Alternative methods of mathematics placement

Although many community colleges are using placement tests as the sole means, or as an important part of making placement decisions, it is not clear that these tests effectively measure a student's readiness for the initial mathematics course. Results of a study comparing alternative methods of placement into the mathematics curriculum indicated that an institutional placement policy prescribing placement by an examination of multiple measures consisting of placement test score and self-reported high school preparation resulted in student placement into higher-level mathematics courses with equal academic success when compared to policies that considered either measure individually.

Introduction

Students come to the American community college because they know they can pursue their postsecondary educational goals at the institution. However, in many cases, institutional placement policies serve as barriers to enrollment in college-level classes. When the policies prescribe necessary remedial instruction, they are crucial to student success (Roueche & Roueche, 1999). But when institutional placement policies prevent students from registering for courses in which they could be successful, the policies often deny access to the instruction that students need to. achieve their educational goals.

Most community colleges choose standardized placement tests as the sole measure of student academic preparedness (Lewis et al., 1996). Grubb (1999) notes, however, that community colleges have rarely analyzed the results of the tests to determine their validity as predictors of academic success. Researchers have questioned the effectiveness of standardized placement test scores as the sole component of an institutional placement policy. They have identified other measures that have implications for a student's academic success. But much of the research examines existing data rather than examining the effectiveness of placement methods which considered measures other than test scores as part of an initial placement policy.

Hypothesis

A study recently completed at one urban community college in the Midwest compares the effectiveness of three alternative methods for initial placement in the mathematics curriculum with the current method of placement by test scores alone. The research sought to determine which of the four placement methods was most effective in assigning an initial course placement. It measured subsequent academic success by higher rates of completion, persistence to enroll in another mathematics course the following semester, and higher course grades.

Prior to the study, the Accuplacer(R) test by ETS placed all students in mathematics courses at the institution. The design of the Accuplacer(R) test differentiates between those ready for college level instruction and those needing some remediation. Over the years, the number of developmental mathematics courses offered at community colleges has expanded to include as many as five levels at some institutions (Lewis et al., 1996). The present study examines the hypothesis that one method of initial placement might be more effective placing students ready for college-level mathematics instruction and another more effective placing students at the developmental level.

Method

Data collection occurred in a controlled randomized experiment. All students who took the placement test between May 1, 2001, and August 17, 2001, and enrolled in a mathematics course at the selected Midwestern institution were randomly assigned to one of four placement methods. Each student's initial mathematics course placement followed examination of either the test score, high school preparation, balancing these two measures, or student choice constrained by these measures. Researchers examined academic outcomes for each student who enrolled in the prescribed math course during fall semester 2001.

Two instruments collected information to determine initial student placement. The college administered the Accuplacer(R) test by ETS to all study participants. The resulting test score constituted one measure of academic preparedness. High school preparation as self-reported on a student survey also became a measure of academic preparedness for the study. It was chosen primarily because of Armstrong's (1999) finding that self-reported high school preparation more strongly correlates to college grades and course completion than a placement test score does.

Researchers chose self-reporting over actual high school transcript evaluation since community colleges have difficulty obtaining high school transcripts prior to enrollment. At the selected institution, approximately 250 new students take the placement test, meet with advisors, and register for classes during the week before fall semester classes begin. If students had to produce actual transcripts before enrollment, they would not be able to enroll at the college. That would not only impact generated credit hours, but might also discourage some students from pursuing their educational goals. Therefore the institution, like many community colleges, chooses not to require high school transcripts prior to enrollment.

Three hundred sixty-one students completed testing and enrolled in an initial mathematics course. Fifty-- seven of the students were placed in error. That is, they enrolled in a course other than the one prescribed by the assigned placement method. Results for the remaining 304 students provided the data used to test the research hypotheses.

Discussion of findings

Comparison of four methods for placing students in the mathematics curriculum sought to determine if one or more methods for placing students led to better academic success than the other methods. Specifically, math course completion and persistence became guidelines to compare all students by placement method. The study found that, overall, there were no significant differences in either measure of academic success among students placed by the four methods. Students performed equally well regardless of the method used for initial mathematics course placement.

Placement in higher-level courses

Perhaps no placement method is optimal for all students. Armstrong (1999) hypothesized that mandatory placement by test score denied access to higher-level mathematics instruction for some students who could have completed a higher class successfully. Isbell (1988) and Jenkins (1991) confirmed that many students succeeded in classes when test scores categorized them as unprepared for the classes. While the present study confirmed the Isbell and Jenkins finding, it found that placing students by examining high school preparation also denied access to higher-level classes for some students who could successfully complete them. In fact, for those students where random selection of placement method made a difference in their placement, the test score method would place 52% of the students at a higher level and the high school preparation method would place 48% of the students at a higher level. Therefore, one cannot conclude that test scores systematically place students at a lower level than examination of high school preparation.

When comparing academic success rates for students placed at a higher level by either test score results or high school preparation than they would have been placed by the alternate method, results show that the students are equally successful. In fact, at the developmental level, students whose test score recommended a higher placement and high school preparation recommended a lower placement completed at a significantly higher rate when placed in the higher level course. Thus, placing students at the higher level indicated by either method did not hurt their chances of academic success and, in fact, increased their chances in some cases.

Since little difference in academic outcomes appeared among the four placement methods, any of the methods could be used to place students with equal success. Thus, the level of math class prescribed by the methods has importance when determining an institutional placement policy. If one method systematically places students into higher-level mathematics courses, and they achieve equal academic success in the higher courses, then the institution should use the method. Mandating placement into lower level classes for students who could achieve success at a higher level denies those students access to acollege education

Distribution of enrollment

Comparing the distribution of student enrollment in the mathematics course sequence by placement method shows a significant relationship between placement method and distribution of enrollments. Single measure methods place students into lower level classes than do the multiple measure methods used in this study. Particularly at the developmental level, a significant difference occurs between students placed by the single measure method of high school preparation and the multiple measure of choice. Moreover, when comparing enrollments for students placed by either single measure method to those placed by either multiple measure method, developmental students place by multiple measures into significantly higher courses.

In contrast, no difference occurs in the distribution of enrollments for students who place at the college level by any of the four methods. However, college-level students suf fer no disadvantage in placement by considering multiple measures of academic preparedness and enrolling at the highest level indicated by any measure. All students placed using multiple measures of academic preparedness can enroll initially in higherlevel classes and, therefore, shorten the time necessary to complete the mathematics requirement for an associate degree or certificate.

Conclusions

The benefit of multiple measures

By using a controlled randomized experiment to investigate the relationship between method of initial placement in mathematics and measures of academic success, researchers tried to establish cause and effect between method of placement and academic outcomes. The findings lead to several conclusions. Most importantly, community college students benefit from institutional placement policies that require consideration of multiple measures of academic preparedness when prescribing an initial mathematics course. The current study confirms the conclusions of Wattenbarger and McLeod (1989) that a combination of several factors provides a more successful placement policy than consideration of a test score alone. Results show that placement methods which consider multiple measures place students collectively into higher-level courses. By using a placement method that considers multiple measures, students place into higher-level courses where they achieve academic outcomes equal to or better than the outcomes of students placed by either test score or high school preparation.

Developmental and college level placement

The result holds true when examined for students at either the developmental or college level, but for different reasons. Developmental students place into higher classes when a placement method considers multiple measures. Students prepared for college-level classes enroll at the same level regardless of placement method and are most successful when multiple measures prescribe the same course. When multiple measures indicate different courses, however, college-level students achieve equal success when enrolled at the higher level. Therefore, a placement method requiring consideration of multiple measures benefits those prepared for college-level courses as well as those in need of some remediation. The study confirms Grubb's (1999) contention that more elaborate decision making mechanisms than test scores alone are necessary to place students for the best educational beginning.

Standardized test scores

Although multiple measure placement methods remain preferable for guiding students into the highest course, Accuplacer(R) test scores provide a reasonably effective means of making placement decisions. Despite contentions by Robinson (1998), Armstrong (2001), and others that measures other than test scores have an important relationship to academic outcomes and should be considered when initially placing students, this study found test scores equally effective. The study confirms that the Accuplacer(R) placement test does provide valuable information for initial placement in the mathematics curriculum. The Illinois Community College Task Force on Remediation (2001) states that standardized tests provide the greatest uniformity for making placement decisions. Administrators in Isbell's (1998) survey preferred standardized tests as a mechanism for prescribing initial placement because of the uniformity of the standard. Standardized test scores present an easy choice for community colleges that want a defensible placement policy.

High school grades

The study also shows consideration of high school preparation to be an effective measure of academic preparedness. Current high school courses may have more congruence with current community college pedagogy and curriculum than test scores. High school grades may be a better indicator of motivation than test scores. When both test score and high school preparation inform the placement decision students benefit by enrolling in a higher course than the lowest indicated by either method. Results show that developmental students do at least as well in higherlevel classes when the two measures recommend different levels of placement and more often complete the higher class if it is recommended by the test score.

College-level students placed by either test score or high school preparation perform equally well on all measures of academic success when placed at the higher level indicated by either measure.

A different method of initial placement does not appear more effective for developmental students than college-level students. No differences in academic outcomes occur for developmental students based on placement method. At the college level, students placed by test score earn higher grades than students placed by the balanced method, but not higher than students placed by high school preparation or student choice. A different placement policy does not seem to be warranted for the two groups of students.

Implications

The results of the current study provide valuable information for community college faculty and administrators interested in initial student placement. The results also inform national organizations, such as The American Mathematics Association of Two-Year Colleges (AMATYC), as they consider position papers on placement, and testing companies, such as the Educational Testing Service (ETS), as they adapt and market their products. The significance of the study lies in the importance of placement policies as they affect students' academic success.

Because the study was conducted at one institution, the results cannot automatically be generalized to all community colleges. However, the findings may have implications for practice at other community colleges as they attempt to formulate institutional policies prescribing initial mathematics course placement.

Administrator, faculty and student objectives in placement

College administrators seek a simple, economical and defensible placement procedure. Mathematics faculty seeks a policy that provides the best match between course objectives and necessary student skills. Institutional placement policies that use multiple measures can address concerns of both groups. The ones employed in this study offer simple, economical, and defensible placement. Though not as simple or economical as placement based on a test score only, procedures that consider multiple measures surely warrant the small increase in cost or complexity. If students can be placed initially at a higher level without risk to their success, they may be more likely to achieve their educational goals and complete their degrees or certificates. As a result, the institution benefits in fulfillment of the college's mission as well as financially.

Placement policies that consider multiple measures may also provide the best congruence between course objectives and student skills. Test scores measure mathematics skills, but high school preparation and grades may have a stronger relationship to college curriculum and student motivation. Allowing students to participate in placement decisions conveys an important message about their responsibility for their own learning and the differences between high school and college.

Position paper on placement

AMATYC (2001) is currently in the process of developing a position paper on the issue of placement in mathematics curricula. The research in this article will help inform the issue. Such position papers from a national organization serve as policy statements on important topics in community college mathematics education. Initial placement is certainly one such topic. Based on the research presented here, AMATYC's position paper should consider recommending multiple measures of academic preparedness and the involvement of mathematics faculty in developing community college placement policies. Faculty involvement is essential when developing the algorithm used to interpret high school mathematics courses and their relationship to the college mathematics curriculum. The position paper should give formal recognition to the importance of initial placement in community college education.

Mandatory placement policies

Mandatory testing may provide important information for placement, but a mandatory placement policy based only on standardized test scores may deny access to a college education for some students. The findings of the current study show that test scores provide valuable information but place developmental students in lower level mathematics classes more often than methods that consider multiple measures of academic preparedness. The problem seems to go deeper than simply adjusting cut scores. If cut scores separating PreAlgebra and Introductory Algebra were set 10 points lower to allow more students to qualify for the higher course, only three additional students in this study would have been placed in Introductory Algebra than if all students had been placed by test score alone. In fact, test scores and high school preparation may measure different components of academic preparedness that are important when determining a student's academic success. Even the makers of standardized tests recommend that test results be used as only one component of an institutional placement policy.

Testing companies, such as ETS, need to promote the value of multiple measures in making placement decisions. ETS manuals provided by the company in 1991 include such a recommendation, but their current marketing materials do not. Promoting multiple measures, one of which is standardized test scores, will provide their product with more credibility rather than less. Armstrong (2001), Isbell (1988), Jue (1993), Robinson (1998), and Spurling (1998) have all raised questions about the use of test scores as the single means of making initial placement decisions. Unfortunately, institutions may move away from mandating a placement test if they feel the tests are losing legitimacy. But standardized placement test scores provide valuable information and should be a part of a mandatory placement policy. Acknowledging that tests play an important part, rather than providing the sole criteria for placement, can enhance a company reputation and educator opinions of the tests.

Recommendations for educational policy and practice

Based on research findings, the author recommends that community colleges adopt institutional placement policies which examine multiple measures of academic preparedness and use the results to place students in the mathematics curriculum. An effective policy provides students with as much information as can be reasonably gathered and then sets parameters for initial placement based on the information. If placement policies direct students to enroll at the developmental level when they could have achieved success in higher-level classes, then access to a college education has been postponed and may, in some cases, have been effectively denied. In order to balance the mission of an open door institution with high academic standards, policies must he developed that optimize a student's chances for success. Analysis of both placement test scores and self-reported high school preparation may help community colleges achieve the needed balance.

A second recommendation suggests that the community college participating in the current research adopts the practice of evaluating all policies at regular intervals with a focus on student success. A review of literature concerning academic placement indicates many institutions use standardized tests as the sole indicator for making placement decisions without doing analysis to examine the effects of such decisions on student success. Isbell's (1988) survey of administrators shows that they will implement mandatory placement policies based solely on standardized test scores because the uniformity of the standard provides a defensible policy. Administrators want a simple, defensible and costeffective placement policy. However, they must not forget that the policy should help students find the best starting point for their postsecondary educational goals. Rather than adopt an easy method, community college administrators should evaluate all college policies in terms of student learning outcomes.

Given the diversity in background and goals of American community college students, no one method of initial placement can prescribe the optimal course for all students. The current study confirms earlier conjectures that placement policies should consider measures of academic preparedness in addition to standardized test scores. For community colleges to promote academic success among diverse students, each institution must regularly review all placement policies. Accepting standardized measures may be an easy method of showing accountability, but it is not in the best interests of the diverse students who rely on American community colleges to provide access to education.

References

American Mathematics Association of Two-Year Colleges, (2001). Position paper on the placement of community college students into the mathematics curriculum. Paper presented at the American Mathematical Association of Two Year Colleges annual conference, Toronto, Ontario, Canada.

Armstrong, W. B. (1999). Explaining community college outcomes by analyzing studentdata and instructor effects. Unpublished doctoral dissertation, University of California Los Angeles, Los Angeles.

Armstrong, W. B. (2001). Explaining student course outcomes by analyzing placementtest scores, student background data, and instructor effects. Paper presented at the Conference for the Study of Community Colleges, Chicago, IL.

Educational Testing Service. (1991). Accuplacer user's notebook, coordinator's guide, background reading. Princeton, NJ.

Grubb, W. N.. Worthen, H., Byrd, B., Webb, E., Badway, N., Case, C., Goto, S., & Villeneuve, J. C. (1999). Honored but invisible. New York and London: Routledge.

Illinois Community College Board (2001). Collaborating to Strengthen Student Preparation. Springfield, IL Task Force on Remedial Education.

Isbell, V. K. (1988). Student placement in entry level courses of reading, writing, and mathematics in community colleges (Doctoral dissertation, University of Florida). Dissertation Abstracts International, 50-07, A1871.

Jenkins, B. G. (1991). Meeting the diverse needs of two-year college students through appropriate course placement. Redlands Community College, OK. (ERIC Document Reproduction Service No. ED 341444).

Jue, P. Y. (1993). Course enrollments and subsequent success after being advised of or 'blind' to assessment test scores and course recommendations. Napa Valley College. (ERIC Document Reproduction Service No. ED356819).

Lewis, L., Farris, E., & Greene, B. (1996). Remedial education at higher education institutions in Fall 1995 (Statistical analysis report NCES 97-584). Washington D.C.: National Center for Education Statistics.

Robinson, S. H. (1998). An analysis of placement systems for new and returning community college students, specifically in the college preparatory and entry,

level college-level mathematics courses (Doctoral dissertation, University of Central Florida, 1990). Dissertation Abstracts International, 59-03, A0707.

Roueche, J. E., & Roueche, S. D. (1999). High stakes, high performance. Washington DC: Community College Press.

Spurling, S. (1998). Progress and success of English, ESL and mathematicsstudents at City College of San Francisco. City College of San Francisco, CA. (ERIC Document Reproduction Service No. ED425782).

Wattenbarger, J. L., & McLeod, N. (1989). Placement in the mathematics curriculum: What are the keys? Community College Review, 16(4), 17-21.

Judith Marwick

Dr. Marwick is the Assistant Vice President for Academic Programs at Moraine Valley Community College, Palos Hills, Illinois.

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