All students entering the California State University (CSU) system are expected to have completed a rigorous sequence of college preparatory subjects. In mathematics, this means three years of college preparatory course-work, while a fourth year of pre-calculus is recommended. Students who are not exempt on the basis of other test scores must take an Entry Level Mathematics Placement Examination (ELM).1 If they do not pass this examination, students are required to take remedial course-work. The failure rate has been steadily increasing over the past several years, and now well above 50% of entering students require remediation.2 The CSU system has recently revised the ELM.1 This report summarizes some of the characteristics of the revised ELM.
The new version of the ELM retains the multiple choice format. A passing grade varies somewhat from exam to exam, but should fall in the range from 58% to 65% correct. Items are 5-alternative, multiple choice format, so 20% correct is expected by chance. Although calculators are now permitted, they are not of great benefit. The examination is divided into three general areas - Algebra (roughly 60% of test items), Geometry (roughly 20% of test items), and Data Interpretation, Counting, Probability and Statistics (roughly 20% of test items). Various subtopics are defined within each of these content areas.1
To assess the target grade level of the ELM against external criteria, individual sample items1 were evaluated for their grade level based on the newly established California Mathematics Standards.3 These standards provide a desirable benchmark for several reasons. They are perhaps the most highly detailed of all the sets of state mathematics standards, greatly facilitating item evaluation. And they have been judged as the best available mathematics standards among all sets of state standards, even better than those from Japan.4
The authors independently judged the grade level of every sample ELM item using California's new mathematics standards as the criteria. The inter-rater reliability was r=.80, which indicates a reasonably high degree of agreement. Where there were differences, the mean of the two ratings was used.
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The item ratings ranged from 4th grade to 10th grade, although most (72%) were judged as measuring standards at the 6th to 8th grade levels. The overall mean grade level rating was 6.92 (SD=1.47). Overall, 68% of items fell below 8th grade level, 24% of items were at the 8th grade level, and 8% of items fell above 8th grade level. |
| The mean grade level rating for the statistical item group (5.3) was significantly lower than the mean for items with geometry (6.8) or algebra (7.3) content (p<.05). |  |
Given the test requirements, a passing grade requires at least some minimal degree of competence in introductory algebra. It should be noted that this is clearly a higher requirement than one often sees for high school graduation, such as in the Texas TAAS examination.5 On the other hand, passing such an examination is no assurance of the knowledge and skills needed for further courses involving quantitative reasoning. Indeed, success on the ELM might signal readiness to study high school geometry or intermediate algebra, but should not be taken as an indicator of readiness for pre-calculus, calculus, other demanding mathematics courses, or other courses requiring a strong mathematics base.
1 Focus on Mathematics: Entry Level Mathematics Placement Examination. CSU Academic
Affairs, Office of the Chancellor, Phillip Emig, CSU Faculty Consultant in Mathematics
http//www.co.calstate.edu/aa/ar/FOM.pdf
2 Fall 1998 Freshman Remediation Rates Campus and Systemwide, CSU
http//www.asd.calstate.edu/remrates98sys.htm
3 Mathematics Content Standards for California Public Schools: Kindergarten Through Grade Twelve, California State Board of Education
http://www.cde.ca.gov/re/pn/fd/documents/math-stnd.pdf
4 State Mathematics Standards, Ralph A. Raimi and Lawrence S. Braden, Fordham Report Volume 2, Number 3, March 1998.
http//www.edexcellence.net/standards/math.html
5 Statewide Mathematics Assessment in Texas, P. Clopton, W. Bishop, and D. Klein
http//www.mathematicallycorrect.com/lonestar.htm