Keywords:
math test - arithmetic difficulties - learning disabilities - ADHD - methylphenidate
Palavras-chave:
teste de matemática - dificuldades aritméticas - dificuldades de aprendizagem - TDAH
- metilfenidato
Attention deficit hyperactivity disorder (ADHD) and arithmetic disorders, both individually
and in combination, have a significant impact on the academic performance of individuals,
as well as on their ability to professionally insert themselves when adults. Despite
the high prevalence of arithmetic disorders in ADHD[1], the literature on this condition is very limited[2]. Although individuals with ADHD generally have more arithmetic difficulties than
the general population[3], the underpinnings of this overlap are not well known.
Arithmetic operations are thought to involve various cognitive dimensions. For instance,
subtraction operations have a different mechanism when it is required to subtract
larger numbers from small numbers (requiring “borrowing”). Since 1993, Geary argues
that forgetting to borrow or borrowing indirectly while attempting to solve a subtraction
problem is related to a poor working memory and attentive skills[4]. Methylphenidate (MPH) is shown to improve numerical abilities related to working
memory functions in children with ADHD[5]. Other studies found that children with ADHD (who were not taking any medication)
were more likely to have arithmetic difficulties than their healthy peers, and that
taking MPH led to an improvement in arithmetic performance[6],[7],[8]. At different doses, MPH administration can increase overall academic performance[8].
To assess arithmetic difficulties, two important issues must be considered: detection
and classification. Therefore, our initial challenge was to develop an appropriate
method to assess arithmetic functions in Brazilian children. However, there is no
consensus as to which test is optimal for this purpose; there is not even a consensus
on the cutoff level used to determine levels of performance[9]. Instead of developing a new test, the strategy was to combine three tests, which
are currently being used in Brazil, to evaluate whether they can collectively identify
difficulties with arithmetic. These three tests were chosen because they tackle a
wide range of arithmetic functions (number comprehension, number production, and calculation),
forming the principles of arithmetic knowledge development according to McCloskey[10]. A comparison was made between the detection of arithmetic difficulties of each
test separately and the combination of them. Each test separately is expected to be
able to assess some arithmetic difficulties in ADHD children, but their combination
is expected to provide a more sensitive detection of arithmetic difficulties and MPHs
effects. In the consulted scientific literature, this is the first time these three
tests have been used together for the same purpose. Furthermore, subtraction performance
was evaluated because of its previous association with (and this study had a particular
interest in that) working memory abilities. This study considered all types of difficulties
as arithmetic difficulties, instead of trying to differentiate the less severe and
more general difficulties in arithmetic from severe forms, such as dyscalculia. Hence,
the purpose of this study was to compare ways of evaluating arithmetic skills in Brazilian
children with ADHD by combining three validated neuropsychological tests and to determine
whether they are sensitive to the methylphenidate treatment.
METHODS
The present study was approved by the Local Research Ethics Committee (CAPPesq/HC
- FMUSP). A written informed consent for study participation was obtained from each
child’s legal guardian.
This interventional prospective study evaluated 42 children: 20 with a diagnosis of
ADHD and 22 matched controls. All participants were 9–12 years old (mean age 9.9±0.9)
with normal intelligence (IQ≥85) and no neuropsychiatric comorbidities, except for
oppositional defiant disorder in three children from the ADHD group. The SNAP-IV for
parents and teachers and “Benczik Scale for ADHD” for teachers[11],[12] questionnaires were used to screen ADHD symptoms. Diagnoses were confirmed by two
experienced pediatric neurologists following the DSM-IV criteria for ADHD, and ADHD
children were referred by the neuropsychiatry team in a large metropolitan pediatric
health neuroscience center. The control group had no clinical evidence of ADHD and
was matched according to age, IQ, and socio-economic status.
In order to assess the intelligence level and arithmetic skills of all participants,
three tests were used: a) Protocol for Calculus and Mathematical Reasoning Test (Bastos
Test)[13]; b) the Academic Performance Test in Arithmetic (TDE Arithmetic)[14]; and c) the WISC-III - Arithmetic Sub-test[15]. Each test is described in further details in the following paragraphs:
a) The Bastos Test[13] is a 50-minute test that addresses lexical and syntactic forms of written Arabic
numerals, number production, transcoding of numbers, and calculations using the four
basic arithmetic operations. The protocol consists of four items:
-
Assessment of lexical and syntactic ability. Participants are asked to: read a number
word and convert it to its numerical symbol. Number words became progressively more
difficult (units, tens, hundreds and thousands); convert a numerical symbol into a
number word with numerical symbols becoming increasingly difficult (units, tens, hundreds
and thousands).
-
Estimation of magnitude: assessment of the knowledge of magnitude with numbers of
increasing difficulty (units, tens, hundreds and thousands).
-
Evaluation of the ability to add, subtract, multiply, and divide, which also became
progressively more difficult.
-
Evaluation of mathematical reasoning ability.
b) The TDE Arithmetic Test[14] test is a written test with no time limit, that assesses fundamental arithmetic
skills (addition, subtraction, multiplication, and division) with 35 exercises that
become increasingly difficult with alternating types of test.
c) Finally, the WISC-III - Arithmetic Subtest[15] is a time-limited verbal subtest of the Wechsler Intelligence Scale for Children
(WISC-III). Children must solve each of the 17 increasingly difficult problems mentally,
without using any pencil or paper. This test assesses addition, subtraction, multiplication,
division, fractions, sense of time, and distance. Each item has a time limit and the
test is stopped after the third consecutive error.
All participants were evaluated for the 3 tests (Bastos Test, TDE Arithmetic, and
WISC-III - Arithmetic Sub-test) at two time points. The ADHD group was assessed at
time 1 without medication and at time 2 under medication. Children in this group were
kept medication-free for at least 1 week, at time 1, and under medication for at least
two months, at time 2. The medication used had a short action MPH 0.3–0.5 mg/kg, administered
90 minutes prior to assessment. The control group underwent the same evaluations as
the ADHD group, with an interval of three months between the first (time 1) and second
(time 2) assessments. Children in both groups were tested, and all of them responded
to the Wechsler Intelligence Scale for Children-Third Edition (WISC-III)[15] (complete) only at time 1.
Assessment for:
-
Arithmetic Difficulties: children were classified as having arithmetic difficulties in each test, according
to the following criteria:
-
Bastos Test: the criterion used was proposed previously[13] for the presence of arithmetic difficulties. A score lower than or equal to 58%
in the Bastos Test was considered a “poor performance”.
-
TDE Arithmetic Test: inferior score[14].
-
WISC-III - Arithmetic Subtest: score lower or equal to 7[16].
-
Besides that, a combination of these three tests was used as follows: children were
considered as having overall arithmetic difficulties when they displayed “poor performance”
in at least two of the three tests described above. The same cutoff levels were used,
but overall arithmetic difficulties were linked to performance in the three tests.
Subtraction performance
Basic numerical knowledge and working memory were also explored via subtraction exercises.
There were seven subtraction operations in each test (Bastos Test and TDE Arithmetic
Test), except for the WISC-III - Arithmetic Sub-test, which is an oral test. These
subtraction operations were categorized as “simple” or “complex”. Simple subtraction
consisted of subtracting small numbers from large ones (e.g. 88–53), and complex subtraction
involved “borrowing” or subtracting bigger from smaller numbers (e.g. 318–189). Thus,
there were seven items for simple subtraction (4 items from the Bastos Test and 3
from the TDE Arithmetic Test) and seven for complex subtraction (3 on the Bastos Test
and 4 on the TDE Arithmetic). The subtraction performance was calculated based on
the total number of correct responses.
Statistical analysis
Fisher's exact test was used to compare differences in arithmetic difficulties between
groups: time 1: ADHD (medication-free) versus control group, and time 2: ADHD (with medication) versus control group.
To determine the effect of MPH on their arithmetic function, the McNemar test was
used to evaluate the concordance of results observed in the ADHD group: ADHD without
medication versus ADHD with medication. The McNemar test was also used to assess the “learning effect”
in the control group, measured by the control performance at time 1 versus time 2.
Fisher's exact test and the McNemar test were performed for the results of each of
the three tests (Bastos Test, TDE Arithmetic Test and WISC-III - Arithmetic Subtest)
separately and for the results from combining these tests. This processing could evaluate
the benefits of using the proposed criterion for classifying arithmetic difficulties.
The results allowed us to see if the same differences between groups and the same
effect of MPH were observed using only one test for each classification criterion.
The Wilcoxon and Mann-Whitney tests were used to test the means subtraction scores
for both simple and complex subtractions. The Wilcoxon test was used to assess subtraction
performance within the same group at the two time points (for example: performance
of complex subtraction in ADHD group without medication versus ADHD group with medication). Following that, the Mann-Whitney test was used to compare
subtraction performance between groups (control vs. ADHD). All analyses were conducted
using the SPSS 13.0 software, and the significance level was set at p<0.05.
RESULTS
Arithmetic performance
[Table 1] summarizes the number of children with arithmetic difficulties according to each
test at time 1. At time 1 (without medication), when comparing ADHD and control children
as to a “poor performance” on the Bastos Test, a worse performance was seen in the
ADHD group (Fisher's exact test: p<0.001). This difference was also found when adopting
only the TDE arithmetic test (Fisher's exact test: p=0.002). However, the WISC-III
Arithmetic Subtest criterion showed that the groups’ classifications were equivalent
(Fisher's exact test: p=0.460).
Table 1
Number of children with arithmetic difficulties at time 1.
|
Group (n)
|
Arithmetic Difficulties at time 1
|
|
Bastos Test
|
•TDE
•Arithmetic Test
|
•WISC-III
•Arithmetic Subtest
|
Combination of the three tests
|
|
ADHD (20)
|
13
|
15
|
3
|
13
|
|
Control (22)
|
2
|
5
|
6
|
2
|
ADHD: Attention Deficit Hyperactivity disorder; TDE Arithmetic Test: Academic Performance
Test in Arithmetic; WISC-III: Wechsler Intelligence Scale for Children - Third Edition
- Arithmetic Subtest; Math: Combination of the three tests
[Table 2] summarizes the number of children with arithmetic difficulties according to each
test at time 2. At time 2, considering each test separately, no difference was found
between groups (Fisher's exact test: Bastos Test p=0.152; TDE Arithmetic p=0.758;
WISC-III Arithmetic Subtest p=0.414). Also, the analysis could not detect a significant
effect of the MPH treatment on ADHD children (McNemar's test: Bastos Test p=0.077;
TDE Arithmetic p=0.289; WISC-III Arithmetic Subtest p=1). There were no differences
between time 1 and time 2 in the control group (McNemar's test: Bastos Test p=1; TDE
Arithmetic p=0.182; WISC-III Arithmetic Subtest p=1).
According to the combination of the three tests ([Table 1]), there were significantly more children in the ADHD group at time 1 with arithmetic
difficulties relative to children in the control group (Fisher’s exact test, p<0.001).
When medicated with MPH at time 2 ([Table 2]), the children with ADHD had fewer arithmetic difficulties than at time 1 (McNemar’s
test, p=0.046). The number of children classified with arithmetic difficulties decreased
from 13 (at time 1) to 6 (at time 2). As expected, control participants showed no
significant difference in their overall arithmetic performance between the two time
points (McNemar, p=1). Most importantly, at time 2 ([Table 2]), the groups did not differ from each other in terms of number of individuals with
arithmetic difficulties (ADHD: 6/20 vs. Controls: 3/22; Fisher’s exact test, p=0.269).
Table 2
Number of children with arithmetic difficulties at time 2.
|
Group (n)
|
Arithmetic Difficulties at time 2
|
|
Bastos Test
|
•TDE
•Arithmetic Test
|
•WISC-III
•Arithmetic Subtest
|
Combination of the three tests
|
|
ADHD (20)
|
7
|
11
|
2
|
6
|
|
Control (22)
|
3
|
10
|
5
|
3
|
ADHD: Attention Deficit Hyperactivity disorder; TDE Arithmetic Test: Academic Performance
Test in Arithmetic; WISC-III: Wechsler Intelligence Scale for Children - Third Edition
- Arithmetic Subtest; Math: Combination of the three tests
Subtraction performance
Complex subtraction
At time 1, children with ADHD (unmedicated) scored significantly worse than control
children on the “complex subtraction” task (mean scores [SD]: ADHD=2.55 [2.11]; Controls=4.32
[1.96]) Mann-Whitney, p=0.007).
At time 2, children with ADHD (medicated) were more accurate on the complex subtraction
task relative to themselves at time 1 (mean scores [SD]: ADHD time 1=2.55 [2.11];
ADHD time 2=4.05 [2.24]) Wilcoxon, p<0.001). Furthermore, their performance was similar
to that of control participants (mean scores [SD]: ADHD=4.05 [2.24]; Control=4.91
[1.66]) Mann-Whitney, p=0.263).
Simple subtraction
The same analyses of the afore mentioned were conducted for the “simple subtraction”
task. No differences were found between patients and controls at either time point
for this task (mean scores [SD]: ADHD time 1=5.30 [1.69]; Control time 1=5.95 [1.09];
ADHD time 2=5.95 [1.15]; Control time 2=6.00 [1.11]; Mann-Whitney time 1, p=0.237;
Mann-Whitney time 2, p=0.915). Moreover, there were no differences in ADHD groups
between time 1 and time 2 (Wilcoxon, p=0.068).
DISCUSSION
ADHD and arithmetic difficulties are frequently associated, and these variables were
studied here in Brazilian children. The choice of which arithmetic test should be
used was the first challenge. There was no guarantee that, by applying each of the
three tests widely used in Brazil (Bastos Test, TDE Arithmetic, and WISC-III Arithmetic
Subtest), the results aligned with current literature, which had already shown that
ADHD children have more arithmetic difficulties than their healthy peers would be
found[3]. This is due to two simple issues: the lack of a “perfect” arithmetic test (no consensus
among researchers of the field) and this being the first time in Brazil that these
tests were applied collectively to detect the presence of arithmetic difficulties
in ADHD children.
The reason for using MPH was to check how aligned the tests were with their known
effects, regarding working memory and attention to improve arithmetic skills[6],[7],[8]. The identification of arithmetic difficulties according to each test in the context
of MPH treatment for ADHD children was analyzed. Separately, the Bastos Test and TDE
Arithmetic Test could identify differences between children with ADHD (without medication)
and the control group, which agrees with those of the literature[3]. However, the WISC-III Arithmetic Subtest could not detect this difference. The
results were statistical similar between controls and ADHD children when the ADHD
children were medicated. This improvement is probably related to MPH, because none
of these children suffered any other interventions, except for the use of MPH. In
the ADHD group, the tests did not show better results separately, before and after
MPH.
However, by combining these three tests the following results were found: there was
a worse performance in unmedicated ADHD children than in the control group; an improved
performance was associated to the MPH treatment, and no significant difference was
seen between medicated ADHD children and the control group.
These results could be explained by the fact that none of the tests individually fulfill
McCloskey’s principles[10] to study arithmetic knowledge: number comprehension, number production and calculation
processing. However, combining these three tests could detect the presence of arithmetic
difficulties and expands the sensitivity of the process.
In terms of mathematical cognition domain, complex subtractions were explored based
on different authors statements, who say that working memory and attention are part
of subtraction skills that involve the borrowing procedure[4],[5]. Thus, combining the complex subtractions of Bastos and TDE Arithmetic tests provided
similar results to the combination of all three tests. Simple subtraction could not
identify any differences between groups. Furthermore, as found by Rubinsten et al.[5], MPH had no effects on simple subtraction performance, probably because this is
a basic processing skill, that relies on the number sense, which is an inherited ability[17]. The improved complex subtraction performance could be attributed to the MPH effects
on executive functions, such as working memory. It may be possible that this discrepancy
regarding simple and complex subtractions in children with ADHD suggests that basic
arithmetic difficulties need to be addressed with specific educational interventions;
those based on working memory and attention might benefit from medication[5],[18].
The study design is controlled for possible experimental placebo-related effects (task
learning and research team interaction effects) and for time-related effects (two
time-points in both groups). However, possible effects of MPH’s medication were not
controlled with a specific placebo-medication. If a medication-wise placebo arm was
used in both groups, the effects could also be present in the control group. Moreover,
the experiment was not double-blinded. However, it is expected that these characteristics
would affect the tests separately and their combination similarly. The placebo effects
would also probably increase the differences between time 1 and time 2 in the ADHD
group. Nonetheless, given that MPH benefits are well established, and only the tests
in combination detected these improvements in the ADHD group, we find that these results
were not altered by placebo effects. Another possible aspect is that the study sample
size is relatively small. Even a small sample could provide strong evidence aligned
with literature as seen with our subtraction data. These results were quite similar
to that of Rubinsten et al.[5]. We reiterate that we are not trying to validate a new test but rather suggesting
that combining tests could increase sensitivity, which could be especially useful
in studies with smaller samples.
In conclusion, instead of creating a new test, the use of existing tests was recycled
to offer a more complete assessment of arithmetical difficulties when applied in combination.
When using this combination of validated tests, arithmetic difficulties could be detected
in Brazilian children with ADHD, besides demonstrating the benefits of methylphenidate.
Currently, the authors are working on a neuroimaging version of this protocol to explore
the neural underpinnings of ADHD and arithmetic disorders. Recycling existing tools
might be a way to align the different world groups that research arithmetic disorders
and establish a consensual criterion to detect the presence of arithmetic difficulties.
