To the Editor:
In their article "Make Math a Gateway, Not a Gatekeeper" (The Chronicle, April 23), Anthony S. Bryk and Uri Treisman describe a problem and how the Carnegie Foundation for the Advancement of Teaching is going to solve it. The problem they describe is that some students are unable to meet the algebra requirements for their degrees—specifically they speak of students who need statistics for their degrees but cannot meet their algebra requirements. The authors claim that they are going to develop a new curriculum that will prepare these students for statistical work but will somehow avoid much of the algebra. I am going to state a set of observations on algebra and statistics and then point out where I see difficulties.
1. Generally people do not retain algebra for more than two years unless they have had calculus. That is where they really learn algebra. Students who have not had algebra for two years and need to use it generally need to retake their last algebra course. Hence many students who are quite capable give up on math because they were encouraged or allowed to take a course they were not ready for. Sometimes the capable student gives up simply because of a bad teacher.
2. Unless students go into areas that require calculus, they are unlikely to use any algebra beyond the most basic.
3. Students who do not need mathematics for their majors can be accommodated with a "math for humanities" course. The ubiquitous course in "finite mathematics" offered at the precalculus level can serve this function.
4. The basic statistics course, whether taught in business or psychology, is meant to familiarize the student with statistical concepts. The algebra required is minimal, and even though the student performs various statistical tests, the course does not give the student proficiency in performing statistical procedures.
5. An enormous body of statistical tests can be performed without use of calculus. However, in practice this statistical work requires the mathematical maturity associated with learning calculus. Statistical theory, even at the undergraduate level, is calculus-intensive.
If the students Mr. Bryk and Mr. Treisman are talking about need only to understand basic statistical concepts, that can be accomplished with a course in basic algebra, a well-designed statistics course, and good teaching. However, if these students need genuine statistical skills, their inability to pass algebra courses implies that they have chosen to pursue the wrong fields—and no curriculum design will change that fact.
James M. Cargal
Professor of Mathematics