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AMBULATORY PEDIATRICS

Copyright ? 2005 by Ambulatory Pediatric Association

Volume 5, Number 5

September–October 2005281

Math Learning Disorder: Incidence in a Population-Based Birth Cohort,

1976–82, Rochester, Minn

William J. Barbaresi, MD; Slavica K. Katusic, MD; Robert C. Colligan, PhD; Amy L. Weaver, MS;

Steven J. Jacobsen, MD, PhD

Objective.—To report the incidence of math learning disorder (Math LD) among school-aged children, overall and

by gender. To compare incidence estimates obtained by using three different methods to identify Math LD cases. To

assess the extent to which children manifest Math LD alone, versus Math LD with comorbid reading disorder.

Methods.—This is a population-based, retrospective, birth cohort study. Subjects included all children born 1976–82

who remained in Rochester, Minn after age 5 (N ? 5718). Using records from all public and private schools, medical

facilities, and private tutorial services, all individually administered intelligence quotient and achievement tests and

extensive medical, educational, and socioeconomic information were abstracted. Math LD was established using research

criteria based on 3 formulas (regression-based discrepancy, nonregression-based discrepancy, low achievement).

Results.—Cumulative incidence rates of Math LD by age 19 years varied from 5.9% to 13.8% according to the

formula used. Boys were more likely to be affected than girls, with relative risk ratios from 1.6 to 2.2 depending on

the formula applied. Many children with Math LD (35% to 56.7%, depending on the formula used to define Math LD)

did not have a comorbid reading disorder.

Conclusions.—These results, from a community-based birth cohort, suggest that Math LD is common among school-

children, and is significantly more frequent among boys than girls, regardless of definition. Many children with Math

LD do not have an associated reading disorder.

KEY WORDS:

incidence; learning disability; math learning disorder

Ambulatory Pediatrics 2005;5:281 289

M

as mathematical ability that is substantially below that ex-

pected for chronological age, intellectual level, and edu-

cational experience.1Understanding mathematical con-

cepts and performing mathematical operations are impor-

tant skills for people living in a technologically oriented

society.2,3Indeed, poor math achievement by US students

has been a source of national concern for some time.4

Despite the importance of mathematics, the majority of

learning disability (LD) research has focused on read-

ing.2,5–9

The DSM-IV also notes the lack of epidemiological

data regarding Math LD, but estimates the prevalence of

Math LD is 1% of school-age children.1This conflicts

with research suggesting that the prevalence ranges from

4% to 6%.5,10–14Variations in the definition of Math LD

and operational criteria for identifying cases in epidemi-

ological research have contributed to uncertainty about the

athematics learning disorder (Math LD) is de-

fined in the Diagnostic and Statistical Manual

of Mental Disorders, Fourth Edition (DSM-IV),

From the Department of Pediatric and Adolescent Medicine, Di-

vision of Developmental and Behavioral Pediatrics (Dr Barbaresi),

Department of Health Sciences Research, Division of Epidemiology

(Drs Katusic and Jacobsen) and Division of Biostatistics (Ms Weav-

er), and Department of Psychiatry & Psychology (Dr Colligan),

Mayo Clinic College of Medicine, Rochester, Minn.

Address correspondence to William J. Barbaresi, MD, Mayo Clin-

ic College of Medicine, 200 First St SW, Rochester, MN 55905

(e-mail: barbaresi.william@mayo.edu).

Received for publication December 3, 2004; accepted April 8,

2005.

prevalence of Math LD.15,16Some researchers have re-

ported that Math LD is more common among boys than

girls.13Others have suggested that girls are equally or

more likely than boys to have Math LD.14,15Previous stud-

ies have suggested that Math LD is as common as reading

learning disorder (Reading LD), and have also reported

widely varying estimates of the extent to which Math LD

and Reading LD occur as comorbid learning disor-

ders.16–18Also, to our knowledge, the literature does not

include any contemporary studies of the incidence of

Math LD in a population-based birth cohort.

In this paper, we report the incidence of Math LD in a

population-based birth cohort of all children born 1976–

82 in Rochester, Minn. We examine the variation in in-

cidence resulting from the use of 3 different definitions

of Math LD, and compare incidence rates between boys

and girls. We also report the extent to which Math LD

occurs as an isolated learning disorder, compared with its

comorbid occurrence with Reading LD.

METHODS

A detailed description of the 1976–82 Rochester birth

cohort and our study methods for determining the inci-

dence of Reading LD in this cohort have been pub-

lished.19,20In this paper, we summarize the methods as

they were applied to our study of Math LD (Figure 1).

Study Setting

In 1990, the population of Rochester, Minn was 70745,

96% white, and primarily middle class; 82% of adults

were high school graduates.19The capacity for population-

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AMBULATORY PEDIATRICS 282 Barbaresi et al

Figure 1. Flow diagram describing identification of learning-disabled children among 1976–82 Rochester, Minn birth cohort. RCDIM

indicates Reading Center/Dyslexia Institute of Minnesota; LD, learning disorder; RFM, regression formula–Minnesota; DS, discrepancy–

nonregression method; LA, low-achievement method; and MLD, math learning disorder. *Evidence of learning/performance concern con-

sisted of Individual Education Program (IEP) reports, report of IEP review, individual assessment/reassessment report forms, referral forms,

medical or medication reports, private tutoring, private evaluation reports, individually administered ability and achievement tests, or any

notation from teacher, parent, or other person related to any type of difficulties in learning or performance.

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AMBULATORY PEDIATRICSIncidence of Math LD in a Population-Based Birth Cohort 283

based epidemiological research on LD in Rochester is the

result of several unique circumstances. Because of Roch-

ester’s geographic isolation in southeastern Minnesota,

greater than 95% of medical care is provided locally by

Mayo Clinic, Olmsted Medical Center, and a few private

practitioners. Through the Rochester Epidemiology Pro-

ject, all diagnoses and surgical procedures recorded at

these medical facilities, including affiliated hospitals, are

indexed for computerized retrieval (Medical Diagnostic

Index).21Each institution maintains a unit or dossier med-

ical record. The medical records contain complete and de-

tailed information from providers of all primary, specialty,

inpatient, and outpatient care to local residents. This in-

cludes psychometric assessments and questionnaires, and

psychological and psychiatric evaluations obtained during

interdisciplinary assessments of children with learning

problems.

Through a contractual research agreement, permission

was obtained to review the records of Rochester public

and private schools (Independent School District #535),

including the complete school records of all children born

in Rochester 1976–82 ever registered at any of the dis-

trict’s public, parochial, or private schools. The district

also maintains records for all home-schooled children.

Under a separate research agreement, we obtained per-

mission to review the records of the Reading Center/Dys-

lexia Institute of Minnesota (RCDIM), the largest private

tutoring agency in Rochester.

Identification of the 1976–82 Rochester Birth Cohort

The birth cohort included all children (N ? 8548) born

between January 1, 1976 and December 31, 1982 to moth-

ers residing in the five Olmsted County townships com-

prising Minnesota Independent School District #535. Sub-

jects were identified through the computerized birth cer-

tificate information from the Minnesota Department of

Health, Division of Vital Statistics. Vital status for each

member of the birth cohort during the 1995–96 school

year was established. Children who still lived in Rochester

until at least age 5 years were included in the study (n ?

5718, Figure 1). An analysis of birth certificate data from

children who moved away versus those who remained in

the community was published previously.19Few differ-

ences were found, and these were unlikely to compromise

the identification of LD cases. The study was approved

by the Institutional Review Boards of Mayo Clinic and

Olmsted Medical Center.

Identification of Potential Math LD Candidates

Phase 1

We reviewed the entire school record for every member

of the birth cohort who enrolled in any public or private

school in the district, including home-schooled children

(‘‘In study’’ subjects). The subject was classified as

‘‘Learning/performance concern–yes’’ if the school record

contained any form, test results, or remarks related to any

learning problem or handicapping condition (n ? 1961,

Figure 1). The subject was classified as ‘‘Learning/per-

formance concern–no’’ if the school record did not con-

tain such information (n ? 3757). Nineteen children with

moderate to severe mental retardation (intelligence quo-

tient [IQ] ? 50) were excluded from further consider-

ation.

For all subjects whose school records were designated

‘‘Learning/performance concern–yes,’’ we completed an

additional, detailed review of each subject’s school, med-

ical, and RCDIM records. If these records contained at

least one set of scores from individually administered IQ

and academic achievement tests, the subject was desig-

nated as an ‘‘LD candidate’’ (n ? 1366 at this stage).

Phase 2

For all 3757 subjects whose school records were des-

ignated ‘‘Learning/performance concern–no,’’ we con-

ducted a computerized search of the Medical Diagnostic

Index, using diagnostic terms for LD as well as a code

indicating that psychometric testing had been completed.

We also cross-matched these subjects with the RCDIM

file. These two sources yielded an additional 143 LD can-

didates.

Phase 3

We then abstracted detailed information from the com-

plete school, medical, and RCDIM records for all 1509

subjects who were designated as LD candidates in the

previous steps. In addition to individually administered IQ

and achievement test scores, we also abstracted other in-

formation including socioeconomic status, medical and

comorbid psychological/psychiatric conditions, and de-

tails regarding any special education services that were

provided.

For each child within each calendar year, all IQ and

achievement test scores were used to form pairs of ability

and achievement measures. All pairs of IQ–achievement

measures were placed in chronological order for each sub-

ject.

Identification of Math LD Cases

We applied 3 different ability–achievement methods to

the IQ and achievement scores of each subject classified

as an LD candidate. In each formula, x is the full-scale

IQ score and y is the achievement standard score.

1) Regression formula, Minnesota (RFM). y ? 17.40 ?

0.62x. This regression-based discrepancy formula is

currently used in Minnesota.

2) Discrepancy formula (DS). For children in kindergarten

through third grade, y ? x ? 15; for grades 4 through

6, y ? x ? 19; for grades 7 through 12, y ? x ? 23.

This nonregression-based discrepancy formula was

used by the local school system during several years

when our subjects were in school.

3) Low achievement formula (LA). x ? 80 and y ? 90.

This formula reflects recent trends toward LD defini-

tions that emphasize low academic achievement among

children with at least low average cognitive skills.22It

is also comparable to the definition used in the most

recently published study of the prevalence of Math

LD.10

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AMBULATORY PEDIATRICS 284 Barbaresi et al

Table 1. Incidence of Math Learning Disorder, Identified by 3 Formulas Among 1976–82 Birth Cohort, Rochester, Minn*

Math LD Formulas

RFM

AllBoys Girls

DS

All Boys Girls

LA

AllBoys Girls

Number with Math LD

Age met criteria, y; mean (SD)

291

8.8 (2.5)

199

8.8 (2.4)

92

8.8 (2.9)

485

8.3 (2.0)

336

8.5 (2.1)

149

8.1 (1.9)

665

9.7 (3.1)

417

9.4 (2.8)

248

10.1 (3.5)

Cumulative incidence, at age (y):

7

9

11

13

15

17

19

1.3

3.8

4.9

5.3

5.6

5.9

5.9

1.4

5.1

6.7

7.1

7.6

7.7

7.8

1.2

2.3

3.1

3.4

3.6

3.8

3.9

2.1

6.9

9.0

9.3

9.6

9.7

9.8

2.6

9.0

12.0

12.4

12.8

13.0

13.2

1.7

4.5

5.8

5.9

6.1

6.2

6.2

2.1

7.1

10.0

11.0

12.5

13.4

13.8

2.4

9.1

12.8

14.1

15.7

16.2

16.7

1.9

5.0

7.0

7.6

9.1

10.4

10.8

RR, boys versus girls; (95% CI)2.1 (1.6, 2.6)2.2 (1.8, 2.6) 1.6 (1.4, 1.9)

*(N ? 5699); Math LD indicates math learning disorder; RFM, regression formula—Minnesota; DS, discrepancy; LA, low-achievement;

RR, risk ratio; and CI, confidence interval.

Comorbidity of Math LD and Reading LD

After identifying all cases of Math LD, we determined

the number of subjects with research-identified Math LD

alone versus research-identified Math LD and Reading

LD, for each of the 3 formulas. Reading LD cases among

birth cohort members had been identified in a previous

study.20

Statistics

Cumulative incidence rates were calculated according

to the method of Kaplan and Meier.23Ninety-five percent

confidence intervals (95% CI) about the point estimates

were calculated using the Greenwood formula for the

standard error. The cumulative incidence rates represent

the likelihood that subjects who remained in Rochester

throughout their school years (ie, by age 19 years) would

be diagnosed as Math LD. Children in the birth cohort

who did not meet research criteria for Math LD were cen-

sored on the initial occurrence of migration from the com-

munity, death, last follow-up date, or age 19 years. Cu-

mulative incidence rates were calculated separately for

boys and girls for each of the 3 LD definitions. Risk ratios

(boys vs girls) and corresponding 95% CIs were deter-

mined using the regression coefficient and standard error

for gender obtained by fitting Cox proportional hazards

models.

RESULTS

Cumulative Incidence of Math LD by 3 Formulas

and by Gender

Table 1 provides the cumulative incidence of Math LD

at various ages up to 19 years, overall and separately for

boys and girls, by each of the 3 formulas. Math LD was

common, with cumulative incidence by age 19 years vary-

ing from a low of 5.9% (RFM) to a high of 13.8% (LA),

depending on the Math LD definition. The mean age at

diagnosis was similar for each Math LD definition and

did not differ by gender within each definition. Males

were more likely to have Math LD than females, with

male:female relative risk ranging from 1.6 to 2.2. Cu-

mulative incidence by each of the 3 formulas is depicted

in Figures 2 and 3.

Among children with IQ scores between 50 and 79 (n

? 91), 38 met the RFM, 33 met the DS, and 50 met the

LA criteria for Math LD. If these children had been ex-

cluded from the analysis, the resulting cumulative inci-

dence estimates by age 19 years would have been similar

to the estimates noted above (5.2%, 9.3%, and 13.0% for

the RFM, DS, and LA definitions, respectively).

On the basis of the ability and achievement measures

that were used to identify a child with a Math LD, 86.7%

of the children with Math LD (79.0%, 85.8%, and 83.9%,

respectively, depending on the formula) had been admin-

istered an age-appropriate Wechsler scale for ability as-

sessment. For math achievement, 76.5% of these children

had been administered a Woodcock-Johnson test (59.1%,

70.3%, and 74.0% depending on the formula), whereas

nearly all remaining children with Math LD had Wide

Range Achievement Test scores.

Comorbidity of Math LD and Reading LD

For the 2 discrepancy-based definitions 56.7% (RFM)

and 35.9% (DS) of subjects with Math LD did not have

a coexisting Reading LD (Table 2). For the LA definition,

35% of the Math LD cases did not have a coexisting

Reading LD.

Overlap Among Children With Math LD Identified

by Different Classification Methods

Among the 5718 children in the birth cohort with Math

LD, some subjects were identified as having Math LD by

more than 1 method. The frequency and overlap of Math

LD cases identified by the 3 formulas are presented in

Figure 4.

Cognitive Profile of Math LD Cases

Children with Math LD had cognitive skills that were

solidly in the average range, regardless of LD definition

(Table 3). As expected, academic achievement in math is

quite poor among the Math LD cases. However, Math LD

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AMBULATORY PEDIATRICSIncidence of Math LD in a Population-Based Birth Cohort 285

Figure 2. Cumulative incidence rates of mathematics learning disorder for males and females combined, identified by each formula among

1976–82 birth cohort, Rochester, Minn, by age. Lines represent cumulative incidence rate with associated 95% confidence interval.

cases identified by the LA and DS formulas appear to

have mean math achievement scores that are better than

the cases of Math LD defined by the RFM formula. In

particular, among the cases identified by more than 1 for-

mula, the median achievement scores were significantly

higher at the time a subject was identified by either the

LA or DS formula compared to the RFM formula (all P

? .001, Wilcoxon signed rank tests).

Site of Assessment and Sources of Data

We did not depend on school identification of Math LD

to determine the incidence rates of Math LD. School-iden-

tified cases had records indicating the presence of an In-

dividual Educational Program (IEP) specifying services

for Math LD. Of the 504 cases of research-identified Math

LD identified by either of the 2 discrepancy formulas, 251

were not identified as Math LD by the schools (ie, did not

have an IEP for math; Table 4). Also, 15 of these 251

Math LD cases were identified by our research criteria

solely by information from the medical and RCDIM re-

cords (ie, the school record did not include any informa-

tion to indicate that the student had problems in learning

or school performance or an IEP for math). Furthermore,

among the 287 Math LD cases identified solely by the LA

formula, 183 were not identified as Math LD by the

school.

Of the 504 cases of research-identified Math LD de-

fined by either of the 2 discrepancy formulas, 238 had at

least some test results from sites other than the school.

Similarly, for the 287 Math LD cases identified solely

with the LA formula, 146 had at least some testing per-

formed at a site other than school.

DISCUSSION

This report of the incidence of Math LD in a popula-

tion-based birth cohort indicates that Math LD is com-

mon, affecting many children at some time during their

school years. Prevalence studies have reported rates rang-

ing from 4% to 6%.5,10–13However, prevalence studies are

subject to bias due to children with Math LD moving into

or out of the community, with no way to determine the

extent, or the effect, of such movement. Birth cohort-

based incidence studies minimize this bias by identifying

cases of Math LD that arise naturally in a well-defined

population. Thus, incidence rates represent a more precise

description of the occurrence of Math LD.24Our results

support the notion that Math LD is an important problem