The Mathematical Association of America Maryland-District of Columbia-Virginia Section

Preface by Lee May, Past Chair of the MD-DC-VA Section:

The mathematical preparation in high school of students who are planning to go to college has long been of interest to me. Consequently, when I was asked to chair the Maryland/District of Columbia/Virginia section of the Mathematical Association of America, the only plank in my platform was to present the members of the section with an opportunity to issue a statement regarding what knowledge, skills, experiences, and attitudes they would like to find in the possession of incoming first-year students at the colleges and universities of the section. The members of the section were, it seemed, as eager as I to produce such a statement, and in the summer of 2003 requested the formation of an ad hoc committee to that purpose. Under the superior guidance of Professor Denny Gulick of the University of Maryland, the committee, consisting of representatives of the secondary schools, two- and four-year colleges, and universities in the MD-DC-VA section, produced the statement which follows. The statement was unanimously approved by the members of the section at their November 2004 meeting.

The statement is an attempt to clarify what mathematical skills and attitudes we members of the section hope to find in students entering college or university -- whether the students choose to major in mathematics or not. The statement is aimed at students in secondary (and, to a lesser extent, middle) schools; their parents, teachers, guidance counselors, principals, and county supervisors of mathematics instruction; and, last but not least, the offices of admission at the colleges and universities in the District of Columbia, Virginia, and Maryland. It is our hope that the statement -- which appears on the section website at www.math.vt.edu/org/maa -- will contribute to the enhancement and enjoyment of the learning and teaching of mathematics at the secondary level. If that outcome is achieved, we are confident that the learning and teaching of mathematics at the post-secondary level will be similarly enhanced.

Members of the Ad-Hoc Committee

• Dave Carothers, James Madison University
• Annie Commito, Frederick Community College
• Jerry Dancis, University of Maryland at College Park
• Frances Gulick, University of Maryland at College Park
• Patrick Lintner, Mathematics Coordinator, Harrisonburg City Public Schools
• Gail Kaplan, Towson University
• Jon Scott, Montgomery College at Germantown
• Susan Schwartz Wildstrom, Walt Whitman High School, Montgomery County
• Denny Gulick, University of Maryland at College Park -- chair of committee

Statement on Mathematics Preparedness: MD-DC-VA Section of the MAA

Recently mathematics teachers from secondary schools and two- and four-year colleges in the Maryland-District of Columbia-Virginia region have been discussing issues relating to students as they enter college. The issues relate both to students' attitudes toward mathematics and student potential for success in college mathematics courses.

Presently large numbers of students are deemed unready (by virtue of their scores on placement tests) to take college-level mathematics courses when they enter college. Moreover, to many students entering college, mathematics consists of obtaining answers rather than understanding the concepts, reasoning out appropriate approaches to problems, and thinking about the validity of answers derived.

In light of these observations and concerns, we offer to the mathematical community, and especially to students, parents, guidance counselors, and college and university admissions officers, the following thoughts concerning mathematical programs in pre-college classes.

1. Mathematics instruction should emphasize student understanding of mathematical concepts and should develop in students the ability to adapt such concepts to a diversity of settings. In particular, mathematics programs should avoid pushing students ahead until they have mastered the appropriate material, and should also minimize teaching to tests.
2. Mathematics instruction should help students to develop enough sophistication and confidence to be able to perform basic calculations, both numeric and symbolic, without the assistance of calculators or computers; to recognize when and how to use technology to best effect; and to formulate word problems mathematically.
3. In all mathematics courses, instruction should emphasize conceptual understanding and ownership of basic concepts. Moreover, each mathematics course (including algebra as well as geometry courses) should enhance logical thinking processes. In addition, mathematics instruction should enhance the ability of students to judge the reasonableness of a given approach to solving a problem, and the reasonableness of a result when it is obtained.
4. By the time students arrive at college they should think of mathematics as relevant to their lives and as offering a very broad lens through which to view the world. They should see mathematics in the same way as they might think of music or art: important, beautiful, complex, worth time and effort to study, and capable of enriching their lives.
5. In terms of potential success in college mathematics courses, there is no substitute for continuity of study of mathematics. Thus we strongly recommend that all college-bound students study mathematics during each year of high school. There are several mathematics courses that could be considered reasonable for study once students have achieved a strong background in algebra and geometry. Such courses may include trigonometry, analytic geometry, mathematical modeling, statistics, probability, discrete mathematics, or calculus, among others. However, we should never place a higher value on exposure to calculus (e.g., a student taking calculus in high school) than on mastery of Algebra I and II and Geometry.

In conclusion, the best mathematics preparation for college is continuous coursework throughout high school that fosters a strong background in algebra and geometry, and brings an ability to solve multi-step "word problems" and an open and positive attitude towards problem solving in general.