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Equity in mathematics education should be one of the most important concerns of
teachers, administrators, policy makers, mathematicians, and mathematics educators. In fact, the Association of Mathematics Teacher Educator (AMTE), the National Council of Supervisors of Mathematics (NCSM), and the National Council of Teachers of Mathematics NCTM), three national organizations that support teacher educators, mathematics teachers, and teacher leaders, have made equity a priority for their organizations (Gutierrez et al. 2008). Position statements, standards documents, and various books identify key equity issues and recommend directions compelling all involved in the mathematics education of students to become aware of equity issues and to take steps toward eliminating the inequities that plague K-16 education.

Laurie H. Rubel (Brooklyn College) discusses a teacher learning community for high school teachers in New York City organized to develop practices of culturally relevant mathematics pedagogy. This project, named CureMap, emphasizes the connections between mathematical concepts, procedures, and facts; focuses mathematics instruction on students’ experiences; and strives to develop students' critical consciousness about and with mathematics.

This article reports findings from a research and professional development project at two high schools located in low-income, urban communities of color. The project collaborates with teachers on improving their instructional practices, using a framework of culturally relevant mathematics pedagogy, which is described in detail here. We present results from a qualitative and quantitative analysis of mathematics instruction in 68 classroom observations of seven teachers. In particular, we use culturally relevant mathematics pedagogy as a lens through which to analyze instruction and the associated opportunities to learn mathematics provided to students.

The central goal of this study was to create a new diagnostic tool to identify organic chemistry students’ alternative conceptions related to acid strength. Twenty years of research on secondary and college students’ conceptions about acids and bases has shown that these important concepts are difficult for students to apply to qualitative problem solving. Yet, few published studies document how students’ prior knowledge of acids influences their understanding of acid strength in organic chemistry contexts. We developed a nine-item multiple-tier, multiple-choice concept inventory to identify alternative conceptions that organic chemistry students hold about acid strength, to determine the prevalence of these conceptions, and to determine how strongly these conceptions bias student reasoning. We identified two significant alternative conceptions that organic chemistry students hold about acid strength. Students who answered items incorrectly were more confident about their answers than peers who answered items correctly, suggesting that after one semester of organic chemistry, students do not know what they do not know. Implications for the teaching of acid strength are discussed.

Despite evidence that it can help students learn higher-order thinking skills and gain deep content knowledge, problem-based learning (PBL) is not deployed on a large scale in K-12 classrooms. This conceptual chapter explores teacher’s past experiences, and resulting habitus, to explain the minimal extent of PBL in K-12 schools. Central to teachers’ abilities to implement PBL is their ability to provide scaffolding, and their habitus may interfere with this process. Implications for teacher education and teacher change are discussed.