mathematics at the interface leslie mustoe loughborough university
TRANSCRIPT
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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
• What’s 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 year’s 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 (2+2)
• 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
PROCESSCHANGING
INPUT
CHANGING
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 3+4+5=3x4, 8+9+10=3x9 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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What’s 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