Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.
Anna F. DeJarnette and Gloriana González
Allison B. Hintz
Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.
Marcy B. Wood
Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used positioning theory to develop a framework of micro-identity and then to examine the identities and learning of 1 fourth-grade student during 1 mathematics lesson. This study demonstrates how mathematical identities can shift in dramatic ways in response to minor changes in context so that a student might be, in one moment, engaged in an identity that undermines learning and then later engaged in an academically productive identity. These shifting micro-identities have important implications for mathematical learning, classroom contexts, and macro-identities.
This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month in the Coaches' Corner, take a closer look at CCSS Standard 3 for Mathematical Practice, Explain and Justify. Coaches may want to demonstrate the integration of math and writing with Speak, Write, Reflect, Revise, a five-step approach for integrating problem solving and the writing process.
Erin Turner, Higinio Dominguez, Luz Maldonado, and Susan Empson
This study investigated discursive positioning moves that facilitated Latino/a English learners' (ELs) opportunities to take on agentive problem-solving roles in group mathematical discussion. A focus on mechanisms that support students' agentive participation is consistent with our view that recurrent experiences participating and being positioned in particular ways contribute to identity development. Findings suggest several ways that discursive positioning facilitated ELs' agentive participation, including via: (a) explicit statements that validated ELs' reasoning, (b) invitations to share, justify, or clarify thinking that positioned ELs as competent problem solvers, and (c) inviting peers to respond to an EL's idea in ways that positioned the idea as important and/or mathematically justified.
Indigo Esmonde and Jennifer M. Langer-Osuna
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.
P. Janelle McFeetors
Communication within the mathematics classroom has captured the interest of mathematics educators over several decades. The National Council of Teachers of Mathematics Standards publications (1989, 1991, 2000) highlight communication as one of the fundamental strands in mathematical processes. Although research has investigated students' written mathematics work (e.g., Masingila & Prus-Wisniowska, 1996; Mason & McFeetors, 2002; Pugalee, 2004), considerable focus has also been given to understanding effective spoken discourse patterns within the mathematics classroom (e.g., Hufferd-Ackles, Fuson, & Sherin, 2004; Lampert & Blunk, 1998; Nathan & Knuth, 2003). Pimm (1994) argues that focusing on “the form and structure of spoken interactions between mathematics teachers and pupils” (p. 134) can inform the way in which classroom discourse is shaped. He encourages the use of discourse analysis as one way of making sense of questions that address the what, how, and why of teachers' forms of language in teaching mathematics. Increasingly, studies using discourse analysis are being used to describe effective classroom communicative practices (e.g., Bills, 2000; Gresalfi, Martin, Hand, & Greeno, 2009; Truxaw & DeFranco, 2008; Zolkower & Shreyar, 2007).
Danielle S. Legnard and Susan L. Austin
A first-grade teacher demonstrates how to serve up this model of inquiry-based instruction in any classroom.
When communicating mathematical ideas to students, teachers must elaborate explicitly on the elements of their discourse. This article focuses on one instructor's and his students' discourse on limits in a beginning-level calculus classroom.