Mathematics at the Interface

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Mathematics at the Interface

• Leslie Mustoe
• Loughborough University

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What is the mathematics problem?

• Fewer candidates
• Lack of basic knowledge and skills
• Shortage of qualified teachers

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Curriculum 2000

• 4 AS subjects at Year 12
• Up to 3 A2 subjects
• Less time for each AS
• Less material in AS than 0.5 x A level
• Mathematics increases AS content

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Facing reality

• The primary problem
• Whats a GCSE worth?
• In 2001 a massive increase in teacher training
  applications led to 78 more secondary mathematics
  teachers
• TTA says that we need 38 of this years graduate
  output in mathematics

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AS and A level in turmoil

• The AS disaster
• Knock-on effects
• Revisions have been proposed

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Outline of revisions

• 4 Pure Mathematics modules (22)
• Applied Mathematics modules flexible
• Mechanics not compulsory
• Content of Pure modules equivalent to first
  three in Curriculum 2000
• More opportunity to bridge the gap
• One Pure module calculator-free

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How deep-rooted are the causes?

• GCSE grade B with little algebra
• Too much of a gap to Advanced level
• Poor grasp of basic mathematics

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Will things get better?

• Not before they get worse
• Not for some time
• Perhaps not for the foreseeable future

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Why does it matter?

• Mathematics is the language of engineering?
• Engineering can be descriptive or analytical
• There are software packages
• I never used much of the mathematics which I
  learned at university.

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Core curricula

• Engineering Mathematics Matters 1999
• SEFI Core Curriculum 2002

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Is there an irreducible core of mathematics for
engineers?

• Will engineering courses have to change?
• Is there an acceptable minimum core?
• What is taught requires time

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The educational process
PROCESS
CHANGING
CHANGING
INPUT
OUTPUT
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Mathematics in context

• Why does it matter?
• Will it hang together?
• Who can teach it?

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The primary problem

• ITT at Durham and IOE, London
• 56 could not rank order five decimals
• 80 could not work out the degree of accuracy in
  the estimated area of a desk top
• 50 were insecure in understanding why 3453x4,
  89103x9 etc

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JIT mathematics

• Have we learned nothing from GNVQ?
• Without coherence, mathematics is a box of tricks
• How can we ensure no overlap, no lacunae, no
  contradictions?

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Whats a GCSE worth?

• Mathematics in tiers
• Grade B at Intermediate level
• Algebra coverage
• Grade inflation
• Problems for Year 12 and Year 13

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A /AS shortfall

• 29 failure rate at AS level in 2001
• 21 failure rate at AS level last year
• 20 fewer offered A level last year
• Solution - reduce syllabus content

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How we might proceed - 1

• Teach first semester engineering modules in a
  qualitative manner
• First semester mathematics will allow catch-up
• Then revisit engineering topics quantitatively

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How we might proceed - 3

• Help for teachers
• What is on offer must be relevant for engineering
• It must relate to the syllabus
• It must be attractive for pupils to use
• It must be easy for teachers to use

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How we might proceed - 2

• Involve the mathematics lecturer as part of the
  teaching team
• Plan a coherent development of mathematics
  through the course
• Seek actively to provide joint case studies

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Mathematics Post - 14
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Epilogue

• Mathematics requires time for its assimilation
• Short cut equals short change
• People who are weak mathematically need longer
  than those who are strong mathematically
• The interests of the students should be paramount