Science Students with Numerical Difficulties:

what are we doing for them?

University of Strathclyde, Glasgow, UK.

Corinne M. Spickett, John Wilson, Jim Boyle

OVERVIEW OF THE PRESENTATION

Numerical difficulties: extent of the problemOverall incidenceRange of problemsStrathclyde study

Support for numerical difficultiesTypical accommodation in HE Is it enough?

Alternative Support Approach: BCalcDescription of BCalc Development of BCalc

Accommodation versus Academic Standards

Difficulties in Mathematics

• There has been an acknowledged decline in standards of numeracy and mathematical ability in recent years.

• Much of this may relate to changes in teaching practice in schools:

• Class size• Use of calculators• teaching methods & lack of ‘drill and practice’

• This has led to anxiety about mathematics, lack of experience and poor motivation.

• A sub-set of these have extreme problems resulting from the learning disability DYSCALCULIA.

Dyscalculia or ‘Mathematics Disorder’

A learning disability that affects numerical and mathematical skills

.… whereas intellectual functioning falls within or above the normal range.

Mathematical ability…. is substantially below that expected given the person’s age and age-

appropriate education ….

Dyscalculia has genetic, cognitive and neurological causes.

Manifestations of DyscalculiaFUNDAMENTAL PROBLEMS Counting Reading and writing numerals Number seriation Numerical procedures Principles, concepts and laws of arithmetic

PROBLEMS IN APPLICATION Telling the time and judging elapsed time Calculating prices and handling change Measuring (e.g. temperature or speed) Problems with ratios, fractions, decimals, changing units

Incidence 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 largely unknown.

Strathclyde Study to assess Numerical Difficulties in University Students (2003)

A self-report questionnaire was distributed to:

1st Year bioscience science students at calculations tutorials at Coventry.

1st and 3rd Year biological science and biology students surveyed in practical classes at Liverpool Hope.

1st and 2nd Year bioscience and pharmacy students in practical laboratories at Strathclyde.

Format of the Questionnaire - General

Format of the Questionnaire - Specific

Algebraic functionsManipulating EquationsLogarithmsPowers of 10Decimal placesFractionsMental arithmetic

Moles and MolarityConversions between

unitsDrawing GraphsDilutions

Findings of the Strathclyde Survey

Strathclyde Coventry Liverpool Number surveyed 400 75 85 No of Respondents (% of total surveyed)

81 (21)

59 (79)

39 (46)

% Respondents reporting numerical difficulties

49 86 36

% Surveyed reporting numerical difficulties

10 68 16

logarithms (p<0.01)

- - Tasks giving discrimination

alegebraic functions (p<0.05)

- -

Implications of the Strathclyde Survey

Prevalence of numerical difficulties among biological science students differs between 3 universities in the UK.

At Strathclyde, numerical skills seem to have declined even further since 2003!

Lower-bound prevalence rate of at least 10% amongst 1st and 2nd years at Strathclyde.

Dyscalculic students will represent a fraction of this (1/10 ?)

Algebra and logs significantly discriminated those reporting problems (75%)

Support for Students with Numerical Difficulties:Remedial Mathematics Support

• Pre-entry classes and testing (e.g. Queen

Margaret)

• Central support schemes for voluntary

participation (e.g. Maths Learning Support

Centre, Loughborough)

• Remedial classes for specific courses on a

voluntary basis.

• Incorporation of remedial maths / numerical

skills teaching into curriculum

Various approaches in many UK universities:

Remedial Support: is it working?

For most students, remedial classes in numerical skills allow them to achieve acceptable standards

“Remedial classes” are becoming incorporated into the curriculum as standard teaching.

Time required to teach numerical skills is detracting from teaching of the main subject

POSITIVE POINT:

CONCERNS:

Support for Students with Dyscalculia

Dyscalculic students are entitled to accommodations that are intended to compensate for their disability.

These are generally similar to those offered to students with other disabilities such as dyslexia.

extra time in examinations use of a calculator access to notes/memory aids alternative formats for questions and answers

Is the Support for Dyscalculia Enough?

Remedial classes are of limited value in this case.

Accommodations such as use of calculators / crib sheets are of limited use as they still require mathematical ability, number recognition, etc.

We attempted to offer a technology-based support for a dyscalculic student who presented on a biological science course at Strathclyde…..

BCalc

The Development of BCalc

Collaborative project between departments of Bioscience, CIS, Special Needs and Psychology

Aimed to produce a software system to help answer specific questions for 2nd year biological calculations:

Interconversions of scientific units Preparation of solutions Dilutions

[Did not attempt to include pH and pKa calculations]

Examples of Biological Calculations

PREPARING A SOLUTION:How much potassium sulfate (MW 174) would you weigh out to prepare 200 mL of a 50 mM solution?

Weight (g) = MW x Conc (M) x Vol (L)

DILUTIONS:a) What volumes of stock and diluent are needed to

prepare 100 mL of 2 mM solution from a 50 mM stock b) What is the dilution factor?

C1 x V1 = C2 x V2 Diluent = V2 – V1

Dilution Factor = C2/C1

BCalc was initially developed for the HP Jornada

• MFC AppWizard to create dialog-based project

• Microsoft eMbedded Visual C++

• 7 separate functions are called from main dialog box

• 8 person-weeks of development effort (CIS project student)

The HP Jornada Screen

The need for training

Less confident than with paper conversion tables

More ‘step by step’ help

Scientific notation vs powers of ten:

5.000e-002 vs 5 x 10-2

Rounding errors difficult to detect and control

New user interfaces are required

Evaluation of BCalc on the HP Jornada

Pocket PC and PalmOS versions

Adaptation of BCalc to more convenient user interfaces:

<LABEL> <NAME>Vol 2</NAME> <TEXT>Vol 2:</TEXT>

</LABEL> <LABEL>

<NAME>Vol2</NAME> <TEXT>??</TEXT>

</LABEL> <BUTTON>

<NAME>CalcVol2</NAME> <ACTION> <TYPE>divide</TYPE> <TRIGGER>CalcVol2</TRIGGER> <MEMBERS>Numerator,

Conc2</MEMBERS> <TARGET>Vol2</TARGET> </ACTION>

</BUTTON>

Latest application: mobile phones

All currently hampered by lack of funding !!!

Further Research and Directions

• Extend the evaluation of current BCalc by MD students.

• Extend the 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.

• 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 solutions (XCalc).

• 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

• Important to distinguish between inability to grasp theoretical concepts, and inability to conduct mathematical routines during application of the concepts.

Support versus Academic Standards

Is this a problem with Dyscalculic Biological Sciencists?

• Many concepts that are fundamental are intrinsically numerical (e.g. moles, statistics)

• Can people learn to use BCalc if they don’t understand the principles ?

• If they don’t understand the principles, can they be biological scientists ?

• Potential for use in employment vs universities?

ACKNOWLEDGEMENTS

• John Wilson • Jim Boyle • Deborah Finn• Graham Martin • Inga Tulloch• Jan Coveney • Simon Wagstaff• Clare Trott

(CIS, Strathclyde)

(Psychology)

(Special Needs Service)

“ “ “

(CIS, Strathclyde)

(Coventry)

(Liverpool Hope)

(LTSN / HEA)

Strathclyde R&D Fund