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## “She's Always Been the Smart One. I've Always Been the Dumb One”: Identities in the Mathematics Classroom

The moment-to-moment dynamics of student discourse plays a large role in students' enacted mathematics identities. Discourse analysis was used to describe meaningful discursive patterns in the interactions of 2 students in a 7th-grade, technology-based, curricular unit (SimCalc MathWorlds®) and to show how mathematics identities are enacted at the microlevel. Frameworks were theoretically and empirically connected to identity to characterize the participants' relative positioning and the structural patterns in their discourse (e.g., who talks, who initiates sequences, whose ideas are taken up and publicly recognized). Data indicated that students' peer-to-peer discourse patterns explained the enactment of differing mathematics identities within the same local context. Thus, the ways people talk and interact are powerful influences on who they are, and can become, with respect to mathematics.

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## Mapping Mathematics in Classroom Discourse

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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## Low-Performing Students and Teaching Fractions for Understanding: An Interactional Analysis

This article presents an analysis of two low-performing students' experiences in a firstgrade classroom oriented toward teaching mathematics for understanding. Combining constructs from interactional sociolinguistics and developmental task analysis, I investigate the nature of these students' participation in classroom discourse about fractions. Pre- and post-instruction interviews documenting learning and analysis of classroom interactions suggest mechanisms of that learning. I propose that three main factors account for these two students' success: use of tasks that elicited the students' prior understanding, creation of a variety of participant frameworks (Goffman, 1981) in which the students were treated as mathematically competent, and frequency of opportunities for identity-enhancing interactions.

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## Mathematical Discourse in Shared Storybook Reading

The purpose of the study reported in this article was to explore the mathematical discourse in which four dyads engaged while sharing the storybook One Snowy Night (Butterworth, 1989) while at home or in other locations (e.g., day care centers). Each dyad consisted of a mother and her four-year-old child. Various discourse patterns were evident, and while there were commonalities across dyads, each pair shared the book in unique ways. In two of the dyads, the mother initiated the mathematical discourse; in the other two, the child did. Size, subitizing, and counting were the most common mathematical concepts that emerged. One dyad attended to a single concept of size, and the other dyads attended to more than one mathematical idea. Some parents scaffolded particular problem-solving strategies; others provided more generic support. Based on our findings, we discuss insights and issues and make suggestions for further research.

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## Discourse Research in Mathematics Education: A Critical Evaluation of 108 Journal Articles

There has been increased engagement in studying discourse in the field of mathematics education. But what exactly is a discourse, and how do researchers go about analyzing discourses? This study examines 108 articles from 6 international journals in mathematics education by asking questions such as these: In which traditions and in relation to which kinds of epistemological assumptions are the articles situated? How is the concept of discourse used and defined? How are mathematical aspects of the discourse accentuated? The results of this study show that a variety of conceptualizations are used for analyzing discourses but also that many articles would benefit from strengthening those conceptualizations by explicitly defining the concept of discourse, situating the article in relation to epistemological assumptions, and relating the work to other discourse studies in mathematics education.

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## Power in Numbers: Student Participation in Mathematical Discussions in Heterogeneous Spaces

In this article, mathematics classrooms are conceptualized as heterogeneous spaces in which multiple figured worlds come into contact. The study explores how a group of high school students drew upon several figured worlds as they navigated mathematical discussions. Results highlight 3 major points. First, the students drew on 2 primary figured worlds: a mathematics learning figured world and a figured world of friendship and romance. Both of these figured worlds were racialized and gendered, and were actively constructed and contested by the students. Second, these figured worlds offered resources for 1 African American student, Dawn, to position herself powerfully within classroom hierarchies. Third, these acts of positioning allowed Dawn to engage in mathematical practices such as conjecturing, clarifying ideas, and providing evidence.

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## Doing Wrong With Words: What Bars Students' Access to Arithmetical Discourses

To investigate mechanisms of failure in mathematics, we adopt the communicational approach to cognition, which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine the arithmetical discourses of two 18-year-old girls with long histories of learning difficulties. The resulting arithmetical discourse profiles of the two students help us substantiate the following two claims: (1) Almost any person may become a skillful participant of arithmetical discourse, provided, first, that a discursive mode is found that makes the best of this person's special strengths and second, that in the process of teaching, the general sociocultural context of learning is taken into account as having a central role in enabling or barring one's access to literate discourses; (2) if the potential for successful participation remains often unrealized, it is mainly because of certain widely practiced abuses of literate mathematical discourse.

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## A Collective Case Study of the Influence of Teachers' Beliefs and Knowledge on Error-Handling Practices During Class Discussion of Mathematics

This collective case study examines the influence of 4 third-grade teachers' beliefs and knowledge on their error-handling practices during class discussion of mathematics. Across cases, 3 dimensions of teachers' error-handling practices are identified and discussed in relation to teacher beliefs and knowledge: (a) intentional focus on flawed solutions in class discussion, (b) promotion of conceptual understanding through discussion of errors, and (c) mobilization of a community of learners to address errors. Study findings suggest that, although teachers' ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.

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## From Intended Curriculum to Written Curriculum: Examining the Voice of a Mathematics Textbook

In this article, I used a discourse analytic framework to examine the “voice” of a middle school mathematics unit. I attended to the text's voice, which helped to illuminate the construction of the roles of the authors and readers and the expected relationships between them. The discursive framework I used focused my attention on particular language forms. The aim of the analysis was to see whether the authors of the unit achieved the ideological goal (i.e., the intended curriculum) put forth by the NCTM's Standards (1991) to shift the locus of authority away from the teacher and the textbook and toward student mathematical reasoning and justification. The findings indicate that achieving this goal is more difficult than the authors of the Standards documents may have realized and that there may be a mismatch between this goal and conventional textbook forms.

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## Steering (Dis)Course Between Metaphors and Rigor: Using Focal Analysis to Investigate an Emergence of Mathematical Objects

This study deals with students' construction of mathematical objects. The basic claim is that the need for communication—any attempt to evoke certain actions by others—is the primary driving force behind all human cognitive processes. Effectiveness of verbal communication is seen as a function of the quality of its focus. Material objects may serve as a basis for creation of such a focus, but in some discourses, focus-engendering objects must be created. Such discursive construction is observed in analysis of one classroom episode. Special attention is given to metaphor, which is the point of departure for the construction process, and to the subsequent dialectical process of closing the gap between the metaphor-induced expectations and the need for a well-defined construction procedure to ensure effective communication.