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

PROCESSCHANGING

INPUT

CHANGING

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

Mathematics Post - 14

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