Craig Roberts
Southeast Missouri State University
I had the privilege of attending a College Algebra Reform Workshop at Prairie View A & M University. Particularly striking to me was the remarkable agreement between the philosophy and goals stated in Contemporary College Algebra and the Reform Workshop and those stated by the National Council of Teachers of Mathematics (NCTM) in the recently released Principles and Standards for School Mathematics. As the workshop progressed, it also was readily apparent that the student-centered instructional strategies advocated in Contemporary College Algebra are consistent with the Principles and Standards. This is especially noteworthy because it provides for a seamless transition from the mathematical experiences we hope our students had at the elementary, middle, and high school levels and the mathematical experiences we hope to engage them in at the college and university level.
The Principles and Standards was officially released at NCTM's Chicago meeting in April 2000, and its purpose is to build on and consolidate the philosophy and goals set forth in previous NCTM publications. It contains a very ambitious vision for mathematics education. It is a vision in which "Students are flexible and resourceful problem
solvers. Alone or in groups and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it." (NCTM, 2000, p. 3) This vision is founded upon six principles, which should be features of any quality mathematics program. These principles are Equity, Curriculum, Teaching, Learning, Technology, and Assessment. Briefly, the Equity Principle advocates high expectations for all students and providing the necessary support to help each one achieve these expectations. The Curriculum Principle emphasizes a focus on important and interesting mathematics pertaining to the real world. The Teaching and Learning Principles stress student-centered instructional approaches that actively engage students in exploration, discovery, and understanding of mathematical concepts with the supportive guidance of their instructor. The Technology Principle views technology as a means for enhancing the understanding of fundamental mathematical concepts and for considering interesting real life applications, not as a substitute for basic understanding. Finally, the Assessment Principle states that an assessment plan must include formal and informal assessments that are consistent with the instructional approaches used and that reflect the important mathematical concepts studied. (NCTM, 2000, pp. 11-27)
While these six principles form consistent themes throughout a quality mathematics program, five Content Standards and five Process Standards describe the knowledge, skills, and processes that students should acquire. The Content Standards are Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. The Process Standards are Problem Solving, Communication, Connections, Representation, and Reasoning and Proof. (NCTM, 2000, p. 29)
The objectives advocated within the Algebra Standard are especially interesting. Students should "understand patterns, relations, and functions" and "use mathematical models to represent and understand quantitative relationships." (NCTM, 2000, p. 37) Nowhere is the emphasis placed on algebraic manipulation and computational skills. Rather the emphasis is placed on understanding fundamental algebraic concepts such as functions and utilizing mathematical models to understand the world from a quantitative perspective.
It is within this context that computational and algebraic skills may be effectively developed and reinforced. It is in relation to the Process Standards that Contemporary College Algebra shines even more brightly in my opinion. While students often forget specific mathematical content over time, the general thought processes and attitudes that each student acquires may remain for a lifetime and profoundly influence the opportunities that become available. If a student can become confident about analyzing problems from a quantitative perspective, flexibly applying various technologies and problem-solving strategies, and working with others to solve problems, then he or she has formed the foundation for becoming a lifelong, exploratory learner and a productive member of the fast-paced, technological world.
As we reflect on the philosophy and goals mentioned in the Preface of Contemporary College Algebra (namely, empower students to become exploratory learners, improve communication skills, participate in group work, use technology, model real life situations, develop confidence as problem solvers, and enjoy doing and applying meaningful mathematics), they are remarkably consistent with those of the Principles and Standards. (Small, 1999, p. vii) While the Principles and Standards were specifically written for prekindergarten through grade 12, I believe the manner in which they are reflected in Contemporary College Algebra should serve as a model for transforming other college and university mathematics texts and courses into student-centered texts and courses. I heartily congratulate Dr. Small and the Editorial Board Members for their visionary approach to College Algebra Reform and their efforts to help every student reach his or her full potential.
(Note: An electronic version of Principles and Standards may be viewed on the World Wide Web at http://www.nctm.org/)
References:
National Council of Teachers of Mathematics,
Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000.
Small, Don. Contemporary College Algebra. New York; McGraw Hill Primus Custom Publishing, The McGraw-Hill Companies, Inc.