DIFFERENTIATING STUDENTS WITH
MATHEMATICS DIFFICULTY IN COLLEGE:
MATHEMATICS DISABILITIES VS. NO DIAGNOSIS


Sean M. McGlaughlin, Andrew J. Knoop, and Gregory A. HoUiday 

Abstract. Difficulties with college algebra can be the gatekeeper 
for earning a degree. Students struggle with algebra for 
many reasons. The focus of study was to examine students struggling 
with entry-level algebra courses and differentiate between 
those who were identified as having a mathematics disability and 
those who were not. Variables related to working memory, math 
fluency, nonverbal/visual reasoning, attention, and reading were 
analyzed using a MANOVA and separate ANOVAs. Significant differences 
were found on all but attention, supporting the findings 
of research on students in elementary and secondary education. 
Implications include a focus on techniques that help to remediate 
these specific deficits. 

SEAN M. MCGLAUGHLIN, M.A., is a doctoral student. University of Missouri-Columbia.
ANDREW J. KNOOP, Ph.D., is a clinical assistant professor, University of Missouri-Columbia.
GREGORY A. HOLLIDAY, Ph.D., is a clinical associate professor. University of Missouri-Columbia.


By understanding students struggling with mathemat-Gerber, 1993). This is especially the case for instrucics 
at the postsecondary level, professionals can offer het-tional or remediation interventions. Consequently, 
ter assistance both during and before college and can researchers often present results involving elementary 
help identify appropriate remediation techniques. and secondary students as part of their literature 
Approximately 5-6% of students have significant diffi-reviews, generalizing this information to students at 
culty in mathematics (Fleischner & Manheimer, 1997), the college level. Because enrollment in postsecondary 
and many struggling students are not identified as settings by students with documented learning diffirequiring 
special services for math during secondary culties is increasing, researchers must begin to focus on 

school. It is becoming increasingly evident that students the needs of this population of students (Mercer, 1997). 
need help understanding mathematics, especially with 
the world rapidly evolving scientifically and mathema-STUDENTS WITH MATHEMATICS 
tically. Many college students encounter mathematics DISABILITY 
difficulties, which can eventually act as a gatekeeper to Research on students with mathematics disabilities 
earning a college degree. often consists of comparisons with other disabilities. 

Little research has been published on college students That is, students with reading disabilities (RD), disorders 
experiencing mathematics difficulties compared to ele-of written expression (WD), and mathematics disabilimentary 
and secondary students having difficulties ties (MD) and combined reading/mathematics disorders 
with mathematics (Strawser & Miller, 2001; Zawaisa & (RD/MD) are compared and contrasted between and 

Volume 28, Summer 2005 223 


among disability groups to establish shared and disparate 
attributes (Benton, 2001; Greene, 2001; Rourke, 
1993; Shafrir & Siegel, 1994). Commonly, these studies 
focus on elementary and secondary students, highlighting 
the need for research at the postsecondary level. 

Normally achieving (NA) students often make up a 
fourth group in such comparisons. From the comparisons 
made, several sources of individual differences 
can be extracted, including deficiencies in (a) reading 
ability, (b) nonverbal/visual skills, (c) working memory, 

(d) poor math fluency, and (e) attention and/or hyperactivity. 
Reading Comprehension and MD 

Fleischner and Manheimer (1997) identified two primary 
reasons why students struggle with mathematics. 
First, some students exhibit difficulty in reading comprehension. 
Comprehension difficulties seem to exacerbate 
difficulties in mathematics, especially for solving 
word or story problems. Examining NA students and 
students with MD, RD, and MD/RD, Jordan and Hanich 
(2000) demonstrated that when asked to solve four 
types of problems (number facts, story problems, place 
value, and written calculation), the students with 
MD/RD performed significantly lower than NA students. 
Further, the students with MD only performed 
lower on complex story problems compared to the NA 
students. Students with RD performed similarly to the 
NA students. Overall, students with MD/RD and MD 
significantly underperformed the students with RD and 
NA students on mathematics-related tasks. 

Nonverbal Reasoning and MD 

Fleischner and Manheimer (1997) also asserted that 
some students exhibit difficulties in nonverbal reasoning 
and/or primary mathematics knowledge. Rourke 
and his colleagues (Rourke, 1993; Rourke & Del Dotto, 
1994; Rourke & Fuerst, 1996) have made significant 
contributions to the field of learning disabilities by 
studying nonverbal learning disability and its relationship 
to reading and mathematics disorders from a neurological 
perspective. 

Rourke (1993) summarized several of these studies 
conducted with children with learning disabilities (LD) 
using a variety of assessment measures, including the 
Wechsler Intelligence Scale for Children (WISC) and 
Woodcock-Johnson Tests of Achievement (WJ). Among 
the three main clinical groups, Rourke and his colleagues 
identified differences between students with RD 
and MD, noting that students with RD typically have 
verbal deficits whereas students with MD typically have 
nonverbal deficits, as measured by the discrepancy 
between VIQ and PIQ measures on the WISC. "Qlder 
group [RD] children exhibit normal levels of performance 
on visual-spatial-organizational, psychomotor. 

and tactile-perceptual tasks; group [MD] children have 
outstanding difficulties on such tasks" (p. 220). 

Additional findings were presented by Rourke and 
Fuerst (1996) and Rourke and Del Dotto (1994). For 
specifics on the range of studies that make up the preceding 
three studies, the interested reader is referred to 
Rourke and colleagues' publications on students with RD 
and MD. Rourke originally referred to MD as MD, but 
later changed to NLD (nonverbal learning disabilities). 
For the purposes of this article, Rourke's NLD group is 
referred to by his initial identification of MD. 

According to Silver, Pennett, Black, Fair, and Balise 
(1999), visuo-spatial deficits may be the core deficit for 
students with isolated mathematics disorders, yet subtype 
stability is poorer for the arithmetic-only group. In 
a literature review, Jordan (1995) found three subtypes 
of mathematics disabilities, including one identified as 
having visuo-spatial deficits, similar to the nonverbal 
deficit discussed by Rourke. 

Geary (1993) examined visuo-spatial deficits as one 
of three core difficulties (along with semantic memory 
and procedural deficiencies) experienced by students 
with calculation difficulties. Cirino, Morris, and Morris 
(2002) further explored Geary's theory on a sample 
of college students using a comprehensive battery 
of assessment instruments, Wechsler Adult Intelligence 
Scale-Revised and Woodcock-Johnson Tests of 
Achievement-Revised, along with a variety of other 
neuropsychological instruments. They determined that 
visuo-spatial deficits did not contribute to the calculation 
difficulties experienced by this sample. However, 
they did find evidence that Geary's other two categories 
of deficiency - semantic memory deficits and 
procedural deficits - contributed to the calculation difficulties 
of college students. 

Working Memory, Math Fluency, and MD 

Geary (1993) described semantic memory deficits 
and procedural deficits, arguing that they could be 
related to an underlying memory deficit. Semantic memory 
deficits include difficulties in fact retrieval and in 
learning mathematic facts to the point that they 
become automatic or retrieved directly from long-term 
memory. Students with this deficit continue to mentally 
calculate the answers rather than obtain them 
through direct retrieval. Procedural deficits are considered 
more problematic and pervasive, causing faulty 
procedures that are learned with errors. Students with 
this deficit are more likely to use inappropriate developmental 
procedures because they appear to struggle 
with remembering the appropriate ways to complete 
certain problems. An oversimplified example of a faulty 
procedure might be to learn that a plus sign means subtracting 
instead of adding. 

Learning Disability Quarterly 224 


Swanson (1993, 1994) investigated working memory 
in children with and without LD. He defined working 
memory as "the system of limited capacity for the temporary 
maintenance and manipulation of information" 
(Swanson, 1994, p. 190). Students were operationally 
defined as having an LD if they had scores that were 
one half standard deviation below the mean or having 
scores on the Wide Range Achievement Test-Revised 
(WRAT-R) that were below the 25th percentile for their 
age. Normally achieving students were identified as 
those having scores equal to or above the 50th percentile 
for their age. Students were excluded in both 
cases if their scores were deemed due to "retardation, 
poor teaching, or cultural deprivation" (Swanson, 1994, 

p. 192). Using a variety of memory measures, Swanson 
found that students with LD had particular difficulties 
in several areas of working memory compared to NA 
students. Further, he (1994) demonstrated that differences 
in verbal working memory were not as discrepant 
from NA students as were students considered to be 
slow learners, but were discrepant nonetheless. McLean 
and Hitch (1999) found that students with arithmetic 
difficulties were impaired on spatial working memory 
and executive processing. 
Geary, Hoard, and Hamson (1999) investigated the 
digit-span scores of first graders and found that "average 
IQ children with low arithmetic achievement scores 
have difficulties retaining information in working 
memory while engaging in a counting task" (p. 235). 
Further, they demonstrated that students with MD/RD 
and students with RD committed higher numbers of 
retrieval errors than the students with RD alone. 
However, the authors acknowledged that this may not 
necessarily be due to a working memory deficit, but 
a deficit in attentional capacity. 

Retrieval and reaction time can be linked to working 
memory as well. For example, Hayes, Hynd, and 
Wisenbaker (1986) found that students with LD had 
difficulty building facts into math fluency. Thus, compared 
to normally achieving peers, groups of students 
with LD had more difficulty in recalling basic facts and 
thus made more errors. In addition, these students were 
more variable when making those errors. 

Geary, Brown, and Samaranayake (1991) found similar 
results in groups of flrst and second graders. When 
comparing NA students and students with MD, the NA 
students were not as likely to rely on counting procedures, 
a less than optimum strategy when building 
math fluency, and were more likely to rely on memory 
for recalling basic facts. Students with MD still relied 
on the counting procedures and not on memory. 
According to Geary et al. (1991), this poor working 
memory not only affects retrieval, it can lead to errors 
in procedure such as counting errors, which can lead 

to memorization of wrong facts (e.g., 7 + 6 = 12). All 
of these compounded can cause further difficulty for 
students struggling with math. 

In studies designed to look at the effects of time on 
students with and without MD, Alster (1997) and 
Jordan and Mantani (1997) demonstrated that students 
with MD in grades 3 through 12 did better on tasks 
when their retrieval ability was not tested by time. Thus, 
both studies demonstrated that when doing algebraic 
and word problems, students with MD performed 
poorer than students without MD when time was 
involved, but were similar to students without MD 
when there was no time limit. Both studies inferred that 
short-term memory and semantic memory difficulties 
may be the reason that timed tests have an effect. 
Jordan and Mantani (1997) found that this is especially 
true for people with speciflc mathematics difficulties 
rather than general academic difficulties. 

AD/HD and MD 

When examining LD subtypes, some researchers 
include students with attention-deficit disorders in their 
analyses and discussion (Hurley, 1996; Marshall, 
Schafer, O'Donnell, Elliott, & Handwerk, 1999; Rourke, 
1993). While 3% of children in the United States have 
LD, approximately 35% of children with AD/HD have 
learning difficulties (Woodrich, 2000). Mayes, Calhoun, 
and Crowell (2000) studied a sample of 8- to 16-yearolds 
with and without AD/HD. The group was set up to 
be as similar as possible to those referred to clinical settings. 
These researchers found that the proportion of 
LD among AD/HD students was significantly higher 
than for the sample of students without AD/HD. 
Mathematics had the second highest comorbidity, with 
approximately 33% of the students with AD/HD also 
having MD diagnoses. 

Research is sometimes conducted with students with 
AD/HD to compare their profiles to those of students 
with LD; at other times, studies address the comorbidity 
of these two disorders. Riccio, Gonzalez, and Hynd 
(1994) suggested that the comorbidity of AD/HD and 
LD is so high that the two may be indistinguishable. 
Attention-related concerns affect achievement and 
must be explored when analyzing students struggling in 
math. 

Postsecondary Intervention 

Thus far, this literature review has focused on common 
difficulties among students with MD in order to 
aid practitioners in identifying students with MD as 
well as begin to focus on remediation. Again, empirical 
evidence for effective interventions for postsecondary 
students struggling with mathematics is, at best, scarce, 
with much of the intervention literature focusing on 
elementary and secondary education. Thus, Strawser 

Volume 28, Summer 2005 225 


and Miller (2001) noted that "the literature is silent" on 
the utility of generalizing to other populations those 
intervention techniques that have been empirically 
demonstrated to be successful with elementary and secondary 
students. 

Current Study 

The following analysis explored the characteristics of 
college students with mathematics difficulties who were 
subsequently identified as having mathematics disabilities. 
Because lower-than-average abilities on measures of 
mathematics achievement were expected among this 
population, mathematics achievement scores were not 
explored in depth. 

The importance of this study lies in its ability to add 
supporting or refuting evidence of the presence of previously 
identified sources of individual differences in 
students with MD by analyzing similar assessment 
measures and examining the results to determine if the 
difficulties that exist in younger populations also exist 
at the postsecondary level. A preliminary discussion on 
remediation techniques based upon the results is also 
included. 

METHOD 

Participants 

Participants consisted of undergraduate students 
attending a public research university in the midwest 
with a student body representative of the general mid-
western population. All participants reported experiencing 
significant difficulties when attempting to complete 
the mathematics course requirements for their degree. 
Participants were full-time students who, at the time of 
the evaluation, needed to earn course credit in at least 
one college-level mathematics course to fulfill their 
degree requirements. 

Potential participants were referred by their academic 
advisors or instructors, or were self-referred through 
"word of mouth." To qualify as a research participant, 
each student underwent and passed an initial screening 
interview conducted by the researchers to document (a) 
the student's need for additional course credit in a college-
level mathematics course, and (b) significant evidence 
of current and previous mathematics difficulty, 
such as low grades in high school mathematics courses, 
low ACT mathematics scores, and/or significant self-
reported difficulties in understanding mathematics-
related concepts compared to concepts in other subject 
areas. Students who successfully completed the screening 
process were asked to volunteer as participants; 
those who agreed were administered the psychoeducational 
assessment battery. 

In all, 205 students completed at least some of the 

psychoeducational battery. A total of 129 participants 

were removed because their diagnostic categories did 
not match the identified groups used in this study - MD 
and no diagnosis (ND) - or because they did not complete 
significant portions of the evaluation. This left 76 
participants for the analysis. 

Overall, 34 participants were identified as MD and 42 
as ND. The database included MD participants ranging 
from 18 to 23 years of age, with a mean age of 20.6 
years, and ND participants ranging from 18 to 43 years 
of age, with a mean age of 22.9 years. The mean 
attained ACT composite score for MD was 21.6 and 21.7 
for ND, with ranges of 14 (scores from 15 to 29) and 
12 (scores from 16 to 28), respectively. The database 
consisted of 53 females (27 ND; 26 MD) and 23 males 
(15 ND; 8 MD), who identified themselves as Caucasian, 
68 (36 ND; 32 MD), African-American, 7 (5 ND; 2 MD), 
and Hispanic, 1 (1 ND; 0 MD). Table 1 shows participant 
characteristics. 

Instrumentation 

To investigate and describe the characteristics of college 
students with math difficulties, the researchers 
administered a complete psychoeducational evaluation 
battery to each of the participants: structured interview, 
the Wechsler Adult Intelligence Scale-Third Edition 
(WAIS-III) (Wechsler, 1997a), the Wechsler Memory 
Scale-Third Edition (WMS-III) (Wechsler, 1997b), the 
Woodcock-Johnson-III Tests of Achievement (WJ-III) 
(Woodcock, McGrew & Mather, 2001), and the Conners 
Adult ADHD Rating Scale (CAARS) (Conners, Erhardt, & 
Sparrow, 1998). 

WAIS-III. The WAIS-III is an appropriate tool for 
measuring general levels of cognitive functioning for 
individuals aged 16 to 89. A complete administration of 
the WAIS-III yields three composite IQ scores (Full Scale, 
Verbal, and Performance) and four index scores (Verbal 
Comprehension, Perceptual Organization, Working 
Memory, and Processing Speed). The WAIS-III consists 
of 14 subtests, 7 each in the Verbal and Performance 
scales (Wechsler, 1997a). 

WMS III. The WMS-III is an individually adminis


tered test of verbal and nonverbal memory for adoles


cents and adults aged 16 to 89. It is useful in educational 

settings to (a) assess the degree to which an individual's 

memory functioning impacts academic performance, 

(b) assist in developing individualized education programs, 
or (c) recommend external strategies or memory 
training to assist those with learning disorders. The 
test consists of 11 subtests, 6 primary subtests, and 5 
optional subtests (Wechsler, 1997b). 
WJ-III. The WJ-III is an individually administered, 
norm-referenced test of academic achievement that can 
be administered to individuals from age 2 to over 90. 
When combined with other pertinent information, the 

Learning Disability Quarterly 226 


Table 1 
Sample Characteristics—Mathematics Disabilities (MD) vs. No Diagnosis (ND) 
Mathematics Disability No Diagnosis 

Numbers: 

Male 

Female 

Total 

Age: 

Mean 

Range 

Race/Ethnicity: 

Caucasian 

African-American 

Hispanic 

Total 

Overall Academic Achievement'' 

Mean 

SD 

Range 

"ACT scores. 

results of the WJ-III aid in developing educational programming 
and appropriate services for reading, writing, 
oral language, or math skills. The test consists of 12 sub-
tests within the Standard Battery, yielding composite 
standard scores in Broad Reading, Broad Mathematics, 
Broad Written Language, and Oral Language Cluster 
(Mather & Woodcock, 2001). 

CAARS. The CAARS is a self-report rating scale that 
provides a quantitative measure of ADHD sjonptoms for 
adults over the age of 18. The CAARS consists of 66 items 
presented in a 4-point Likert-style format that contribute 
to nine empirically derived scales. The CAARS includes 
four factor-derived subscales: Inattention/ Memory Problems, 
Hyperactivity/Restlessness, Impulsivity/Emotional 
Lability, and Problems with Self-Concept. Additionally, 
three ADHD symptom subscales are generated, including 
Inattentive Symptoms, Total ADHD Symptoms, and Hyperactive-
Impulsive Symptoms. The CAARS may be utilized 
to help identify, assess, and treat adults with ADHD-
related symptoms and behaviors (Conners et al., 1998). 

8 
26 
34 

20.6 
18-23 
32 
2 
0 
34 

21.6 
3.3 
15-29 

15 
27 
42 

22.9 
18-43 
36 
5 
1 
42 

21.7 
3.1 
16-28 

From this battery of tests, six individual variables were 
selected to analyze differences between students with 
MD and ND. These variables, representing the sources 
of individual differences identified by previous research, 
were as follows: (a) the WMS-III Working Memory 
Index score (WM), (b) the WJ-III Math Fluency (MF) 
subtest score, (c) the WJ-III Passage Comprehension 
(PC) subtest score, (d) the WAIS-III Performance 
Intelligence Quotient (PIQ), (e) the WAIS-III Verbal 
Intelligence score (VIQ) minus the PIQ score, and (f) the 
CAARS DSM-IV Total Symptoms Index score (DSM-IV 
TSI). 

Procedure 

To test the significance of observed differences in the 
mean scores of the two groups on each of the six variables 
that represent sources of individual differences, a 
multiple analysis of variance (MANOVA) was used. 
MANQVA is an extension of the ANQVA method to 
cover cases where there is more than one dependent 
variable. 

Volume 28, Summer 2005 227 


Conducting the MANOVA reduced the chances of a 
Type I statistical error. Assumptions of MANOVA must 
be met before analysis was completed; namely (a) independence 
of observations, (b) multivariate normality, 
and (c) a check of covariance among the variables. First, 
independence of observations was assumed for the data. 
Due to the difficulty of checking for multivariate normality 
in SPSS (Stevens, 1999), the variables were tested 
for univariate normality. The assumption of univariate 
normality was met for each of the variables; thus, the 
second assumption was met. Because Box's test is 
affected by non-normality, it can be a good indicator of 
violations of multivariate data. Also, it helps to determine 
any covariance among the three variables, and is 
the third assumption of MANOVA. Box's test determined 
covariance among the variables and was not significant. 
Thus, the third assumption was also met 
(Stevens, 1999). 

With Type I statistical error ruled out, a one-way 
analysis of variance (ANOVA) was used to test the significance 
of observed differences in the mean scores 
between the two groups on each of the six variables that 
represent sources of individual differences. ANOVA is a 
statistical analysis that utilizes one categorical independent 
variable (diagnostic group) and one continuous 
variable (source of individual difference). 

Table 2 

RESULTS 

The results of the MANOVA indicated significant differences 
among the variables. Thus, all four of the statistics 
produced by SPSS were significant. The Pillai's 
Trace, Wilk's Lambda, Hotelling's Trace, and Roy's 
Largest Roots all had the same statistical value, significance 
level, p value, effect size, and power. The statistic 
was F(6, 69) = 8.499, p < .000, with an effect size of .425, 
indicated by a partial eta squared and a power of 1.000. 
Separate ANOVAs were run to determine which of the 
variables were significantly different between the two 
groups. Results showed that the PIQ, WM, MF, and PC 
were all significantly different when comparing students 
with MD and ND. Results of the ANOVA for PIQ 
indicated an f(l, 74) = 6.960, p < .01, with an effect 
size, indicated by a partial eta squared, of .086 and a 
power indicated at .740. Results of the ANOVA for WM 
indicated an f (1, 74) = 16.050, p < .000, with an effect 
size, indicated by a partial eta squared, of .178 and a 
power of .977. Results of the ANOVA for PC indicated 
an f(l, 74) = 3.991, p < .049, with an effect size, indicated 
by a partial eta squared, of .051 and a power of 
.505. Results of the ANOVA for MF indicated an F{1, 74) 
= 33.939, p< .000, with an effect size, indicated by a 
partial eta squared, of .314 and a power of 1.000. The 

Descriptive Statistics—Mathematics Disabilities (MD) vs. No Diagnosis (ND) 

Instrument 

PIQ"* 

VIQPIQDF 

WJPASCOM" 

WJMTHFLU"** 

WMSWM"** 

DSMIVADHD" 

'n=42. 

''n=34. 

•^Normative sample mean = 100; SD = 15. 
""Normative sample mean = 50; SD = 10. 
*p<.05. "p<.01.***p<.000. 
Mathematics Disability^ No Diagnosis'' 
Mean SD Mean SD 

98.59 12.82 106.02 11.71 
9.59 12.52 4.17 11.70 
101.29 11.77 106.14 9.40 
82.94 8.41 97.10 11.97 
92.65 11.75 101.74 7.97 
50.97 15.88 50.45 8.88 
Learning Disability Quarterly 228 


results for the other two variables (VIQ/PIQ difference 
and ADHD Total Symptoms) were not significant. Table 
2 shows the mean and standard deviations for students 
with MD and ND on each of the variables analyzed. 

DISCUSSION 

The results of this study suggest that students with 
mathematics disabilities at the college level tend to mirror 
research findings for students identified with mathematics 
disabilities at the elementary and secondary 
levels. 

Among the similarities, college students identified 
with mathematics disabilities demonstrate significant 
weaknesses in reading comprehension, nonverbal reasoning, 
working memory, and math fluency. Interestingly, 
attention difficulties, which have been identified 
as a source of individual differences in elementary and 
secondary students, were found not to be a significant 
distinguishing factor between students with MD and 
ND in this study. 

Reading Comprehension 

The results support previous findings that students 
with MD have difficulty with reading comprehension 
(Fleischner & Manheimer, 1997; Jordan & Hanich, 
2000). For example, on the WJ-III Passage Comprehension 
score, students with MD scored lower than students 
with ND, indicating that they had more difficulty 
understanding contextual clues relating to reading 
comprehension. 

Nonverbal Reasoning 

Rourke (1993), Rourke and Fuerst (1996), and Rourke 
and Del Dotto (1994) discussed nonverbal/visual-spatial 
discrepancies among students with MD. Our results 
indicate that when compared to students with ND, the 
students with MD had significantly lower WAIS-III PIQ 
subtest scores; however, the VIQPIQDF scores were not 
significantly different. This provides some supporting 
evidence to findings of visual-spatial deficits and nonverbal 
difficulties for students with MD at the college 
level. 

Working Memory and Math Fluency 

Previous researchers have concluded that memory, 
especially working memory, is a deficit area for students 
with MD (Geary, 1993; Geary et al., 1991; McLean 
& Hitch, 1999; Swanson, 1993, 1994). In the current 
study the WMS-III measure demonstrated that college 
students diagnosed with mathematics disorders had 
difficulty with working memory above and beyond 
that of students who struggle with mathematics who 
are not diagnosed. 

Math fluency scores based upon the WJ-III Math 
Fluency subtest score were, on average, one standard 
deviation lower for students with MD than for students 

with ND. In fact, on average, their score nearly fell in 
the low instead of low-average range. This is consistent 
with past findings showing math fluency to be problematic 
(Geary 1993; Geary et al., 1991; Hayes et al., 
1986; Jordan & Mantani, 1997). 

While math fluency may be closely related to working 
memory capacity, it may also be affected by other variables. 
Students with higher levels of math fluency (or 
automaticity with math facts) are more likely to utilize 
their finite working memory capacity for other calculation 
processes, or "chunking" more relevant content at 
one time. However, the level of math fluency can also 
be negatively impacted by inattention, depression, and 
high or low degrees of anxiety, as well as other factors 
that are not directly related to working memory. 

AD/HD 

The results of the AD/HD measure did not distinguish 
the two groups. Thus, our results with a college student 
population do not support Riccio and colleagues' (1994) 
assertion that the comorbidity of AD/HD and LD is so 
high that the two may be indistinguishable. However, 
this does not preclude the likelihood that attention-
related symptoms are important factors that need to be 
addressed. We strongly advocate that further research 
be conducted to examine the effect of AD/HD symptoms 
on students with mathematics disabilities and students 
in general at the college level. 

Intervention 

We now turn to remediation and/or accommodation. 
While not meant to be comprehensive, this discussion 
is intended to spark further research into effective remediation 
and intervention strategies suitable for college 
students with mathematics difficulties. 

Based upon our results, it appears there are factors 
other than IQ-achievement discrepancies that affect 
classroom performance. When faced with trying to 
meet the needs of students with LD in mathematics, 
universities have traditionally emphasized academic 
supports, such as classroom accommodations (e.g., 
extended time to complete examinations) and increased 
access to tutoring and individualized assistance. 
While these supports are aimed at increasing the 
performance of students with documented disabilities, 
they do little to address the wider variety of differing 
abilities of students who do not have documented disabilities 
but experience significant difficulty when performing 
math tasks. 

One emerging trend in providing support for all 
learners, regardless of disability status, is to implement 
classroom presentation methods that engender concepts 
aligned with the universal design for learning 
(UDL), as advocated by Rose, Meyer, Strangman, and 
Rappolt (2002). The three principles of the UDL frame-

Volume 28, Summer 2005 229 


work promote classroom instruction that provides for 

(a) multiple, flexible methods of content presentation; 
(b) multiple, flexible methods of content expression; 
and (c) multiple, flexible options for individual engagement 
in the material being presented. Within the UDL 
perspective, existing curriculum materials can be presented 
with the necessary flexibility to support the 
diverse learning needs of a variety of students. UDL 
instructional concepts intentionally provide multi-
modal learning support for all students in a classroom, 
allowing each student to assimilate new content in ways 
that are most efficacious for the individual learner, as 
opposed to a traditional, single instructional method. 
Students with MD not only need remediation with 
specific mathematics techniques, they also need remediation 
techniques specifically designed to address 
deficits in reading comprehension, nonverbal/visual 
skills, working memory, and math fluency. Levine 
(1999) identified academic strategies that can be used to 
provide learning support for these deficits. With regard 
to math fluency deficits, Levine suggested that students 
utilize flashcards to develop automaticity for basic 
arithmetic and more advanced algebraic concepts, calculations, 
and manipulations. Mathematics-related 
computer software will help hold a student's attention 
while rehearsing common calculations. Finally, students 
may choose to rehearse, or automatize, common 
calculation methods and multiple-step processes within 
an overall solution. 

For working memory deficits, Levine (1999) advocated 
that students concentrate on performing one task 
or subtask at a time, develop definite and consistent 
stepwise approaches to problem solving as opposed to 
tackling the entire problem at once, use self-monitoring 
techniques (talking their way through a problem) to aid 
in problem solution, and practice extended arithmetic 
problems in their head (such as 23 x 22, or 4 x 7 x 3) to 
develop working memory capacity. Students may also 
find it beneficial to summarize complex instructions or 
solution processes before attempting the solution. 

For nonverbal reasoning deficits,' Levine (1999) recommended 
the use of graph paper to aid in the spatial 
placement of numbers and as well as the use of manipulatives 
or concrete applications of the math concept as 
an example of the problem to be solved. Instructional 
techniques should incorporate a highly verbal approach 
of explaining mathematical or geometric concepts 
rather than relying solely on algebraic notations and 
graphical plots. 

Finally, for reading comprehension deficits, Levine 
(1999) suggested that students incorporate visual models 
to accompany written explanations. Students should 
also develop an individualized mathematics glossary of 
terms and concepts used in class so they can be 

reminded of these definitions as they complete homework 
assignments. Math-related computer software can 
increase mathematical conceptual understanding, and 
the development of good estimating skills can serve as 
a self-check mechanism. Further, Levine suggested that 
instruction, including ways to translate specific words 
into numerical symbols or processes, would support a 
student's mastery of word problems. 

Implications for Practice 

For practitioners working with students with MD, two 
important pieces of information are gained from this 
research. First, once students have been identified as 
having MD, it is important to focus on each individual 
to determine his or her specific strengths and weaknesses. 
Although we present common characteristics for 
the sake of simplicity, it is important to recognize that 
students with MD are a heterogeneous group of individuals 
with different weaknesses that contribute to 
their difficulties in math (Fleischner & Manheimer, 
1997; Parmar & Cawley, 1997; Strawser & Miller, 2001). 
Information gained from this study can aid in creating 
initial hypotheses to gain insight into the strengths and 
weaknesses of individual students. Specific remediation 
techniques must subsequently be explored. 

Second, it is important to recognize the need for techniques 
that not only focus on intervention of specific 
mathematics weaknesses, but also on intervention in 
areas where students have other identified weaknesses. 
For example, students struggling with mathematics who 
are identified as having working memory deficits 
should receive instruction in mathematics geared 
toward the difficulty in math together with the working 
memory deficit to attempt to maximize their ability to 
gain information. Such interventions must be studied 
and examined empirically to identify their utility. 
Further research needs to address the effects of specific 
strategies and techniques already identified as useful 
interventions at elementary and secondary levels to 
determine their usefulness at the postsecondary level. 

Limitations 

It is important to note that the students who made up 
the two groups in this study all presented with mathematics 
difficulties. Thus, a major limitation in understanding 
students with MD is that there is no purely 
random comparison group, and the design is not truly 
experimental. Future research is needed to compare 
these findings with a normative group, which would 
allow for the data to be treated as a true experimental 
design. 

Another limitation is the presence of comorbidity in 
the sample. For the purposes of this study, students with 
mathematics difficulty were included and the difference 
between the diagnoses of MD and ND was the focus. 

Learning Disability Quarterly 230 


However, in 14 cases comorbidity was an issue. Future 
research is needed to focus on students with MD alone 
compared with students with MD and other disorders. 

CONCLUSIONS 

With the growing demand for mathematics competency, 
it is becoming increasingly important to understand 
what differentiates postsecondary students with 
mathematics disorders/difficulties from their peers. Past 
researchers have focused on identification and remediation 
of students with MD in elementary and secondary 
grades. This article examined information from these 
studies to determine if the same weaknesses exist in a 
sample of college students identified as MD. This article is 
the beginning of what we hope will become an extensive 
body of research on individuals with LD in mathematics 
at the college level. Future research must not only focus 
on what weaknesses these students have, but also on 
determining which remediation techniques are useful. 

Overall, these analyses demonstrated that working 
memory, math fluency, reading comprehension, and 
visual/spatial/nonverbal ability weaknesses are significant 
contributors to difficulties for college students with 
mathematics disabilities compared to students who are 
struggling in math but are not diagnosed. Academic 
supports for these deficits must not only address specific 
mathematics difficulty areas but also the individual 
underlying difficulties that exacerbate poor math performance. 
For example, if a student has a relative and/or 
normative weakness in working memory and is struggling 
with mathematics, it is not enough to focus on 
helping the student learn the importance of a certain 
mathematical skill or concept. Instructors must also 
support the working memory deficit that is a contributing 
factor to the mathematics difficulty. By supporting 
both the math difficulty and the underlying processing 
deficits that exacerbate poor math performance, 
instructors and tutors will significantly increase students' 
ability to assimilate and utilize the mathematics 
concepts and skills needed to meet college-level mathematics 
requirements. 

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AUTHOR NOTE 
This material is based on work supported by the National Science 
Foundation under Grant 0099216. We thank the individuals who 
participated in the study and all those who graciously aided the 
progress of this manuscript in its many stages. 

Requests for reprints should be addressed to: Sean McGlaughlin, 
205 Lewis Hall, University of Missouri, Columbia, MO 65211. 
Email: smm302@mizzou.edu 

Learning Disability Quarterly 232