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.
Beth A. Herbel-Eisenmann
Beth A. Herbel-Eisenmann
A way to introduce and use mathematical language in mathematics classrooms that draws on multiple representations and student language.
Samuel Otten, Michelle Cirillo and Beth A. Herbel-Eisenmann
Reconsider typical discourse strategies when discussing homework and move toward a system that promotes the Standards for Mathematical Practice.
Beth A. Herbel-Eisenmann and M. Lynn Breyfogle
Teachers pose a variety of questions to their students every day. As teachers, we recognize that some questions promote deeper mathematical thinking than others (for more information about levels of questions, see Martens 1999, Rowan and Robles 1998, and Vacc 1993). For example, when asking, “Is there another way to represent or explain what you are saying?” students are given the chance to justify their thinking in multiple ways. The question “What did you do next?” focuses only on the procedures that students followed to obtain an answer. Thinking about the questions we ask is important, but equally important is thinking about the patterns of questions that are asked.
Beth A. Herbel-Eisenmann and Elizabeth Difanis Phillips
Recent literature has shown that having teachers examine student work can enhance teachers' thinking about what constitutes mathematical understanding (Crespo 2000; Crockett 2001). There is also evidence that teachers need to experience unconventional mathematics problems to see the value of using them in their own classrooms (Ball 1988; Crespo 2003).
M. Lynn Breyfogle and Beth A. Herbel-Eisenmann
When viewing videotaped examples of his classroom teaching, Anthony, a veteran ninth-grade teacher, was surprised that he focused more on the students' responses than on the students' thinking. For example, he realized that he was not asking questions to understand what or how the students were thinking but rather to test their knowledge.
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.
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.
Jon R. Star, Beth A. Herbel-Eisenmann and John P. Smith III
New mathematics curricula serve middle grades students well when they provide students with richer and more accessible introductions to a wide range of mathematical content. New curricula also serve teachers well when they lead us to examine and reflect on what and how we teach. When these curricula enter our working lives and conversations, we are often forced to question exactly what is “new” about them and how this “newness” may affect our students' learning. To address this issue and, we hope, to support further reflection and discussion, we take a closer and more careful look at what is new in one middle school curriculum's approach to algebra. The curriculum we examine is the Connected Mathematics Project (CMP) (Lappan et al. 1998), particularly the eighth-grade units, but the issue of what is new in algebra is relevant to many other innovative middle school curricula, as well.