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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 PROCESS CHANGING 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

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