still Numeracy Matters From the Classroom to Employment

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stillNumeracy Matters From the Classroom
to Employment

• Vicki Tariq

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Todays workshop presentation

• Definitions and skills
• What employers do
• What employers say
• What do students think?
• Factors affecting numerical competency
• Classroom experiences common errors and
  misconceptions

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Higher Education for Capability (1988)
Enterprise in Higher Education (1989)
Employability issues are at the very core of
contemporary higher education in the UK (Cranmer,
2006)
Student Skills Policy 2000
DELs Success through Skills (2006)
Dearing Report (1997)
Student Employability and Skills Policy 2007
Development of key skills (communication,
numeracy, IT, learning how to learn) within all
disciplines in HE
Demand-led skills creativity, innovation,
enterprise, management and leadership
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Definitions of education employability

• Education

• Employability

Instruction or training
Bringing up
Fitness for employment
Ability to be employed
Culture
The character or quality of being employable
Strengthening of the powers of body or mind
Imparting of knowledge or skill
A set of skills, knowledge and personal
attributes that makes an individual more likely
to secure and to be successful in their chosen
occupation(s) to the benefits of themselves, the
workforce, the community and the economy (Mantz
Yorke)
Formation of character
Development of powers
The systematic instruction, schooling or training
given to the young (or adults) in preparation for
the work of life

• Determined by
• Capabilities/characteristics
• of the individual
• Labour market health of economy

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What do we mean by numeracy?

• Numeracy OR mathematical literacy OR numerical/
  quantitative literacy OR functional
  maths/numeracy? all have a practical purpose
• A lack of numeracy goes beyond employability

Numeracy is a mastery of the basic symbols and
processes of arithmetic numbers addition
subtraction simple multiplication simple
division simple weights and measures money
counting telling time
Mathematical competence a competence in the
mathematical skills needed to cope with everyday
life and an understanding of information
presented mathematically, e.g. in graphs, charts,
or tables
The application of basic mathematical knowledge
and skills within a variety of practical contexts
Ability to use or understand numerical techniques
of mathematics
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Top 10 graduate skills and qualities

• The Council for Industry and Higher Education,
  Feb. 2008

• Institute of Directors Skills Briefing
  Graduates Employability Skills, Dec. 2007

• Communication skills
• Team-working skills
• Integrity
• Intellectual ability
• Confidence
• Character/personality
• Planning organizational skills
• Literacy (good writing skills)
• Numeracy (good with numbers)
• Analysis
• 28. Leadership skills
• N 233 employers)

• Honesty and integrity
• Basic literacy skills
• Basic oral communication skills (e.g. telephone
  skills)
• Reliability
• Being hardworking and having a good work ethic
• Numeracy skills
• A positive can do attitude
• Punctuality
• The ability to meet deadlines
• Team working and co-operation skills
• N 500 directors

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Order of importance of graduate skills

• Basic skills
• Basic literacy
• Basic oral communication skills
• Numeracy skills
• ICT skills
• General employment skills
• Ability to meet deadlines
• Problem-solving
• Attention to detail
• Creative and innovative thinking skills
• Advanced oral communication skills (e.g.
  presentations)
• Decision making skills
• Advanced written communication skills (e.g.
  Formal reports, letters)
• Business acumen

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Order of importance of graduate skills

• People and social skills
• Team working and cooperation skills
• Etiquette and good manners
• Self-confidence
• Appropriate dress and appearance
• Networking skills
• Influencing and negotiating skills
• Leadership skills
• Foreign language skills

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Order of importance of graduate skills

• Personal qualities
• Honesty and integrity
• Reliability
• Being hard-working and having a good work ethic
• A positive can do attitude
• Punctuality
• Willingness to take on responsibility
• Adaptability and flexibility
• Ability to work independently
• 27/28 skills or qualities rated as
  very/quite important by gt70 of members
• Only exception - foreign language skills
  only 39
• Institute of Directors Skills Briefing
  Graduates Employability Skills, Dec. 2007

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Every Student Counts employer survey 2008

• 154 graduate employers (by Sept. 2008)
• 56 multinational 31 national (UK) 13 local
• Percentage response by size of graduate workforce

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Economic sectors
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What employers do

• 51 use numeracy test(s) as part of their
  recruitment procedures
• 58 national
• 49 multinational
• 45 local

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Numeracy tests in graduate recruitment

• Using numeracy tests

• NOT using numeracy tests

• Accountancy or professional services (9/12)
• Armed forces (3/3)
• Bank/financial institution/services (12/17)
• Engineering or industrial (5/9)
• Local government (4/7)
• National government (4/4)
• Police (2/2)
• Sales (4/4)
• Chemical/pharmaceutical (1)
• Facilities management (1)
• Leisure (1)
• Oil company (1)

• Charity/voluntary (5/7)
• Consulting (12/20)
• Healthcare (3/5)
• IT/telecoms (9/13)
• Law firms (5/5)
• Marketing (3/4)
• Recruitment/HR (5/8)
• Teaching (2/3)
• Childcare (1)
• Construction firm (1)
• Electricity/gas/water supply (1)
• Fashion design (1)
• Investment bank (1)
• Media company (1)

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Occupations for which numeracy tests are used
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Types of tests qualifications

• 62 use commercially available tests (38 use
  bespoke)
• 34 use SHL tests (others incl. PSYTECH, ASE,
  GMA)
• In 70 of companies/organizations its essential
  that applicants pass the test
• 50 required a minimum of GCSE in Maths or a
  maths-related discipline 33 required a higher
  qualification only 8 didnt stipulate any
  minimum requirement (requirements dependent upon
  role)

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Degree classification vs. subject specialism

• 74 of employers considered the classification of
  the applicants degree important in the selection
  of graduates
• 54.5 of employers considered the degree subject
  important
• CBI education and skills survey 2008 ranked
  degree subject (56) higher than degree results
  (32)
• 57 wouldnt be satisfied if recruits were
  technically competent but didnt understand the
  underpinning mathematical concepts
• Only 40 provide opportunities for numerical
  skills training

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Pilot student survey 2008

• 140 UCLan undergraduates participated
• 52 nursing 31 biological/biomedical sciences
• 14 physiotherapy 3 history
• 94 full-time students (vs. part-time)
• 94 face-to-face learners (vs. distance/online)
• 81 females
• 69 possessed GCSE (or O-level) Mathematics only
  17 possessed a higher level Mathematics
  qualification
• 15 in Level 0 80 in Level 1 1 in Level 2 4
  in Level 3
• 53 18-22 years old 22 23-30 years old 19
  31-40 years old 6 gt40 years old

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Students views

• 62 recognized that their numeracy skills could
  influence their graduate employability
• 39 were unaware that employers are increasingly
  adopting test procedures
• 51 were anxious about attempting such a test
  21 indifferent only 28 confident they could
  pass

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Confidence v. anxiety
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Students views

• I feel competent at maths although my dyslexia
  means I often read numbers backwards (Nursing
  female 23-30)
• I feel quite nervous regarding mathematics, and
  although I have passed tests in the past, still
  feel anxious, and know I need to learn more as I
  find a lot of it quite difficult. (Nursing
  female 23-30)
• I think my problem lies with the fact that its
  been a long time since I did maths at school, so
  my confidence is low on the subject.
  (Biomedical/Biological Sciences female 23-30)
• We need support and tutoring. (Biomedical/Biologic
  al Sciences female 36-40)
• We were just given the drug calculations exercise
  and expected to understand it! (Nursing female
  23-30)

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Numerical skills competencies
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Underlying problems

• 326 volunteer 1st-year bioscience undergraduates
• from 7 universities (26 from three pre-1992
  and 74 from four post-1992)
• Paper-based, 20-item test
• 10 abstract maths questions
• fractions, powers of ten, volume, surface area,
  transposing equations, prefixes for SI units,
  converting units of measurement
• 10 brief word problems
• maths topics set within biological contexts
• allowed calculators
• up to I hour to complete
• asked to provide details of calculations

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Overall test performance

• M 38.5 (SD 18.5) 60 scored 40 only 6
  scored 70-90
• Sig. diff between mean scores for students from
  pre-1992 (44.5) and
• post-1992 (36.5) universities (p lt 0.01
  effect size r 0.2)

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Performance on individual questions
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Summary of performance

• gt 50 students incorrect answer or no attempt
  in 13/20 questions
• ve correlation between scores on abstract
  items and contextualized word problems (r
  0.5, p lt 0.01)
• Scores sig. higher on 10 abstract items (M
  55) than on 10 contextualized word problems (M
  23) (p lt 0.01 effect size r 0.82)
• Greater reluctance to attempt the word problems
  (11-75) than the abstract calculations (2-12)

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Fractions

• 21/4 x 13/4 ? 11/8
• Convert to improper fractions, invert and cancel
• Lack of awareness of inversion rule and
  cancelling
• Confusion between procedures for adding/
  subtracting with multiplying/dividing fractions
• Visual misinterpretation of items, e.g. 2 x 1/4,
  21 ? 4
• such perceptual errors may be linked to dyslexia
  and/or dyscalculia
• may have been inadvertently encouraged by layout
  of worksheet

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Powers of 10

• (7.52 x 109) x (0.036 x 10-5) ? (4.8 x 10-8)
• Lack of understanding re handling negative
  indices in the context of division
• e.g. 4 - (-8) -4 or -5 - (-8) -13
• Perceived power as combination of sign and the
  number dealt with number first and then the
  sign
• Failure to appreciate that 10-8 ? 1?108
• Wrote out all zeros, then made slips
• Presented answer as 6.8115 (calculator), instead
  of 6.81 x 1015

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Volume surface area

• Volume of a sphere If the diameter
  of a sphere is 6 mm, what is its volume in cm3?
• Failed to halve the diameter believed d r2 r
  2d 33 9
• Failed to convert to cm3 or converted
  incorrectly, e.g. divided by 10

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Errors misconceptions

• Many traced to secondary (even primary) level
  mathematics learning
• poor understanding of the concept of number and
  the many meanings of the minus symbol
• Similar to those common amongst 13- to
  14-year-olds (based upon data from Mathematics
  Assessment for Learning and Teaching MaLT
  database, Ryan Williams, 2007)
• Perform better on problems that can be solved
  directly, without any (less) interpretation and
  transformation of information
• e.g. those not involving additional conversion of
  units of measurement

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Factors influencing performance

• Basic maths knowledge and skills
• Memory (working, short- and long-term)
• Math anxiety e.g. abandoning test, high
  percentage not attempting the word problems
• Attitude finding maths interesting/enjoyable
• Perceived usefulness and difficulty of maths
• Level of confidence
• Word problems context, relevance,
  problem-solving skills
• More than any other aspect of elementary
  arithmetic, except perhaps fractions, word
  problems cause panic among the math-anxious
  (Tobias, 1993)

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Factors influencing performance

• Speed time available for task particularly
  processing information in word problems
• Carelessness
• Ability to use a calculator efficiently and
  effectively
• Visual discrimination spatial awareness
• Ability to transfer maths learning from one
  context to another
• Flexibility in cognitive (thinking) style and
  conceptual ability
• Dyslexia and dyscalculia may occur concurrently
• 3.6 of 1st-year undergraduates registered as
  dyslexic (HESA statistics for 2005/06)

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Thinking (cognitive) style

• inchworm 1
  10grasshopper
• - likes formulae - good sense of numbers
• - fixed methods - rarely writes down anything
• - sees details of a problem - looks at the whole
  picture (has
• - good at detailed work overview)
• using formulae - confined by formulae (sees
  no reason to use them)
• - good at mental arithmetic
  estimating
• - often goes straight to the answer
• How do you view yourself?

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What is dyscalculia?

• A condition that affects the ability to
  acquire arithmetical skills. Dyscalculic learners
  may have difficulty understanding simple number
  concepts, lack an intuitive grasp of numbers, and
  have problems learning number facts and
  procedures. Even if they produce a correct answer
  or use a correct method, they may do so
  mechanically and without confidence. (DfES,
  2001)
• 3 - 8 of the population believed to be affected
• 50-60 of dyslexics also experience difficulties
  with maths, e.g. interpreting word problems,
  decoding mathematical notation and symbols
• DyscalculiUM a screener for dyscalculia in HE

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Dyscalculia dyslexia

• Experience particular difficulties with
• learning and recalling number facts
• using rules and procedures to build on known
  facts
• money transactions
• telling the time, concepts such as speed and
  temperature
• basic arithmetic (addition, subtraction,
  multiplication, division)
• sequencing of numbers (short-term memory
  problems)
• spatial orientation difficulties following
  directions or map reading
• abstract mathematical, symbolic graphical
  representations

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To summarise ...........

• Employers are increasingly using numeracy tests
  as part of their graduate recruitment processes
• Need to ensure our graduates are confident and
  competent enough to pass such tests
• Need greater awareness and understanding of
• reality of students pre-university maths
  learning experiences, which may underpin
  persistent misconceptions
• affective factors
• Embed numeracy within curricula and/or provide
  extra-curricular opportunities to support further
  development and practice
• Need variety of support mechanisms one size
  wont fit all!

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Sources of information

• CBI (2008) Taking Stock CBI Education and Skills
  Survey 2008. Available at www.cbi.org.uk/pdf/edus
  kills0408.pdf
• Council for Industry and Higher Education (2008)
  Graduate Employability What do employers think
  and want? Available at www.cihe-uk.com/publicatio
  ns.php
• Dyscalculia and Dyslexia Interest Group at
  http//ddig.lboro.ac.uk
• Institute of Directors (2007) Institute of
  Directors Skills Briefing Graduates
  Employability Skills. Available at
  www.iod.com/intershoproot/eCS/Store/en/pdfs/policy
  _paper_graduates_employability_skills.pdf
• Tariq, V. N. (2008) Defining the problem
  mathematical errors and misconceptions exhibited
  by first-year bioscience undergraduates.
  International Journal of Mathematical Education
  in Science and Technology 39(7), 889 904.
• Tariq, V. N. (2005) Introduction and evaluation
  of peer assisted learning in first-year
  undergraduate bioscience. Bioscience Education
  Ejournal (BEE-j) Vol. 6. Available at
  www.bioscience.heacademy.ac.uk/journal/vol6/beej-6
  -3.htm