Students in higher education with mathematical difficulties: The scope

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Students in higher education with mathematical
difficulties The scope nature of the problems
implications for support

• J Boyle, M Dunlop, D Finn, M Mattey,
• C Spickett, I Tulloch J Wilson
• University of Strathclyde,
• Glasgow

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(No Transcript)
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Difficulties in Mathematics

• Concern about standards of attainment in
  mathematics
• Reason for apparent fall in standards is unclear
• Class size calculators lack of drill and
  practice class organisation teaching methods
  individual maths schemes
• Anxiety about mathematics, lack of experience and
  poor motivation
• Sub-set of those experiencing difficulties in
  mathematics will have problems resulting from
  dyscalculia

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Dyscalculia or Mathematics Disorder

• Mathematical ability, as measured by individually
  administered standardized tests, is substantially
  below that expected given the persons
  chronological age, measured intelligence, and
  age-appropriate education.
• Developmental and Acquired
• Underlying causes
• Genetic
• Neurological
• Cognitive

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Dyscalculia Common Problems

• Counting reciting the number words in the
  correct order and being able to count a number of
  objects
• Reading and writing numerals being able to
  understand that a number is a symbol that
  represents a value
• Number seriation placing numbers in order of
  size
• Number facts being able to understand that
  224 or 7x10 70
• Numerical procedures counting on to add,
  borrowing and carrying to subtract
• Principles, concepts and laws of arithmetic
• Telling the time and judging elapsed time
• Calculating prices and handling change
• Measuring (e.g. temperature or speed)
• Problems with ratios, fractions, decimals, place
  value, changing units

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Prevalence of Dyscalculia

• Large-scale surveys of school-children suggest a
  prevalence of around 6-7 with no gender
  differences
• Half of those with dyscalculia have problems with
  number only and the rest have comorbid problems
  with reading
• Prevalence of dyscalculia in adults and in
  students in higher education is unknown
• Strathclyde University Survey lower bound
  prevalence rate of self-reported mathematical
  difficulties in 1st and 2nd Year Bioscience
  students of around 10 (42/400, with response
  rate of 21)

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Recognition of the need for support

• Increasing awareness and concern at low levels of
  mathematical competence for students entering HE
  programmes in science and engineering
• Emerging awareness of the presence of dyscalculic
  students in HE, though little understanding of
  the obstacles faced
• Disabled Students Allowance is available to
  dyscalculic students with study support needs but
  we need to identify the most effective support
  methods

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Compensatory Support

• Compensatory support is typically provided in
  acknowledgement of a permanent area of
  difficulty, not susceptible to improvement
  through remedial programmes
• For dyscalculic students, it can include
• extra time in examinations
• use of a calculator
• access to notes/memory aids
• alternative formats for questions and answers
• Use of a calculator can assist with computational
  inaccuracies, but still requires considerable
  mathematical and conceptual understanding

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Compensatory Support (cont.)

• Not all types of compensatory support are
  regarded as academically valid, depending on core
  learning and assessment criteria
• Software to support specific academic/professional
  calculations could allow dyscalculic students to
  succeed in key tasks, but may be controversial
• Learning support staff can negotiate
  accommodations for a disabled student, but this
  requires clarity on core learning/assessment
  criteria

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Whats missing?

• To develop effective support systems for
  dyscalculic students in HE we need
• More understanding of the obstacles/solutions for
  dyscalculic students in HE, so we can develop
  guidance for HEIs
• Better understanding of accessibility issues for
  dyscalculic students (and dyscalculic/dyslexic
  students)
• Development of best practice teaching and
  assessment materials/methodologies
• Accessible software to support students in
  numeric tasks

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Strathclyde University Dyscalculia Project

• Second year student with difficulties in coping
  with the mathematics content of Biosciences
  courses
• Long-standing history of problems in number at
  school which necessitated tutorial support
• Assessment confirmed marked problems in both
  mathematical reasoning and numerical operations
• To develop an IT-based intervention, BCalc, to
  support students experiencing problems with
  mathematics, including those with dyscalculia
• Multidisciplinary project involving Computer
  Science, Bioscience Psychology Departments and
  Special Needs Service

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Exam question
0.1 ml
1 ml
1 ml
1 ml
1 ml
9.9 ml
9.0 ml
9.0 ml
9.0 ml
9.0 ml
E coli culture
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1
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5

1. If the original E.coli culture contains 5.4 x 109
   cfus ml-1 calculate the number of cfus ml-1 in
   bottle 5 after the serial dilution of the
   original culture, which was performed as
   described in the diagram above
2. If bottle 5 is found to contain 1.9 x 104 cfus
   ml-1, what is the number of cfus ml-1 in the
   original culture

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BCalc software

• Designed for HP Jornada
• Microsoft eMbedded Visual C
• 7 separate functions are called from main dialog
  box
• 8 person-weeks of development effort (CS graduate)

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BCalc on the Jornada
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HP Jornada screen
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Evaluation

• The need for training
• Confident with paper conversion tables
• More step by step help
• Scientific notation vs powers of ten
• 5.000e-002 vs 5 x 10
• Rounding errors difficult to detect and control

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Future direction of research

• Extend the evaluation of software that we have
  already developed for use by MD students.
• Extend our current study to other subjects and
  organisations   
• Identify particular areas of need that can be
  used as a basis for developing systems to help
  with particular problems.
• To improve the user-interface of our pilot
  software support system and assess its value to
  students with MD
• To investigate the feasibility of scalable
  software solution.

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Pocket PC and PalmOS versions
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Future direction of research

• Extend the evaluation of software that we have
  already developed for use by MD students.
• Extend our current study to other subjects and
  organisations   
• Identify particular areas of need that can be
  used as a basis for developing systems to help
  with particular problems.
• To improve the user-interface of our pilot
  software support system and assess its value to
  students with MD
• To investigate the feasibility of scalable
  software solution.

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Towards a scalable solution
ltLABELgt ltNAMEgtVol 2lt/NAMEgt ltTEXTgtVol
2lt/TEXTgt lt/LABELgt ltLABELgt ltNAMEgtVol2lt/NAMEgt
ltTEXTgt??lt/TEXTgt lt/LABELgt ltBUTTONgt
ltNAMEgtCalcVol2lt/NAMEgt ltACTIONgt
ltTYPEgtdividelt/TYPEgt ltTRIGGERgtCalcVol2lt/TRIGGER
gt ltMEMBERSgtNumerator, Conc2lt/MEMBERSgt
ltTARGETgtVol2lt/TARGETgt lt/ACTIONgt lt/BUTTONgt
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Conclusion two conflicting viewpoints
Some students have fundamental difficulties that
prevent them from ever developing mathematical
ability necessary for a science course. Providing
a prosthetic to enable to them overcome these
difficulties is the equivalent of destroying the
integrity of the course for these individual
students. This is far more than a 'reasonable
adjustment'.
A student might be capable of understanding
theoretical concepts without being able to carry
out consistently and accurately the mathematical
processes that underlie these concepts. If we can
provide the maths element with an effective aid
and this aid can continue to be used once the
student enters employment then a prosthetic is a
reasonable adjustment to make.