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Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
by
Elizabeth (Beth) D. C. Taylor
Thesis Submitted in Partial Fulfillment
of the Requirements for the Degree of
Master of Science
Clinical Psychology
College of Saint Joseph
May, 2015
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Acknowledgments
Please allow me to thank my thesis committee: Dr. Ronald Hedgepeth (chair,) Dr. Robert
Walsh, and professor Jonathan Gilmore, all from the College of St. Joseph. I am deeply
grateful for their ongoing support, advice, and patience. They were always available to
answer questions and share their expertise, and without their tutelage and commitment to
my thesis project, this research would not have been possible.
I am also grateful to the nine young adults who gave up their time to participate in this
research. For purposes of confidentiality I will not include their names here, but they, as
well, made this research possible.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Abstract
This research attempted to document a positive correlation between the life-long
phonological processing deficit such as in developmental dyslexia and arithmetic fact
fluency deficit. Previous research has shown a possible connection. These deficits
continue into adulthood and continue to affect behavior, reading, and general functioning.
This research failed to obtain a large enough sample size to make meaningful
conclusions; however, unlike previous research designs, this research design is relatively
easy to replicate. By preserving our data, we have made it possible for other researchers
to continue to grow the sample size. This bodes well for the future because researchers
interested in how developmental dyslexia affects adults may continue to add to the
database and we will be able to draw meaningful conclusions regarding the lifetime
connection between phonological processing deficits and arithmetic fact fluency deficits.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Table of Contents
List of Tables
i
List of Figures
ii
1.0 Introduction
1
1.1 Reading Difficulties and Dyslexia
1
2.0 Literature Review
2
2.1 Phonological Deficit Hypothesis
2
2.2 Double-Deficit Hypothesis
3
2.3 Triple-Deficit, Multiple-Deficit, and Visual Deficit Hypotheses
4
2.4 Auditory Temporal Processing Deficit Hypothesis
Auditory Rhythmic Entrainment
Syllable Stress
Phonological Awareness
5
6
7
7
2.5 Cerebellar Hypothesis
8
2.6 Dyslexia and Mathematics
Dyscalculia
9
9
3.0 Method
10
3.1 Participants
10
3.2 Instrumentation
Phonological Awareness
Reading Comprehension
Arithmetic
Control Test of Working Memory
11
11
12
13
13
Analysis 4.0
14
4.1 Cancellation Test
14
4.2 General Reading Ability
Reading Rate
Reading Comprehension
15
15
16
4.3 Phonological Processing
18
4.4 Test of Arithmetic Fact Fluency
19
5.0 Discussion and Conclusions
Cancellation
Reading Rate
Reading Comprehension
Phonological Awareness and Arithmetic Fact Fluency
Weaknesses in This Study
Strengths in This Study and Moving into the Future
21
21
23
24
25
28
28
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
References
30
Appendix A: Demographic Data and Cancellation Test Data
32
Appendix B: Phonological Awareness Data
33
Appendix C: Arithmetic Fact Fluency Data
34
Appendix D: Reading Rate and Reading Comprehension Data
35
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
i
List of Tables
Table 1, Male/Female Demographic
10
Table 2, Diagnoses
11
Table 3.a, Cancellation All Participants
15
Table 3.b, Cancellation Exclude Low Score
15
Table 3.c Cancellation Means
15
Table 4, Reading Rates
15
Table 5, Reading Comprehension
16
Table 6, Reading Percentages
17
Table 7, PACS
19
Table 8, AFFCS
20
Table 9, Reading Rate Chi Square
24
Table 10, Percentage Correct
24
Table 11, PACS
25
Table 12, PACS Chi Square
26
Table 13, PACS & AFFCS
27
Table 14, AFFCS chi square
28
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
List of Figures
Figure 1, Reading Comprehension Scaled Scores
17
Figure 2, Percentage Correct
18
Figure 3, PACS
19
Figure 4, AFF
20
Figure 5, Cancellation SS
22
Figure 6, Cancellation Raw Scores
22
Figure 7, Nelson-Denny Reading Rates
23
ii
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
1
1.0 Introduction
Reading fluency is the ability to read accurately, with comprehension and with
expression at a reasonable rate of speed. Fluent reading is a vital skill to be learned
during the appropriate developmental window, as reading and writing are tantamount to
functioning well in today's world. Many young school children are considered for a
diagnosis of developmental dyslexia when they fail to develop reading fluency in spite of
innate intelligence, appropriate instruction and personal motivation. Our current
understanding of developmental dyslexia is that it is a neurobiological learning disability
that affects reading and spelling in spite of intelligence, educational opportunity, and
motivation to learn.
Both the criteria for diagnosis of developmental dyslexia as well as the theories regarding
the cause of the disorder are numerous. Studies as recent as the 1990's have varied in
their criteria for inclusion in either the dyslexic or typical reading group confounding any
discoveries. However, if we are going to successfully help dyslexic children learn to read
and function as best they can, we must come to a better understanding of what causes
dyslexia and how the dyslexic brain works. The way to do this is to continue to study
dyslexic and reading disordered behavior at all points in life.
1.1 Reading Difficulties and Dyslexia
Developmental dyslexia is considered a learning disability with a neurobiological basis.
Some of the disagreement among professionals as to what causes dyslexia may be due to
past research lumping varied reading disorders together. In order to understand
developmental dyslexia, it is necessary to separate dyslexia from other reading disorders
and learning disabilities.
Vukovic, Lesaux, and Siegal (2010) wrote that while dyslexic students have difficulty
decoding due to phonological deficits, phonological processing is not implicated in all
reading difficulties. Students who show problems with reading comprehension but are not
necessarily dyslexic often suffer from problems with intact word reading ability. (Other
researchers consider intact word reading ability as part of dyslexia.)
Vukovic, however, considers it a problem that studies on reading disorders prior to her
research in 2010 did not separate dyslexic students from those with other, more broadly
construed reading difficulties. The various theories of dyslexia structure how we define
dyslexia, and not the other way around. Therefore, continued research and observation of
how dyslexic students function is necessary for us to discover accurate definitions of
dyslexia and craft appropriate curricula and interventions for dyslexic students.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
2
2.0 Literature Review
This literature review examines different theories behind the etiology of dyslexia, and
focuses on both research plus other literature reviews published from 2002 to the present.
2.1 Phonological Deficit Hypothesis
The phonological deficit hypothesis states that dyslexia is caused by a neurological,
phonological deficit. The phonological deficit causes decoding to be a slow, laborious
and difficult process. This presents as problems learning to read, to write, and to spell.
Phonological information is stored in long-term memory. Recent research by Ferreira de
Carvalho, de Souza Batista Kida, Aparacida Capellina, and Brandao (2014) examined
phonological deficits in students ranging in age from 8 to 15 years. These dyslexic
students had trouble decoding written words and holding pseudo-words in short-term
memory. The fact that the same dyslexic students did not have trouble with digit span
recall as compared to their typical peers was interpreted to mean their problem was a
phonological deficit and not a short-term memory deficit.
Earlier studies have found the same lack of difference between dyslexic subjects and
typical controls in digit span, validating the theory that dyslexia is not caused by a shortterm memory deficit. (Huss, Verney, Fosker, Mead and Goswami, 2011; Leung,
Hamalainen, Fruzsina and Goswami, 2011.) Because phonological information is stored
in long-term memory, the typical functioning of the short-term memory validates the
phonological theory.
This phonological deficit hypothesis also explains why dyslexic readers have more
difficulty with reading comprehension than with listening comprehension. In the same
2014 study referenced above, dyslexic students showed no significant difference from the
control group in understanding text that was read to them. However, their ability to
answer questions about text they had read silently to themselves was significantly poorer.
This lack of reading comprehension coupled with a typical short-term memory score on
digit span indicates the deficit is phonologically based in long-term memory. During
silent reading, the dyslexic short-term memory is unable to retrieve the necessary
phonological information from long-term memory in order to comprehend individual
words in the text. In this study, the ability of the students to understand information
presented in a fashion other than silent reading showcases the phonological hypothesis at
work.
The phonological deficit hypothesis holds that problems with decoding are due to a
neurological, phonological deficit and this is the marker for developmental dyslexia as
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
3
opposed to other reading disorders. Also, it is logical to say this hypothesis holds that
presentation of reading disorders not phonologically based is not specifically dyslexia.
2.2 Double-Deficit Hypothesis
The double-deficit hypothesis considers naming speed a second core deficit in dyslexia,
in addition to (not instead of) the core phonological deficit. Rapid naming speed (RAN)
is the speed at which a subject can name a color, object, or sight-read a word. RAN
studies often use colors, objects, and numbers in order to remove the variable of reading
from the test. People diagnosed with reading difficulties sometimes do have trouble with
RAN. One question is whether trouble with RAN is a marker for dyslexia or a different
reading disability.
The double-deficit hypothesis expects dyslexic readers to fall in one of three categories:
phonological deficit only, phonological deficit and RAN deficit, or RAN deficit only.
Subjects with low RAN sometimes have sight word reading difficulties. Sight-reading is
the ability to recognize a word immediately, without sounding it out. While these two
skills, RAN and sight reading, seem to go together, some people have trouble with sight
reading but can name non-word visual stimuli as quickly as typical readers, which poses
additional questions.
Vukovic and Siegal (2006) performed a comprehensive review of the double-deficit
hypothesis. They looked for evidence in past research of the three possible subtypes of
dyslexia mentioned above, but the definition of "dyslexic readers" in the 29 studies they
included in their review varied from a lack of definition, "Dyslexia not defined; boys
selected from a pool of 56 children referred for dyslexia who showed 'unusual hesitancy'
in rapidly naming a series of colors" to lags in oral reading skill, to word reading
percentile scores. One of the more comprehensive dyslexia identification protocols was,
"Dyslexia defined as a history of reading and spelling problems and significant
discrepancy between reading or spelling and cognitive abilities" in 2001. This criterion is
most closely related to the current understanding of the definition of developmental
dyslexia.
In the end, the accumulated evidence in this 2006 review consistently found evidence of
RAN deficits in some children and adults with learning disabilities, but failed to support
the premise that people with dyslexia have problems with RAN. While some dyslexic
subjects may have both, RAN may not be a symptom of dyslexia, but rather an additional
complication. Vukovic and Siegel emphasized the importance of further research before
conclusions are made regarding the double-deficit hypothesis.
Later, in 2010, Vukovic, et alia discussed problems with lumping reading disabilities
together, and stressed the importance of defining dyslexia and other reading disabilities
with specificity and care. Based upon the evidence, this would lead one to consider RAN
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
4
and sight-reading deficits as reading disabilities often separate from the difficulty with
phonological decoding inherent in a diagnosis of dyslexia.
2.3 Triple-Deficit, Multiple-Deficit, and Visual Deficit Hypotheses
The triple-deficit hypothesis accepts the premise in the double-deficit hypothesis that
both phonological deficits and RAN deficits are at the core of dyslexia. The triple-deficit
hypothesis adds another innate and causative deficit into the mix: an orthographic deficit.
A deficit in orthography causes the subject to be unable to move from processing
information about letters to information about words. Groups of letters (i.e., written
words) do not make sense to these subjects. (Suk-Han Ho, Wai-Ock Chan, Tsang, and
Lee, 2002.)
There is evidence to conclude that there is an association between the number of deficits
and level of reading impairment (Suk-Han Ho, et alia, 2002.) Essentially, dyslexic
students with all three deficits perform less well in school than those with only two
deficits, who then still perform less well than those with a single deficit. While this
makes intuitive sense, there is still the question whether the dyslexia is caused by a tripledeficit in some subjects. This hypothesis states that all three deficits are innate in dyslexic
people.
Suk-Han Ho, et alia (2002) found evidence of multiple deficits including visual,
phonological, and orthographic in Chinese children with dyslexia. Chinese children learn
to write in both English and Mandarin; Mandarin orthography is not phonological. We
might expect dyslexic children learning to write with phonological orthographies (such as
English or Greek) to experience difficulty, but if the core deficit in dyslexia is
phonological only, then we should not see so much trouble in Chinese children with
dyslexia. Ho's work added validation to the triple deficit hypothesis.
People with dyslexia often read more slowly than typical peers. This could, in theory, be
caused by a visual deficit, a temporal deficit affecting reading comprehension (discussed
below,) or a purely phonological deficit affecting decoding.
In 2010, Skottun and Skoyles re-analyzed data from 2009 that charted dyslexic and
typical controls' ability to perceive which of a pair of visual stimuli appeared first (the
one on the left, or the one on the right.) Dyslexic subjects needed more time between the
appearance of the first and second visual stimuli in order to know which was presented
first. The original paper interpreted the difference as a deficit in temporal order judgment.
Skottun and Skoyles concluded in their analysis that the difference could just as easily be
caused by a visual deficit. If the results were caused by a visual deficit in dyslexic
subjects, this would support the multiple-deficit hypothesis. Their paper concluded that
the data is equivocal and, therefore, supports neither the temporal processing deficit
hypothesis nor the multiple deficit hypothesis.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
5
2.4 Auditory Temporal Processing Deficit Hypothesis
Auditory and speech perception problems are well represented among those with literacy
problems. Temporal processing refers to the rate at which a person processes auditory
information. Auditory temporal processing is a larger category that often includes people
with phonological deficits. The temporal processing deficit theory of dyslexia holds that
an innate auditory processing deficit or deficits causes the phonological deficits seen in
dyslexia, and causes additional problems seen in dyslexia. Proponents of the temporal
deficit hypothesis recognize that a cognitive hallmark of developmental dyslexia is
impaired phonological processing.
Usha Goswami is the director of the Center for Neuroscience in Education at Cambridge
University. She has been instrumental in conducting research examining the neural basis
of developmental dyslexia, the neural basis of speech and language impairments, and the
neural basis of rhythmic motor behavior since the 1980's. In 2011 Goswami published "A
Temporal Sampling Framework (TSF) for Developmental Dyslexia" in which she
proposed that the root cause of dyslexia is a temporal deficit, not a phonological
processing deficit. Goswami posits that temporal issues affect a child's development and
cause phonological deficits post birth. This is in contrast to the phonological processing
deficit that posits an innate neurological difference in phonological processing as the
cause of dyslexia.
Aspects of temporal processing that she and other researchers have isolated and shown a
weakness in dyslexic readers include rise time, rapid naming, rhythm, phonological
awareness and syllable stress.
Amplitude Rise Time Envelope
Amplitude rise time envelope is the amount of time it takes for a sound to reach full
amplitude, or loudness. In English language speech, each syllable or sound in a word has
a rise time that contributes to the rhythm and prosody of speech. Deficits in perceiving
rise time in developmental dyslexia have been documented in more than one study and
across languages, including English, Spanish, Chinese, French, Dutch, Finnish and
Hungarian. (Goswami, Huss, Mead, Fosker, and Verney, 2013.)
Huss, Verney, Fosker, Mead, and Goswami (2011,) found dyslexic children were less
able to single out sharper beats, in other words, dyslexic subjects could not distinguish
sounds with shorter rise times from sounds with longer rise times. The shorter the rise
time, the sharper the beat. Typically developing controls were able to perform this task
significantly better than dyslexic subjects.
Leong, Hamalainen, Soltesz, and Goswami, 2011, found evidence that even adults with
developmental dyslexia continue to have a statistically significant difficulty
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
6
discriminating between sounds based upon rise time. These data support the idea that
temporal processing is an innate and lifelong deficit in dyslexia.
Auditory Rhythmic Entrainment
In Goswami's TSF (2011,) we expect the auditory rhythmic entrainment in dyslexic
subjects to be impaired. Rhythmic entrainment is, essentially, synchronization to an
external rhythm. There are rhythms in speech that children as young as infants attend to
as part of learning their language. The perception of rhythms in speech continues to be
important for communication on a lifelong basis.
Auditory rhythmic entrainment impairment in dyslexic children affects perception of
syllables, rhymes, and phonemes. This impairment likely also affects auditory-visual
integration and even attention. Goswami's TSF synthesizes some of the different theories
discussed herein and may serve to connect or integrate seemingly contradictory literature
on developmental dyslexia.
Studies have found problems with rhythmic motor entrainment in children with
developmental dyslexia (Corriveau and Goswami, 2009.) Children with dyslexia, reading
problems, and speech language impairments (SLI) have shown trouble tapping their
fingers to a beat when compared to typical controls. Similar impairments in both auditory
and motor rhythm abilities have also been found in adults with developmental dyslexia.
Corriveau and Goswami (2009) worked with sixty-three, 7 to 11 year old children. The
clinical group had a statement of language impairment from the local educational
authority. There were two control groups, one was matched to the SLI group for
chronological age, and the other control group was matched to the SLI group for
language ability. All children participated in the metronome task.
The metronome task required the subjects to tap their fingers to three different beats in
both a paced and an unpaced condition. In the paced condition, the children tapped along
to the rhythm of metronome beeps. In the unpaced condition, the children had to continue
to tap the rhythm at the same rate without the help of ongoing metronome beeps. All
children performed poorly in the unpaced condition.
In the paced condition, significant group differences were found during two of the three
tapping rates, 2 Hz and 1.5 Hz. There were no significant differences during the fastest
rate, 2.5 Hz. Further analysis of the data showed that the slower the rate of tapping, the
more inconsistent the tapping of the SLI group. It was also determined that, on average,
the SLI group started tapping earlier than both of the control groups. These results are
consistent with the hypothesis that children with SLI also have a rhythmic processing
deficit.
Huss, et alia (2011, including Goswami) explored how auditory sensitivity to rhythmic
cues affected phonological development and metrical perception. Huss and team worked
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
7
with sixty-four children ages 8 to 13 years of age. The clinical group were either already
known to have developmental dyslexia, or showed severe literacy and phonological
impairments on the researchers' test battery. One of the control groups was matched for
chronological age, the other for reading level.
In the perception of musical meter task, subjects had to ascertain whether two sets of
series of notes in a metrical arrangement were the same or different. In the different trials,
the accented note was longer on the second delivery. Children with developmental
dyslexia performed significantly worse than the chronological age matched controls in all
of the trials except for the shortest, 5 note sequence.
The poor performance on the musical meter task was associated with problems detecting
rise time, and was also a strong predictor of reading and spelling. This lends credence to
the theory that perception of metrical structure is necessary for phonological development
in children. Dyslexic children have a phonological deficit, and it may be caused by
temporal processing deficits.
Syllable Stress
Meter in music is syllable stress in speech. There is evidence that dyslexics may have an
inability to perceive syllable stress. "Dee-dee" tasks have been done in more than one
research study documenting this deficit. (Leong, et alia, 2011; Goswami, Mead, Fosker,
Huss, Barnes and Leong, 2013.) Dee-dee tasks remove the phonemes from words and
focus on syllabic stress. A subject may be shown a picture of Harry Potter, whose
syllabic stress name pronunciation is DEE-dee DEE-dee, or Strong-Weak Strong-Weak
(SWSW.) The participant is asked whether the person's name sounds like DEE-dee DEEdee, or DEE-dee dee-DEE (SWSW or SWWS.)
In Goswami, et alia's 2013 research, children with developmental dyslexia did more
poorly on the Dee-dee task than both age-matched controls and younger, reading-level
matched controls.
Phonological Awareness
In Huss, et alia's 2011 research discussed above, the researchers also gave the children a
rhyme oddity task to test their phonological awareness. The children listened through
headphones to twenty sets of three words, such as "gap, nap, Jack." The task was to
identify the word that did not rhyme with the others. The dyslexic group performed
significantly worse than their chronological age matched controls, but not much more
poorly than their reading level matched controls.
Huss and her team also tested children's phonological short-term memory. Children
listened to four monosyllables and were required to repeat them back. There were sixteen
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
8
trials. Again, the dyslexic children performed significantly below their chronological age
matched controls, but not very different from their reading level matched controls.
The children in Huss, et alia's 2011 study were 8 to 13 years of age, and seemed to lag
behind their chronological age matched controls. Vandermosten, Boets, Luts, Poelmans,
Wouters, and Ghesquiere (2011) performed a longitudinal study on 11-year-old dyslexic
children who were being followed up from kindergarten. This study served more than one
purpose. First, the study found that children with dyslexia have trouble with phonological
awareness and categorization when listening to both speech and non-speech sounds.
Second, that the deficit is temporal in nature, and not connected to the character of the
speech. Dyslexic children had more trouble labeling sounds with rapidly changing
information than labeling sounds with steady rates of change.
Third, when compared with results from the same study design performed with different
age groups, including adults, we see developmental progress in dyslexic children running
parallel to and lagging behind their typical age-mates. The size of the temporal
processing deficit does not change over time; therefore, dyslexic readers lag behind their
peers consistently as they all develop. This gap continues into adulthood.
2.5 Cerebellar Hypothesis
And finally, studies indicate that dyslexic brains have cerebellar anatomical differences
from brains of typical readers. Technologies such as functional magnetic resonance
imaging (fMRI) have given us the ability to see what areas of a subject's brain are
activated during specific tasks. In 2009, Baillieux, Vandervliet, Monto, Parizel, De Deyn,
and Marien presented a new hypothesis: the cerebellar hypothesis of dyslexia.
Baillieux and team worked with a small group of dyslexic and typical children from 10 to
12 years of age with similar intelligence quotient scores. The average verbal IQ score
among dyslexic children was 113, and the average verbal IQ score among their typical
reading peers was 110. All of the subjects were given fMRI's during a noun-verb
association task, in which the subjects heard a noun and were asked to come up with a
verb associated with it. For example, the subject might hear "boat" and think of the verb
"sailing." Nouns were presented through headphones every three seconds.
Typical readers presented with bilateral activation in the cerebral hemispheres during
verb generation. Dyslexic children presented with more widespread and diffuse
activations on the cerebral and cerebellar level. Dyslexic activation was more scattered
all over the left hemisphere and in different spots in the right hemisphere than typical
readers. Typical subjects activated anterior sections of the right hemisphere, but dyslexic
readers presented with activation in the right occipital lobe. These results caused
Baillieux and his team to theorize that developmental dyslexia is due to a core deficit in
the processing of information in the cerebellar cortex.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
9
Christodoulou, Del Tufo, Lymberis, Saxler, Ghosh, Traintafyllou, Whitfield-Gabrieli,
and Gabrieli (2014) used fMRI technology to compare neural correlates of reading
fluency in adults with and without developmental dyslexia. Not only were the adult
dyslexic readers slower and less accurate than typical readers, dyslexic subjects also
showed less activation, primarily in the left hemisphere and also in the cerebellum. This
supports the premise that developmental dyslexia is a lifelong condition. The researchers
concluded that the weakened engagement of the brain could be the cause of reading
fluency deficits seen in developmental dyslexia.
2.6 Dyslexia and Mathematics
De Smedt and Boets (2010) refer to cognitive neuroimaging data suggesting "a neural
overlap between phonological processing and arithmetic fact retrieval in the lefttemporal-parietal junction, in particular in the left angular and supramarginal gyri." The
same area of the brain in which phonology is processed is also used during arithmetic fact
retrieval; therefore, it makes sense that dyslexics, due to their deficit in phonological
processing, would also have trouble with mathematics.
Also in 2010, Vukovic, et al., explained that there was a compilation of research pointing
toward mathematical deficits in children with reading comprehension difficulty (RD,) but
this body of research did not distinguish between dyslexia and other forms of RD.
Operations refer primarily to the ability to perform mathematical operations using
previously learned rules, such as addition. Arithmetic fact fluency refers to a student's
ability to quickly and efficiently remember math facts and apply them. Arithmetic fact
fluency relies on an understanding of operations as well as working memory, and is
necessary for solving word problems.
The Vukovic team (2010) examined the mathematical abilities of students with RD,
developmental dyslexia, and their typically developing peers. They found that it was the
children with dyslexia who had the most trouble with arithmetic fact fluency, operations,
and applied problems, respectively. Children with RD did not show arithmetic fact
fluency deficits. The findings in this research support the hypotheses that phonological
processing underlies the development of arithmetic fact fluency.
Dyscalculia
Dyscalculia is a diagnosis for impairment with mathematics. It represents a pattern of
difficulties with processing numerical information. In 2009, Landerl, Fussenegger, Moll,
and Willburger clarified that dyslexia and dyscalculia have two separate cognitive
profiles. Subjects with dyscalculia have trouble understanding magnitude, which is a
different deficit than arithmetic fact fluency.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
10
Dyslexia is sometimes comorbid with dyscalculia. Vukovic's 2010 research showed
evidence that dyslexic subjects who do not have dyscalculia do have arithmetic fact
fluency problems.
3.0 Method
The purpose of this research was to further investigate the possible connection between
the phonological processing deficit often present in developmental dyslexia and deficits
in arithmetic fact fluency. We were inspired by Bert De Smedt and Bart Boets' 2010
research, "Phonological processing and arithmetic fact retrieval: Evidence from
developmental dyslexia." Their research built on cognitive neuroimaging data, which
suggested a neural overlap between phonological processing and arithmetic fact retrieval.
De Smedt and Boets examined arithmetic fact retrieval and its relation with phonological
processing in adults with developmental dyslexia and matched controls. They did find
that adults with developmental dyslexia were slower in single-digit arithmetic.
3.1 Participants
We looked for subjects between the ages of 18-24 who had at some point in their lives
been diagnosed with a reading disorder as well as controls in the same age group. We
hypothesized that those participants who exhibit a phonological deficit will also exhibit
an arithmetic fact fluency deficit.
We advertised on two college campuses, the College of St. Joseph in Rutland, Vermont
and Castleton State College in Castleton, Vermont. Taylor also recruited two participants
via her social acquaintances.
Table 1, Male/Female Demographic
All participants between the ages of 19-23:
Control Group (N=7)
Experimental Group (N=2)
Male
Female
Male
1
6
2
Female
0
Testing was performed on three separate days. One student at the College of St. Joseph
showed up to participate on the first day. Taylor recruited two participants for the second
day. On the third day at Castleton State College, another six students volunteered to be
tested. We had a grand total of nine participants.
All volunteers were given a statement of informed consent to read and sign, and were
given the opportunity to ask questions. They were guaranteed confidentiality; Taylor
gave each profile a number and letter code. Taylor was the only researcher who had
access to which participants had a diagnosis and which did not.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
11
After signing the statement of informed consent, volunteers filled out a short form
indicating whether they have ever been diagnosed a with reading disorder, when they
were diagnosed and by whom (for example, an educator or a pediatrician, etc.) They were
asked whether they had a diagnosis of ADHD or dyscalculia.
None of the females reported any diagnosis. All three males reported one diagnosis, as
seen below, in Table 2.
Table 2, Diagnoses
ADHD
Dyslexia
RD (and
minor
hearing
disorder)
Control Group
Male
1
Experimental Group
Male
1
1
"RD" = other reading disorder.
3.2 Instrumentation
Four tests were given to each participant: one phonics test and three written tests. The
phonics test was given one-on-one in a private room, and the three written tests were
administered in a group, classroom setting. At CSJ, the single participant took all four
tests in a private room.
Phonological Awareness
D&B found significant differences between the phonological processing of dyslexic and
control subjects using phoneme deletion and spoonerisms.
We received permission from Pro-Ed to make copies of two subtests from the
Comprehensive Test of Phonological Processing (CTOPP): Elision (EL) and Blending
Words (BW.) EL is a 20-item subtest that measures a subject's ability to say a word, and
then say the word while dropping out one sound. It begins with items simply requiring
dropping a whole word from a compound word (for example, say "toothbrush" without
saying "tooth.") The test proceeds with increasingly smaller segments at increasing
higher levels of linguistic complexity, from words, to syllables, to onset and rime units,
and individual phonemes. For example, a subject may be asked to say the word, "bold."
After complying, the subject is asked, "Now say the word 'bold' without saying /b/." The
correct response is "old."
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
12
BW measures a subject's ability to combine sounds to form words. Blending sounds into
words is an important phonological skill for readers at all levels. New words are decoded
by sounding out individual letters and word parts. Readers then blend these sounds
together to match words in their vocabulary. For example, the subject listens to a
recording that asks, "What word do these sounds make? /t/ and /oi/" The correct response
is "toy."
EL and BW make up the phonological awareness composite for subjects 7 through 24
years of age. The composite measures an individual's awareness of and access to the
phonological structure of oral language. The composite standard score has a mean of 100
and a standard deviation of 15. We hypothesized that reading disordered students would
show less aptitude for these subtests.
We used the Comprehensive Test of Phonological Processing (CTOPP) manual published
by in 1999 to hypothesize our a priori expectations. A CTOPP subtest scaled score of 7 is
equivalent to a CTOPP composite score of 85. EL and BW are the two components of the
Phonological Awareness Composite Score (PACS.) These scores are the equivalent of a
t-score of 40 and a percentile rank of 16. We hypothesized that our EX would score here
or below.
A CTOPP subtest scaled score of 8 is the equivalent of a PACS of 90, a t-score of 43 and
a percentile rank of 25. We hypothesized a priori that all CG participants would score
here or above.
Reading Comprehension
We gave the Reading Rate and Comprehension sections of the Nelson-Denny (ND) to the
group to ascertain level of reading fluency. The original ND was used from 1929 to 1959,
and was revised in 1960. Its primary purpose is to rank student ability in vocabulary
development, reading comprehension and reading rate. We did not administer the
vocabulary section of the test. The ND is normed on students in grades 9 through 16, and
is used to test the reading ability of adults.
We used the test to measure whether subjects in the EX do have a measurable reading
difference or disorder. We hypothesized that dyslexic and reading disordered students
would score lower on reading rate (which is reading speed) on the ND than controls.
The Riverside Publishing Company in Chicago, Illinois published the Nelson-Denny
Manual for Scoring and Interpretation in 1993. The scaled scores for all subtests have a
mean of 200 and a standard deviation of 25. Percentile ranks are different for populations
in high school, two-year colleges, and four- year colleges and universities. We set our a
priori cut-off points via Grade 13, before January 15, for four-year college and university
students. We expected EX participants to score at or below the 15th percentile in Reading
Rate and Reading Comprehension. The 15th percentile correlates with a scaled score of
180.5 for Reading Rate, and 181 for Reading Comprehension.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
13
We also expected, a priori, that CG participants would score in the 20th percentile or
above for reading rate and reading comprehension. The 20th percentile correlates with a
standard reading rate score of 183.5, and a standard reading comprehension score of 185.
A slower reading speed may result in a lower Comprehension score, as the ND gives one
point for each correctly answered question. When a student is able to answer fewer
questions, this decreases the potential score. We are interested in percentage of questions
answered correctly out of questions answered, and are including this third measure in our
data. We hypothesize that a reading disorder will continue to slow down adult readers
and, therefore, their reading rate scores will be lower than controls. This, however, does
not necessarily correlate with how much they understand what they read. We
hypothesized that the percentage of questions answered correctly will not differ between
the two groups, but will remain in the average or above average range for participants in
both nominal groups. In other words, we expected that adult college students with a
diagnosis of reading disorder will take longer to read, but will comprehend what they
read as well as the rest of the population. We chose a priori to assume that college
students would understand at least 80 percent of what they read on a timed test. We chose
to assume that our participants would earn a "B."
Arithmetic
D&B measured arithmetic fact fluency in their subjects via spoken responses. They found
that dyslexic subjects took longer to complete single digit arithmetic problems. We used
the Wechsler Individual Achievement Test, third edition (WIAT-III) subtests of
arithmetic fact fluency. WIAT-III is published by Pearson. The three arithmetic fact
fluency subtests are single-digit addition, subtraction and multiplication. Each subtest
measures how many single-digit problems a person answers correctly in one minute.
There are 48 addition, 48 subtraction, and 40 multiplication problems. We expected to
find a deficit in arithmetic fact fluency among dyslexic subjects.
The WIAT-III is a complex test of academic achievement and abilities normed on kids as
young as pre-K to 12+ grade. It is appropriate to use on undergraduate college students
and adults. Standardized scores of arithmetic fact fluency have a mean of 100 and a
standard deviation of 15. Our a priori cut-off points for the EX on arithmetic fact fluency
were 90 or below on the standard scale and 95 or above for the CG.
Control Test of Working Memory
We gave the non-verbal, picture-based Cancellation subtest from the Wechsler Adult
Intelligence Scale, fourth edition (WAIS-IV,) published by Pearson, to ascertain nonverbal working memory and processing speed. Cancellation measures skills that
do not require language processing. We expected a priori that a reading disorder will not
have an effect upon a student's ability to work with non-symbolic figures; therefore, we
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
14
expected both groups to do equally well on this test. We originally planned to throw out
any data on subjects who scored below average on this test. Scaled scores on this test
have a mean of 10 and a standard deviation of 3. Therefore, our a priori expectation is
that every participant in this study will earn a standard score of 7 or higher on the
Cancellation test.
Analysis 4.0
Our ability to analyze the data was compromised by the small sample size. Our
Experimental Group (EX) consists of two people, and our Control Group (CG) consists
of seven people.
We do not have a large enough sample size to run MANOVA, but hope that in the future
more data may be added to our data in order to do so. We have, however, taken a close
look at scores between the two groups for each test, as well compared variances among
the many factors.
4.1 Cancellation Test
The standardized scores for Cancellation have a mean of 10 and a standard deviation of 3.
Therefore, our a priori expectation was that all participants in both groups would score 7
or higher on this test. However, post hoc we see that one subject in the CG scored below
one standard deviation on this test (she earned a scaled score of 6.) When we exclude her
data, our mean goes up and the standard deviation decreases. Unfortunately, this also
brings our control group sample down to six individuals.
We have the added problem that one of our two EX participants did not understand the
instructions for taking the Cancellation test. His Cancellation test is therefore spoiled.
However, he presented as intelligent and highly motivated. Therefore, because of our
small sample size, we assume he would have scored within average or above average
range and choose to preserve his data.
The other experimental participant scored 14, which is above one standard deviation
above the mean.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Table 3.a Cancellation All Participants
All participants:
CG (N=7)
Mean
SD
Cancellation
11.71
3.99
DX (N=2)
Mean
14 /spoiled
SD
spoiled
DX (N=2)
Mean
14 /spoiled
SD
spoiled
Standard Mean: 10, SD: 3
Table 3.b Cancellation Exclude Low Score
Excluding low control group score:
CG (N=6)
Mean
Cancellation
12.67
SD
3.5
CG = control group. DX = experimental group.
Table 3.c Cancellation Means
All participants, N=8 (excluding one spoiled test)
Mean
SD
12
3.99
Cancellation
Because of the low sample size, we decided to keep all participant data in our
calculations and not exclude any participant data.
4.2 General Reading Ability
We gave the Nelson-Denny Comprehension and Reading Rate subtests as additional
measures for separating the two nominal groups.
Reading Rate
Table 4, Reading Rates
Standardized* Reading Rates
Control
Mean
197
SD
*Mean: 200, SD: 25
21.76
Experimental
Mean
SD
175.5
4.5
15
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
16
While the reading rates of participants in the experimental group are lower than controls,
they are officially within one standard deviation of the norm. Our a priori expectation for
the EX was a scaled score of 180.5 or below on reading rate, which correlates with the
15th percentile. Our a priori expectation for the CG was at or above the 25th percentile,
which correlates with a standard score of 185.
On average, our two experimental subjects read more slowly than our control subjects.
The EX mean of 175.5 is below our cut-off of 180.5. With such a small sample size it is
not possible to interpret from this data alone whether reading disordered individuals read
more slowly in adulthood than age-matched controls.
Reading Comprehension
In order to compare reading comprehension between the two groups, we looked at two
different measures. The reading comprehension scaled score is based upon number of
questions answered correctly out of the total, 38. We expected the EX group to earn
scaled scores of 181 or below, and our CG to earn reading comprehension scaled scores
of 185 and above.
Because slower readers will not answer as many questions on a timed test, we also looked
at what percentage of questions answered were correct.
Table 5, Reading Comprehension
Comp.
Mean
SD
CG SS
205.14
18.36
EX SS
174
2
Norms: Mean: 200, SD: 25
CG SS = Control Group Scaled Scores; EX SS = Experimental Group Scaled Scores
Our post hoc results seem to confirm our expectations. Figure 5 shows the actual standard
reading comprehension scores for each participant. Only one CG participant scored lower
than expected.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
17
Figure 1
Reading Comprehension Scaled Scores
250
Scaled Scores
200
150
219
210
223
223
204
172
176
185
CG Scaled
Score
172
100
Exp. SS
50
0
1
2
3
4
5
CG N=7; Exp. N=2
6
7
The relatively lower experimental scores could be a factor of reading rate, because a
slower reader will answer fewer questions on a timed test. Therefore, we also looked at
percentage of questions answered that were correct.
Table 6, Reading Percentages
Mean
SD
CG Comp Perc.
80.14
10.51
EX Comp Perc.
64.5
3.5
Our a priori expectation was everybody would get a "B," or 80 percent correct. Both EX
scores fall in the "D" range, and below the standard deviation for the CG. This may
indicate that the EX participants had more difficulty understanding what they read than
CG participants. Figure 2 shows the percentage of correct answered questions for each
participant.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
18
Figure 2
Percentage Correct
100
Percentage
80
60
61 61
72 68
78
85
88
88
89
CG
40
Exp.
20
0
1
2
3
4
5
CG N=7, Exp. N=2
6
7
4.3 Phonological Processing
Two subtests from the CTOPP help us determine our subject's phonological awareness
and ability to process phonological information efficiently. Elision (EL) and Blending
Words (BW) require the subject to listen to sound and demonstrate oral fluency dealing
with phonetic information. EL begins with items simply requiring dropping a whole word
from a compound word (for example, say "toothbrush" without saying "tooth.") The test
proceeds with increasingly smaller segments at increasingly higher levels of linguistic
complexity, from words, to syllables, to onset and rime units, and individual phonemes.
BW requires participants to listen to the separate sounds that make up a spoken word,
then say the word. Blending sounds into words is an important phonological skill for
readers at all levels. New words are decoded by sounding out individual letters and word
parts. Readers then blend these sounds together to match words in their vocabulary.
The scores from these two tests are standardized and together make the Phonological
Awareness Composite Score (PACS.) One phonological processing test with a control
group participant was spoiled via clinical error; therefore, we have 6 control and 2
experimental PACS.
Our a priori expectation for EX participants was a PACS of 85 or below, and for CG
participants we expected a PACS of 90 or above.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
19
Table 7, PACS
CG PACS
104.17
10.68
Mean
SD
EX PACS
90
0
Norms: Mean: 100, SD: 15
The mean of the CG PACS is 104.17 with a standard deviation of 10.68. Both EX PACS
are 90, which is higher than our a priori cut off of 85.
It is interesting to note that the one dyslexic subject mentioned that he had taken many
phonics tests. Without the practice effect, it is reasonable to wonder if he would have
done as well.
Figure 3
PACS
140
Composite Scores
120
100
115
90
110
90
105
110
100
85
80
CG PACS
60
EX PACS
40
20
0
1
2
3
4
CG N=6. EX N=2
5
6
4.4 Test of Arithmetic Fact Fluency
This test of arithmetic fact fluency from the WIAT-III is integral to our hypothesis that
phonological processing deficits and arithmetic fact fluency deficits are correlated.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
20
The Arithmetic Fact Fluency composite scores (AFFCS) combine the subject's speed
correctly solving single-digit addition, subtraction, and multiplication problems. Subjects
are given one minute to complete each test. Addition includes 48 problems, subtraction
also has 48 problems, and multiplication is only 40 problems. Credit is not given if a
problem is solved incorrectly.
The WIAT-III standard scores have a mean of 100 and a standard deviation of 15. Our a
priori cut-off points for the EX on arithmetic fact fluency were 90 or below on the
standard scale and 95 or above for the CG.
Table 8, AFFCS
CG AFFCS
96.43
12.74
Mean
SD
EX AFFCS
98.5
11.5
Norms: Mean: 100, SD: 15
Figure 4 displays each participant's composite score in Arithmetic Fact Fluency.
Figure 4
Arithmetic Fact Fluency
140
120
100
80
116
109
110
91
93
100
86
80
87
AFF CG Composite
60
AFF Exp Composite
40
20
0
1
2
3
4
5
CG N=7; Exp. N=2
6
7
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
21
5.0 Discussion and Conclusions
Developmental dyslexia is an extremely complicated learning disability that is not well
understood. Among the various theories of the etiology of dyslexia, most agree that
developmental dyslexia includes a neurological, phonological deficit. There is evidence
to suggest that this phonological deficit is correlated with deficits in arithmetic fact
fluency, and that these learning variances are life-long.
Cancellation
The results of what we thought of as a control, or equalizing test, were thought provoking.
The Cancellation sub-test of the WAIS-IV is a non-verbal test of working memory, and
we expected everyone to score within one standard deviation of the mean or higher.
Cancellation scaled scores have a mean of 10 and SD of 3; therefore, we expected
everyone to have a score at or above 7. We chose the mean, or 10, as our a priori
expectation for both groups.
One EX participant earned a score of 14. Due to a miscommunication or some confusion,
our other EX participant did not understand the directions for this subtest; however, he
presented as intelligent and highly motivated. The Control Group Cancellation scaled
scores ranged from 6 to 19. (Due to small sample size, we kept data from the participant
who scored 6.) Therefore, we had a relatively high-functioning group of voluntary
participants. This may make it easier for us to extrapolate that lower scores on any other
tests are due to diagnoses of organic reading problems and not overall level of
functioning.
The following Figures 5 and 6 display standard scores and raw scores for both groups on
the Cancellation test.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Figure 5
Cancellation Scaled Scores
19
Cancellation Scaled Score
20
18
16
14
12
15
14
12
11
11
10
8
8
CG SS
6
6
EX SS
4
2
0
1
2
3
4
5
CG N=7, EX N=1
6
7
Mean =10; SD = 3
Figure 6
Cancellation Raw Scores
80
68
70
Raw Scores
60
50
57
54
47
44
45
36
40
CG Raw
29
30
EX Raw
20
10
0
1
2
3
4
5
CG N=7, EX N=1
6
7
22
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
23
Reading Rate
Because people with dyslexia often read more slowly than their typical peers, our a priori
expectation was that EX participants would score in the below average range on the
Nelson-Denny reading rate test. The 15th percentile is in the below average range, and
for Grade 13 before January 15 in four-year colleges and universities, the 15th percentile
correlates with a standard reading rate score of 180.5 or below. We applied the NelsonDenny Grade 13 (Before Jan. 15) percentile ranks to all of our participant scores. We also
stated our a priori expectation that CG participants would score in the average range or
higher with the lowest CG standard score no lower 183.5 which correlates with the 20th
percentile.
Both of our EX participants scored in the below average range for reading rate; however,
4 out of 7 of our CG participants also scored below the 15th percentile for reading rate. In
other words, more than half of our CG college students scored as below average in
reading rate. This begs the question of whether they did not give full effort. Perhaps due
to the fact that they are likely required to read often as part of their schoolwork, they did
not strain themselves during this test because it was not a part of their curriculum. It is
also possible that they happen to be slow but efficient readers.
The following scatterplot shows the distribution of reading rates among our total of nine
participants.
Figure 7
Nelson-Denny Reading Rates
100
90
89
80
Percentile Rank
70
69
60
50
CG
40
40
EX
30
20
10
9
5
0
0
50
100
150
Standard Scores
13
200
250
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
24
Table 9 Chi Square Reading Rate Percentile Rank
Reading
Rate
CG
EX
Observed
Expected
36
25
10
15
A chi square test on Table 9 rendered a critical value of 0.039. We cannot reject the null
hypothesis that the reading rates among our participants are due to random sampling error.
Reading Comprehension
Nelson-Denny reading comprehension scores are based upon how many questions a
student answers correctly. It stands to reason that a student who reads more slowly would
answer fewer questions on a timed test. Therefore, we looked at both reading
comprehension scaled scores as well as the percentage of questions answered that each
student got right.
We expected to find that EX participants would earn lower scaled scores due to slower
reading rates. We also expected the EX participants to understand the same percentage of
questions answered as the CG participants. We chose a priori to assume that college
students would understand at least 80 percent of what they read on a timed test. We chose
to assume that our participants would earn a "B."
We were surprised to find that in addition to our Experimental Group participants
answering fewer questions, they also seemed to comprehend less than their Control
Group peers. Table 10 shows the mean of each group's percentage of questions answered
correct.
Table 10, Percentage Correct
CG
EX
observed
expected
80.14
80
64.5
80
Table 10 was put to the chi square test, which returned a value of 2.58 which is below the
critical value of 3.84. Therefore, the null hypothesis was not rejected.
At first blush, it looks as though reading disordered adults in college still do not
comprehend as much as control subjects, but our results do not reject the null hypothesis.
These scores could be due to random sampling error.
However, there are a multitude of possible reasons that we are seeing these scores. It was
surprising to see post hoc that three out of seven CG participants got less than 80 percent
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
25
of the questions answered correct. Perhaps some CG students are struggling with
undiagnosed reading issues. It could also be that this test was not as high-stakes as the
required reading many college students must comprehend for classes, and participants
may not have given it the same degree of attention and concentration they would for their
schoolwork. It is also possible that our a priori expectations were too high.
It is also interesting to note that the lower percentage of comprehension questions
answered correctly by our EX participants may be due to sampling error. Perhaps if we
had a greater number of participants in both groups, our chi square value would change.
Alternatively, not rejecting the null hypothesis may bode well for dyslexic adults. If other
researchers choose to replicate this research and add to this sampling of data, we may
gain increased understanding of whether dyslexic adults are successfully learning, on
average, to comprehend what they read.
Phonological Awareness and Arithmetic Fact Fluency
The possible correlation between phonological processing and arithmetic fact fluency is
the very heart of our hypothesis. We are testing the theory that a phonological processing
deficit, such as that associated with developmental dyslexia, is correlated to an arithmetic
fact fluency deficit and continues into adulthood.
Our a priori expectation was that dyslexic individuals would score no better than 7 on
Elision (EL) and 7 on Blending Words (BW) subtests. We expected to see and 85 on the
Phonological Awareness Composite Score (PACS.) These score would put students in the
16th percentile or lower. We expected a EL and BW scores of at least 8 and PACS of 90
or better from our CG; these scores equate with the 25th percentile. The post hoc results,
however, were surprising.
Table 11 PACS
Profile
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
DX15 M21
DX16 M20
EL SS
9
12
10
4
5
10
8
BW SS
spoiled 5
14
13
10
17
14
12
PACS
n/a
115
110
85
105
110
100
Percentile
n/a
84
75
16
63
75
50
8
10
8
6
90
90
25
25
CG = Control Group, DX = Experimental Group
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
26
Both EX participants earned a PACS of 90, placing them above our expectation. DX16
was not specifically dyslexic, but rather, was diagnosed with a reading disorder when in
elementary school. He did, however, mention a minor hearing problem that may have
affected his ability to score higher on phonics-based tests. He had trouble with BW,
which requires listening to a series of speech sounds and putting them together to make a
word. This would be extremely difficult for anybody with hearing problems.
DX15, the only participant with a diagnosis of dyslexia, mentioned that he has taken
many of these phonics tests in the past. He scored consistently in the 25th percentile,
above our cut-off point. It is possible that he scored as well as he did due to the practice
effect. It is also possible that his brain has developed ways of compensating that serve
him well. With only one dyslexic participant so far, it is difficult to speculate on why he
scored as well as he did, or if we may expect dyslexic adults to do as well or better on
phonological tests.
It is especially interesting to note that the CG participant with a diagnosis of ADHD
earned the only low PACS. His PACS was 85, putting him in the 16th percentile which is
where we expected our EX participants to score. This student had a difficult time with EL.
When he was asked to remove a sound from a two-syllable word, for example, "say
powder without saying [d]," he answered "pow" instead of "power." A minority of CG
participants had some difficulty with this, but they raised their composite scores well
within the average range due to their performance on the BW subtest.
It is unclear whether ADHD would inhibit a person's ability to focus on speech sounds,
especially when in other ways this participant was high functioning. His Cancellation
scaled score was 15, indicating above average non-verbal working memory and
processing speed.
Table 12, PACS Chi Square
PACS
CG
EX
observed
expected
104
90
90
85
Mean: 100, SD: 15
A chi square analysis on Table 12 returned a value of 0.175, which is lower than the
critical value of 3.84. We are surprised to retain the null hypothesis for the phonological
processing subtests.
While our scores could be due to sampling error, this is not surprising given our small
sample size. We would like to see this research design copied by others to increase the
sample size and, eventually, have a large pool of data.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
27
Our hypothesis is that the phonological processing deficit that we expected to see in our
EX would positively correlate with an arithmetic fact fluency deficit. The Arithmetic Fact
Fluency subtests of the WIAT-III render a composite score on a scale with a mean of 100
and a standard deviation of 15. Our a priori expected cut-off point for the EX was 90 on a
standard scale. Our a priori expectation was for the CG to score no less than 95. We were
incorrect on both counts.
Table 13 PACS and AFF
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
EL SS
9
12
10
4
5
10
8
BW SS
spoiled 5
14
13
10
17
14
12
PACS
n/a
115
110
85
105
110
100
Percentile
n/a
84
75
16
63
75
50
AFFCS
91
109
93
116
86
100
80
Percentile
Rank
27
73
32
86
18
50
9
EX
DX15 M21
DX16 M20
8
10
8
6
90
90
25
25
87
110
19
75
CG
AFFCS: Mean 100, SD: 15
EL SS: Mean: 10, SD: 3
BW SS: Mean: 10, SD: 3
PACS: Mean: 100, SD: 15
Our CG earned AFFCS anywhere from 80 to 116. Two CG scores are below our cut-off
of 90.
DX16, our participant with a history of general reading disorder, did especially well on
the math tests with a score of 110, in spite of his poor performance on Blending Words.
Of course, his BW score may be due to his hearing deficit; we cannot say with certainty
that he is dysphonic.
DX15, our dyslexic subject, scored 87 putting him in the 19th percentile. This may
indicate our hypothesis is correct and that a phonological processing deficit is correlated
with an arithmetic fact fluency deficit. However, two CG members scored worse on
arithmetic fact fluency than DX15. Neither of these two CG members with low AFFCS
did poorly on PACS, they may simply struggle with math. Their scores do not indicate a
positive correlation between phonological processing and arithmetic fact fluency in
people who do not have dyslexia. DX15's score profile, however, does seem to confirm
our hypothesis.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
28
CG14, who has ADHD, did poorly on PACS as discussed above, but earned the highest
AFFCS at 116, putting him in the 86th percentile. There seems to be no positive
correlation between the two sets of test scores for this subject, but we don't expect ADHD
to cause a phonological processing deficit. He may have scored poorly due to other issues,
especially if he has difficulty paying attention to sound.
We also cannot discount the possibility that the lack of pressure to do well may have
affected participant scores. College students are often under pressure to perform well and
earn good grades. The testing they agreed to do for us was not "high stakes," and their
performance on these tests will have no impact on their grade point averages in school.
We wonder if these facts may have caused them to unintentionally relax and not give full
effort. In a higher stakes environment, we wonder if they would have scored higher.
It is especially interesting to note that, on average, our EX performed better than our CG
on arithmetic fact fluency. This is the exact opposite of what we expected to find.
Table 14, AFFCS chi-square
AFFCS
CG
EX
observed
expected
96.42
95
98.5
90
Mean: 100, SD: 15
A chi square analysis on Table 14 returned a value of 0.135, which is lower than the
critical value of 3.841. We retain the null hypothesis that all of this is due to sampling
error.
Weaknesses in This Study
Our inspiration for this study, as discussed above, is the 2010 research by D&B. These
researchers had access to computer equipment and software that allowed them to monitor
a subject's reaction time to individual test questions, giving them a much more detailed
window into both motor reaction time as well as time it took their subjects to process
information. We do not have access to equipment necessary to administer tests requiring
this level of exactitude.
The most obvious weakness in this study is the low sample size. Rife with the possibility
for sampling errors, we have confirmed nothing at this time.
Strengths in This Study and Moving into the Future
Unlike the valuable research performed by D&B, this study is relatively easy and
inexpensive to replicate. If more researchers in more geographic areas wish to perform
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
29
the same study, they may include our data with their own. Over time, the sample size will
grow and we will have the opportunity to interpret a large database of young adults with
developmental dyslexia and matched controls. These eventual results will give us an
increased understanding of developmental dyslexia, deficits in phonological awareness,
and the connection to arithmetic fact fluency into adulthood.
Our data is preserved in the appendices of this thesis.
In this study, we chose to include diagnoses of reading disorders in the experimental
group. This was solely because of our small sample size. Ideally, we would have enough
subjects with developmental dyslexia that we would be able to exclude data from those
with other reading disorders, those with a diagnosis of ADHD, and those with a diagnosis
of dyscalculia or other deficits, including uncorrected hearing loss. We would also prefer
to exclude participants whose Cancellation scaled score was below one standard
deviation below the mean.
If other researchers choose to replicate this study, they may add their participant profiles
to our own. As the database grows, we may choose to exclude outliers such as low
Cancellation scores and additional diagnoses such as ADHD or dyscalculia. Then
someday we may get a clearer picture of how the phonological processing deficit
associated with developmental dyslexia affects arithmetic fact fluency into adulthood.
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
30
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Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
32
Appendix A: Demographic Data and Cancellation Test Data
Demographic:
Control Group
ID
Sex
Age
Diagnosis
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
F
F
F
M
F
F
F
19
22
23
22
21
21
21
ADHD
M
M
21
20
dyslexia
remedial reading
Notes
Experimental Group
DX15 M21
DX16 M20
Cancellation:
Control Group
ID
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
Cancellation
Scaled Score
11
19
12
15
6
8
11
Experimental Group
DX15 M21
DX16 M20
Mean: 10
SD: 3
spoiled
14
hearing problem
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
33
Appendix B: Phonological Awareness Data
Control Group
ID
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
Phonological
Awareness
Elision SS
9
12
10
4
5
10
8
Blending Words SS
spoiled 5
14
13
10
17
14
12
PACS
n/a
115
110
85
105
110
100
Percentile
n/a
84
75
16
63
75
50
8
10
8
6
90
90
25
25
Experimental Group
DX15 M21
DX16 M20
SS: Mean:10, SD:3
PACS Mean: 100, SD: 15
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
34
Appendix C: Arithmetic Fact Fluency Data
Control Group
ID
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
Arithmetic Fact Fluency
Raw
40 / 35 / 27
45 / 37 / 40
39 / 36 / 30
48 / 47 / 38
34 / 35 / 26
39 / 45 / 30
30 / 27 / 23
Raw Total
102
122
105
133
95
114
80
AFFCS*
91
109
93
116
86
100
80
Percentile
Rank
27
73
32
86
18
50
9
38 / 34 / 24
48 / 45 / 33
96
126
87
110
19
75
Experimental
Group
DX15 M21
DX16 M20
*AFFCS = Arithmetic Fact Fluency Composite Score; Mean: 100, SD: 15
Examining The Correlation Between Phonological Deficit and Arithmetic Fact
Fluency Deficit in Adults
Appendix D: Reading Rate and Reading Comprehension Data
Reading Rate:
Control Group
ID
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
Nelson-Denny
Rate, Raw
154
211
261
339
137
137
154
Rate, Scaled Score
180
198
213
236
175
175
180
Experimental
Group
DX15 M21
DX16 M20
123
154
171
180
SS: Mean: 200, SD: 25
Comprehension:
Control Group
ID
CG11 F19
CG12 F22
CG13 F23
CG14 M22
CG17 F21
CG18 F21
CG19 F21
Nelson-Denny
Comprehension
Scaled Score
172
219
210
223
223
204
185
Comprehension
Percentage Correct
72
88
89
88
78
85
61
Experimental
Group
DX15 M21
DX16 M20
Scaled Score: Mean:200, SD:25
172
176
61
68
35