A Study of Core-Plus Students Attending Michigan State University

1. INTRODUCTION. One important measure of the effectiveness of a high school mathematics program is the success students have in subsequent university mathematics courses. Yet this measure is seldom considered in studies of high school curricula. This article describes a study that we undertook to quantify this measure for one particular curriculum. Readers of this MONTHLY may be aware of the general context leading to the need for such evaluative studies. Over the past two decades there has been a growing awareness of the inadequacy of the mathematical skills of American high school graduates. That was the assessment of the 1983 report A Nation at Risk [14] and confirmed by many subsequent studies. A recent National Assessment of Educational Progress (NAEP) Report [3] concluded that only 17 percent of U.S. twelfth graders were “proficient” at mathematics. 1 International comparisons also indicate a relatively low level of mathematics achievement by U.S. high school students. The Third International Mathematics and Science Study (TIMSS) assessed the “Mathematics Literacy” of end-ofsecondary students in twenty-two countries and found that U.S. students outperformed only two countries, Cyprus and South Africa [18]. Related studies suggest that the mathematics courses taken by American high school students are often at a lower level than those taken by their international peers and that U.S. high schools are offering a wide assortment of courses that lack the focus and coherence found in many foreign curricula [19]. This situation has been of particular concern on college and university campuses, where large numbers of entering students require remedial courses to bring their mathematical knowledge and skills up to what is required for a wide variety of college courses. One effort to improve school mathematics began in 1989 with the publication of Curriculum and Evaluation Standards for School Mathematics (generally known as “The NCTM Standards”) by the National Council of Teachers of Mathematics [5]. The National Science Foundation (NSF) subsequently funded the development and implementation of thirteen elementary, middle, and high school mathematics curricula based on theseStandards, programs variously referred to as “reform,” “Standardsbased,” or “NSF-sponsored” by their publishers and others. Many of these programs have been controversial. In particular, there has been concern that the NSF-sponsored curricula moved from pilot testing to large-scale implementation without sufficient independent evaluations of their efficacy in preparing students for college mathematics and science courses. Although studies of the effectiveness of these curricula have yielded promising conclusions (see, for example, the collection of such evaluations in [17]), most have been conducted by persons associated with their writing or implementation. A recent National Research Council (NRC) report, On Evaluating Curricular Effectiveness [8], also expresses concerns about the methodological adequacy of these studies. This NRC 1 The notion of “proficient” used in this statistic is identified by the National Assessment Governing Board