Teach an Understanding of Sets

Much of the algebra we teach at the beginning college level deals with solving equations and inequalities.

Without debating the validity of the above statement, it is then logical to conclude that our students should understand what “solving”  means.  Therefore we ought to teach them that solving means to determine the solution set for an equation or an inequality.

Now simple logic dictates that we should teach our students that a solution set is a set.  Furthermore we should teach them a bit about unions and intersections as well as common language.

The concept of a set is not difficult, simplifies and clarifies many discussions, and is used far beyond mathematics.  The concept is helpful in the discussion of  nearly every topic in the beginning algebra classes.

The concept of set and basic operations with sets seems to have vanished from high school classes (or at least the memories of the students).  Those of us teaching at the college level must recognize the fact but the work-around is not to avoid using the concept.

The concept of set and fundamental operations with sets should not be avoided, but should instead be the beginning and the foundation of the algebra we teach at the college level.

One of the central goals of any beginning mathematics course is to improve the student’s ability to use deductive reasoning.  It seems to me that the current norm of omitting the concept of sets from those early algebra courses demonstrates a failure to use deductive reasoning.