High Expectations: A "How^" of Achieving Equitable Mathematics Classrooms

ABSTRACT: Dramatic changes are occurring in the teaching and learning of in the nation's classrooms. It is no longer sufficient to be proficient in basic skills; students are now expected to develop deep conceptual understanding of a broad range of mathematical content areas. While there has been an increased focus on the need for equal opportunities for students, African American students continue to score below their white counterparts, particularly in these critical areas. This paper suggests that low expectations play a significant role in the level of achievement of African American students in mathematics. It then examines the teaching of an effective teacher in an urban middle school and finds that high expectations are at the core of his teaching. Examples are given to illustrate three facets of his high expectations. As the vision of what it means to be mathematically literate in our society has shifted from a basic skills curriculum for some to a more demanding standard for all, the limits of past pedagogical practice have become increasingly apparent. In response to this, the National Council of Teachers of Mathematics (NCTM, 1989) published its Standards for education. These Standards reoriented conventional sequencing of concepts, encouraging the introduction of geometric and algebraic concepts as early as the first grade. They also emphasized the development of conceptual understanding through a range of exploratory strategies including manipulatives, word problems, and open-ended questions. Basic skills continue to have an important role, however they are greatly de-emphasized relative to past practice, and they are envisioned as emerging through the application of conceptual understanding, rather than through direct instruction. Over the past two decades, the underachievement of minority students in has been well-documented (Secada, 1992; Tate, 1997). Tate (1997) examined the achievement of diverse groups from national trend studies and found that African American and Hispanic students continue to score at significantly lower levels than white and Asian American students. He further reported that while minority students have made achievement gains in recent years, these gains were only on low-level and basic skills. This is problematic since basic skill proficiency is not enough for true knowledge and mastery of mathematics (Secada, 1992, p. 630). Recognizing the disparity between minority students and their white counterparts, NCTM (2000) published a revised version of the standards of education entitled Principles and Standards for School Mathematics which attempts to include one of the important omissions of the previous standards document (i.e., NCTM, 1989). This omission includes the importance of high expectations for students in order to implement the new visions of curriculum and teaching as suggested by the previous document. NCTM (2000) provides the education and education research communities with an Equity Principle which suggests that equity [in education] requires high expectations and worthwhile opportunities for all (p. 12). The issues here are: what constitutes worthwhile opportunities at the secondary level and what can be done to promote high expectations of minority students among the education community? Worthwhile Opportunities for All NCTM (2000) asserts that schools have an obligation to ensure that students participate in a strong instructional program that supports their learning. Such programs are built around worthwhile opportunities that elicit learning among students. These opportunities include, but are not limited to, problem solving, reasoning, and communication. Moreover, such opportunities should embody aspects of abstraction, invention, proof and application (Romberg, 1987)). …