Remedial Mathematics and Open Admissions

Theodore EisenbergNorthern Michigan University*Marqiiette, Michigan 49855

INTRODUCTION

Political and social forces in the United States have led many state-funded universities to endorse the open-admissions policy; that is, an ad-missions policy which claims that even students with minimal academicachievements have the right to pursue a higher education. As a result ofopen admissions, many universities have been faced with an influx ofstudents ill-equipped to handle university level work. As a consequence,many universities have increased their remedial offerings. In the shortrun, open admissions seem to be devaluing the overall level and meaningof the baccalureate degree. But, in the long run, open admissions mightwell be a significant educational innovation, for it is making highereducation non-elitist and reducing social stratification. Finally, sincestandards for the baccalureate remain higher than those required for thehigh school diploma, open admissions is helping raise the overall educa-tional level of the country.The short run criticism of open admissions has been well chronicled by

the press with exposes on low level courses being offered and increasingnumbers of students having to take them. Witness, for example, TimeMagazine’s comment: ’Test results have shown that one-third of thefreshmen at state colleges in New Jersey are almost illiterate." ’ Suchcriticism by the press appears to be a well orchestrated effort to expose tothe public the deteriorating state of higher education and the fiscal irre-sponsibleness of open admissions programs. Nevertheless, it is a fact thatthroughout the United States, large numbers of entering university stu-dents require substantial amounts of remedial work. Remedial work inthe mathematical domain usually falls under the rubric of "pre-calcu-lus" course offerings. Here too it is easy to criticize as we see in the com-ment: (< . . . The fastest growing subject in freshmen college mathe-matics is grade school arithmetic!" 2 More relevant, however, is thatmathematicians tend to simply ignore the problem as was recently doneby the blue-ribbon committee of the PRIME-80 conference (Prospectivesin Mathematics Education in the 1980’s) whose recommendations willprobably be used as a blue-print for mathematical education in the nextdecade.3The purpose of this article is to discuss the results of a follow-up study

of students in a remedial mathematics course and its implications. Direc-* Written while a Visiting Professor in the Department of Science Teaching, Weizmann Institute of Science, Rehovot,

Israel

341

342 School Science and Mathematics

tions one can take to systematically study the long-term effects of openadmissions will also be considered.

THE FOLLOW-UP STUDY

Northern Michigan University is an open admissions university whichoffers a substantial number of pre-calculus courses. Collectively, thesecourses account for more than 70 percent of all students taking mathe-matics in any given semester. MA100 (four credits) is the lowest levelcourse in the pre-calculus sequence; in it one systematically studies alge-braic operations, graphing linear equations, exponents, and quadraticfunctions. It is a skill oriented course whose objectives are to provide thestudent with tools he will need to handle mathematics encountered in hischosen course of study. After successfully completing MA100 (usuallywith a grade of A, B, or C), the student can take college algebra (MA105)or intermediate math (MA170). The former leads to courses in trigonom-etry, analytic geometry and calculus; the latter is usually followed by acourse in statistics which is required of all students majoring in businessadministration and psychology. Admission to MA100 is based on thescores obtained on a departmental placement examination. Great effortis made to enroll only those students who are unable to complete moreadvanced mathematics courses. It should be noted that it is seldom thecase that mathematics, engineering, or physical science majors com-mence their study of collegiate mathematics with MA100.One assumption posited to justify the offering of MA100 and other

remedial level courses is that the students are acquiring skills which willenable them to progress in their other courses of study. Because mostdisciplines at Northern Michigan University have a mathematics require-ment which is not satisfied by MA100 alone, most students have to fol-low MA100 with another mathematics course. The progress of more than1600 students enrolled in MA100 over a four year period was studied todetermine the relative effectiveness of the course. This was done byexamining their performance in the subsequent courses of MA105 andMA170. About equal numbers of students took MA100 during each yearof the study, in sections with no more than 35 per class taught by a regu-lar staff member. The courses were taught in a variety of ways: Lectures,small groups, mastery learning, contract learning, with the aide of TVand CAI, and combinations thereof.Table 1 lists the grades and percent of students from MA100 who en-

rolled in another mathematics course within a four semester period aftercompleting MA100. For the most part, the second course was taken thesemester immediately following MA100 and represents an almost evensplit between those taking MA105 (45 percent) and those taking MA170(55 percent).

Remedial Mathematics

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Table 2 lists the grades students from MA100 received in their nextmathematics course. A departmental recommendation states that stu-dents receiving a D, F, or W in MA100 should be strongly advised to re-peat MA100, and encouraged not to take other mathematics courses un-til skills with basic algebra are developed. Nevertheless, some studentsdid take other courses; their grades are found in Table 2.

TABLE 2GRADES RECEIVED IN MA 105 OR MA 170 % OF N

Grades ReceivedA B C D F W

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* Not really eligible for MA 105 or MA 170

Table 3 lists the number and grades of students who repeated MA100.

TABLE 3REPEATED MA 100: GRADE % OF N

Grade Second TimeA B C D F W

EA0%0%0%0%0%0%N = 0FB06733000N= 32C2502525025N= 4ED11163726110N = 19-SF0221417398N = 36-W9143661818N= 22

DISCUSSION

An unsettling finding of this study is how few students take a secondmathematics course. Overall, 60 percent of the A, B students did not takeanother mathematics course; approximately 67 percent of the C, D stu-dents and roughly 78 percent of the F,W, students did not opt for moremathematics. These percentages were roughly constant each semester.The Department had no idea the percentages of students electing to dis-continue mathematics were this high. Because satisfactory completion ofMA100 is not considered to be sufficient to meet the mathematics re-quirement of most disciplines, many students (if they graduate) had toswitch disciplines of study to those with more relaxed mathematics re-

Remedial Mathematics 345

quirements. (Because of the large number of students transferring toother schools, it was impossible to detect a trend of how many studentsactually obtained the university degree.)

Seventy-five percent of the students who received an A in MA100 didnot receive an A in their next mathematics course. Almost 15 percent ofthem received a D, F, or W. For B students, 72 percent received a C, D,F, or W and 73 percent of the C students dropped at least one grade intheir next mathematics course. For all practical purposes, D, F, and Wstudents had no chance of success (C or better) in their next course, evenif they repeated MA100.

IMPLICATIONS

In addition to providing some insight into the relative effectiveness ofthe MA100 course in remediating mathematical deficiencies, this studycan be viewed within the overall framework of a curriculum for an openadmissions university.

It appears that only 35 percent of the MA100 population will try moremathematics, and of them, 45 percent will fail (grade of D, F, or W). Aninitial assessment suggests the MA100 course is a dismal failure, for it isspecifically designed as a feeder course to MA105 and MA170. But wtiatabout the 19 percent of beginning MA100 students who did succeed?Over the four year period this accounted for approximately 310 students.Perhaps these 310 students were salvaged at a high price in view of thenumber who did not succeed. Also to be accounted for is the cost of theirremediation.Over the years, the number of students being helped by such courses

will cumulatively be significant and, hopefully, raise the overall educa-tional level of the country. Similarly, although students failing MA100had to change career goals, certainly they too learned something fromthe course. In other words, even the "failures** can contribute to ageneral increase in the educational level of the citizenry.How to systematically study the hypothesis that the overall knowledge

level is rising is discussed below. Such studies will naturally provide dataon whether or not remediation at the collegiate level is worth the humanand financial expenditures required. This has been the subject of muchdebate and the idea of introducing courses whose content is lower thanthat of MA100 has met serious opposition.4The cost of remediation is staggering from financial and psychological

points of view. It is easy to argue that MA100 and thousands of courseslike it throughout the country, do not justify, as measured by the numberof successful graduates, their existence in the collegiate curriculum. Butsociety in general and universities in particular must subsidize some pro-

346 School Science and Mathematics

grams for such students. For example, few public transportation systemsare financially self-supporting. They do, however, provide a vital service.The same can be said for remedial courses offered at the collegiate level.The major problem is to demonstrate that students in MA100, even thosewho failed, gained something of value from the course.

This study suggests that MA100 does not remediate specific skilldeficiencies. But how does one measure the serendipitous rewards ofstudying mathematics? One studies mathematics not only to learn specif-ic skills, but also to acquire an enriched perceptual-conceptual set bywhich problems can be examined rationally and systematically. Studentsof mathematics learn to recognize problems, utilize data, choose a pathof solution, test, formulate and re-evaluate hypotheses. These are thereal skills one learns while studying mathematics, even remedial mathe-matics. These skills can generalize to help students master other subjectmatter and even help them perform more adequately in vocational set-tings. Research on open-admissions should focus on these goals and noton the specific goal of skill development. The problem is to first demon-strate that these goals are attained through remedial programs, and thento illustrate that they are being achieved in a cost-efficient manner. If thiscan be done, open admissions will have justified its place in the educa-tional philosophy of our country.

REFERENCES

(1) Time Magazine International (October 9, 1978), p. 42.(2) STEEN, LYN ARTHUR, "Math is a four letter word," The Mathematical Intelligences,

Vol. l,No.3, 1978, p. 171.(3) A copy of the PRIME-80 report can be obtained by writing to: Al Wilcox, Executive

Director, Mathematical Association of America, 1529 Eighteenth Street, N.W.,Washington, D.C. 20036.

(4) GEMIGNANI, MICHAEL, C. "Remedial mathematics: An administrator’s viewpoint."American Mathematical Monthly, Vol. 84, No. 6, 1977, p. 481.

OLD FOSSILS

What are "probably the oldest fossil whales" have been found in Pakistan ona geological expedition led by a University of Michigan paleontologist. The backpart of a skull and several teeth found probably belong to whales that inhabitedthe ancient Tethys Sea about 45 to 50 million years ago, called the Eocene age,when India and Pakistan formed a continent separate from the rest of Asia.The remains may help provide information about the little known ancestors of

whales, mammals that are believed to have lived on land before adapting com-pletely to an aquatic environment.