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.