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Daniel L. Reinholz and Niral Shah

Equity in mathematics classroom discourse is a pressing concern, but analyzing issues of equity using observational tools remains a challenge. In this article, we propose equity analytics as a quantitative approach to analyzing aspects of equity and inequity in classrooms. We introduce a classroom observation tool that focuses on relatively low-inference dimensions of classroom discourse, which are cross-tabulated with demographic markers (e.g., gender, race) to identify patterns of more and less equitable participation within and across lessons. We argue that equity analytics can support researchers and practitioners in identifying subtle patterns of inequity in classroom discourse. As we show, even in classrooms with highly experienced, equityminded teachers, subtle inequities can emerge that are detectable through this quantitative methodology. To conclude, we discuss how equity analytics can complement qualitative approaches in the study of equity and inequity in classrooms.

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Beth A. Herbel-Eisenmann and Samuel Otten

This article offers a particular analytic method from systemic functional linguistics, thematic analysis, which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content, allows for content comparisons to be drawn between classroom episodes, and identifies points of possible student misinterpretation. Analyses of 2 middle school classroom excerpts focusing on area—1 that derives triangle area formulas from the rectangle area formula and another that connects parallelogram and rectangular area— are used to delineate the method. Descriptions of similarities and differences in the classroom discourse highlight how, in each classroom, mathematical terms such as base and height were used in semantically related but distinct ways. These findings raise the question of whether students were aware of and able to navigate such semantic shifts.

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Beatriz S. D’Ambrosio

Classroom discourse is often understood as the process of engaging the members of the classroom community—students and teachers—in talking with one another. In this discussion 1 use the term classroom discourse to mean the process of engaging the classroom community in real dialogue, wherein meaning is negotiated and assumptions are questioned. An underlying assumption throughout the discussion is that classroom discourse can help shape the views of the nature of mathematics that are held by students. The goal of this article is to raise questions and invite the readers to reflect on the issues raised rather than to answer any specific questions.

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Mary P. Truxaw and Thomas C. DeFranco

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Grounded theory methodology and sociolinguistic tools were used to move from classroom observations and interviews to line-by-line coding of classroom discourse, to mapping the flow of talk and verbal assessment moves, to a multilevel analysis of the relationships of forms of talk and verbal assessment, and, ultimately, to models of teaching that promote discourse on a continuum from univocal (conveying meaning) to dialogic (constructing meaning through dialogue). Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated with each model are illustrated and discussed.

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Beth A. Herbel-Eisenmann, Michael D. Steele, and Michelle Cirillo

We describe our ongoing efforts to design materials for supporting secondary mathematics teachers in using a set of Teacher Discourse Moves purposefully in order to develop classroom discourse that is both productive and powerful for students' learning. We focus on secondary mathematics classroom discourse because mathematical language and meanings get increasingly complex beginning in middle school, and most discourse-related work in mathematics education has focused on elementary school classrooms. We make explicit both the concepts we use and the translation of these theoretical concepts into ideas useful for practice. This article contributes to ongoing discussions about making visible the work of developing research-based professional development materials.

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Sarah Kate Selling

To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical practices explicit in classroom discourse. Analyses of 26 discussions from 3 mathematics classes revealed that teachers made mathematical practices explicit primarily after students had participated in them. I present a framework of 8 types of teacher moves that made mathematical practices explicit and argue that they did so without turning practices into prescriptions or reducing students' opportunities to engage in them. This suggests a need to expand conceptions of explicitness to promote access to mathematical practices.

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Jessica H. Hunt, Beth MacDonald, Rachel Lambert, Trisha Sugita, and Juanita Silva

Anticipating and responding to learner variability can make using talk moves complex. The authors fuse Universal Design for Learning (UDL), differentiation, and talk moves into three key planning and pedagogy considerations.

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Victoria Hand and Tamsin Meaney

Our connected world is exploding with images and sounds of cultural hybridity and fluidity. Mathematics classrooms, however, remain frozen in time. One consequence of this inertia is that mathematics education, rather than being a way to provide opportunities that lead to better lives for students, continues to limit those opportunities by reproducing existing societal inequities (Ernest, 2009). The inertia continues despite Herculean efforts by a range of stakeholders in mathematics education to broaden and diversify the voices participating in classroom mathematical conversations. What does the contrast between the increasingly dynamic and “flattened” (Friedman, 2005) nature of our global culture and the static and hierarchical nature of the mathematics classroom have to do with a book about classroom mathematical discourse and issues of equity?

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Norma G. Hernandez

In order to describe cognitive aspects of teacher discourse that could be related to possible ATI interactions, an observation system was designed using Guilford's structure-of-the-intellect model together with a model of the theory of language and discourse due to Kinneavy. 12 videotaped lessons were analyzed via the observation system in which 13 of the 19 categories exhibited a correlation coefficient greater than .70. The data indicated that the 4 teachers studied differed in the percent of discourse coded managerial, convergent, reinforcement, and questions. Memory was the most frequently coded inferred cognitive process, while classification, narration, and evaluation comprised 45% of the nonmanagerial discourse. The semantic mode was the most frequently used. Suggestions for further use of the category system are made.

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Clayton M. Edwards, Rebecca R. Robichaux-Davis, and Brian E. Townsend

Three inquiry-based tasks highlight the planning, classroom discourse, positive results, and growth in one class's journey.