Dyscalculia an overview of research of a learning disability

Dyscalculia an overview of research of a learning disability Teresa Guillemot Teacher Education Programme [Mathematics and Computing] toc99001@student.mdh.se 1.1 Abstract Dyscalculia is a mathematical learning disorder that some researchers claim to have proven that it exists. Other researchers beg to differ. Students with mathematical learning disabilities can today in some schools in Sweden be diagnosed with dyscalculia and get directed education fitting their needs. This is not the case on every school around the world. The concept of dyscalculia is still being discussed, researched, tested and scrutinized in several institutions in different countries. Test results indicate that somewhere between 3-6% of the population suffers from severe mathematical learning disorders. Some even to the extent that it impairs their daily life. Recently there have been discoveries made that mathematical operations are connected to an area in the left side of the brain. If this fact can be scientifically proven, then we are one step closer to solve the mystery of number blindness. 1.2 Introduction In the pedagogical and neuropsychological branches today, different views exist of mathematical learning disorders. Dyscalculia has been defined as a specific mathematical learning disorder (MLD), where the mathematical ability is far below normal for a person s age, intelligence, and education. Researchers and scientists have different opinions on whether dyscalculia is a scientific fact or not, or where it originates from in case of existence. This survey is focused on recent work from both perspectives, looking into possible explanations of the phenomenon. Teachers, parents and students are often aware of the fact that there are a number of persons with special difficulties learning mathematics. Persons with learning disorders may feel uncomfortable in learning situations, unless they are being treated in an appropriate way that facilitates learning. In order to give the proper education to a person with a learning disorder, it is essential to understand the best suitable ways persons with learning disabilities can acquire mathematical understanding, which is closely associated with abstract thinking. Early findings pointing towards an area in the brain connected to abstract thinking were discovered by the French neurologist Paul Broca in 1861 (Brian Butterworth, The Mathematical Brain, 1999). The German Dr Josef Gerstmann examined patients in 1924 that had lost their ability to perform mathematical operations due to damage to the left side of the brain, later called Gerstmann s syndrome. The disposition of this paper starts with definitions of the topics discussed [1.3], followed by a survey of recent work from different authors in the field of research [1.4], not necessarily in chronological order. The surveyed work will be discussed in [1.5] and ended with references in [1.6]. References in text are given as end notes and are found on the last page.

1.3 Definitions Different types of dyscalculia: Developmental dyscalculia: dyscalculia due to a specific impairment in brain function 1, not yet fully acknowledged by the research community but the neuroscience research field has increased, where studies are conducted concerning the brain (Wilson & Dehaene, 2007). Acalculia: where a person has lost all sense of meaning of numbers or where the person still understands numbers but is unable to perform basic calculations like addition and multiplication, due to neurological damage. General difficulties in learning math. Pseudo-dyscalculia: finding math difficult, based on emotional blockage or a confidence problem Different reasons for dyscalculia: Core deficit hypothesis (Wilson & Dehaene, 2007) analogies are made between dyslexia 2 and dyscalculia. Even though the knowledge of its behavioural manifestations is incomplete, neuroimaging results point to a specific region in the brain when it comes to numerical handling. Wilson & Dehaene examine the evidence to support their hypothesis that some types of dyscalculia are caused by an impairment of function in different regions in the brain. Working memory; Wilson and Dehaene 3 suggest a controversial definition of dyscalculia, namely a deficit in the components of the working memory, which is supported by the Swedish neuropsychologist, Björn Adler, author of What is dyscalculia (2001). Adler runs Cognitive Centre in Sweden and offers solutions for diagnosing and handling dyscalculia. 1.4 Result In an overview 4, Von Aster (2000) wrote about the current state of dyscalculia, also describing a study made in Zürich, defining three subtypes of dyscalculia. The Verbal subtype was defined as children with the largest difficulty when counting, especially when counting mentally. Subtraction is most problematic and also remembering methods of counting. Children with verbal subtypes also had other deficits. In nine of eleven in the study, Von Aster found dyslexic similar conditions, and six of them also had ADHD. The Arabic subtype included children with problems reading Arabic numbers out loud and writing them from hearing the numbers, but with no further learning disabilities. The third group, the Pervasive subtypes, included disabilities with most mathematical thinking, writing, spelling and also possessed emotional and behavioural problems. Gunnar Sjöberg (2006) is of the opinion that the results pointing towards dyscalculia as an indication of difficulties in mathematics are inconclusive, rather the pupils have not put enough effort and time into their work with math. Sjöberg (2006) claims that research results showing that 6% of compulsory school pupils suffer from dyscalculia are incorrectly interpreted. Sjöberg (2006) presents his conclusions in a thesis where he studied 200 pupils from Year 5 in the Swedish compulsory school, to Year 2 in the upper secondary school during a six year period. 13 of these students were having specific mathematical problems. Material was gathered regularly where pupils filled in questionnaires. 100 classroom

observations were made, 40 of them video recorded. On two occasions Sjöberg conducted indepth interviews with the 13 pupils who had specific mathematical problems. Sjöberg noticed other components that could affect the pupil s low understanding of math, like a low work rate during the lessons, disturbance in the classroom environment, large groups, and emotional stress about test situations. The results of the study did not refute an existence of dyscalculia as a concept, but the findings made Sjöberg draw the conclusion that diagnosing dyscalculia should be exercised cautiously or not at all. All the students finished math studies in upper secondary school with satisfying results. This led Sjöberg to the conclusion that to make a diagnose the whole environment has to be examined, not only the pupil with the mathematical learning disorder. According to Shalev, Gross-Tsur et al. (2000) there are about 3 6% schoolchildren with dyscalculia. The range was interpreted as a consequence of different definitions of developmental dyscalculia. To determine prevalence we must develop a scientific and clinical consensus as to what constitutes a learning disability and which definition best describes the problem. (2000). The definitions of dyscalculia were not precise, Shalev, Gross-Tsur et al. are referring to different options like; a specific, genetically determined learning disability in a child with normal intelligence and a learning disability in mathematics, the diagnosis of which is established when arithmetic performance is substantially below that expected for age, intelligence and education. The first study of prevalence was made by Kosc in Bratislava in 1974, using different mathematical assignments of basic character. Kosc regarded the children with results below the 10 th percentile as dyscalculic, which was 6.4% of the 375 fifth-graders participating in the study. Several other studies 5 have been made in other countries showing similar figures. Margin of errors in these studies are reading difficulties, dyslexia, ADHD 6 and other disabilities, since children with these difficulties tend to show poorer arithmetic skills than if only having dyscalculia. Shalev and Gross-Tsur (2000) acknowledge that other authors emphasize other reasons than brain dysfunctions for dyscalculia; lower social and economic status, mathematical anxiety, large classes and less well thought-through curricula and teaching. Dr Cohen Kadosh 7 (Cohen Kadosh et al., Virtual Dyscalculia Induced by Parietal-Lobe TMS Impairs Automatic Magnitude Processing, 2007) discovered through tests using functional Magnetic Resonance Imaging (fmri) that a specific part of the brain, the intraparietal sulcus (IPS), see figure A, is associated with automatic magnitude processing 8. In order to cope with ambiguous results regarding the left and the right side of the brain, a transcranial magnetic stimulation (TMS) was used to block the activation of the IPS on one side at a time. When blocking the right side of the brain, the test persons appeared to obtain dyscalculic behaviour, as opposed to without the blocking, where there was no appearance of dyscalculic behaviour. The experimenters also took into consideration that other areas communicating with the brain could be affected by the TMS, but according to the fmri no other areas showed any activity during automatic magnitude processing. However, the researchers do not claim to have found the cause of dyscalculia, since it is not clear to whether developmental dyscalculia and effects produced through TMS are identical deficits. The experimental procedures were carefully described in the report. ONLY 5 subjects were tested. Earlier studies have been made, one of them by Professor Brian Butterworth 9, identifying the IPS as the centre responsible for handling number information 10.

Figure A 11 Rubinstein and Henik (2009) regard the IPS findings as surprising. Reasons stated are; heterogeneous behavioural deficits, comorbidity 12 and number processing represented in more than one brain area. Developmental disorders often generate multiple problems. How is it possible to sort out the dyscalculia? Rubinstein and Henik (2009) focus on three different views; single restricted biological deficit, cognitive deficits due to instances of biological damage, and finally neurocognitive damage causing developmental dyscalculia may result in several, not related, behavioural disorders. Rubinstein and Henik consider brain dysfunction as a possible reason for dyscalculia and state that evidence has been found that IPS is involved in attention and related cognitive processes. Injury in the IPS area can thus result dyscalculia. The authors recommend future researchers to examine the whole brain, since developmental disorders are heterogeneous. Focusing on single brain-behaviour deficits exclusively could prevent understanding of the variety of deficits connected to developmental dyscalculia and MLD, yet standardized tests of arithmetic computation can be a helpful screening tool to detect and separate dyscalculia from MLD. Geary et al. 13 (2009) refers to other authors 14 when it comes to predicting the amount of children diagnosed with a mathematical learning disorder (MLD), which is between 5-10%. It is critical on multiple levels that the diagnosis is made early and measures can be taken in order to help the child developing their mathematical abilities in the future. The early stages of mathematical learning are essential for later outcome in the education. The authors point out that the reason for mathematical learning disorders are still being investigated, even if some conclusions have been drawn about the main areas contributing to the disorder. Comparisons between normal achieving children and children with a MLD have been made. The latter group s counting strategies are less mature, their understanding of counting is not fully developed and they have continuous hardships with learning math and recalling basic arithmetic facts stored in the long-term memory (2009). Working memory has come to develop a central role in the area of MLD. Children with MLD probably have a dysfunction in the basic recognition of numbers and their magnitude (2009). Number Sets Tests were designed by Geary et al. (2009) to measure the speed and correctness to which the children solved basic number and quantity recognition. The further developed test was meant to serve as a quick screening to find sensitivity for numbers and predict MLD. Participants in the test were 228 children from kindergarten, first, second and third grade. In the analysis proficiency scores and first grade IQ, working memory, and mathematical cognition test scores were taken into consideration. The IQ scores were measured using a test

by Wechsler Abbreviated Intelligence Scale 15. Examples of understanding numbers see example item in figure B. Figure B (Geary et al., 2009) Number estimation was assessed through number lines with a blank line with two endpoints; 0 and 100. The assignment was to mark on the line where the number presented should lie on the line. The score was defined as the absolute difference between the marking of the number and the correct position of the number. The overall score was calculated as the mean of these differences across the trials. Measuring the children s counting ability was made by letting the child look at a puppet counting red and blue chips. The child had to tell if the puppet had made a correct calculation, and not double-calculated, by saying OK or Not OK. Geary et al. noted that children with MLD made errors throughout the test when the first chip was counted twice like one one two three etc. The score for this part of the test was calculated as a percentage of the number of times the child successfully identified wrong calculations. To further asses the children s addition strategies, a mix of simple and complex addition problems were showed one at a time. Each problem should be solved as quickly and correctly as possible. The child could use any strategy to get the answer, but without pen and paper. The answer was to be told out loud. Geary et al. (2009) classified the trials into six different categories; specifically, counting fingers, fingers, verbal counting, retrieval, decomposition 16 or other/mixed strategy. The percentage of correct direct-retrieval trials for simple problems was correlated with the mathematics achievement scores, and used in the analysis (2009). The Working Memory Test Battery for Children 17 is composed by nine subtests in order to assess the central executive, phonological loop, and visuospatial sketchpad (Geary et al., 2009). The tests have six items from one to six to one to nine, where four were to be

remembered to get to the next level. To get to the next level after that, the numbers remembered increased by one. The test ended when the child failed three times in a row. The central executive was tested through three different tests; Listening Recall, Counting Recall and Backward Digit Recall. The idea of the first test is listening to a sentence, then determining if it was true or false and then repeat the last word in a series of sentences. The second test then demands of the child to count a set of dots on a card, maximum seven, and then remember the number of counted dots at the end of a series of cards. The third test, Backward Digit Recall is a standard format backward digit span 18 (Geary et al., 2009). The Phonological loop was tested by Digit Recall, Word List Recall, and Nonword List Recall, for instance by repeating words spoken by the experimenter in the same order. Series of words were presented to the child in the Word List Matching task. Then the words were presented again, maybe in another order, and the child had to decide whether the second list had the same order as the first list. The Visuospatial sketch pad was tried with other span tasks, like Block Recall. A board was set up with nine one-sided numbered blocks in a random arrangement. The numbers could only bee seen by the experimenter. Then the experimenter touches series of blocks and the child should repeat the order. Mazes Memory task is conducted like this; the child gets a picture of a maze with more than one solution. A picture of an identical maze with a one solution drawn is presented. The child s task is to replicate the solution when the picture is removed. After a successful trial, the maze increases with one wall. The tests were conducted every term for each age group, except for the children in kindergarten who were tested one time in spring. The location was at their schools in a quiet place most of the time. Some of the children s tests were executed on the university campus or in a mobile testing van. A score below the 15th percentile on the mathematics achievement test characterized the child as having a MLD. Results between the 15th and 30th percentiles considered as low achieving pupils (Geary et al., 2009). Pupils with results above the 30th percentile were considered normal achieving. To find the most accurate measure to predict third grade mathematics achievement, all measures were compared in independent regressions. The central executive and sensitivity measures predicted 25% in the variation; the number line scores predicted 27%. The number line measure appears to somewhat assess children s intuitive understanding of numerical quantity. The researchers claim that their results provide initial support for their hypothesis. Competencies assessed by the sensitivity score are unrelated to reading achievement and achievement in general or to IQ or working memory (Geary et al., 2009). 96% of the non-mld children in third grade were correctly identified in first grade. According to Geary et al. (2009) the Number Sets Test is a potential screening tool for discovering children prone to MLD at an early stage. The results from the test in early first grade can be used to detect 67% of children risking MLD at the end of third grade and to correctly identify nearly 90% of non-mld children. Benefits of early identification of children at risk for MLD would be; early remedial services, and low costs. The authors emphasize that the Number Sets Test is not yet ready for use as a diagnostic tool since the test is not normed and it can not be used for predictions for after third grade. To enable further tests, the authors are willing to provide the test on request.

1.5 Discussion Dyscalculia is a topic widely discussed in pedagogical and neuropsychological forums. The cousin Dyslexia has previously been established as a proper diagnose of learning disorder after years of controversies between scientists and researchers. Still the researchers and paper writers have not reached consensus about how to regard dyscalculia. There are those who find the matter settled and have already started to sell solutions to diagnosing and handling this learning disorder. Björn Adler has been on the market for at least a couple of years, providing screening tests to diagnose dyscalculia. Gunnar Sjöberg (2006) on the other hand, is of the opinion that dyscalculia has not been defined and indicates that other reasons may be cause. Rubinstein and Henik (2009) are not satisfied with defining dyscalculia as being a separate disorder, but rather depending on various disorders. Kosc was one of the first researchers to make a large scale test on mathematical disorders (Gross-Tsur et al., 2000). He came up with the result that 3-6% of the tested children suffered from a mathematical learning disorder. Later performed studies by other researchers show around the same percentage. Still others point to other parameters like large groups, disturbing environments, bad teaching and mathematical anxiety. Recent research has although been made in this area, indicating that mathematical abilities can be connected to the left side of the brain, in the IPS. Roi Cohen Kadosh et al. (2007) have performed clinical studies on the brain using fmri, with results confirming the IPS as a centre for number cognition. It is however not proven that this mathematical ability is not in need of other parts of the brain. Despite the research work, the fact remains that there still are pupils in school with hardships when it comes to math. Normal, social, intelligent adolescences with on the surface no seemingly disorders, but when it comes to math, their whole world falls apart. The main reason to why research on dyscalculia is made is hopefully to give remedy to these persons and to help them find a way to not feel excluded from the possibility to understand a core subject. I look forward to the day when I as a math teacher have the perfect tools to help all of my students prevail in math.

1.6 References Number sense and developmental dyscalculia. Anna J. Wilson & Stanislas Dehaene in Donna Coch, Geraldine Dawson, and Kurt Fischer, editors, Human behavior, learning and the developing brain: Atypical development. Guilford Press, New York, 2007 The Mathematical Brain. Brian Butterworth, London: Macmillan, 1999 If it isn t dyscalculia then what is it? A multi-method study of the pupil with mathematics problems from a longitudinal perspective. Gunnar Sjöberg, 2006, (ISBN 91-7264-047-2) (http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-777) Virtual Dyscalculia Induced by Parietal-Lobe TMS Impairs Automatic Magnitude Processing. R. Cohen Kadosh, K. Cohen Kadosh, T. Schuhmann, A. Kaas, R. Goebel, A. Henik and AT. Sack, 2007 Discrete and analogue quantity processing in the parietal lobe: A functional MRI study. Fulvia Castelli, Daniel E. Glaser and Brian Butterworth. (http://www.pnas.org/content/103/12/4693.full) Developmental Dyscalculia: heterogeneity might not mean different mechanisms. Orly Rubinsten and Avishai Henik, 2009. Developmental cognitive neuropsychology of number processing and calculation:varieties of developmental dyscalculia. Michael Von Aster, 9: II/41 II/57 Steinkopff Verlag, 2000. Developmental dyscalculia: prevalence and prognosis. R. S. Shalev, J. Auerbach, O. Manor, V. Gross-Tsur, Steinkopff Verlag, 2000. Predicting Mathematical Achievement and Mathematical Learning Disability With a Simple Screening Tool - The Number Sets Test. David C. Geary, Drew H. Bailey, Mary K. Hoard. University of Missouri. Printed in Journal of Psychoeducational Assessment, Volume 27, Number 3, 2009.

Footnotes: 1 Kosc, 1974, Shalev & Gross-Tsur, 1993, 2001, Wilson & Dehaene, 2007 2 Dyslexia; : learning disability involving difficulties in processing language in reading, spelling, and writing (http://www.merriam-webster.com/dictionary/dyslexia) 33 Stanislas Dehaene, Professor at Collège de France, has a Masters degree in applied mathematics and Computer science, PhD in Experimental Psychology, chair of Experimental Cognitive Psychology. 4 Developmental cognitive neuropsychology of number processing and calculation: varieties of developmental dyscalculia, 2000 5 In Germany by Badian (1983), Klauer (1992), in Switzerland by Von Aster (1997), in England by Lewis, Hitch and Walker (1994) 6 ADHD; Attention-Deficit/Hyperactivity Disorder 7 Roi Cohen Kadosh, doctor at Institute of Cognitive Neuroscience, University College London, researcher in numerical cognition, parietal lobe functions and neurocognitive mechanisms amongst other areas. 8 Automatic magnitude processing: determining the magnitude of a number when compared to another number that also differs in appearance and physical size. 9 Brian Butterworth, professor of Cognitive Neuropsychology at University College, London 10 Discrete and analogue quantity processing in the parietal lobe: A functional MRI study, 2006 1111 Figure taken from http://dericbownds.net/uploaded_images/vis_perf.gif 12 The presence of one or more disorders 13 Predicting Mathematical Achievement and Mathematical Learning Disability With a Simple Screening Tool. The Number Sets Test. David C. Geary, Drew H. Bailey, Mary K. Hoard. University of Missouri, 2009. 14 Gross-Tsur, Manor, & Shalev, 1996; Kosc, 1974; Ostad, 1998; Shalev, Manor, & Gross-Tsur, 2005 15 WASI; Wechsler, 1999 16 7 + 8 by decomposing 8 into 5 and 3 and then adding 7 + 3 = 10, 10 + 5 = 15, (Geary et al., 2009) 17 WMTB-C; Pickering & Gathercole, 2001, (Geary et al., 2009) 18 Recalling numbers in reversed order (Wikipedia).