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- 1. Adaptive Computer Assisted Instruction (CAI) for Students with Dyscalculia (Learning Disability in Mathematics) A. Brunda J. Bhavithra Senior Lecturer, Lecturer, Department of Computer Science & Engineering, Department of Computer Science & Engineering, Dr. Mahalingam College of Engineering and Dr. Mahalingam College of Engineering and Technology, Pollachi, Tamilnadu, India. Technology, Pollachi, Tamilnadu, India. rambru@drmcet.ac.in bavi@drmcet.ac.inABSTRACT General TermsDyscalculia refers to a persistent difficulty in the learning or Experimentationunderstanding of number concepts (e.g. 4 > 5), countingprinciples (e.g. cardinality – that the last word tag, such as Keywords“four”, stands for the number of counted objects), or arithmetic Dyscalculia, Learning Disability (LD), Multi dimensional(e.g. remembering that 2+ 3 = “5”). These difficulties are often Learning Algorithm, Educational Software, E-learning, Adaptivecalled a mathematical disability. Learning-disability (LD) E-learning.students face difficulties in processing and retaining informationand thus have problems in time keeping up with classroom 1. INTRODUCTION Mathematics difficulties are widespread in the United States asinstruction. It follows that students with dyscalculia may have well as in other industrialized nations [13]. The consequences ofdifficulty with numerical operations, both in terms of such difficulties are serious and can be felt into adulthood. Lowunderstanding the process of the operation and in carrying out math achievement is especially pronounced in students from low-the procedure. Further difficulties may arise in understanding income households. Children with weaknesses in basic arithmeticabstract mathematical concepts, symbolic and graphical may not develop the conceptual structures required to support therepresentations. The lack of specialized teacher training, as well learning of advanced mathematics. Although competence in high-as unavailability of effective study material and traditional LD- level math serves as a gateway to myriad careers in science andfriendly curricula further worsen the educational problems technology, many students never reach this stage. Some childrenLearning-Disabled student must challenge. Here we develop a gradually learn to avoid all things involving math and evenE-learning and an Adaptive E-learning tool, that trains develop math anxieties or phobias. In recent years, there has beendyscalculia children on an entertaining numerical comparison growing interest in children with mathematics difficulties, in parttask, by presenting problems adapted to the performance level of because of the relatively large body of research on children‟sindividual child and the adaptation was implemented using mathematical cognition more generally [3].Multidimensional Learning Algorithm to constantly adapt the Research on children with mathematics difficulties has beendifficulty of the problem to the Childs difficulty level. This influenced by the wealth of studies in phonetic based readingMultimedia tool for students with math learning disabilities difficulties, studies that have led directly to the development ofgives students an opportunity to maximize learning and skill evidence-based methods for determining who is going to needimprovement through Educational software. Multimedia tutoring support and how to provide help [5, 6, 7]. As in reading,provides students the opportunity to proceed at a self-guided longitudinal research is critical for understanding how mathpace with immediate feedback. difficulties develop and change over time. Difficulties with number combinations reflect basic weaknesses in number sense,Categories and Subject Descriptors such as the ability to grasp counting principles or to manipulateK.3.1 [Computers and Education]: Computer Uses in quantities mentally .There may also be underlying problems inEducation– Computer-assisted instruction (CAI). working memory, spatial representation, and attention.K.4.2 [Computer and Society]: Social Issues – HandicappedPersons/ Special Needs. Longitudinal research on subgroups of mathematics difficulties is beginning to bear fruit for the development of instructional methods [9]. For example, Fuchs, and Prentice (2004)Permission to make digital or hard copies of all or part of this work for demonstrate that children with mathematics difficulties who arepersonal or classroom use is granted without fee provided that copies are good readers respond differently to instruction than children withnot made or distributed for profit or commercial advantage and that mathematics difficulties who are also poor readers [6]. Thiscopies bear this notice and the full citation on the first page. To copy investigation was concerned with the emergence of mathematicsotherwise, to republish, to post on servers or to redistribute to lists,requires prior specific permission and/ or a fee. difficulties. If children‟s learning needs can be identified early on,A2CWiC 2010, September 16-17, 2010, India. we may be able to design interventions that prevent failure inCopyright © 2010 978-1-4503-0194-7/10/0009… $10.00. math. The importance of different components of „„n umber
- 2. sense‟‟ to mathematics achievement is not well understood, years are less researched and understood. Fortunately, attention isalthough the aforementioned research on mathematics difficulties now being directed to helping students who struggle learningin elementary school is suggestive [2]. basic mathematics skills, mastering more advance mathematics (e.g., algebra), and solving math problems. [4, 5, 7] explains inAlthough no two researchers define number sense in exactly the detail about math disability, the sources that cause such asame way [5, 6, 7], most agree that the ability to subitize small disability, and how a math disability impacts students at differentquantities, to discern number patterns, to compare numerical grade levels.magnitudes and estimate quantities, to count, and to performsimple number transformations are key elements of number sense 2.1 Number Sensein young children [7]. Most children develop fundamental number In mathematics education, number sense can refer to “an intuitivesense before they receive formal instruction in elementary school, understanding of numbers, their magnitude, relationships, and howalthough there is significant variation by social class and cognitive they are affected by operations” [5]. Some definitions emphasizeability. Even infants appear to be sensitive to small numbers and an ability to work outside of the traditionally taught algorithms, e.g.,number transformations. Preschool children learn basic counting “a well organized conceptual framework of number informationprinciples and can perform addition and subtraction calculations. that enables a person to understand numbers and numberThese foundational aspects of number sense are important to the relationships and to solve mathematical problems that are not“higher order” mathematical thinking that results from formal bound by traditional algorithms”.education. The following are the components of Number sense: Counting,1.1 Objective Number knowledge, Arranging Numbers, Big and Small Numbers,To design e-learning and adaptive learning tool for students with Simple Addition and Subtraction [6, 7].Dyscalculia by presenting problems adapted to the performancelevel of the individual child. Department of education and 2.2 Multidimensional Learning Algorithmprofessional organization should increase their efforts and The multidimensional learning algorithm constantly adapts thecontinue to support the dissemination of research based practices difficulty of the program to the childs performance level [2].especially given the goals of “No Child Left Behind”. Adaptation was implemented using three dimensions of difficulty, which were based on our instructional principles and our2. LITERATURE REVIEW knowledge of the key determinants of performance in basicA learning disability (LD) is a neurological disorder that affects numerical cognition in adults and children. The three adaptivethe brains ability to receive process, store and respond to dimensions are: Distance, Speed, Conceptual complexity.information. The term learning disability is used to describe theseeming unexplained difficulty a person of at least average 2.2.1 Distance Dimensionintelligence has in acquiring basic academic skills. Studies show The first dimension, “distance”, increases difficulty of thethat mathematics content is especially challenging for students numerical comparison by decreasing the numerical distance (aswho have learning disabilities. Learning-disabled (LD) students measured by the Weber ratio) between the two comparedface difficulties in processing and retaining information and thus quantities [4]. This dimension is designed to adapt to the precisionhave problems time keeping up with classroom instruction [2]. of the childrens quantity representation and to push children to progressively increase this precision.For this reason, it appears that learning disabled students mayvastly benefit from self-paced computer-assisted instruction. The 2.2.2 Speed Dimensionpurpose of this project is to review literature that: (1) clarifies The second dimension, “speed”, implements an increasingly shortproblematic areas of instruction for LD students, (2) discusses deadline by which the child must respond. This is designed tosuccessful teaching strategies that can be applied to software, and increase speed and automaticity of to quantity representations, and(3) reviews optimal characteristics of current motivational to encourage more efficient calculation and eventually memoryeducational software. This information allows the formation of a recall of simple number facts. At the lower end of this dimension,general overview on the design of multimedia / software for there is no deadline, so that if children are particularly slow at astudents with math learning disabilities. task, they will still be able to succeed.Recently [12, 13], increased attention has focused on students 2.2.3 Conceptual Complexitywho demonstrate challenges learning mathematics skills and The third dimension, “conceptual complexity”, is a compositeconcepts that are taught in school across the grade levels. dimension which is designed to move children along aBeginning as early as preschool, parents, educators, and pedagogical progression which teaches them about numberresearchers are noticing that some students seem perplexed symbols and elementary arithmetic. Difficulty is increased in twolearning simple math skills that many take for granted. For ways: 1) by decreasing the ratio of non-symbolic to symbolicexample, some young children have difficulty learning number information available to make a choice between the two quantitiesnames, counting, and recognizing how many items are in a group. on the “choice screen”, and 2) by introducing addition andIn fact [13], we know that that 5% to 8% of school-age children subtraction at higher levels.are identified as having a math disability. Research on These steps were designed to cement links between symbolic andunderstanding more completely what a math disability means and non-symbolic representations of number, and to increasewhat we can do about it in school have lagged behind similar understanding and of and fluency of access to simple arithmeticalwork being done in the area of reading disabilities. Compared to facts. However the dimension includes some other aspects, suchthe research base in early reading difficulties [8], early difficulties as restricting magnitude range at times, and adding hazards to thein mathematics and the identification of math disability in later board.
- 3. Table 1: Conceptual Complexity Table Non Symbolic: Range Dot Symbolic Addition Symboli Verbal Restriction? Fading Subtraction Levels : Arabic Required Instructional goal c (dot (Spoken (Numbers Present? Required? (Digits) ? clouds) numbers) 1-5 only) (Duration) Attention to and 1 Yes No No Yes No No No Processing of small non symbolic quantities Attention to and 2 Yes No No No No No No Processing of large non symbolic quantities Link small non symbolic 3 Yes Yes Yes Yes No No No quantities to symbolic codes Link large non symbolic 4 Yes Yes Yes No No No No quantities to symbolic codes Increase reliance on 5 Yes Yes Yes Yes Yes No No symbolic codes Further Increase reliance 6 No Yes Yes Yes Yes No No on symbolic codes Require complete reliance 7 No Yes Yes No No No No on symbolic codes Require complete reliance 8 No No Yes Yes No No No on Arabic codes Attention towards exact 9 No No Yes Yes No Yes Yes quantity Comprehension and 10 No No Yes No No Yes Yes fluency of small addition problems Comprehension and 11 No No Yes No No Yes Yes fluency of large addition problems Comprehension and 12 No No Yes Yes No No Yes fluency of small subtraction problems Comprehension and 13 No No Yes No No No Yes fluency of large subtraction problems Distinguishing between 14 No No Yes No No Yes Yes addition and subtraction3. EXISTING SYSTEM 3.1 Limitations of Existing SystemMathematical difficulties are widespread in all industrialized The following are the limitations of the existing system:nations. Elementary school and Kindergarten students with 1.Instruction principles not relevant to the remediation oflearning disabilities often struggle to learn math. They have Dyscalculia. 2. Same set of questions presented in same order.trouble in counting, naming numbers, remembering numbers etc. 3. Children‟s get uninterested in using these tools. 4. DesignedChildren with Learning disabilities, particularly Dyscalculia, have only to particular group of children. 5. Not adaptive to children‟sless “Number Sense” [5]. Children with weakness in basic performance level.arithmetic may not develop the conceptual structures required tosupport learning of advanced mathematics. 3.2 Need for the Proposed System Many training institutions are not teaching scientifically basedCompetence in high level math serves as a gateway to a numerous practices. Beyond an emphasis on the dissemination of researchcareers in Science and technology; many students never reach this based practices, teacher preparation programme should infusestage. Some children gradually learn to avoid all things involving information about screening and formative assessment procedures,math and even develop math anxieties [3]. specific content area instruction methodologies and methods ofE-Learning tool is available in the market to enhance the key individual and small group instruction into curricular for allelements of Number Sense in young children. The areas include: educators, not just for special educators. Towards that end,Counting, Number Knowledge, Number transformation, Dot Department of education and professional organization shouldenumeration, Number Patterns. increase their efforts and continue to support the dissemination of
- 4. research based practices especially given the goals of “ No Child 5.2.1 CountingLeft Behind”. In counting children can learn counting by clicking on the particular number. On clicking, they get the corresponding4. PROPOSED SYSTEM number of objects and their representation in English on theIn modern societies, computers have become so ubiquitous that screen (see Figure 1). Children can also select Autoplay to playcomputer-aided instruction is now low-cost, and can be used in automatically till twenty five.either the home or the school environment. The use of computeraided instruction also allows us to capitalize on the fascinationthat children have for computer games, which makes it easier toprovide intensive training on exercises which might otherwisebecome boring for them.Adaptive Tutoring train‟s children on numerical task, bypresenting problems adapted to the performance level of theindividual child. The tool uses an algorithm to adapt to anindividual child‟s ability and provide intensive training in anentertaining context. This approach for remediation of Dyscalculiaprovides intensive training in number sense.The instruction principles may be equally pertinent to theinstruction of mathematics for younger non-Dyscalculia children.The most important design principle was that of enhancing qualityrepresentation or number sense, cementing the links betweenrepresentations of number, conceptualizing and automizingarithmetic, and maximizing motivation. Figure 1. Counting NumbersA multidimensional learning algorithm constantly adapts thedifficulty of the tool to the child‟s performance level. Adaptation 5.2.2 Arranging Numberscan be implemented using three dimensions of difficulty. The In arranging children learn the number sequence by moving theDistance dimension increases difficulty of numerical comparison. numbers to the correct boxes. They can also select autoplay toThe Speed dimension implements an increasingly short deadline move the number automatically to appropriate boxes (see Figureby which the child must respond. 2).The third dimension “Conceptual Complexity” which teaches thechildren about number symbols and elementary arithmetic.Difficulty is increased by decreasing the ratio of symbolic andnon-symbolic information and by introducing addition andsubtraction at higher levels.5. IMPLEMENTATIONThe Computer Assisted Instruction system includes two modules:E-Learning and Adaptive E-Learning. The Students of age 6-7registers and logins to the system, the system displays the menufor E-learning and Adaptive Tutoring.Through E- Learning, the students can learn the basics ofmathematics. Students can undergo tests through AdaptiveTutoring. The adaptive tutoring contains 14 different levels of test.Response time is calculated at each level and a report is generated.A general report is generated at the end of 14th level. Figure 2. Arranging Numbers5.1 Login ModuleEach user has to login using their Name, Age and School. After 5.2.3 Number Knowledgelogging in they will be taken to a menu where they can select E- In Number knowledge children comes to know the number namesLearning or Adaptive Learning. The registered details will be used and representation. Here they have to move the golden balls to theto generate reports in each of the 14 levels and a consolidated appropriate position in the 5x5 Matrix given or select autoplay toreport. place the numbers automatically (see Figure 3).5.2 The E-Learning Module 5.2.4 Simple Addition and subtraction In E-Learning module students can learn the basics of Here children learn simple and basic addition by a method calledmathematics like counting, number knowledge, and number line addition and line subtraction. To add a number, move to thenames, simple Addition and subtraction. Students can select any right on the number line (see Figure 4). To subtract, move to theone of the above mentioned basics using the E-Learning Menu. left on the number line (see Figure 5).
- 5. difficulty of the program to the childs performance level. It contains 14 levels. A Child will be taken to the next level only if he clears the current level else he will be taken to the E-Learning tool. Level 1: Questions will be presented in the form of dot clouds and there is number restriction of 1 to 5 (see Figure 6); Level 2: Questions will be presented in the form of dot clouds and there is no number restriction; Level 3: Includes both dot cloud and numbers with a restriction 1 to 5; Level 4: Includes both dot cloud and Numbers with no number restriction; Level 5: Includes a new concept called Dot Fading in which the question fades in 4 seconds. Children have to select the correct option after fading. This concept is used to enhance the memory of the children (see Figure 7); Figure 3. Number Knowledge Level 6: Uses Dot fading but with fading time of 1 second; Level 7: Used to provide complete reliance on symbolic codes. Questions contain Arabic digits; Level 8: Used to provide complete reliance on Arabic digits; Level 9: Used to provide Attention towards exact quantity; Level 10: Provides Comprehension and fluency of small Addition problems; Level 11: Provides Comprehension and fluency of larger Addition problems; Level 12: Provides Comprehension and fluency of small subtraction problems; Level 13: Provides Comprehension and fluency of larger subtraction Problems (see Figure 8); Level 14: Provides questions to Distinguishing between addition and subtraction; 6. RESULTS AND DISCUSSION We and others have suggested that dyscalculia may involve impairment in quantity representation or its access via symbolic Figure 4. Simple Addition representations .In order to enhance number sense; we firstly selected number comparison as the primary task of the software. Number comparison is a simple task which draws heavily on quantity representation, and which produces activity in the area of the brain thought to underlie a neuronal code for numerical quantity, the horizontal intra-parietal sulcus (HIPS). The difficulty of the task and degree of associated brain activity is modulated by numerical distance in adults and children. Dyscalculia children and children who are at risk for mathematical under-achievement perform slowly or inaccurately in numerical comparison. Our comparison task included varying levels of numerical distance, thus allowing the software to adapt to the current level of precision of the childs quantity representation. We also included an adaptable response deadline to encourage faster, increasingly automatic access to quantity representation. The software was also designed to emphasize the association Figure 5. Simple Subtraction between representations of number and space, which are known to be closely linked. One previous highly successful number sense5.3 The Adaptive E-Learning Module intervention achieved this by capitalizing on the key features ofThe Adaptive Tutoring tool trains children on an entertaining board games, in which the number/space link is concretized asnumerical comparison task, by presenting problems adapted to the playing pieces are moved along the board; the distance of theirperformance level of the individual child. This tool uses a moves being enumerated or estimated numerically by children.multidimensional learning algorithm to constantly adapt the
- 6. level. The consolidated report contains mark and time of all the levels. The software is tested by nine children with mathematical learning difficulties. The results indicate that the software adapts well to varying levels of initial knowledge and learning speeds. Feedback from children, parents and teachers was positive. A companion article [6] describes the evolution of number sense and arithmetic scores before and after training. The following graph (see Figure 9) shows the score of a tested student (age 7). The graph exposes that the student performs good in Level 1, 5, 9, 10 and 14. He performs poor in level 4 and 6. Overall statistics says that most of the students find difficulty in dot fading (level 6) and no number restriction (level 2, level 4). Figure 6.Report for Level 1 Figure 9.Graph exposing a student performance in different levels of test Figure 7.Adaptive E-Learning Level 5 (Dot Fading 4 sec) 7. CONCLUSION AND FUTURE SCOPE This Project describes the cognitive and algorithmic principles underlying the development of software for dyscalculia. The software is based on current understanding of the cerebral representation of number and the hypotheses that dyscalculia is due to a "core deficit" in number sense or in the link between number sense and symbolic number representations. The design of the software was based on several instructional principles relevant to the remediation of Dyscalculia. Our comparison task included varying levels of numerical distance, thus allowing the software to adapt to the current level of precision of the childs quantity representation. We also included an adaptable response deadline to encourage faster, increasingly automatic access to quantity representation. Children‟s confidence in their mathematical ability improved. Profiles generated at each level showed the performance of children across different dimensions. The software may have applications to the general instruction of number sense for normal children at younger age (3- 6 yrs). Figure 8.Adaptive E-Learning Level 13 The software tool used to investigate different causes andThe performance of the software was evaluated by Adaptive subtypes of dyscalculia. The software tool may be useful forlearning module .A report is generated at the end of each level and remediation of dyscalculia for children aged 7-8 and under. Fewconsolidated report containing results of all the level is generated. aspects of software tool: speed deadlines, complexity, soundThe report contains percentage of marks and time in particular feedback, characters were found entertaining. The results indicate
- 7. that the software adapts well to varying levels of initial knowledge [4] Bradley S. Witzel, Christine J. Ferguson, and Dale S. Brown,and learning speeds. Feedback from children, parents and teachers 2007, Developing early Number sense for students withwas positive. The tool may also be useful for general instruction disabilities, LD Online.of normal preschool children. The learning algorithm reported is [5] David Kaplan, Leslie Nabors Ola´h, Nancy C. Jordan, andhighly general, and may be applied in other domains.Further this Maria N.Locuniak, 2006, Number sense Growth in kinder-work can be extended using Touch Screen implementation, garten: A longitudinal Investigation of children at risk forChildren with age 5-7 have less or no knowledge in computer mathematics difficulties. Child Dev , Jan-Feb, 77(1), 153-75.operation, Tool with Voice recognition for interactive learning,Dyscalculia Assistant which is a talking calculator will be an [6] Daniel B.Berch, 2008, A Remedial Teaching program to helpappropriate tool for people with Dyscalculia. The synthesized children with mathematical disability.voice output of a talking calculator provides feedback to the user [7] Griffin, Sharon, 2004, Building number sense with numberthat helps them identify any input errors. Additionally, hearing the worlds, Early Childhood Research Quarterly, 19(1), 173-180.calculated answer can provide a check against the transposition of [8] Mary Rack, 2005, Learning Disabilities: A Handbook fornumbers commonly reversed in reading by people with Dyslexia Instructors and Tutors, Sabbatical Project, Fall 2005.or Dyscalculia. [9] Regina G. Richards, 2008, Strategies to Facilitate math8. REFERENCES concepts, LD Online.[1] Baer, R., Referral Consultant, 1991, An Expert System for [10] Scharg.J, 2000, Discrepancy approaches for Identifying Guiding Teachers in Referring Students for Special Learning Disabilities, National Association of state Directors Education Placement, Logan, Utah State U., Center for for Special Education. Persons with Disabilities, 84. [11] Siegler R S, 2004, Development of numerical estimation in[2] Berch, D.B. 2005, Making sense of number sense: young children, Child development. Implications for children with mathematical disabilities, Journal of Learning Disabilities, 38, 4 (Jul-Aug 2005), 333. [12] National Center for Learning Disabilities, 2006, DOI= http://ncld.org/LDInfoZone/InfoZone_FactSheetLD.cfm.[3] Bhoomika. R Kar, Rao, S. L., Chandramouli, B.A., Tennarasu, K., 2004, Clinical Validation of the NIMHANS [13] The Access Center, 2006, “Using Mnemonic Instruction to Neuropsychologi-cal Battery for children, Psychological teach math”. DOI=http://www.k8accesscenter.org. Studies, 53, 271-277.

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Regards,

Dr. Anna J. Wilson, College of Education, University of Canterbury

Original works (from which Brunda & Bhavithra plagiarized):

Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 19.

Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 20.