College Algebra can stay on its current path of a technique-driven curriculum. In this case, techniques are emphasized and applications or problems are chosen that are susceptible to the specific technique. Data shows this approach is unsuccessful in attracting students who have other choices or encouraging students to proceed on to calculus.
Or, College Algebra can become problem-based quantitative mathematics. In the latter case, the curriculum-design task is choosing generic problems and the mathematical techniques needed to solve them. In this alternative approach, College Algebra is divided into two roughly equal parts. The first half of this new course is "Mathematics for Planning." Students learn how to efficiently allocate four kinds of resources: money, as in budgets; time, as in schedules; space, as in architecture or space planning; and staff, as in staff requirements. The second unit is called "Modeling Systems" and teaches students to understand, monitor, and design systems. Students learn – at a deep level – what exactly graphic and symbolic representations of reality imply. A pilot study, using the second approach in Algebra II led to student success.
College Algebra:
As another paper to be presented at this conference makes clear, College Algebra is the last mathematics course many students take. A majority may enter the classroom having already decided that it will be their final mathematics course. Recent data, contained in the preliminary report of an MAA Task Force, indicate that only one in ten College Algebra (CA) students go on to take a full length calculus sequence. Not coincidentally, one in ten of these students are enrolled in a mathematics intensive field i.
Many would skip College Algebra if they did not have to pass it to get the degree they need to enter their chosen career field. Enrollment in CA tends to fall dramatically when colleges make quantitative reasoning or intermediate algebra the requirement. Finally, a few years after finishing the course, getting their degree, and starting their professional life, they cannot recall anything they learned. Or, equivalently, they have never used anything they learned in College Algebra.
All of this is unfortunate and related. Mathematics courses that seem hard, boring, and irrelevant prior to College Algebra establish the expectation that College Algebra will be more of the same. Moreover, the course – as conventionally taught – does nothing but confirm the foreboding.
Look at a typical description:
This course is a modern introduction to the nature of mathematics as a logical system. The structure of the number system is developed axiomatically and extended by logical reasoning to cover essential algebraic topics: algebraic expression, functions, and theory of equations.
Who decided that "algebraic expression, functions, and theory of equations" is essential, and if so, essential to who or what? The course covers the following topics: Radicals, Complex Numbers, Quadratic Equations, Absolute Value and Polynomial Functions, Equations, Synthetic Division, the Remainder, Factor, and Rational and Conjugate Root Theorems, Linear-Quadratic and Quadratic-Quadratic Systems, Determinants and Cramer's Rule, and Systems of Linear Inequalities.
That is a long list of topics; yet, it is only half the topics listed. How much can students learn in two days and what will they remember? How close is this official curricula to the one actually taught? Is this the topic list the mathematics department would present if it were an elective course for those not majoring in mathematics or engineering or intending to go on to graduate or professional school? For too many students it looks like – and is -- a painful experience that they would prefer to skip.
Presumably, these kinds of questions led to this conference at West Point. What should CA accomplish? One way to answer is to consider how to evaluate a changed CA course. What empirical evidence would this audience want to see before they called a new CA course successful? More students taking subsequent mathematics courses would please some. More students leaving college who could be deemed quantitatively literate would please others.
College algebra can stay on its current path of a technique-driven curriculum. In this case, techniques are emphasized and applications or problems can be chosen that are susceptible to the specific technique. Or, CA can become problem-based quantitative mathematics. In the latter case, the decision is what generic problems should be included and what mathematical techniques are needed to solve them.
