Responding to Calls for Change in High School Mathematics: Implications for Collegiate Mathematics

1. INTRODUCTION. Nearly all mathematicians, mathematics educators, teachers, parents, and students agree on the need to improve the mathematical learning of students in our nation's schools. Yet there are widely differing viewpoints concerning appropriate directions for school mathematics curricula that might help accomplish this goal. With its publication of the Curriculum and Evaluation Standards for School Mathematics in 1989 [5] and subsequent supporting documents on standards for teaching [20] and for assessment [2], the National Council of Teachers of Mathematics (NCTM) provided a vision of school mathematics that was both broadly embraced [18] and intensely debated (see, for example, [13], [26], or [27]). In the case of curriculum recommendations for high school mathematics reform, the NCTM Standards reflected earlier expressed views of the mathematics community. In particular, in its 1983 report " The Mathematical Sciences Curriculum K–12: What Is Still Fundamental and What Is Not " [15], the Conference Board of the Mathematical Sciences (CBMS) recommended that the secondary school curriculum be streamlined to make room for new topics and techniques from discrete mathematics, statistics, and probability, and that the content, emphases, and approaches in algebra, geometry, and precalculus be reexamined in the light of emerging computing technologies. The report suggested that " technology provides an opportunity to devote less time to traditional [manipulative] techniques while boosting understanding and allowing more time for more complex, realistic problem-solving, " but cautioned that " there is little research data on the feasibility of such changes, and there are almost no prototype school curricula embodying the new priorities " [15, p. 5]. The broad CBMS recommendations received further elaboration in the 1983 National Science Board Commission on Precollege Education in Mathematics, Science, and Technology report " Educating Americans for the 21st Century " [8]. In addition, that report challenged the sequence of separate year-long courses in algebra, geometry, and precalculus topics and called for serious consideration of the development of an integrated secondary school mathematical sciences curriculum. This report, like the CBMS report that preceded it and the NCTM Standards that followed, sketched directions for change. These reports did not provide guidance for the specifics of day-today , week-to-week, or even year-to-year practice. That burden was left to curriculum developers and teachers. The decade of the nineties was characterized by efforts funded by the National Science Foundation to develop curricula that interpreted the broad recommendations for change and to evaluate their effects in …