (Herbst et al. 2011(Herbst et al. , 2012(Herbst et al. ,2014(Herbst et al. ,2016. In Bannister et al. (2018), we describe in detail how we adapted the original storyboard to suit the purposes of our digital course assignment (see https ://sites .googl ...
Learning to name and notice students’ mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students’ mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students’ mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students’ mathematical strengths. The paper concludes with implications for future research in teacher education.
... Rendahnya pemahaman konsep matematika siswa berdampak pada proses pembelajan sehingga siswa kesulitan menyelesaikan permasalahan matematika. Salah satu solusi yang dapat meningkatkan pemahaman konsep matematika siswa adalah penggunaan macromedia flash (Herbst, Chieu, & Rougee, 2014;Moradmand, Datta, & Oakley, 2014) Macromedia flash merupakan software yang menampilkan animasi sederhana untuk menjelaskan konsep matematika. Penggunaan macromedia flash dapat memvisualisasikan konsep matematika yang abstrak menjadi kongkrit, meningkatkan perhatian siswa pada pembelajaran dan memungkinkan pengulangan berulang (retensi) bagi siswa dalam meningkatkan pemahaman konsep matematikanya. ...
Penelitian ini berfokus pada peningkatan kemampuan pemahaman konsep siswa dalam pembelajaran matematika. Pendekatan pembelajaran yang efektif yang digunakan dengan memanfaatkan media teknologi informasi dalam bentuk pembelajaran digital adalah aplikasi macromedia flash. Macromedia flash dapat membantu menjelaskan konsep matematika yang kepada siswa dengan tampilan yang menarik. Tujuan penelitian ini adalah untuk menganalisis; (1) kemampuan pemahaman konsep matematika siswa yang menggunakan macromedia flash; (2) respons siswa terhadap penggunaan macromedia flash dalam pembelajaran. Penelitian ini merupakan kuasi eksperimen dengan desain kelompok pretes-postes menggunakan macromedia flash dalam pembelajaran matematika. Populasi dalam penelitian ini adalah seluruh siswa kelas IX SMP Negeri di Majalengka. Instrumen penelitian berupa tes kemampuan pemahaman konsep matematika dan angket. Analisis data menggunakan Paired t-test. Penelitian menghasilkan: (1) peningkatan kemampuan pemahaman konsep matematika siswa dengan kategori sedang, dan (2) respon positif siswa terhadap penggunaan macromedia flash diatas skor netralnya.
Kata Kunci: Aplikasi Macromedia flash, Geometri, Pemahaman Matematis, Pemahaman Konsep Matematika.
... The use of technology and multimedia is an effective and efficient way of conveying information (Kaharuddin, 2019). Computer is one of information technology that has great potential to improve the quality of learning, especially in mathematics learning (Herbst, 2014;Moradmand, 2014). The development of Information and Communication Technology which together with the development of multimedia technology, makes the products of Information and Communication Technology increasingly diverse. ...
This study aims to describe the characteristics of storyboard design and to find out the multimedia storyboard design of mathematics learning in the production of BTIKP (Center for Information and Communication Technology Education) of the Jambi Provincial Education Office according to the rules based on ADDIE framework learning design. The researcher uses the ADDIE framework learning design because this design is more effectively used as a reference for the creation and development of a learning media. From the results of the identification carried out by the researcher in three stages. For the characteristics of the multimedia storyboard design of mathematics learning produced by the BTIKP (Center for Educational Information and Communication Technology) of the Jambi Provincial Education Office, there is one storyboard that satisfies the assessment, namely in the third stage (evaluating and revising) for multimedia storyboards learning mathematics with Geometry Transformation material. Overall the design of the five multimedia storyboards of mathematics learning produced by the BTIKP (Center for Educational Information and Communication Technology) of the Jambi Provincial Education Office which has been investigated by researchers is still a design that is not in accordance with the design of ADDIE framework learning.
... 42). And, teacher candidates, not only their instructors, can be the creators of these artifacts (Herbst, Chieu, & Rougée, 2014;Rougée & Herbst, 2018). Teacher candidates can represent practice that they are observing, and they can represent their own attempts to engage in practice. ...
... Frequently, teacher educators are the creators and rarely do PSTs themselves create animations or depictions, yet recent studies point to possible affordances of PST-created animations or depictions as a form of practice-based work (de Araujo et al., 2015). Herbst, Chieu, and Rougée (2014) specifically describe using depictions through storyboarding as a way to approximate practice and argue this provides "opportunities for preservice teachers to learn to teach by doing" (p. 356). ...
In this mixed methods study, we used a convergent paral- lel design to create and analyze a task that was implement- ed across four US institutions with 99 preservice teachers (PSTs) using one of two multi-media platforms: LessonS- ketch or GoAnimate. We analyzed PSTs’ comic-based depic- tions or animations to examine teacher questioning and ut- terances, use of visual information, and format of classroom interaction. PSTs who used GoAnimate included significantly more utterances than those who used LessonSketch, yet the level of questioning was statistically equivalent across both mediums. Artifacts created with GoAnimate tended to convey small group interactions, whereas LessonSketch depictions typically portrayed whole class interactions and included ad- ditional visual information. We discuss these findings and their implications for teacher educators to select and align use of such multi-media platforms for particular instructional aims.
... While such efforts can be quite compelling for providing mechanisms for teacher growth, some have continued to express doubts about the extent to which actual classrooms can serve educative purposes beyond the socialization of teachers into the typical schooling routines (see Ellis, 2010;Zeichner, 1981Zeichner, , 2012. Some scholars have taken a different tack, investigating ways to engage teachers in practice-based pedagogies through the use of simulated envi-ronments (Amidon, Chazan, Grosser-Clarkson, & Fleming, 2017;Brown, Davis, & Kulm, 2011;Dieker, Hughes, Hynes, & Straub, 2017;Herbst, Chieu, & Rougée, 2014;Lampert et al., 2013;Shaughnessy & Boerst, 2017). For example, Lampert and colleagues (2013) describe rehearsals as a kind of simulated activity distinct from more typical run-throughs or microteaching found in teacher education courses. ...
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.
... This virtual eld placement is similar to several of the virtual eld experiences described above in that it does not take place in a real classroom with actual students; Azul's Room is a set of images created with the Lesson-Sketch platform's Depict tool (for detail on this tool, see Herbst, Chieu, & Rougee, 2014) that Amidon's teacher candidates are asked to treat as a setting to learn teaching. Different from these other virtual eld experiences, though, Azul's Room is not a place to view interaction; instead, it is a space where teacher candidates can represent student thinking or responses to student thinking. ...
This article explores the ways in which a teacher educator uses digital technology to create a virtual field placement as a way to blur the boundaries between a university methods course and teacher candidates' field placements. After describing his goals for the course, the teacher educator provides a description of three Lesson Sketch experiences his teacher candidates complete in this virtual field placement site and how these experiences create opportunities for teacher candidates to learn to teach mathematics. The design process and choices of these virtual field placement experiences are explored via interviews with the first author. Reflecting on these Lesson Sketch experiences, all of the authors then explore affordances of virtual and hybrid placements as resources for supplementing real placements and bridging theory/practice divides in teacher education.
... Chen (2012) had PSTs create comic-based lesson depictions of classroom interactions. Similarly, Herbst, Chieu, and Rougee (2014) have engaged mathematics methods students in creating representations of teaching through static animation sketches. Amador and Earnest (2016) explored PSTs' use of animations for lesson planning and to approximate enactment, but the focus was on curricular use as opposed to noticing mathematics content. ...
In an effort to elicit elementary preservice teachers' mathematical noticing, mathematics teacher educators at 6 universities designed and implemented a 3-step task that used video, writing, and animation. The intent of the task was to elicit preservice teachers' mathematical noticing—that is, noticing specific to mathematics content and how students reason about content. Preservice teachers communicated their noticing through both written accounts and self-created animations. Findings showed that the specificity of mathematical noticing differed with the medium used and that preservice teachers focused on different mathematical content across the methods sections, illuminating the importance for mathematics teacher educators understanding of the noticing practices of the preservice teachers with whom they work. This report includes implications for using the task in methods courses and modifying course instruction to develop noticing following task implementation.
... Activities of approximating practice could conceivably involve novices' interactions with a simulator . Herbst, Chieu, and Rougee (2014) show how they have been able to engage preservice teachers (PSTs) in practice-based homework assignments where they demonstrate how they would do a practice by authoring a classroom storyboard. Once authored, these storyboards support the learning of teaching by enabling novices to visualize a lesson that provides feedback on their demonstration. ...
This chapter focuses on how digital technologies provide affordances for Practice-Based Mathematics
Teacher Education (PBMTE) and maps needed research on technologically mediated teacher education.
The chapter elaborates on Grossman’s pedagogies of practice, describing how they can be enacted in
digital environments. Using LessonSketch as a prototype of an online platform for PBMTE, the chapter
describes what those pedagogies look like when mediated through technology by narrating three cases.
The chapter maps needed research by describing how various research approaches including design
research, teaching effectiveness, ecological, and instrumental genesis might be used to organize research
on environments that support technologically mediated, practice-based mathematics teacher education.
The aim of this qualitative study was to examine prospective mathematics teachers’ instructional visions and engagement in an approximation of practice during the Methods of Teaching Algebra course during a 14-week spring semester. One such approximation to practice is scripting tasks, which can reveal the visions of prospective teachers. Each of the 25 prospective teachers completed three scenarios, held group discussions, and revised individual scenarios. The main findings indicated that while prospective teachers had an instructional vision that aligned with ambitious instruction, they were unable to adequately reflect these visions in their engagement in the approximation to practice.
https://authors.elsevier.com/a/1kF5s,Gtqw3ed5
The purpose of this study was to investigate whether a TMSSR (Teacher Moves for Supporting Student Reasoning)-based intervention could enhance prospective middle school teachers' abilities for supporting student reasoning on quadratic functions. Participants (N = 17) engaged with quadratic functions, practiced the TMSSR framework through scriptwriting assignments, received feedback and revised their scripts, compared and contrasted scenarios, and discussed ways to achieve high-potential moves during the intervention. Data sources included participants' pre/post scriptwriting tasks along with take-home assignments across the intervention. Results indicated the TMSSR-based intervention was effective in improving prospective teachers' repertoire of high-leverage moves for eliciting, responding to, facilitating, and extending student mathematical reasoning. Specific areas of improvement included eliciting understanding, promoting error correction, providing guidance, encouraging reflection, and pressing for generalizations. This study suggests a framework that mathematics teacher educators can use to improve prospective teachers' abilities for supporting student reasoning.
Bu nitel çalışmada, matematik öğretmen adaylarının cebir öğretimine yönelik öğrenmelerinin gelişiminde uygulamaya dayalı pedagojik yaklaşımlardan biri olan senaryo tamamlama uygulamasından yararlanılmıştır. Katılımcıları 3. sınıf seviyesinde “Cebir Öğretimi” dersini alan ilköğretim matematik öğretmeni adayları oluşturmaktadır. Ders sürecinde teorik konu anlatımları gerçekleştirilmiş ve ardından araştırmacılar tarafından hazırlanan senaryolar öğretmen adaylarına verilerek bunların öğretmen-öğrenci etkileşimi temelinde tamamlanmaları istenmiştir. Takip eden süreçte grup tartışmaları ve bireysel revizyonlarla öğretmen adaylarının eksik öğrenmelerini tamamlamaları hedeflenmiştir. Veriler içerik analizi kullanılarak öğretmen öğrenmesi kavramsal çerçevesinin önerdiği dört bileşen temel alınarak analiz edilmiştir. Bulgulara göre, öğretmen adayları genellikle öğrenci merkezli vizyonu benimsemiştir. Ancak çoğunun vizyonlarını düşündükleri şekilde senaryolarına yansıtamadıkları görülmüştür. Grup çalışmalarından elde edilen veriler, öğrenciye daha fazla söz hakkı tanıyan, öğretmenin rehber konumunda olduğu, öğrencilerin birbiriyle tartıştığı ve keşfettiği bir ortam oluşturma eğilimlerinin genel olarak tüm gruplarda arttığını göstermiştir. Bireysel revizyonlarda öğretmen adaylarının alan ve öğrenci bilgilerinin ve öğrenci merkezli eğilimlerinin çoğunlukla arttığı görülmüştür. Uygulama bağlamında senaryo tamamlama sürecinin, öğretmen adaylarının öğrenmelerini geliştirdiği ve gerçek sınıf ortamına hazırlanmalarına katkı sağladığı düşünülmektedir.
Approximations of practice create valuable opportunities for preservice teachers (PSTs) by engaging them in components of teaching. By reviewing the literature, this study explored PSTs’ learning through approximations and the extent approximated practices preserve the complexity – or authenticity – of teaching. A review of 25 empirical studies related to approximations of mathematics teaching indicated that mathematics teacher educators are currently exploring an expansion of opportunities through approximations wherein PSTs could experience a higher degree of authenticity. The existing conceptualization of authenticity emphasizes the complexity of practices but overlooks how approximated practices prepare PSTs for their future teaching. An alternative definition is proposed for the emerging conceptualization of authenticity to highlight how PSTs’ learning through approximations prepares them for their future teaching.
This article explores secondary teachers’ opportunities to learn from an innovative real analysis course, as reflected in their actual classroom teaching. The course used cases of teaching as a site for applying mathematics and developing pedagogical mathematical practices. This article explores particular teaching moments in ( N = 6) secondary teachers’ classrooms, and the attributions they gave for why they engaged in those teaching practices. Teachers engaged in instructional practices that exemplified course objectives, and their attributions for their actions contribute a teacher perspective on opportunities to learn in teacher education from (advanced) mathematical coursework. Results highlight cases of teaching and modeled instruction as catalysts of change and as opportunities to develop pedagogy from mathematical activity, and vice versa.
Developing expertise in professional noticing of students’ mathematical thinking takes time and meaningful learning experiences. We used the LessonSketch platform to create a learning experience for secondary preservice teachers (PSTs) involving an approximation of teaching practice to formatively assess PSTs’ noticing skills of students’ mathematical thinking. Our study showed that approximations of teaching practice embedded within platforms like Lesson Sketch can enable mathematics teacher educators (MTEs) to carry out effective formative assessment of PSTs’ professional noticing of students’ mathematical thinking that is meaningful for both PSTs and MTEs. The experience itself as well as its design features and framework used with the assessment can be applied in the work of MTEs who develop teachers’ professional noticing skills of students’ mathematical thinking.
In this article the authors discuss the process of designing a digital experience to support prospective teachers to learn to enact an equity-based complex practice of mathematics
teaching, namely to notice students’ mathematical strengths rather than notice gaps and deficits in their thinking. LessonSketch is a web-based platform purposefully designed to support the work of teacher educators. After theorizing how approximations of practice provide prospective teachers with ways and means for leveraging complex, equity-based pedagogical practices, the authors describe how they used LessonSketch
to design a flexible digital learning experience for prospective teachers in mathematics methods courses. The authors reflect on the design choices they made, the challenges
they faced, and the educational potential of their LessonSketch experience. They conclude by sharing design considerations and challenges that guided their work together and that could guide other mathematics teacher educators to support prospective teachers’ learning of complex pedagogical practices.
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 describes a set of activities in a professional development intervention with in-service geometry teachers that engaged them in role-playing a lesson summary. The activities included discussion of animations of classroom instruction with examples of how to lead a summary of a problem-based lesson. The animations were representations of teaching that supported the development of shared knowledge about how to summarize a lesson. In addition, the teachers decomposed the practice of summarizing prior to their engagement in a role-play of a summary. This role-play constituted an approximation of practice that enabled the teachers to envision how a summary would unfold in real time and required the teacher leading the summary to make tactical decisions. Observations of a teacher leading a summary in his classroom provided evidence of teacher learning. Overall, the professional development included a sequence of activities that validated teachers’ knowledge and provided them with the capabilities for engaging in an authentic approximation of practice in a safe environment.
The topic survey on the education of prospective secondary mathematics teachers (PSMTs) provides significant new trends and development in research and practices related to aspects of preparing PSMTs from 2005 – 2015. An overview of the current state-of-the-art and recent research reports from an international perspective are provided. The development of PSMTs’ mathematics content and pedagogical content knowledge, the emergence of PSMTs’ professional identities, PSMTs’ field experiences, and the impact of the increasing availability of various technological devices and resources on preparing PSMTs are discussed. The authors conducted a thorough review of the literature by examining major journals in the field of mathematics education and some well-known cross country studies. In the report, dominant methodologies and theoretical perspectives are addressed as well as main findings to indicate current trends.
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.
Elementary preservice teachers at six universities engaged in a task that provided them opportunities to articulate their professional noticing within video representations, written decompositions, and animated approximations of practice. The preservice teachers’ written accounts indicated that a majority attended to students or student thinking; however, when asked to illustrate their noticing through animation, focus shifted to the classroom teacher. Findings indicate the extent to which preservice teachers articulated specific mathematics concepts within and across pedagogies of practice and highlight the critical importance for selecting and utilizing multiple types of tasks to better understand preservice teacher noticing. Implications for eliciting and supporting preservice teacher noticing are discussed.
The topic study group on the mathematics education of prospective secondary teachers is dedicated to sharing and discussing significant new trends and developments in research and practices related to various aspects of the education of prospective secondary mathematics teachers from an international perspective. As Ponte and Chapman (2016) stated, teacher education is an area in which, although we have developed an understanding about the process of becoming a teacher, many questions still remain open. Our goal in this topic group is to address some of these questions. We discuss major areas in the field, including the nature and structure of teachers’ knowledge and its development, models and routes of mathematics teacher education, development of professional identities as prospective mathematics teachers, field experiences and their impact on prospective secondary mathematics teachers’ development of the craft of teaching, and use of various technological devices and resources in preparing prospective secondary mathematics teachers. To facilitate the discussion of these issues, the authors of this survey conducted a systematic literature review of studies published in nine international mathematics education during the last decade focused on the following four areas: Teacher knowledge; Technologies, tools and resources, Teachers’ professional identities, Field experiences.
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