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Using Designed Instructional Activities to Enable Novices to Manage Ambitious Mathematics Teaching

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  • New Visions for Public Schools

Abstract

If teacher education is to prepare novices to engage successfully in the complex work of ambitious instruction, it must somehow prepare them to teach within the continuity of the challenging moment-by-moment interactions with students and content over time. With Leinhardt, we would argue that teaching novices to do routines that structure teacher–student–content relationships over time to accomplish ambitious goals could both maintain and reduce the complexity of what they need to learn to do to carry out this work successfully. These routines would embody the regular “participation structures” that specify what teachers and students do with one another and with the mathematical content. But teaching routines are not practiced by ambitious teachers in a vacuum and they cannot be learned by novices in a vacuum. In Lampert’s classroom, the use of exchange routines occurred inside of instructional activities with particular mathematical learning goals like successive approximation of the quotient in a long division problem, charting and graphing functions, and drawing arrays to represent multi-digit multiplications. To imagine how instructional activities using exchange routines could be designed as tools for mathematics teacher education, we have drawn on two models from outside of mathematics education. One is a teacher education program for language teachers in Rome and the other is a program that prepares elementary school teachers at the University of Chicago. Both programs use instructional activities built around routines as the focus of a practice-oriented approach to teacher preparation. KeywordsExchange routines–ambitious teaching–instructional activities–teacher preparation–deliberate practice
... During the last two decades, significant attention has been paid to ambitious teaching (Franke et al., 2007;van Es et al., 2017) in different subject matters, including mathematics (e.g., Lampert et al., 2010), science (e.g., Tekkumru-Kisa et al., 2020), literacy (e.g., Hatch & Grossman, 2009), and history (e.g., Fogo, 2014). Defined as work with all students that is "intellectually demanding and attentive to students' work" (Cohen, 2011, p. 47), ambitious mathematics teaching aims at engaging all students in mathematically challenging work that affords them opportunities to reason mathematically and explain their thinking (Lampert et al., 2010). ...
... During the last two decades, significant attention has been paid to ambitious teaching (Franke et al., 2007;van Es et al., 2017) in different subject matters, including mathematics (e.g., Lampert et al., 2010), science (e.g., Tekkumru-Kisa et al., 2020), literacy (e.g., Hatch & Grossman, 2009), and history (e.g., Fogo, 2014). Defined as work with all students that is "intellectually demanding and attentive to students' work" (Cohen, 2011, p. 47), ambitious mathematics teaching aims at engaging all students in mathematically challenging work that affords them opportunities to reason mathematically and explain their thinking (Lampert et al., 2010). The significance of ambitious teaching for promoting deep learning has been documented in a growing body of research (e.g., Boaler, 2008;Forzani, 2014;Franke et al., 2007) and different educational policy documents (e.g., Australian Government Department of Education, 2014; National Council of Teachers of Mathematics, NCTM, 2014). ...
... The significance of ambitious teaching for promoting deep learning has been documented in a growing body of research (e.g., Boaler, 2008;Forzani, 2014;Franke et al., 2007) and different educational policy documents (e.g., Australian Government Department of Education, 2014; National Council of Teachers of Mathematics, NCTM, 2014). In mathematics, in particular, ambitious teaching has been considered a key lever for helping students develop deep conceptual understanding; compose and share convincing argumentation; use skills of reasoning to comprehend and solve complex and authentic problems; and produce high-quality academic work (Lampert et al., 2010). ...
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Over the past decade, teaching mathematics ambitiously has received increased attention. In this paper, we argue that to materialize this vision in contemporary classes we need to understand how practicing teachers experiment with certain aspects of this teaching and what challenges they encounter. Toward this end, we focus on an aspect of teaching ambitiously—designing and using enablers and extenders—and examine how four elementary schoolteachers experimented with it in their practice while also participating in a video-club setting. Drawing on a corpus of data including lesson plans, videotaped lessons, pre- and post-lesson interviews, end-of-program interviews, and videotaped video-club sessions, and looking across the four cases, we sketch how these teachers worked with enablers and extenders and the challenges they faced. Our analysis helped identify certain components entailed in working with enablers and extenders during the phases of lesson planning and enactment; it also yielded a classification of observed and reported challenges encountered as teachers engage with this work. This mapping of work associated with designing and using enablers and extenders, along with the classification of challenges generated, can inform professional learning development attempts aiming to support teachers enact ambitious teaching by identifying and naming separate components of practice that merit consideration and by providing insights into the types of scaffolds needed to support teachers in teaching ambitiously.
... Many scholars studying research-based teaching practices stress that students interacting with the instructor and each other are critical components of such teaching (e.g., Jacobs & Spangler, 2017;Lampert et al., 2010;Larsen et al., 2015;Laursen & Rasmussen, 2019;Stein et al., 2008). For instance, a defining characteristic of inquiry-based instruction is that instructors inquire into their students' thinking (Laursen & Rasmussen, 2019), which requires eliciting and building on students' ideas to drive the mathematical agenda of the class. ...
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Background Implementing research-based teaching practices has been repeatedly cited as an important factor for student success in university mathematics courses. Many research-based practices increase the amount of student–student and/or student–instructor interaction. However, some instructors are hesitant to implement such practices because they anticipate their students reacting negatively to experiencing an interactive classroom. As part of a larger project studying introductory undergraduate mathematics courses in the United States, we investigated students’ perceptions of the helpfulness of various classroom characteristics, particularly those that require interaction. Results From analyzing quantitative student data, we found that students reported interactive classroom characteristics (e.g., group work) as less prevalent than other classroom characteristics (e.g., lecture). Moreover, the students tended to regard characteristics that they reported experiencing often as helpful for their learning. From analyzing qualitative data from student focus groups, we found that students considered several indicators when identifying if a characteristic was helpful for their learning. In particular, students suggested that they can identify a characteristic as helpful for their learning when it supported them in solving assigned problems and understanding why the procedures work, earning good grades, building on their knowledge or applying it in different contexts, and teaching others. Conclusions The key finding from our work is that students are likely to view classroom characteristics that they experience more often as more helpful for their learning and are less likely to view characteristics that they rarely experience as helpful for their learning. Students view the characteristics that they regularly experience as helping them to solve problems and understand why the procedures work, earn good grades, build on their knowledge or apply it in different contexts, and teach others. We discuss important implications for practice, policy, and research as it relates to both student and instructor buy-in for increasing interactions in class.
... In a study of recent graduates from a teacher education program, Jansen et al. (2020) show that teacher preparation experiences can influence teachers' instructional vision into their early years of teaching. Arbaugh et al. (2021) investigated the connections between pedagogies of practice (Grossman et al., 2009;Lampert et al., 2010) and changes in preservice teachers' instructional vision, which they characterize as "broadening visions" of the role of the teacher. Taken together, these studies suggest that engaging in professional learning opportunities can lead to changes in instructional vision as well as practice. ...
... In spite of the emergence of some deeply insightful research into teaching of mathematics (e.g., Lampert, 2001;Lampert, Beasley, Ghousseini, Kazemi, & Franke, 2010;Stein, Engle, Smith, & Hughes, 2008), the field focused overwhelmingly on studies of learning. An analysis we have recently reported elsewhere (Visnovska, Cortina, & Vale, in press) is illustrative in this regard. ...
Article
We address two of the challenges that were recently raised in APJTE editorial. The editorial aimed to encourage the APJTE research community, and the field of teacher education broadly, to engage in research, in which a complex view of teaching is assumed, explored, and proactively supported. We offer a perspective on the standing of two of the outlined challenges in mathematics education research and notes on what pursuing these challenges may entail. Specifically, we comment on the challenges of (1) reclaiming a practically meaningful, intellectually rigorous and politically astute conception of teaching, and (2) dealing well with and rigorously theorising the complexity of education, teaching, and teacher education. We start with a brief (and necessarily reductive) account of the history of mathematics education research domain and highlight how the conceptions of teachers and teaching were shaped through the research endeavours. We bring to the fore the implications that the dominant research approaches had for resources for teaching school mathematics. In this context, we turn to design research methodology in mathematics education and illustrate how the methodology, when coupled with the orientation of designing for teachers, can assist in the researchers’ pursuits of the outlined challenges.
... There is little debate that the intentional use of instructional strategies to facilitate rich classroom discussions is an essential component of high quality or "ambitious" mathematics teaching (Lampert et al., 2010;Stein et al., 2008). In fact, Correnti et al. (2015) argued that orchestrating productive conversations is an "important and universally recognized dimension of teaching" (pg. ...
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Chapter
This chapter provides a set of recommendations for teacher educators interested in using simulated teaching experiences to support teacher learning of pedagogical practice in the post-COVID era. Built from existing research, the recommendations from the study come from lessons learned as five elementary mathematics and science teacher educators used a simulated teaching experience to support preservice teacher learning during the COVID-19 pandemic. The authors begin by situating this work in the larger context of practice-based teacher education and then provide an in-depth description of how five teacher educators at different universities integrated a simulated teaching experience into their elementary mathematics or science methods course. The chapter ends with a discussion of lessons learned and how educator preparation programs and teacher educators can leverage the opportunities created by using simulated teaching experiences in the post-COVID era.
Thesis
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Thesis
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