This article shares the authors' views on language-diversity issues in research in mathematics education. Described are tensions, questions, and myths that they have regularly faced as researchers. They use similarities and differences in two settings (multilingual classrooms in South Africa and U.S. mathematics classrooms with Latino/a students) to illustrate the complexity of this work and illuminate research findings.

### Mamokgethi Setati Phakeng and Judit N. Moschkovich

### Margaret Schwan Smith and Edward A. Silver

Current reform efforts have emphasized the need to change the way that mathematics is taught and learned so that all students have access to a mathematics education rich in opportunities for thinking, reasoning, and problem solving. Reaching all students may not be easy, however, since students in a mathematics classroom may be considerably diverse, not only with respect to prior mathematics achievement but also with respect to ethnicity, language, and life expelience. The challenge is even greater because teachers often do not share the ethnicity, primary language, or life experiences of the children they teach. The *Curriculum and Evaluation Standards for School Mathematics* (NCTM 1989) and the *Professional Standards for Teaching Mathematics* (NCTM 1991) urge teachers to consider classroom diversity by-

The title of this focus issue—“Human Dimensions of Mathematical Diversity”—is meant to evoke the phenomenal variation found in the development of mathematical ideas between and within cultures and communities of practitioners. We use the term human dimensions because we want to highlight the social, cultural, and historical aspects of mathematical activity. We use the term mathematical diversity because we want to emphasize the various forms of mathematical activity one finds in any community or culture.

### Kanwal Singh Neel

To paraphrase john dewey, diversity is one word, but many things. It could describe students from diverse backgrounds and refer to ethnicity, culture, gender, language, learning style, socioeconomic level, intellectual ability, and physical capability. The question arises as to how one should teach mathematics to all learners, regardless of their diversity. The experiences that students bring to the classroom; the ways they interpret their learning experiences; and the knowledge, skills, and attitudes with which they leave the classroom will vary.

### Maisie L. Gholson and Danny Bernard Martin

Six books on equity and diversity are explored.

### Darinka Radovic, Laura Black, Christian E. Salas and Julian Williams

The construction of positive mathematical identities (MIs) is a complex and central issue in school mathematics, where girls are usually “counted out” of the field. This study explores positive MIs (high achiever and positive relationship with mathematics) of 3 girls. We employed a nested model of identity based on a case study approach (i.e., female mathematics students nested within a cluster of students nested within a mathematics classroom). The results highlight diversity in how these girls experienced mathematics: They valued different forms of doing mathematics (independent and collaborative; wider and complex; and straightforward, procedure-oriented mathematics), showed different forms of engagement (detachment, protagonist and challenging, and compliant and support-seeker), and narrated different MIs (efficient, different, and responsible). The study also explores and discusses the roles of mathematical practice and belonging to different peer clusters in these different forms of identification.

### Woong Lim, Hongjoong Kim, Lynn Stallings and Ji-Won Son

A classroom vignette presents teaching practices that develop an appreciation of diverse thinking.

### Tonya Bartell, Anita Wager, Ann Edwards, Dan Battey, Mary Foote and Joi Spencer

The *Common Core State Standards for Mathematics* (CCSSM) do not make any promises about the teaching practices that should be used to support students' enactment of the standards. Thus, equity gets framed as achievable through making the standards a goal for all students. We know from research on past reform efforts that standards without explicit (or companion) teaching practices, and teaching practices without explicit attention to equity, will inevitably result in the failure of the standards to achieve goals for students. This commentary provides a framework for future research that hypothesizes research-based equitable mathematics teaching practices in support of the CCSSM's Standards for Mathematical Practice, connecting research, policy, and practice in order to realize the equity potential of the CCSSM.

### Abbe H. Herzig

Commenting on the film *Good Will Hunting*, a mathematician noted, “We would do well to remember, in our efforts to include members of underrepresented groups in mathematics, that there can be as much resistance to our efforts from the students we work with as from the system we work in– (Saul 1998, p. 501). In other words, try as we may to include people in mathematics—in *our version* of mathematics—they might not be interested. Alternatively, some individuals may reject mathematics not out of a sense of choice but because they feel that mathematics has rejected them. Students' reactions to mathematics are affected both by their interests, abilities, and goals and by the particular ways that mathematics is conceived and taught within the mathematics classroom. It is possible that the people who succeed in mathematics are those who are able or willing to adapt themselves to the existing structure of mathematics education in schools. Individuals whose talents, values, skills, or interests make it difficult or undesirable for them to adapt to that structure may not be able to negotiate successfully the educational systems in a way that allows them to succeed in mathematics. In this argument I turn attention away from features of students—for example, their preparation or their ability—and toward our assumptions about mathematics education itself, presenting a unique challenge for us to build a context for mathematics education that is truly accessible and inviting to a broad range of students.

### Lawrence M. Lesser

At this time in American education, many educators (e.g., Manning [1995]) continue to struggle with the balance of highlighting differences and highlighting common ground among individuals with diverse backgrounds. Giving full educational opportunities to all students, however, not only is the right thing to do as a matter of justice but also enriches the educational experience of all individuals involved. The National Council of Teachers of Mathematics (1997, 5) explains one reason that these opportunities are essential for the algebra course: “In recent years, [algebra] has become a ‘gateway’ course to higher education, particularly for minority students. Those students who steer away from algebra early often forfeit some of their options for the future.”