• Vol. 28, No. 6, December 1997

    William F. Tate
    The purpose of this article is to document changes in U.S. mathematics achievement by reviewing national trend studies, college admissions examinations, and Advanced Placement tests. This article examined this quantitative research literature to determine trends in mathematics achievement of various social groups defined along lines of race, class, gender, ethnicity, and language proficiency. The findings of this review indicate that over the last 15 years all demographic groups have improved in mathematics achievement--specifically, in basic skills. Moreover, the mathematics achievement gap is slowly closing between White students and students of color on assessments of basic skills. Males tended to outperform females on standardized measures; however, gender differences were small and generally not significant. Consistent with past reviews of mathematics achievement, course taking was a powerful variable, often resulti! ng in similar achievement gains across diverse groups. This finding has serious implications for equity-related policy. The article concludes with two other recommendations: the need for fiscal and cultural policy to support standards-based reform.
    Christine E. Sleeter
    Multicultural education grew out of the civil rights movement and, as such, is grounded in a vision of democracy, social justice, pluralism, and equality--ideals that have yet to be realized in U.S. society and its schools. For the past 25 years, multicultural education has served as a mobilizing focus for struggles to articulate visions of schooling that are consistent with the ideals of the U.S. and for the development of theory and research that offer a countervision to the way that schooling is usually conducted, particularly for children from historically marginalized groups. As this body of theory and research has grown so also have the implications for restructuring various dimensions of the education enterprise. Mathematics is one such dimension and is the focus of this article. First, however, I contextualize the discussion that follows within a vision of what multicultural education means.
    Gloria Ladson Billings
    Mathematics education has been heralded for its leadership role in the U.S. school reform effort (Stein, Grover, & Henningsen, 1996; Grant, Peterson, & Shojgreen-Downer, 1996). Prominent in the reform of mathematics education is the call for students not merely to memorize formulas and rules and apply procedures but rather to engage in the processes of mathematical thinking, that is, to do what mathematicians and other professional users of mathematics do. The revamped mathematics education program is based on engaging students in problem posing and problem solving rather than on expecting rote memorization and convergent thinking. These changes in mathematics education suggest that mathematics teaching must build on students' learning and on their ability to pose and solve problems previously considered too difficult for their age-grade levels (Carpenter & Fennema, 1988; Fennema, Franke, Carpenter, & Carey, 1993).
    Eric Gustein, Pauline Lipman, Patricia Hernandez, Rebeca de los Reyes
    This article examines mathematics instruction and its intersection with culturally relevant teaching in an elementary/middle school in a Mexican American community. The findings are based on a collaborative-research and school-change project involving university researchers, teachers, and the school's principal. On the basis of ethnographic data and an interdisciplinary theoretical framework, we propose a three-part model of culturally relevant mathematics instruction. The 3 components are (a) building on students' informal mathematical knowledge and building on students' cultural and experiential knowledge, (b) developing tools of critical mathematical thinking and critical thinking about knowledge in general, and (c) orientations to students' culture and experience.
    Karen C. Fuson, Steven T. Smith, Ana Marie Lo Cicero
    Year-long classroom teaching experiments in two predominantly Latino low-socioeconomic-status (SES) urban classrooms (one English-speaking and one Spanish-speaking) sought to support first graders' thinking of 2-digit quantities as tens and ones. A model of a developmental sequence of conceptual structures for 2-digit numbers (the UDSSI triad model) is presented to describe children's thinking. By the end of the year, most of the children could accurately add and subtract 2-digit numbers that require trading (regrouping) by using drawings or objects and gave answers by using tens and ones on various tasks. Their performance was substantially above that reported in other studies for U.S. first graders of higher SES and for older U.S. children. Their responses looked more like those of East Asian children than of U.S. children in other studies.
    Khaula Murtadha-Watts, Beatriz S. D'Ambrosio
    In the work described here we report on our collaborative efforts to produce a multicultural mathematics curriculum for Grades K–6 that was socially transformative. We drew insights and direction from the following discourses: multicultural education, socially proactive mathematics, and preservice and in-service teacher deliberations. Through group deliberations, the analysis of existing mathematics and multicultural curricula, and the sharing of personal histories, we planned our teacher-research activities. Our goal was to define mathematics as a tool for social analysis. In this article we describe the perplexity of issues related to the definition of multicultural curricula and mathematics curricula for social transformation, the complexities of the group deliberative process, and the demands involved in the teacher-research process.