Placement tests the placement testing process

An Institutionally Developed Placement Test
At Pembroke State University in North Carolina, the Mathematics Department created its own test to assess math skills and place students in remedial or first-year university math courses (Truman, 1992). Development and piloting of the process took about two years. A large part of the paper deals with how the test was constructed, and how the content, validity, reliability and other statistical aspects of the test were assessed and improved. The author then reviews the success of the placement and remediation process over the most recent three-year period.
The placement test was administered to all entering students during summer freshmen orientation. Based on scores, students were assigned to one of two remedial courses, and one of three first-year math courses. Students who felt they were misplaced could apply for a retest; only 2% of 1375 students have done so in the three-year period reported on in the paper (Truman, p62). To evaluate the effectiveness of following recommendations, the final grades of first-year students in the Fall term were compared with their choice of course level for three consecutive years.

Table 6: Accumulated results for Fall semesters: 1988, 1989, and 1990.
Student Enrollment Category ( N)	Final Grades
	A	B	C	D	F	W
Below Placement Level (262)	52	78	57	42	21	12
At Placement Level (461)	58	112	136	81	53	21
Above Placement Level (52)	5	6	13	16	10	2

(adapted from Truman, 1992, p63)
Reviewing the figures in this table, we see that a large proportion of students - 262/775 or 34% - took courses below the placement level. As might be expected, this group shows a relatively high average grade. The 461 students who followed recommendations include 53 who failed, or 11.5%. This can be described as an 11.5% false-positive error for the placement test, ie. the test placed that portion too high. Finally, 52 out of 775, or 6.7% took higher courses than recommended and, not surprisingly, show a low mean grade. However, 24 of these students were successful as defined in the previous study, meaning that 24/775 or 3% were placed too low by the initial test. (The reader might compare this to the 6-8% low placement error for the test in the first study.) As far as Truman is concerned the evidence from these results is clear:
After 5 years of mathematics placement testing at Pembroke, the mathematics department is convinced that this program provides an efficient, practical, and workable method of placing students in mathematics courses which give them the best chance for educational success (Truman, p64).
Is this conclusion reasonable? Certainly, the rate of failures is relatively low, as is the rate of dissatisfaction with placements. But,something does not seem quite right with some of the numbers. For example, if 1,375 students took the math placement test in the period described above why are there only 775 students in the table of grades? What happened to the remaining 600? And if just 2% of 1,375, or 23 students (Truman, p. 62) asked for a retest, how is it that 52 students took courses higher than placement level? Of these 52 students, 24 of them were successful. This calls to question the claim that only 3% were placed too low. The fact that 46.2% of the students who took the initiative to get placed in a higher than initially recommended course were successful suggests that the potential for inappropriate placement in this direction merits further attention. This false-negative error rate is unacceptably high. In addition, there is no follow-up data presented to indicate if successful underprepared students are enrolling in college-level math and what their success rates in those courses might be. Omission of this type of data in studies evaluating remedial math programs is unfortunately relatively common (Akst, 1986). The papers by Sturtz and McCarroll (1993) and Truman (1992) clearly support the use of math placement testing and remediation in post-secondary institutions. They provide evidence to show that the process is beneficial to students. These papers also present, either implicitly or explicitly, indications that a score from a placement test alone does not tell the whole story. For example, though placement was nominally mandatory at both institutions, each one also provided a way for students to challenge and alter placements. Many students who had been tested never took any math courses at all. Did placement testing scare them away from math courses, confirming one more time that they can't do it? There must be other factors that affect a student's success in college-level mathematics. In the next section, criticisms of the math placement process and some views opposed to placement testing will be explored.