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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 References 1. Agus, Trevor R.; Carrion-Castillo, Amaia; Pressnitzer, Daniel; Ramus, Franck (2014). Perceptual Learning of Acoustic Noise by Individuals With Dyslexia. Journal of Speech, Language, and Hearing Research. Volume 57, pps. 1069-1077. 2. Baillieux, Hanne; Vandervliet, Everhard J.M.; Monto, Mario; Parizel, Paul M.; De Deyn, Peter P. and Marien, Peter. (2009). Developmental dyslexia and widespread activation across the cerebellar hemispheres. Brain and Language, 108 pps. 122-132. 3. Boets, Bart and De Smedt, Bert; (2010). Single-digit Arithmetic in Children with Dyslexia. Dyslexia 16; pps. 193-191. 4. Boets, Bart; Wouters, Jan; van Wieringen, Astrid; and Ghesquiere, Pol (2007). Auditory processing, speech perception and phonological ability in preschool children at high-risk for dyslexia: A longitudinal study of the auditory processing theory. Neuropsychologia 45; pps. 1608-1620. 5. Christodoulou, Joanna A.; Del Tufo, Stephanie N.; Lymberis, John; Saxler, Patricia K.; Ghosh, Satrajit S.; Traintafyllou, Christina; Whitfield-Gabrieli, Susan; Gabrieli, John D. E. (2014). Brain Bases of Reading Fluency in Typical Reading and Impaired Fluency in Dyslexia. Plos One, Volume 9, Issue 7. 6. Corriveau, Kathleen H. and Goswami, Usha (2009). Rhythmic motor entrainment in children with speech and language impairments: Tapping to the beat. Cortex 45, pps. 119-130. 7. De Smedt, Bert; Boets, Bart (2010). Phonological processing and arithmetic fact retrieval: Evidence from developmental dyslexia. Neuropsychologia 48, pps. 3973-3981. 8. Ferreira De Carvalho, Carolina; de Souza Batista Kida, Adriana; Aparacida Capellini, Simone; and Brandao, Clara Regina (2014). Phonological working memory and reading in students with dyslexia. Frontiers in Psychology. 9. Goswami, Usha. http://www.neuroscience.cam.ac.uk/directory/profile.php?ucg10 10. Goswami, Usha (2011). A temporal sampling framework for developmental dyslexia. Trends in Cognitive Sciences, Volume 15, No. 1. 11. Goswami, Usha; Huss, Martina; Mead, Natasha; Fosker, Tim and Verney, John P. (2013). Perception of patterns of musical beat distribution in phonological developmental dyslexia: Significant longitudinal relations with word reading and reading comprehension. Cortex 49, pps. 1363-1376. 12. Goswami, Usha; Mead, Natasha; Fosker, Tim; Huss, Martina; Barnes, Lisa and Leong, Victoria (2013). Impaired perception of syllable stress in children with dyslexia: A longitudinal study. Journal of Memory and Language 69, pps. 1-17. Examining The Correlation Between Phonological Deficit and Arithmetic Fact Fluency Deficit in Adults 31 13. Huss, Martina; Verney, John P.; Fosker, Tim; Mead, Natasha and Goswami, Usha (2011). Music, rhythm, rise time perception and developmental dyslexia: Perception of musical meter predicts reading and phonology. Cortex 47, pps. 674689. 14. Landerl, Karin; Fussenegger, Barbara; Moll, Kristina; Willburger, Edith; (2009). Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology 103 pps. 309-324. 15. Leong, Victoria; Hamalainen, Jarmo; Soltesz, Fruzsina and Goswami, Usha (2011). Rise time perception and detection of syllable stress in adults with developmental dyslexia. Journal of Memory and Language 64, pps. 59-73. 16. Nosworthy, Nadia; Bugden, Stephanie; Archibald, Lisa; Evans, Barrie and Ansaril, Daniel. (2013). A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children's Arithmetic Competence. Plos One. 17. Simmons, Fiona R. and Singleton, Chris; (2008). Do Weak Phonological Representations Impact on Arithmetic Development? A Review of Research into Arithmetic and Dyslexia. Dyslexia 14, pps. 77-94. 18. Skottun, Bernt C.; Sloyles, John R. (2010). Temporal order judgement in dyslexia -- task difficulty or temporal processing deficiency? Neuropsychologia 48, pps. 2226-2229. 19. Suk-Han Ho, Connie; Wai-Ock Chan, David; Tsang, Suk-Man; and Lee, Suk-Han (2002). The Cognitive Profile and Multiple-Deficit Hypothesis in Chinese Developmental Dyslexia. Developmental Psychology, Volume 38, No. 4, pps. 543-553. 20. Valdois, Sylviane; Bosse, Marie-Line and Tainturier (2004). The Cognitive Deficits Responsible for Developmental Dyslexia: Review of Evidence for a Selective Visual Attentional Disorder. Dyslexia 10, pps. 339-363. 21. Vandermosten, Maaike; Boets, Bart; Luts, Heleen; Poelmans, Hanne; Wouters, Jan and Ghesquiere, Pol (2011). Impairments in speech and nonspeech sound categorization in children with dyslexia are driven by temporal processing difficulties. Research in Developmental Disabilities 32, pps. 593-603. 22. Vukovic, Rose K.; Lesaux, Nonie K.; Siegel, Linda S. (2010). The mathematics skills of children with reading difficulties. Learning and Individual Differences 20 pps. 639-643 23. Vukovic, Rose K. and Siegel, Linda S. (2006). The Double-Deficit Hypothesis: A Comprehensive Analuysis of the Evidence. Journal of Learning Disabilities, Volume 39, Number 1, pps. 25-47. 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