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.
M. Lynn Breyfogle and Beth A. Herbel-Eisenmann
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.
Eva Thanheiser, Amy Ellis and Beth Herbel-Eisenmann
In this Research Commentary, 3 JRME authors describe the process of publishing their research in JRME. All 3 authors published parts of their dissertation in JRME and are sharing their stories to help (new) researchers in mathematics education better understand the process and to offer (experienced) researchers in mathematics education a tool that can be used to mentor their less experienced colleagues and students. The authors address preparing, conceptualizing, and writing a manuscript as well as responding to reviewers.
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.
Julia Aguirre, Beth Herbel-Eisenmann, Sylvia Celedón-Pattichis, Marta Civil, Trena Wilkerson, Michelle Stephan, Stephen Pape and Douglas H. Clements
In 2005, the NCTM Research Committee devoted its commentary to exploring how mathematics education research might contribute to a better understanding of equity in school mathematics education (Gutstein et al., 2005). In that commentary, the concept of equity included both conditions and outcomes of learning. Although multiple definitions of equity exist, the authors of that commentary expressed it this way: “The main issue for us is how mathematics education research can contribute to understanding the causes and effects of inequity, as well as the strategies that effectively reduce undesirable inequities of experience and achievement in mathematics education” (p. 94). That research commentary brought to the foreground important questions one might ask about equity in school mathematics and some of the complexities associated with doing that work. It also addressed how mathematics education researchers (MERs) could bring a “critical equity lens” (p. 95, hereafter referred to as an “equity lens”) to the research they do. Fast forward 10 years to now: Where is the mathematics education researcher (MER) community in terms of including an equity lens in mathematics education research? Gutiérrez (2010/2013) argued that a sociopolitical turn in mathematics education enables us to ask and answer harder, more complex questions that include issues of identity, agency, power, and sociocultural and political contexts of mathematics, learning, and teaching. A sociopolitical approach allows us to see the historical legacy of mathematics as a tool of oppression as well as a product of our humanity.
Michelle L. Stephan, Kathryn B. Chval, Jeffrey J. Wanko, Marta Civil, Michael C. Fish, Beth Herbel-Eisenmann, Clifford Konold and Trena L. Wilkerson
Mathematics education researchers seek answers to important questions that will ultimately result in the enhancement of mathematics teaching, learning, curriculum, and assessment, working toward “ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement” (National Council of Teachers of Mathematics [NCTM], 2014, p. 61). Although mathematics education is a relatively young field, researchers have made significant progress in advancing the discipline. As Ellerton (2014) explained in her JRME editorial, our field is like a growing tree, stable and strong in its roots yet becoming more vast and diverse because of a number of factors. Such growth begs these questions: Is our research solving significant problems? How do we create a system and infrastructure that will provide an opportunity to accumulate professional knowledge that is storable and shareable as we work together to address significant problems (Hiebert, Gallimore, & Stigler, 2002)? How do we “facilitate research and development that is coordinated, integrated, and accumulated” (Lesh et al., 2014, p. 167)?
Beth Herbel-Eisenmann, Nathalie Sinclair, Kathryn B. Chval, Douglas H. Clements, Marta Civil, Stephen J. Pape, Michelle Stephan, Jeffrey J. Wanko and Trena L. Wilkerson
In this commentary, we identify key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that we identify–including the media, companies and foundations, and other academic domains–affect the public's perception of mathematics and mathematics education. Identifying this set of influences in particular is important because these groups often shape policymakers' viewpoints and decisions, but there is not always agreement between mathematics education researchers and these groups about the ways in which mathematics and mathematics education are framed. Whenever a conflict is brought to the foreground, it can be difficult to raise issues without appearing defensive or sounding querulous. It is helpful, then, to bring to bear a theory that can help us interpret this reality (Mewborn, 2005); theories can provide a way to encode, read, and examine a problem as well as offer insights into the design of new practices (Silver & Herbst, 2007). In this case, we use positioning theory to examine potential conflicts between mathematics education researchers and other groups because it offers interesting interpretive insights into the phenomenon and because it can lead to potential strategies for working toward different positionings for mathematics education researchers. We begin by explaining relevant ideas from positioning theory, including storylines, positions, and communication actions. We then use these ideas to highlight current storylines underlying communication by the abovementioned groups about mathematics and mathematics education and trace some of their historical and contextual roots. We argue that mathematics education researchers can intervene to shift these storylines and positionings and to have greater impact on policy, practice, and public perception in the future. Finally, we end by offering specific suggestions for beginning this work.