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Mathematics at the Interface. Leslie Mustoe Loughborough University. What is the mathematics problem?. Fewer candidates Lack of basic knowledge and skills Shortage of qualified teachers. Curriculum 2000. 4 AS subjects at Year 12 Up to 3 A2 subjects Less time for each AS
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Mathematics at the Interface Leslie Mustoe Loughborough University
What is the mathematics problem? • Fewer candidates • Lack of basic knowledge and skills • Shortage of qualified teachers
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
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
AS and A level in turmoil • The AS disaster • Knock-on effects • Revisions have been proposed
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
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
Will things get better? • Not before they get worse • Not for some time • Perhaps not for the foreseeable future
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.”
Core curricula • Engineering Mathematics Matters 1999 • SEFI Core Curriculum 2002
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
The educational process CHANGING PROCESS CHANGING INPUT OUTPUT
Mathematics in context • Why does it matter? • Will it hang together? • Who can teach it?
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
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?
What’s a GCSE worth? • Mathematics in tiers • Grade B at Intermediate level • Algebra coverage • Grade inflation • Problems for Year 12 and Year 13
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
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
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
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
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