Developmental Mathematics Revival!

Prerequisites

Prerequisites are placed on courses for various reasons, from convenience to supporting student success. Few prerequisites are placed on courses based on validation studies … some prerequisites are used based on professional validity, while others have even less of a scientific basis.

Let’s say that you are working for the department of education in a state such as mine (Michigan), and you have been getting more concerned about the possibility that academic standards are not consistent across regions or levels of education. You look at mathematics, and notice that college courses use a different organizing system than high schools … and you do not want students to get credit for a college math course that is really a high-school level course. An easy, and somewhat logical, approach is to enact a rule (or law) that says any college level math course needs to have at least an intermediate algebra prerequisite.

What’s so bad about that arrangement? If intermediate algebra is at the level of 1oth to 11th grade high school, this seems like a pretty low standard for ‘college’; when challenged, you might add that the really logical rule would be that a college level math course needs to have at least a college-algebra prerequisite … and you’d like to do this, if WE would just make up our minds about what ‘college algebra’ really is.

However, the problems with this approach are too basic to be resolved by this framework. First, it assumes that all mathematics builds on the stuff in an intermediate algebra course; several basic areas, most notably statistics, do not have any relationship to the concepts and skills of intermediate algebra. By requiring intermediate algebra as the minimal prerequisite, we mislead students and cause them to take unneccessary courses … both problems are non-trivial.

Second, this approach assumes that a subtle concept like ‘rigor’ can be measured by the prerequisite. This is not one of the valid uses of prerequisites; rigor is measured by properties of the course in question (the content, concepts, assessment and practices) … which do not necessarily change just because we list “IA” (intermediate algebra) as a prerequisite. If we want sufficient rigor in college level mathematics classes (and I hope we do), we need to measure those courses — not a prerequisite to those courses.

Third, prerequisites tend to disproportionately affect underrepresented groups. At my institution, it is not unusual to have 30% of a pre-algebra class be minority; the courses which immediately follow intermediate algebra are often 90% majority. Sadly, our curriculum is still not a pump … more filtering happens, so any unvalidated prerequisite can lead to wasteful reductions in minority completion.

I’m pleased that my own institution has 5 college-credit math classes that do not have an intermediate algebra prerequisite. Two of these 5 courses transfer to several institutions in the state. However, students are still advised to take intermediate algebra “just in case” … they don’t really need it, but they might change their mind later.

If this topic is of interest to you, you will want to follow a position statement being worked on in the Developmental Mathematics Committee (DMC) of AMATYC. The DMC web site is http://groups.google.com/group/amatyc-dmc?hl=en The motivation for this position statement is to help institutions and states use appropriate prerequisites, based on validation — not prerequisites to enforce an abstract policy on ‘rigor’.

In the long term, we will replace “IA” with a more reasonable course like the New Life Transitions course — at least for the majority of students who do not need a pre-calculus type course later. We will also replace beginning algebra with something like Mathematical Literacy for College Students, and this kind of course could really serve all students. Until this change happens, we can work on better prerequisites relative to IA … and for all courses (including Transitions).