Providing directions for the new millennium for the teaching of mathematics.

Purpose:

To define the knowledge, skills and abilities necessary to succeed in the first year of college mathematics. To make this information available to all aspects of the educational endeavor: students, parents, teachers, advisors, and educational policy makers.

Definition of Success:

A student is successful in the first year of college mathematics if the following three conditions are met:

1. The student is prepared for the first college mathematics course required by the student’s choice of major or interest area.
2. The student completes each mathematics course attempted during the freshman year with a grade of C or better.
3. The student is able to transfer knowledge gained in the mathematics course(s) into other courses, particularly into courses of the major.

The overwhelming consideration is that mathematical skill, or the lack thereof, should not be the determining factor in the choice of major or career.

Primary concerns for Teachers:

Content:

• The traditional four courses of mathematics – two years of algebra, geometry and precalculus – are the minimum.
• Strong algebra and trigonometry skills are needed to continue in college mathematics.
• Conceptual understanding of algebra is critical.
• Students must be able to translate written descriptions into mathematical language and also the reverse.
• Sketching graphs by hand is as critical as sketching using some form of technology.
• Exposure to "real-life" problems is critical for students’ appreciation and understanding of mathematics.
• Basic technological skills are necessary for success in college mathematics courses.

Instruction Methodology:

Teachers should provide classroom instruction which achieves the following:

1. Develops approximation skills.
2. Avoids "monkey mathematics" – mindless, repetitive assignments.
3. Fosters in students the ability to read and use a formula, understanding it as a process in addition to the rules of symbolic manipulation
4. Requires students how to compare numbers, functions and processes. The development of patterns is essential in mathematics.
5. Views mathematical processes as useful in a variety of interdisciplinary and/or historical settings.
6. Emphasizes connections to other mathematical and interdisciplinary material.
7. Recognizes that minimal facility in current material almost guarantees failure in future material for your students.
8. Recognizes that taking comprehensive final exams are important for retaining knowledge. Exemptions from final exams are detrimental to success in college study, and particularly in college mathematics.

Technology:

Technology aids the understanding of mathematics by promoting:

• The understanding of the concepts of function and functional behavior.
• The visualization of solutions and functions.
• The understanding of estimation and its applications.
• The appreciation of the advantages of theoretical understanding.

Best Teaching Practices:

• Teachers maintain an enthusiastic attitude towards mathematics.
• Class size remains below 25.
• Maintain the use of comprehensive finals as a means of preparing students for college experiences.
• Use technology to enhance conceptual development and to allow access to "real-life" problems.
• Assign homework in appropriate amounts on a daily basis.
• Maintain a good pacing of lectures and presentations, using manipulatives when they add to the presentation.
• Develop high mathematical expectations for your students.
• Remain committed to professional development, especially in content areas.

The report in its entirety contains information regarding content recommendations, technology recommendations, teaching and environmental issues, and teacher training recommendations. Interested persons are encouraged to obtain a copy either on the Internet or by mail. Copies should also be housed in college and high school libraries.

Committee:

Mary B. Martin, Chair, Winthrop University
Roger Allen, Francis Marion University
Eddie Brown, Burkett CPA’s
Charles Cleaver, The Citadel
Lin Dearing, Clemson University
Ron Goolsby, Winthrop University
Hugh Haynsworth, College of Charleston
John Long, Midlands Technical College
Mary Ellen O’Leary, University of South Carolina at Columbia
Julia Robbins, Rock Hill School District III
Suzie Schembri, Northwestern High School, Rock Hill
Wade Sherard, Furman University
Chris Tisdale, Winthrop University
Jane Upshaw, American Management Association
Keith Wilks, Rock Hill High School, Rock Hill

Funded by a grant from the South Carolina Commission on Higher Education (based upon Act 359) as part of the "Great Expectations" Project.