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Mathematics at the Interface

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

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  1. Mathematics at the Interface Leslie Mustoe Loughborough University

  2. What is the mathematics problem? • Fewer candidates • Lack of basic knowledge and skills • Shortage of qualified teachers

  3. 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

  4. 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

  5. AS and A level in turmoil • The AS disaster • Knock-on effects • Revisions have been proposed

  6. 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

  7. 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

  8. Will things get better? • Not before they get worse • Not for some time • Perhaps not for the foreseeable future

  9. 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.”

  10. Core curricula • Engineering Mathematics Matters 1999 • SEFI Core Curriculum 2002

  11. 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

  12. The educational process CHANGING PROCESS CHANGING INPUT OUTPUT

  13. Mathematics in context • Why does it matter? • Will it hang together? • Who can teach it?

  14. 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

  15. 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?

  16. What’s a GCSE worth? • Mathematics in tiers • Grade B at Intermediate level • Algebra coverage • Grade inflation • Problems for Year 12 and Year 13

  17. 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

  18. 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

  19. 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

  20. 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

  21. Mathematics Post - 14

  22. 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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