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Lambert, T ; Moss, D (Ed.)Negative perceptions held by teachers toward students with disabilities create environments that make students feel uncomfortable and often incapable of participating actively in classrooms. Much of the research about these perceptions is focused on teachers of students with learning disabilities, which leaves out teachers’ perceptions toward students with other disabilities. We are developing a responsive online survey to access what mathematics teachers identify as disabilities and their behavior toward students with disabilities in their classroom. In this paper, we describe the process we have developed for constructing this survey. We also share our conceptualization of the relationship between teachers’ perceptions and equity affirmations toward disability, and the results of applying that conceptualization to our research context.more » « less
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Lamberg, T ; Moss, D (Ed.)Past research has identified factors that help maintain the cognitive demand of tasks, including drawing conceptual connections. We investigated whether teachers who were engaging in the teaching practice of building—and thus focusing the class on collaboratively making sense of their peers’ high-leverage mathematical contributions—drew conceptual connections at a higher rate than has been found in previous work. The rate was notably higher (54% compared to 14%). By comparing multiple enactments of the same task, we found that this higher rate of drawing conceptual connections seemed to be supported by (1) eliciting student utterances that delve more deeply into the underlying mathematics, (2) giving students more time to explore the underlying math, and (3) using previously learned abstractions to help move the class toward understanding the new abstract concepts underlying a task.more » « less
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Ayalon, M ; Koichu, B ; Leikin, R ; Rubel, L ; Tabach, M (Ed.)We used videotaped enactments of high cognitive demand tasks to investigate whether teachers who were engaged in the teaching practice of building—and thus were focused on having the class collaboratively make sense of their peers’ high-leverage mathematical contributions—provided scaffolding that supported the maintenance of high cognitive demand tasks. Attempting to build on high-leverage student thinking seemed to mitigate the teachers’ tendencies to provide inappropriate amounts of scaffolding because they: (1) believed the building practice required them to refrain from showing the students how to solve the task; (2) wanted to elicit student reasoning about their peer’s contribution for the building practice to utilize; and (3) saw the benefits of their students being able to engage in the mathematical thinking themselves.more » « less
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To better understand how researchers with existing research projects that were not designed to address concerns for equity can contribute to current needs in mathematics education research, we investigated one such research team’s existing products, including tools designed for use by others, in light of the team’s stated goals to support the learning of all students. We identified several ways that existing research can retroactively be modified in authentic ways that explicitly address concerns for equity and justice. These ways range from incorporating explicit language about the project’s equity intent in the project dissemination to annotating specific connections with equity for each tool in a way that supports using the tool to disrupt inequities.more » « less
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Lischka, A. E. ; Dyer, E. B. ; Jones, R. S. ; Lovett, J. N. ; Strayer, J. ; Drown, S. (Ed.)The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers' use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broadways teachers used public records—manipulating and referencing—to support establishing and maintaining students' thinking as objects in sense-making discussions.more » « less
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Lischka, A. E. ; Dyer, E. B. ; Jones, R. S. ; Lovett, J. N. ; Strayer, J. ; Drown, S. (Ed.)Productive use of student mathematical thinking is a critical aspect of effective teaching that is not yet fully understood. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper, we begin to unpack this complex practice by looking closely at its third element, Conduct. Based on an analysis of secondary mathematics teachers' enactments of building, we describe the critical aspects of conducting a whole-class discussion that is focused on making sense of a high-leverage student contribution.more » « less
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Olanoff, D. ; Johnson, K. ; Spitzer, S. M. (Ed.)Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first element, establish. Based on an analysis of secondary mathematics teachers' enactments of building, we describe two critical aspects of establish—establish precision and establish an object—and the actions teachers take in association with these aspects.more » « less
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