Understanding teachers’ noticing of children’s mathematical thinking in written work from different sources

Expertise in teacher noticing of children's thinking is central to a vision of responsive teaching in which teachers regularly elicit and build on children’s thinking during instruction (Richards & Robertson, 2016). In mathematics classrooms, this core instructional practice of noticing children’s mathematical thinking repeatedly occurs during instruction and involves attending to and making sense of children's mathematical thinking (Sherin, Jacobs, & Philipp, 2011). Teachers daily have opportunities to notice children’s mathematical thinking during their conversations with students and in students’ written work. However, expertise in noticing children’s mathematical thinking does not develop automatically or through years of teaching, and teachers need support developing noticing expertise. To help teachers develop noticing expertise, professional developers often employ artifacts of practice (e.g., video clips and student written work) from teachers’ own classrooms as well as strategically selected artifacts from classrooms taught by teachers unfamiliar to the PD participants. This study explored the potential differences in teachers’ noticing with written work from these two sources—teachers’ own classrooms and classrooms unfamiliar to the teachers. Drawing on the construct of framing (Goffman, 1974), particular attention was paid to the various frames (or lenses) teachers used during noticing. Using a context of professional development focused on children's mathematical thinking in the domain of fractions, this three-phase study explored teachers’ noticing and their use of frames by investigating the relationship between teachers' noticing of children's mathematical thinking in written work from their own classrooms versus unfamiliar classrooms. In the first phase, this study identified the frames individual teachers used when noticing children’s thinking in written work from their own classrooms. The second phase explored the frames that small groups of teachers used when collectively noticing children’s thinking in written work from unfamiliar classrooms during professional development. The third phase used in-depth interviews to investigate the relationship between the quality of teacher noticing and the use of frames of six teachers who were asked to notice children’s thinking in written work on the same problem from their own classrooms and from unfamiliar classrooms. Findings identified six frames teachers used while noticing children's mathematical thinking in written work from the two sources, and they fell into three broad categories: (a) noticing focused on the child’s current mathematical performance, (b) noticing focused on the child’s non-mathematical performance, and (c) noticing that compared the child’s performance to the expected performance based on the child’s past performance, the performance of the rest of the class, or curricular or testing guidelines. Confirmation of these frames in three data sets highlighted the variety of ways teachers reason during noticing, suggesting that frames are a useful construct for understanding the complexity of teachers’ noticing because frames capture the multiple and sometimes competing ideas that teachers need to coordinate. When comparing teachers’ noticing of children’s thinking in written work from their own classrooms versus unfamiliar classrooms, a lack of substantial evidence was found to distinguish the sources in terms of the use of particular frames, the prevalence of particular frames, or the quality of teachers’ noticing of children’s thinking. Further, there was evidence that teachers “imagined” insider knowledge of children from unfamiliar classrooms to assist with their noticing, which might explain why engaging with written work from either source did not seem to change the quality of teachers’ noticing. On the other hand, comparative analyses identified a distinction between teachers’ use of frames when they were considering one child’s strategy versus several children’s strategies regardless of whether the written work came from the teachers’ classrooms or unfamiliar classrooms. Specifically, when teachers’ noticing focused on more than one child, more frames and a greater variety of frames were invoked. Implications for professional development focus on the need to appreciate and address teachers’ coordination of multiple frames and the idea that the use of these frames depends less on the source of the written work and more on the number of children involved in the task

New Working Group: Teaching Mathematics for Social Justice in the Context of University Mathematics Content and Methods Courses

There are three goals for this new working group: 1) To create a community of mathematics teacher educators (MTEs) who are (or are interested in) collaboratively teaching mathematics for social justice (TMfSJ) in their university content and/or methods classes. 2) To collaboratively select/develop/modify TMfSJ tasks and implement those in mathematics content/methods classes. 3) To research the implementation of TMfSJ tasks in content and methods classes

Reimagining the STEM Education Pipeline for Teachers of Color

Increasing the presence and representation of people of Color is essential to giving more children and communities access to diverse, highly qualified, STEM educators. As Black authors, and scholars of Color, each of our careers is a reflection of that reality, with our combined 50 years as STEM educators. Throughout the United States, and in the Caribbean, we have taken on roles as mentors, guides, advisors, and leaders of STEM programs to specifically caretake how people of Color experience and navigate them. These roles have been both paid and voluntary roles, grounded in our membership in communities of Color and our commitment to diversity and equity in STEM. From this perspective, we draw upon both our expertise as well as the extant literature to collectively give voice to powerful ways that the teacher pipeline must be disrupted. We wish to not only advocate for change in the pipeline but also to impact how teachers of Color advocate for themselves

Reimagining the STEM Education Pipeline for Teachers of Color

Increasing the presence and representation of people of Color is essential to giving more children and communities access to diverse, highly qualified, STEM educators. As Black authors, and scholars of Color, each of our careers is a reflection of that reality, with our combined 50 years as STEM educators. Throughout the United States, and in the Caribbean, we have taken on roles as mentors, guides, advisors, and leaders of STEM programs to specifically caretake how people of Color experience and navigate them. These roles have been both paid and voluntary roles, grounded in our membership in communities of Color and our commitment to diversity and equity in STEM. From this perspective, we draw upon both our expertise as well as the extant literature to collectively give voice to powerful ways that the teacher pipeline must be disrupted. We wish to not only advocate for change in the pipeline but also to impact how teachers of Color advocate for themselves

Teacher noticing from a sociopolitical perspective: the FAIR framework for anti-deficit noticing

In this paper, we respond to the continued harm of deficit discourses in mathematics education, focusing on discourses that systematically devalue the knowledge and abilities of students of color in classrooms in the United States. We specifically aim to (1) develop a sociopolitical framework for conceptualizing mathematics teacher noticing and (2) conceptualize and illustrate the enactment of noticing that challenges deficit discourses about these students and their communities—anti-deficit noticing—through the lens of our framework. We address our first research aim by introducing the FAIR framework, which foregrounds the role of sociopolitical Framing as an essential component of noticing that shapes and is shaped by Attending, Interpreting, and Responding, processes that have frequently been discussed in studies of teacher noticing. We show how an analysis using FAIR can contribute to understanding deficit noticing. We then conceptualize and illustrate anti-deficit noticing using the case of Oscar, a college mathematics instructor who worked with many Black and Hispanic students and himself identified as Hispanic. We discuss the local context that supported Oscar’s anti-deficit noticing and conclude with implications for future research and practice. © 2021, FIZ Karlsruhe.12 month embargo; first published online 17 February 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Tensions of trust in preservice teachers’ consideration of challenging mathematics tasks

Drawing on a larger, cross-institutional study that examines equitable elementary mathematics education, this article reports initial findings related to tensions that emerged for preservice teachers (PSTs) related to trusting students with open-ended, challenging mathematics tasks. Data composed of 194 PSTs’ written responses to a survey question. Using methods of qualitative analysis, findings indicate two prominent tensions that emerged for PSTs related to trusting students with open-ended challenging tasks: productive struggle versus unproductive failure and teacher control versus student control. These findings suggest that reform efforts that encourage teachers to implement open-ended, challenging tasks may not come to fruition if underlying issues of (mis)trust teachers may have related to students are not unpacked and addressed

On Aboriginal Representation in the Gallery

Originating from a series of workshops held at the Art Gallery of Ontario and the Vancouver Art Gallery in March 2000, the 24 essays in this book address the subject of Aboriginal representation in the gallery. The authors analyse issues stemming from the production, collection and exhibition of historical and contemporary Aboriginal art. Includes the programme for the workshop series. Text in English, with a French abstract. List of illustrations. Notes on contributors. Circa 450 bibl. ref