Are placement tests for incoming undergraduate mathematics students worth the expense of administration?

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jun 2003 by Latterell, Carmen M, Regal, Ronald R

ABSTRACT: One of the tasks faced by undergraduate mathematics departments is placing incoming students into the appropriate mathematics classes for their abilities. This is often accomplished through giving a placement test at the time of student orientation. Dissatisfaction with the results of the placement test used at our university prompted us to write a new one. In this paper, we describe the writing of the new placement test and provide detailed results of a validity study on the test. Our results led us to conclude that placement testing does not work very well, and to suggest that undergraduate mathematics departments consider using existing data rather than give a separate placement test. In spite of this conclusion, we do decide to continue with our placement test, and we offer reasons for doing so.

KEYWORDS: Placement testing, incoming undergraduate mathematics students, ACT mathematics test.

INTRODUCTION

One of the tasks faced by undergraduate mathematics departments is placing incoming students into the appropriate mathematics classes for their abilities. Ninety percent of postsecondary institutions have placement tests [14]. Correctly placing students is becoming quite difficult as the issues surrounding this task are becoming increasingly complex [11]. Certainly, professors would like to see students placed into the appropriate courses according to students' abilities. Not only does this make courses easier to teach, but correct placement also reduces the level of frustration for the students [13, 17]. Students who are successful in their beginning courses are more likely to continue in mathematics courses [13, 15].

Yet, studies show that the relation between placement test score and course grade is weak and other issues (such as grading variability between instructors) contribute more strongly to variance in outcomes [3]. Other predictors (such as high school courses taken and grades received) are often better predictors of course success than a placement test score [10]. Some studies show that having a placement test score does not significantly affect the course students chose to take nor does it affect the success they have in that course [8]. Yet, other studies show that students who take the course recommended are in fact more successful than students who take a course beyond what is recommended [4, 6, 7, 11, 12, 16].

In this article, we describe our own struggles with placement in order to clarity the issues that need to be addressed to ensure success. In particular, we describe how we validated our own placement test and how we reached the conclusion that the placement test adds little information beyond what one finds from ACT mathematics test results. Since we had a valid placement test, we suggest that other undergraduate mathematics departments consider carefully whether their own placement tests are worth the cost.

BACKGROUND

We teach at a regional university with 11 bachelor's degrees in 70 majors, a two-year program at the School of Medicine, and graduate programs in 18 different fields. The campus views itself as an alternative to both large research universities and small liberal arts colleges. It is a medium-sized campus of a major university. In our mathematics department, we had a mathematics placement test that was purchased and used for many years with approximately 1000 students taking the test each fall. In the fall of 1999, out of the students taking the test, 8% placed into prealgebra (housed under "Supportive Services", not considered a college course), 54% into college algebra (although housed in the mathematics department, college algebra did not receive credit toward graduation), 32% into precalculus, and only 7% into calculus. In Pall 2000, the results were similar with 10% placing into prealgebra, 51% placing into college algebra, 31% placing into precalculus, and 7% placing into calculus.

Based on the courses the students had taken in high school, it was reasonable to expect the majority of students to place into calculus. Since students were placing so low, we began to question if the placement test was working. In addition, the test that we were using was quite dated.

ALTERNATIVES

What would be a better alternative? One option would be to eliminate the placement test and let students self-place. Another option might be to purchase a different placement test. Other alternatives include students being placed based on their scores on a standardized test taken for other reasons (e.g., ACT, SAT) or students' high school grades in mathematics courses placing the students into the appropriate college courses. Some combination of these options could be employed, or we could write our own placement test.

We decided to write our own placement test. The reasons for this decision were many, including cutting down on costs and our knowing we were capable of writing our own test. In addition, we decided to give some college credit to the college algebra course, partially to encourage students to take the course into which the test places them.