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Mathematical and Statistical Support for Dyslexic Undergraduates Clare Trott and Glynis Perkin Mathematics Education Centre Loughborough University HELM conference Thursday 15 th September 2005

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Maths support for dyslexic and dyscalculic students One-to-one basis Wide range of departments All have some element of maths in their course, which they struggle with as a result of their SpLD

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Characteristics of Dyslexia A marked inefficiency in working or short- term memory -Problems retaining the meaning of text -Failure to marshall learned facts effectively in exams -Disjointed written work or omission of words Inadequate phonological processing skills -Affects the acquisition of phonic skills in reading and spelling, -Affects comprehension

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Difficulties with motor skills or coordination -Particularly difficulty with automatising skills e.g. listening and taking notes simultaneously Visual processing problems - Affecting reading, especially large strings of text From: Dyslexia in Higher Education: policy, provision and practice. The National Working Party on Dyslexia in Higher Education (1999)

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Mathematical difficulties experienced Poor arithmetical skills Difficulty learning theorems and formulae Mathematical procedures, sequences of operations Holding various aspects of a problem in mind and combining them to achieve a final solution In multi-step problems, frequently lose their way, omit sections Reading the words that specify the problem

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Substituting names that begin with the same letter e.g. integer/integral, diameter/diagram Remembering and retrieving specialised mathematical vocabulary Problems associating the word, symbol and function Errors when transferring between mediums Copying errors from line to line Overload occurs more frequently, forced to stop

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Mathematics Support for students with dyslexia and dyscalculia Dyslexia and no dyscalculia Dyslexia and dyscalculia No dyslexia and dyscalculia Mathematically able Mathematical difficulties Language based Working memory Reading Understanding text Presentation Moving from concrete to abstract Maths Physics Engineering Economics Human Sciences Business Language based Working memory Reading Understanding text Presentation Number related Number relations Number concepts Number operations Human Sciences Social Science Business Number related Number relations Number concepts Number operations Human Sciences Social Science Business Framework for Dyslexic and Dyscalculic students

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Case Study 2 – Nick Economics Dyslexic, not dyscalculic no problems with basic number difficulties in generalisation, in translating from concrete to abstract slow processing speed poor sequencing ability short term memory is weaker for symbolic material

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Demand = Supply Qd = 25 -0.3P - 0.2P 2 Qs = - 5 + 2P + 0.01P 2 Put demand equal to supply, Qd = Qs 25 -0.3P - 0.2P 2 = - 5 + 2P + 0.01P 2 25 - 0.3P - 0.2P 2 = - 5 + 2P + 0.01P 2 0 = 0.21P 2 + 2.3P - 30

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Given the Lagrangian for the long run cost minimisation problem H = 0.25K+L+h(100 - L 0.5 K 0.5 ) Determine the optimal level of labour(L).

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H = 0.25K + L + h(100 - L 0.5 K 0.5 ) H = 0.25K + L + 100h - L 0.5 K 0.5 h HKHK HLHL HhHh 0.25 - 0.5 L 0.5 K -0.5 h 0.25 - 0.5 L 0.5 K -0.5 h = 0 0.5 L 0.5 K -0.5 h = 0.25 L 0.5 K -0.5 h = 0.5 (1) 1 - 0.5L -0.5 K 0.5 h 1 - 0.5L -0.5 K 0.5 h = 0 0.5L -0.5 K 0.5 h = 1 L -0.5 K 0.5 h = 2 (2) 100 - L 0.5 K 0.5 100 - L 0.5 K 0.5 = 0 L 0.5 K 0.5 = 100 (3) (2) (1)L -0.5 K 0.5 h = 2 L 0.5 K -0.5 h 0.5 K / L = 4 K = 4LSubstitute in (3) L 0.5 K 0.5 = 100 L 0.5 (4L) 0.5 = 100 2L = 100L = 50, K = 200

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Case Study 3 – Maria Psychology Dyslexic and Dyscalculic very poor numerical skills, problems with basic concepts difficulty seeing numbers inter-relationships 0.4 percentile for numeracy acutely anxious

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Independent Samples Test.605.4462.57819.0183.62731.40721.681946.57260 2.55017.288.0213.62731.42259.629666.62489 Equal variances assumed Equal variances not assumed Number of words recalled FSig. Levene's Test for Equality of Variances tdfSig. (2-tailed) Mean Difference Std. Error DifferenceLowerUpper 95% Confidence Interval of the Difference t-test for Equality of Means Independent samples t-test

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Facilitating mathematics learning for dyslexics Break down multi-step problems into small, manageable steps Break up large sections of text Sans serif fonts (e.g. Arial) Procedural flow diagrams or tree diagrams Left justify text, easier to read Coloured overlays, coloured paper, reducing glare Use of colour to highlight Colour cells on spreadsheets

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Provide “memory aids”, e.g. large wall posters. Use of card indexes and “card carrying” cases Mind maps for with more extended work. Use colour, and show connections. Graph functions – helpful to SEE the functions “Gallery" of graphs showing various functions or transformations Square paper for rows and columns e.g. matrices Designing graph paper specific to the students needs http://incompetech.com/beta/plainGraphPaper/ http://incompetech.com/beta/plainGraphPaper/

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Progress is often slow and frequent revision is necessary. The same ground may need to be covered many times. However, by providing the student with appropriate strategies and a framework they can relate to, it is possible for the dyslexic or dyscalculic student to grow in confidence, become independent in their learning and, above all, to succeed.

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THE FUTURE IN FRONT OF YOU 82% A* - C (163 out of 212 students) English C or better (89%) MathsC or better (89%) Subject 1C or better Subject 2C or better.

THE FUTURE IN FRONT OF YOU 82% A* - C (163 out of 212 students) English C or better (89%) MathsC or better (89%) Subject 1C or better Subject 2C or better.

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