College Mathematics Placement Tests

How well do Core-Plus students perform on mathematics placement tests at the college level?

On a Mathematics Department Placement Test from a large Midwestern university, students completing field-test versions of Core-Plus Mathematics Courses 1-3 plus the precalculus path of Course 4 performed as well as students in traditional precalculus on basic algebra and advanced algebra subtests and better on the calculus readiness subtest.

The Mathematics Placement Test, compiled from a bank of items developed by the Mathematical Association of America, that is presently used at a major university was administered in several field-test schools in May 1999 at the end of CPMP Course 4 and traditional Precalculus courses. This test contains three subtests - Basic Algebra (15 items), Advanced Algebra (15 items) and Calculus Readiness (20 items). The first two subtests consist almost entirely of algebraic symbol manipulation, and the third subtest measures some of the important concepts that underlie calculus. A graphing calculator (with no symbol manipulation capability) is allowed on this test.

The CPMP Course 4 students included in the comparison below are all those in the 1998-99 Course 4 field test who completed the 6-unit "preparation for calculus" path as the last course in their sequence of CPMP Courses 1-4 (N = 164). The Precalculus students, also from field-test schools, completed a traditional precalculus course following a sequence of Algebra, Geometry and Advanced Algebra (N = 177). The two groups were further restricted to those students who indicated on a written survey their intention to attend a four-year college or university in the next school year. Eighth-grade mathematics standardized test scores for both groups were, on average, at about the 85th national percentile. Means by group and subtest are plotted in Figure 1. The CPMP Course 4 mean was significantly (p < 0.05) greater than the Precalculus mean on the Calculus Readiness subtest, while the group means did not differ significantly on the Basic Algebra or Advanced Algebra subtests.

Figure 1:

The Mathematics Department at the university that provided this placement test combines the subtest scores by a formula to recommend enrollment for each student in one of four college mathematics courses - Calculus I, Precalculus, Intermediate Algebra, and Beginning Algebra. Using that formula, the percent of CPMP Course 4 and Precalculus students who would be recommended for each course is illustrated in Figure 2. A much higher percentage of CPMP Course 4 students (50.6%) than traditional Precalculus students (39.0%) would be recommended for Calculus I suggesting that the CPMP curriculum with this sequence of Course 4 units better prepares students for this examination and presumably for college calculus.

Figure 2:

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