What Mathematics Should Adults Learn? Adult Mathematics Instruction as a Corollary to Two Decades of School Mathematics Reform

Abstract

Twenty-five years ago, the United States Department of Education published A Nation at Risk: The Imperative for Educational Reform, sounding alarm that the United States educational foundations were in grave danger, eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people (National Commission on Excellence in Education, 1983, p. 5). The National Research Council (1989, 1990, 1993) followed with a trilogy of texts specifically addressing the condition of United States mathematics education. In 1989, the National Council of Teachers of Mathematics (NCTM) released their groundbreaking Curriculum and Evaluation Standards for School Mathematics, followed by two additional publications promoting standards for the profession and for assessment (1991, 1995). The three original Standards volumes were revised and consolidated in 2000, and in 2006, NCTM released Curriculum Focal Points, a handbook concerning the grade at which specific mathematics content should be taught from pre-school through 8th grade. In 2008, the National Mathematics Advisory Panel released its report with recommendations concerning K-12 mathematics education in the United States. In the intervening years since 1989, other mathematics professional organizations have addressed the issue of standards for post-secondary institutions. The American Mathematical Association of Two-Year Colleges (AMATYC) published Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus and, recently, Beyond Crossroads: Implementing Mathematics Standards in the First Two Years of College. The Mathematical Association of America (MAA) released Undergraduate Programs in the Mathematical Sciences: CUPM Curriculum Guide 2004, making recommendations for service and mathematics major courses. This year, the MAA released the latest entry in its sequence, Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education, which explores the disconnect between the education of prospective teachers and the practical applications of mathematics in adult life. Those practical applications, called interchangeably numeracy and quantitative literacy in the reports to be examined, have been explored within and outside the mathematics communities. With the exception of the Equipped for the Future project, adult mathematics education experts were noticeably absent from the preparation of the standards documents summarized here. A corollary is, by definition, an immediate consequence or easily drawn conclusion, a natural consequence or result (Stein, 1975, p. 300). This paper terms our work as adult educators a corollary to the reforms of the past 20 years because it is primarily subsequent and reactive to the principles proposed by the school and academic establishment. While there is substantial overlap, the recent shift by the National Math Panel towards a traditional view of mathematics education represents a divergence from many of the values we hold for adult mathematics education that challenges the corollary analogy and gives cause to suggest a new and different theorem for our students. School Mathematics The National Council of Teachers of Mathematics (NCTM) is the largest and most powerful player on the school mathematics field. In their Principles and Standards for School Mathematics, they describe a curriculum as than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades (NCTM, 2000, p. 14). This definition of curriculum was global, and, over time, it became evident that the community could benefit from a more directive NCTM statement suggesting a judicious sequence of topics within the curriculum framework. Furthermore, a mapping of topics to grade levels would provide a consistent timeline for designers, authors, and publishers of curricula. The resulting product, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, provides descriptions of the most significant mathematical concepts and skills at each grade level (NCTM, 2006, p. …