Managing Attrition and Improving Instruction in College Algebra:
A Radical (?) Approach

by Dr. Philip Owens, Adjunct in Mathematics, Northridge Campus
Feb. 10, 2003
Revised: June 3, 2003

In an attempt to control attrition in my College Algebra classes, I instituted two radical procedures for dealing with it in my Spring 2003 sections:  (1) enforcing the prerequisite, and (2) dropping students who were failing after 4 weeks of class.  The following describes why and how these procedures were implemented, and what the results were.
Table of Contents
Introduction
Method and rationale
The results: some statistics
Benefits and deficits of this approach
Recommendations


Introduction

Attrition rates at ACC (as at many other community colleges) are notoriously bad, especially in technical areas (see the ACC Effectiveness Review , Vol. 9, Fall 2002). Also, a study conducted by the Math Department in 1992 showed failure rates ranging from 40% to 55%, the worst being College Algebra, the subject I teach.

For Fall 2002, the overall attrition rate ( % of W's and F's) for College Algebra was 41%, ranging from 13% to 81% per section (with one outlier at 0%).  The average number of students per class with passing grades was 17 (about half of what it could be at classroom capacity).  This means that at zero attrition we would need to offer only half the number of classes that we do now to teach the same number of students, or, we could double our capacity to teach College Algebra with current resources.  In other words, we could double our productivity.  Of course, 0 attrition cannot be reached, but I think we can do much better than we are doing now.

There are lots of reasons for attrition: students taking on more than they can handle, family issues intervening to distract attention from school work, work issues doing the same, lack of preparation for the course they have chosen, etc.

Most people in math, at least, will agree that lack of preparation (compounded, perhaps, by a lack of aptitude for mathematics) is the main factor in our particularly troublesome attrition rates.

I believe we are doing a great (some might say inexcusable) disservice to students to allow them, year after year, to register for and attempt course work for which they clearly are not adequately prepared.  One of the main culprits in this crime is the fact that many students who register for College Algebra do not have either the formal prerequisites or the prerequisite skills necessary for success in College Algebra.  I did a study of 88 students on my rolls at various times in Fall 2002.  It was determined (with the help of Sarah Pokolski in NRG Advising) that 39/88 = 44% did not have the prerequisite.  This semester, as best I am able to determine, as many as 60% of 90 students did not have the prerequisite.  The actual number is probably somewhat lower than that, because some test scores, Intermediate Algebra from another institution, etc. cannot be found (by instructors) on the Datatel database.

But the trouble does not stop there.  Even those who have the formal prerequisite may not have:

required for success in College Algebra.

For example, many would agree that a C in Intermediate Algebra (which satisfies the prerequisite) is nowhere good enough to go on to College Algebra.  In the Fall 2002 study, 10 students qualified on the basis of such a C, for Spring 2003, 11.  These numbers represent over 10% of the registering population.

Another problem is that some students equate "College Math" with "College Algebra".  They register for College Algebra to satisfy their General Ed math requirement, not realizing that College Algebra is primarily for those that will be moving on to Calculus.

The above phenomena result in the chaos of classes flooded on the first day with unprepared students, and eventually:

What can we do about this?

Several things:

Method and rationale
Basically, the method consisted of doing two things:
  1. enforce the prerequisite
  2. drop students who are failing after Test 1 (over Chapter 1)
However, this has to be done with care and consideration toward the students, some of whom may not be used to having academic discipline exercised on their behalf.

Check (and enforce) prerequisites

The Math Manual states very clearly (p. 12):

The most important way to reduce attrition is to make sure that all students meet the prerequisites for the course.  ...  If you discover that students do not have the prerequisites, you may ask the students to withdraw or withdraw them yourself from the course. Ideally, one should try to make this discovery during the first or second class ...
On page 23 we read:
You should not assume that all of your students in any of your courses have the prerequisite and you are expected to do something to check prerequisites on the first day of class.  Usually that will mean having them fill out a student information sheet  . . .  and possibly have them to work problems, depending on the course. . . .   By the beginning of the second class . . ., please give each student appropriate advice about course placement . . .  You are your students' most important and influential math advisor.
I don't believe that a "Prerequisite Check" questionnaire will work effectively for College Algebra, for the following reasons: In spite of these faults, the Task Force expects us to check for the prerequisite and attempt to prevail upon students to act responsibly on their own behalf.  The Math Manual makes it clear that enforcing the prerequisite is not mandatory.

On the other hand, ACC takes prerequisites more seriously.  On page 16 of the ACC Spring 2003 Course Schedule we read:

Courses with course prerequisites have a plus (+) before the synonym.  You must provide proof of this prerequisite (grade slip, transcript, etc.) at the first class meeting.  Prerequisites are listed in the ACC Catalog.  Without proof you will be dropped from the class.
In accordance with this, the very first thing I did on the first day of my Spring 2003 classes was to inform the students (very gently) what the prerequisite was, and that they would need to supply documented proof that they possessed the prerequisite when they appeared the next class day.  Such proof  is available from Advising, and Advising has expressed that they are willing to cooperate in this endeavor.  So that they knew exactly what was required, each student received a Proof of Prerequisite form from me when they entered class.

The prerequisite discussion took about 10 minutes, after which I had a short break, during which I invited those that know for sure that they do not have the prerequisite to consult with me and/or leave immediately and register for an appropriate course.  Many left.

Notify the students that "having the prerequisite" is not the same as "having the prerequisite skills"

I informed those who remained that even though they had the formal prerequisite, they still may not possess the necessary skills:

They were requested to assess their own skills by doing the following: I have learned that a poor score on the Prerequisite Review has little effect on many students.  They seem to think that they will, by virtue of extra study, extra help, and, perhaps some miraculous epiphany, be able to overcome any obvious lack uncovered by the Prerequisite Review.  This rarely happens.

"College Math" is not equal to "College Algebra"

On the student information form that I use, I had the students complete an Appropriateness Check (disguised as a questionnaire).

Early warning

I can usually tell from the first homework that a student hands in whether s/he will be able to work at the level required by College Algebra.  So during the first week, prompted by what I observed, I gave those students that I thought were in trouble already with the work of the course an Early Warning form (with appropriate items checked).

3-week progress report

At the end of the third week, each student received a Three-week Progress Report , with appropriate selections checked.

4-week report

I insist that students show progress in their work. Students who are not progressing are doing themselves a disservice by subjecting themselves to daily failure, and become a drag on the class and the instructor.  The Student Handbook (p. 20) states: "An instructor may withdraw a student who is not meeting course requirements".  Test 1 over Chapter 1 is at the end of week 4, just before the last day to withdraw without record and receive a refund.  As a matter of fact, Chapter 1 covers mostly Intermediate Algebra topics, with the exception of "Higher-degree equations of quadratic form", "Rational exponent equations", and "Polynomial and rational expression inequalities".  Only the last significantly (and refreshingly) departs from the Intermediate Algebra curriculum.  Thus, students failing the course (based on homework and Test 1) at that point received a Drop Notice (attached to their test) and were dropped (code = 29 "lack of progress").

Students falling into the "D" category (they, too, will almost surely fail) received a Drop Recommendation Notice .

The results:  some statistics

The bottom line

Of the 62 students who attended on the first day, only about 20 appeared on the second day.  Succeeding days saw the appearance of 8 more students. Of 90 students that were on my class rolls at various times, only 16 students (8 in each class) remained at the end of four weeks.  What happened to the other 74?

How did I misplace 74 students out of 90?

Of the 35 that appeared and had the prerequisite: Of the 16 remaining students: If we count the 16 as the official class roll (the way ACC should do it, since students who drop themselves during the first month do not appear on the final class roll), then the attrition rate is 5/16=31%.
 

Benefits and deficits of this method

Deficits of this methodology

This method excludes students who do not have the prerequisite, but who may have the prerequisite skills.  For example, of the 40 students from Fall 02 that did not have the formal prerequisite, 5 succeeded, 3 with D's and 2 with C's. Under an enforcement regime, these 5 would have been forced to enroll in Intermediate Algebra, which would have been just as well, since C's or D's in College Algebra do not bode well for those going on in math.

Benefits of this methodology

Recommendations

Recommendation 1:  The automated registration system should enforce the prerequisite.

If Datatel enforced the prerequisite, the number of sections of College Algebra could be reduced by up to 50% (this might raise a political issue, but the educational issue remains clear), and we would start with classes of 36 students that have the prerequisite.  Presumably, we would end up with significantly more that the 17 students which was the median number of (A-D) students per class in the Fall of 2002.  This would almost certainly improve our official success rate, as well.

This is not an impossible "filtering" program for the Datatel folks to implement.  Eight little subqueries could retrieve MATH 0390, TASP, SAT, ACT, T-COMP, CPT, ASSET and HS Algebra II scores, do the appropriate logic (it's not hard), and make one of three announcements:

"You have successfully registered for College Algebra"
"You do not have the Prerequisites for College Algebra"
"You have fallen into a Decision Zone.  Please see an advisor to confirm the prerequisite."
Recommendation 2:  Make the prerequisite for College Algebra an A or B in Intermediate Algebra, or an appropriate score on T-COMP.