Really listening to students reveals that how data analysis is taught affects their mathematical competence.
Lynn Liao Hodge
Lynn Liao Hodge and Ashley Walther
Although it is not a new idea, discourse continues to be a topic of discussion among teachers, teacher educators, and researchers in mathematics education. NCTM (1989; 2000) and the Common Core State Standards for Mathematics (CCSSM 2010) describe mathematics classrooms as discourse communities in which whole-class discussions give students opportunities to share their thinking. In such discourse communities, different problem-solving approaches become explicit topics of conversation that can challenge, extend, and support all students' understanding. Further, opportunities to engage in discourse support students in becoming more confident problem solvers (Ball 1993; Kazemi and Stipek 2001).
Lynn Liao Hodge and Michael Lawson
Collaboration is central to impacting mathematics teaching and learning. As a university mathematics education professor (the first author) and a graduate student in mathematics education and former high school mathematics teacher (the second author), we have initiated partnerships with urban and rural middle schools, families, and preservice teachers during the past five years, using Family Math Nights (FMNs) as the vehicle for collaboration. FMNs are events that usually take place in school gyms, libraries, or cafeterias to promote awareness and inspire interest in K-12 mathematics education. The events are highly interactive, with stations that allow both adults and students to interact with teachers to better understand what inquiry and best practices in mathematics look like. The approach that we facilitated is quite different from the typical approach to designing and implementing FMNs.
Paul Cobb, Melissa Gresalfi and Lynn Liao Hodge
Our primary purpose in this article is to propose an interpretive scheme for analyzing the identities that students develop in mathematics classrooms that can inform instructional design and teaching. We first introduce the key constructs of normative identity and personal identity, and then illustrate how they can be used to conduct empirical analyses. The case on which the sample analysis focuses concerns a single group of middle school students who were members of two contrasting classrooms in which what it meant to know and do mathematics differed significantly. The resulting analyses document the forms of agency that students can legitimately exercise in particular classrooms, together with how authority is distributed and thus to whom students are accountable, and what they are accountable for mathematically. In the final section of the article, we clarify the relation of the interpretive scheme to other current work on the identities that students are developing in mathematics classrooms.