A preliminary investigation of placement and predictors of success for students with learning disabilities in university-required mathematics courses.

Abstract

The number of students with learning disabilities attending institutions of higher education has dramatically increased in the last ten years and will continue to do so. Since federal laws in the United States and other counties require appropriate accommodations for students with learning disabilities, it is important for universities to evaluate the effectiveness of accommodations and services. This study was designed to evaluate the effectiveness of a class reserved for students with learning disabilities and to identify predictors of success based on student documentation. Evaluation of the relationship between student success and specific student documentation will facilitate the development of sound, researched policies for making accommodation and placement decisions.

Introduction

Increased attention to and legal support for those with learning disabilities in education has led to a dramatic increase in the number of students with learning disabilities attending colleges and universities. Unfortunately, few institutions are monitoring performance, graduation rates, attrition, satisfaction, or other indicators of success for students with learning disabilities in their learning services programs (Vogel & Adelman, 1992). Evaluation of what little information there is available for these programs suggest that there is reason to be concerned with success of students with learning disabilities (Vogel & Adelman, 1992). Most universities have ways to assess academic courses through student evaluations of teaching but few have a system in place for feedback on their learning services programs. This raises serious questions about the assessment and implementation of good accommodation and placement practices and the importance of evaluating the services that are in place.

Mathematics learning is crucial to the overall academic success of students with learning disabilities. A significant number of students with learning disabilities have difficulty with mathematics learning (Miller & Mercer, 1997) and other learning disabilities may interfere with testing ability and mathematics learning even if students are not diagnosed with specific mathematics learning impairments (Nolting, 2000). Students with learning disabilities are more likely to fail to organize information, both mentally and physically, in a way that allows for easy retrieval, use, and generalization (Scheid, 1990). Often, students with learning disabilities achieve approximately one year of mathematical understanding for every two years of school attendance (Miller & Mercer, 1997). This progress continues into adulthood, leaving students with learning disabilities behind their contemporaries (Raskind, Goldburg, Higgins, & Herman, 1999). All of this suggests the placement and accommodations associated with mathematics learning are important in the success of students with learning disabilities in higher education.

Placement and Accommodations Practices

Ofiesh and McAfee (2000) surveyed ninety-one college learning services programs to examine current use of psycho-educational evaluations such as the Wechsler Adult Intelligence Scale (WAIS) and the Woodcock-Johnson Tests of Cognitive Abilities and Tests of Achievement (WJ). They found that these tests were being consistently used for eligibility, placement, and accommodation determinations. For eligibility purposes, a diagnostician has a formal and systematic process for interpreting scores supported by research.

However, the process of how test scores are being used to determine accommodations and placement is much less structured and is widely undocumented through survey or empirical data at the postsecondary level. There is a strong need for further research to validate the practice of interpreting specific parts of psycho-educational test scores to make accommodation decisions (Ofiesh & McAfee, 2000). These decisions are often left to a learning services specialist who must make practical connections between test scores and available accommodations or courses. Many learning services providers do not feel comfortable with this process (Ofiesh & McAfee, 2000). This discomfort is due to lack of substantiating research as well as varying education and training levels of the providers asked to interpret testing results. Service providers are often forced to rely solely on their personal judgment, rather than validated criteria, when placing students.

At lower levels of education, psycho-educational and academic test scores are often used to place students and plan educational interventions, but the individuals who are interpreting the scores have an intimate relationship with the child's disability through school records and contact with the child, parents, and teachers. This intimate knowledge is often not available at the college level. Moreover, Ofiesh and McAfee (2000) stress an important difference in service at the postsecondary level: service needs to change from educational interventions to an emphasis on independence as well as accommodations. The psycho-educational diagnostic instruments may or may not provide the information needed to translate to specific accommodations and to place students in appropriate courses.

Research specific to the success of students with learning disabilities in university-required mathematics courses is lacking. Since the number of students with learning disabilities attending institutions of higher education is increasing dramatically (Henderson, 2001) and learning disabilities may change into adulthood (Nolting, 2000; Maller & McDermott, 1997; Gerber, Schnieders, Patadise, Reiff, Ginsberg, & Popp, 1990), it is important to know if university programs are adequately accommodating these students and placing them in courses appropriate to their needs.

Method

The goal of this study was to evaluate the effectiveness of a class reserved for students with learning disabilities and to make recommendations for placement criteria. The researcher hopes that using results from data that is readily available and provided to the university and the support services for students with learning disabilities will improve placement and accommodations decisions in university-required mathematics courses.

The population for this study is a group of students identified as having a learning disability who attended a university in the US between 1998-2002. These students had been diagnosed as having a learning disability by a licensed specialist and had used the academic support services at the university. The population selected consisted of 143 students who had full documentation and had taken the university-required mathematics course.

The research was conducted in three parts and included both qualitative and quantitative methods in analyzing student success (a grade of C or 2.0 on a 4.0 scale) in university-required mathematics courses. After approval from the university, data collection began with student information obtained through the Department of Mathematics and Statistics, Academic Support Center, and Enrollment Services.

The first part of the study examined success in the course enrolled. All students take a mathematics placement exam to ensure enrollment in an appropriate course. Of those who place in the lowest-level courses which will fulfill the university mathematics requirement, students have the choice of enrolling in one of two College Algebra-level courses: an open section of Finite Mathematics (Finite) or an open section of Elementary Mathematical Models (EMM). Students with learning disabilities may enroll in any open section but also have the option of enrolling in a special section of Elementary Mathematical Models reserved for students with learning disabilities (EMM-LD). The students served in these courses usually have at least one year of algebra in high school but are not necessarily headed for calculus. Both courses prepare students to go on to pre-calculus and calculus. They cover the same basic mathematical concepts but with very different approaches, one being a non-traditional mathematical modeling course and the other a traditional mathematics course. The non-traditional mathematical modeling course tends to look at the bigger picture and helps students to use their intuition in solving mathematical problems. The course is designed to teach students the mathematical concepts and language they need to succeed in this course as well as in general education classes such as economics, statistics, and chemistry. The traditional course is very textbook driven and consists of learning formulas and answering questions. Student performance in each of the three courses, EMM-LD, EMM, and Finite, was analyzed.

The second part of the research involved examining student documentation for predictors of student success for the course in which they were enrolled. Student documentation included: SAT scores; high-school GPA; high-school transcript information; full-scale intelligence and achievement test scores; gender; and grades in university-required mathematics courses. These previously identified variables were analyzed, individually and in combinations, for predictor variables for the students' performance in their university-required mathematics course. Regression analysis was used to explore variance in performance among the students.

The final part of the study was a survey of student satisfaction with accommodations in their university-required mathematics course. The survey was a small sampling of the population of students with learning disabilities who took the university-required mathematics course and was conducted through self-selection only. This qualitative data provided information on student perceptions of their experiences in university-required mathematics courses and the accommodations afforded them within the university.

Results

The researcher first examined the performance of students with learning disabilities overall and within the courses taken (see Table 1) using univariate analysis of variance and regression analysis testing where appropriate. The study population of 143 students with documented learning disabilities included 70 students enrolled in an open section of Finite Mathematics, 18 students in an open section of Elementary Mathematical Models, and 55 students in the section of Elementary Mathematical Models reserved for students with learning disabilities. Students enrolled in the reserved section (EMM-LD) performed significantly better (p=.003) than their peers enrolled in the open sections. The proportion of students enrolled in EMM-LD with passing is significant within the study group (All) (z=1.75, p=.0401). Approximately ninety-five percent of the students with learning disabilities in this section earned a grade of C or better (2.0 on a 4.0 scale) and the average grade for students with learning disabilities enrolled in this section was a B (3.13 on a 4.0 scale). Enrollment in the open sections of Finite and EMM is not significant (p=.947), which suggests that the students enrolled in the open sections perform similarly, with a grade of C or 2.46 and 2.44 (on a 4.0 scale) respectively. Enrollment in EMM-LD is significant when compared to the open sections of EMM (p=.032) and Finite (p=.001) individually.

Since students with learning disabilities perform significantly better in the reserved section, which suggests that the class format is important to their success, it is important to examine the differences between the reserved section and the open sections. All of the Finite Mathematics courses take a common final and have a set curriculum. The Elementary Models courses do not have a common final but follow the same basic curriculum. A quick review of the finals for all of the Elementary Models courses, including the LD course, did not reveal any significant differences in the amount or difficulty of the course material covered. The major differences between the reserved section of Elementary Models and the open sections of Finite Mathematics and Elementary Models are the limited enrollment, which allows for more personalized attention, and access to a class mentor. The class mentor meets with students on a regular basis to discuss class ideas, note-taking strategies, and general mathematics questions. The reserved section also meets three times a week, which gives students fifty minutes of instruction a week more than some of the open enrollment courses. All students with learning disabilities, regardless of course enrolled, are afforded general accommodations as recommended by their diagnostic specialist including, but not limited to, extended time on tests, a note taker, and a quiet place to take tests. The results of this study also suggest that students with learning disabilities tend to perform better in a non-traditional modeling course than they do in a traditional mathematics course.

The researcher next investigated predictors of student success (defined as the students' final grade in the university-required mathematics course), overall and within the courses taken, for each of the specified variables individually and in various combinations. Since reserved sections are not always available, it is important to know if students of a certain profile would have more chances for success if placed in a particular type of course and if the currently used placement criteria are sufficient in this manner. The first group of combinations tested included high-school transcript information, gender, SAT scores, and university-required mathematics course enrollment. Next, the researcher chose to look at combinations of these tests individually with selected variables from the first combination of high-school transcript information.

Overall, students with learning disabilities who performed well in eleventh-grade English, twelfth-grade English, and the Broad Written Language subtest of the Woodcock-Johnson Test (WJ), individually, may perform well in any section of the university-required mathematics course (see Table 2). The combination of enrollment in the Reserved Section of Elementary Models, ninth-grade mathematics performance, Broad Reading score (WJ), and eleventh-grade English performance was also shown to be significant in predicting student performance in university-required mathematics.

For students enrolled in open sections of Finite Mathematics, twelfth-grade English was the only individually significant predictor of student success (see Table 3). Students with high twelfth-grade English grades tend to also do well in Finite Mathematics. The most significant combination model to predict the success of students enrolled in Finite Mathematics includes performance in eleventh-grade mathematics and the Mathematics SAT score, although only eleventh-grade mathematics was the individually significant factor within the model and the Mathematics SAT score had a negative coefficient within the model.

Students with learning disabilities who perform well in ninth-grade mathematics, eleventh-grade English, twelfth-grade English, Vocabulary, and Applied Problems individually were significantly more likely to perform well in any section of Elementary Models than those students who did not perform well in these areas (see Table 4). The most significant combination model to predict student success for all sections of Elementary Models includes ninth-grade mathematics performance, eleventh-grade English performance, verbal SAT score, and the Full Scale IQ score from the WAIS. All the variables in the combination had positive coefficients within the model except Full Scale IQ.

Female students tend to get better grades than male students in the open sections of Elementary Models (see Table 5). The only other individual predictors for this section are within the Woodcock-Johnson subtests but, since few students from this group reported these scores, these results cannot be stated with confidence and are for reference only. Students with high Calculation (WJ), Applied Problems (WJ), and Dictation (WJ) subtest scores may perform well in the open sections of Elementary Models. The most significant combination to predict student success in the open sections of Elementary Models includes Performance IQ (WAIS), Verbal IQ (WAIS), overall high-school GPA, eleventh-grade mathematics performance, eleventh-grade English performance and gender. For the gender coefficient in the model, female students outperformed male students. Also, performance in eleventh-grade mathematics and eleventh-grade English had negative coefficients within the model. All the other in the combination model coefficients were positive. The researcher was not able to include the WJ-R in the combinations for the open sections of Elementary Models because there were too few reported cases.

Students who were successful in the reserved section of Elementary Models may have also performed well in ninth-grade mathematics, tenth-grade mathematics, tenth-grade English, eleventh-grade English, and twelfth-grade English (see Table 6). There were two highly significant combination models to predict student success in the reserved sections of Elementary Models. The first includes eleventh-grade English performance, ninth-grade mathematics performance, and ninth-grade English performance. Within this combination model, ninth-grade English performance and tenth-grade mathematics performance had negative coefficients. The second significant model includes gender, Broad Reading (WJ), Broad Mathematics (WJ), letter-word identification (WJ), passage comprehension (WJ), ninth-grade English performance, tenth-grade English performance, and eleventh-grade English performance. Within this combination model, female students outperformed male students and the Broad Mathematics score, letter-word identification score, and passage comprehension score had negative coefficients.

It is interesting to note that in no case, overall or within groups, did SAT Scores or overall high-school GPA present itself as an individually significant predictor of student success in university-required mathematics courses. Also, the most commonly used measure for placing students, mathematics course and test information, was not shown to be a good predictor of how a student will perform. Gender (females outperforming males) was shown to be a significant predictor for students success in the open sections of Elementary Mathematical Models but not for the reserved sections.

It is important to note that the Academic Support Center places many of the students in the mathematics course they feel is most appropriate given their learning disability profile. The factors considered for placement include, but are not limited to: WAIS Verbal IQ and Performance IQ; high-school math courses; WJ-R Calculation, Applied Problems, and reading subtests; and the student's report of strengths and weaknesses. Analysis of these placement factors showed no significant influence on student final grades in the mathematics course. However, since these factors affect placement and placement affects the final grade, it is import not to neglect the importance of these factors.

Finally, student satisfaction with accommodations in their university-required mathematics courses was tested. Overall, students with learning disabilities are satisfied with the accommodations they receive. Also, there is no significant difference in satisfaction between the students with learning disabilities in the reserved section of Elementary Models and the students with learning disabilities in open sections of Finite Mathematics and Elementary Models. This suggests that students with learning disabilities are receiving the accommodations they feel are necessary in all section of university-required mathematics.

Conclusions

Based on the results of this study, there are some important implications for many different groups within the university. Academic support services and those who make accommodation and placement recommendations should note that student documentation that is readily available to them can and should be used to support accommodations and placement of students into appropriate mathematics courses. Statistically significant predictors of student success were identified in this study which did not necessarily include the items widely thought to predict student success and used to place students, including many mathematics scores. SAT scores, overall GPA, and many of the achievement and intelligence test and subtest scores. This suggests that current placement and accommodation criteria should be further analyzed for validity.

Also, for university departments of mathematics, students with learning disabilities perform better in the non-traditional modeling course and significantly better in the reserved section, which suggests that the different learning approach and extra accommodations associated with this course are beneficial to their performance. Perhaps more universities should consider offering such courses.

For all involved in the mathematical education of students with learning disabilities, high-school English and, therefore, reading comprehension present themselves as significant factors in the success of students overall and within groups, while mathematics scores were much less significant, which highlights the importance of language and communication skills for students with learning disabilities enrolled in any section of university-required mathematics.

Implications for Future Research

Based on the results of this study, the researcher believes there are several courses available for additional research in this area. This study was limited to the data available for students with learning disabilities with full documentation who had taken one of the university-required mathematics courses at a particular university during a four-year time period. This certainly limits the number of participants and the amount of usable data. The researcher would recommend a larger study involving various universities. With a larger study, a researcher could also examine more closely predictors for various types of learning disabilities and the effectiveness of specific accommodations and be more confident in making generalizations to other programs.

This research was also limited in that there was no data on the amount and type of services utilized by students or when the students disclosed their learning disability to the university and requested services. The researcher would recommend a study to examine the effect these factors on student performance in university-required mathematics courses.

Also, the survey of satisfaction component to this study was limited to a self-selected group of students surveyed after completing the course and receiving a grade. Their perceptions of how well they were accommodated may have been influenced by their final grade in the course. They students may have also forgotten many of the accommodations afforded them by the time they completed the survey. The researcher recommends a study of LD student satisfaction with accommodations where the survey is given to all students before the end of the course in a manner similar to course evaluations.

Reading comprehension and high-school English scores emerged as significant predictors of LD student success in university-required mathematics courses. This suggests that more research needs to be conducted on the importance of reading comprehension in university-level mathematics courses as well as how to compensate for deficiencies in this area.

Selected References

Alster, E.H. (1997). The effects of extended time on algebra test scores for college students with and without learning disabilities. Journal of Learning Disabilities, 30(2), 222-227.

Gerber, P.J., Schnieders, C.A., Patadise, L.V., Reiff, H.B., Ginsberg, R.J., & Popp, P.A. (1990). Persisting problems of adults with learning disabilities: Self-reported comparisons from their school-age and adult years. Journal of Learning Disabilities, 23(9), 570-573.

HEATH Resource Center. (n.d.). Success in college for adults with learning disabilities. HEATH Resource Center: The National Clearing House on Postsecondary Education for Individuals with Disabilities. Retrieved December 17, 2001, from http://www.heath.gwu.edu/Success.html

Henderson, C. (2001). College freshmen with disabilities: A biennial statistical profile. Washington, DC: American Council on Education.

LaMorte, M.W. (2002). School law: Cases and concepts. Boston: Massachusetts: A Pearson Education Company.

Maller, S.J., & McDermott, P.A. (1997). WAIS-R profile analysis for college students with learning disabilities. School Psychology Review, 26(4), 575-585.

Miller, S.P., & Mercer, C.D. (1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1), 47-56.

National Joint Committee on Learning Disabilities (NJCLD). (1999, January). Learning disabilities: Issues in higher education. ASHA Desk Reference, 1999 Edition, in press.

Nolting, P.D. (2000). Mathematics and learning disabilities handbook: Guide to processing deficits and accommodations. Bradenton, FL: Academic Success Press.

Ofiesh, N.S., & McAfee, J.K. (2000). Evaluation practices for college students with L.D. Journal of Learning Disabilities, 33(1), 14-25.

Raskind, M.H., Goldburg, R.J., Higgins, E.L., & Herman, K.L. (1999). Patterns of change and predictors of success in individuals with learning disabilities: Results from a twenty-year longitudinal study. Learning Disabilities Research and Practice, 14(1), 35-49.

Renaud, A. (1996). Marginal beginnings but great endings. In L.L. Walling (Ed.), Hidden abilities in higher education: New college students with disabilities [Monograph] (pp. 77-53). Columbia, SC: University of South Carolina.

Scheid, K. (1990). Cognitive-based methods for teaching mathematics to students with learning problems. Columbus, Ohio: LINC Resources, Inc.

Thomas, S.B. (2000). College students and disability law. The Journal of Special Education, 33(4), 248-257.

Vogel, S.A., & Adelman, P.B. (1992). The success of college students with learning disabilities: Factors related to educational attainment. Journal of Learning Disabilities, 25(7), 430-441.

Brooke Evans, Ph.D.

The Metropolitan State College of Denver 

Table 1. LD Student Success in the University-Required Mathematics
Course.

        Mean Class Grade Point  Proportion of Students with
Course  Average (GPA)           Passing Grades(n)

All     2.71                    .88 (143)
Finite  2.44                    .86 (70)
EMM     2.46                    .78 (18)
EMM-LD  3.13                    .95 (55)

Table 2. Predictors of Student Success, All LD Students (n=143)

Variable Tested                                       Significance

Eleventh-Grade English Performance                    p=.048
Twelfth-Grade English Performance                     p .001
Broad Written Language WJ Score                       p=.035
Combination of enrollment in the Reserved Section of  p=.017
  Elementary Models, ninth-grade mathematics, Broad
  Reading WJ, and eleventh-grade English

Table 3. Predictors of Student Success, Finite Mathematics (n=70)

Variable Tested                                           Significance

Twelfth-Grade English Performance                         p=.006
Combination of mathematics SAT scores and eleventh-grade  p=.014
  mathematics performance

Table 4. Predictors of Student Success, All Sections of EMM (n=73)

Variable Tested                                          Significance

Ninth-Grade Mathematics Performance                      p=.019
Eleventh-Grade English Performance                       p=.009
Twelfth-Grade English Performance                        p=.002
Vocabulary Score                                         p=.036
Applied Problems Score                                   p=.026
Combination of ninth-grade mathematics performance,      p=.003
  eleventh-grade English performance, verbal SAT score,
  and the Full Scale IQ Score

Table 5. Predictors of Student Success, Open Sections of EMM (n=18)

Variable Tested                                            Significance

Gender                                                     p=.004
Calculation WJ* Score                                      p=.032
Applied Problems WJ* Score                                 p=.012
Dictation WJ* Score                                        p=.04
Combination of WAIS Performance IQ Score, WAIS Verbal      p=.025
  IQ Score, Eleventh-Grade Mathematics Performance,
  Eleventh-Grade English Performance, Overall High-School
  GPA, and Gender

*Not enough data to be reported with confidence--for reference only

Table 6. Predictors of Student Success, Reserved Section of EMM (n=55)

Variable Tested                                             Significance

Ninth-Grade Mathematics Performance                         p .001
Tenth-Grade Mathematics Performance                         p=.032
Tenth-Grade English Performance                             p=.008
Eleventh-Grade English Performance                          p=.001
Twelfth-Grade English Performance                           p=.003
Combination of eleventh-grade English performance, tenth-   p=.001
  grade mathematics performance, tenth-grade English
  performance, ninth-grade mathematics performance, and
  ninth-grade English performance
Combination of gender, Broad Reading Score (WJ), Broad      p .001
  Mathematics Score (WJ), letter-word identification score
  (WJ), passage comprehension score (WJ), ninth-grade
  English performance, tenth-grade English performance,
  and eleventh-grade English performance.