Celia Hoyles

1
Increasing the Supply of Mathematics
GraduatesWhat education is doing and what might
it do

• Celia Hoyles
• www.ioe.ac.uk/tlrp/technomaths

Celia Hoyles Chief Adviser for Mathematics
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Post-14 Maths Inquiry (UK-wide)

• Impetus (DfES point of view) recommendation on A
  levels in Roberts report to Treasury on STEM
  subjects, Set for Success, published in April
  2002
• Announced by Chief Secretary to the Treasury in
  July 2002 but taken forward by DfES
• Three broad areas spanning both the school and FE
  sectors addressed
• Curriculum and Qualifications
• To make recommendations on changes to curriculum
  qualifications and pedagogy for young people aged
  14 and over to ensure they have the mathematical
  knowledge and skills necessary to meet the needs
  of employers and further and higher education.
• Teacher Supply
• Support for Teaching and Learning
• To put forward costed options for establishing a
  National Centre for Excellence in the Teaching of
  Mathematics (NCETM).

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Some dates The Post-14 Maths Inquiry

• Autumn 2002

Adrian Smith commissioned to undertake inquiry
Post-14 Maths Inquiry Report published

• February 2004

It made clear the importance of mathematics to
the economy and was critical of most aspects of
mathematics provision
Charles Clarke both welcomed the report and took
an active part in the development of measures in
response.

• 28 June 2004

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a new date Oct 6 2005
The procurement exercise for National Centre for
Excellence in Teaching Mathematics (NCTEM) has
been successfully completed and an announcement
made on Oct 6 by Bill Rammell The Department for
Education and Skills has announced that the
Tribal Group plc will run the National Centre for
Excellence in the Teaching of Mathematics (NCETM)
with Government funding of 15 million over the
next three years. Tribal Group plc, in
partnership with the Centre for Innovation in
Mathematics Teaching at Plymouth University will
take forward this agenda. Contract signed
yesterday (Nov 3 2005) ...... at last
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Ofsted mathematics in secondary schools

• post-16 mathematics courses
• students' achievement is good in 7 out of 10
  schools below average
• teaching is judged to be very good or excellent
  in over a quarter of schools, almost double the
  1998/99 figure, and good or better in more than
  four fifths of schools but below average
•  
• lack of engagement and motivation for many Key
  Stage 4 pupils results in limited take-up post-16
  in too many schools. 
• need to revitalise teaching in Key Stage 4 in
  order to address this trend.

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Major challenges to increase supply of
mathematics undergraduates

• Pre -16
• raise attainment at Level 1 and Level 2 (problems
  in KS4)
• and enhance engagement in motivation for
  mathematics
• Post -16
• increase uptake in mathematics
• this means must at all phases
• widen participation
• sustain engagement at transitions

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an outcome of NCETM

• an improved output of students motivated to
  continue to study mathematics
• How?
• key to success is teaching and learning with
  teachers who appreciate what maths is, can
  unpack maths have the chance to engage with
  students in exploring maths
• need to identify
• needs of teachers at different phases in their
  career (regional, phase)
• gaps
• target coordinate resources

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CPD model based on research, practice and
experience

• Three components
• mathematics content knowledge NOTE this
  is a necessary but not sufficient condition for
  good teaching
• functional mathematics for teaching (I call
  it this to be consistent with the more general
  policy agenda- not sure if it is wise!?). I mean
  the mathematical knowledge needed to carry out
  the work of teaching mathematics
• effectiveness in teaching resides not simply in
  the knowledge a teacher has accrued but how this
  knowledge is used in classrooms
• embedding effective mathematics teaching in
  practice

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Mathematical content knowledge
There is a need for all teachers to have the
opportunity to simply learn new mathematics
according to the needs of their work But
usually most effective in the context of their
work
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Functional Mathematics for Teaching
Even strong mathematicians, as well as those
lacking subject knowledge, need to work on
functional mathematics for teaching.
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Examples of FM for Teaching

• can understand the personalised mathematical
  knowledge of students
• can build on this knowledge by designing
  appropriate tasks, asking appropriate questions
  and promoting discussion of different but
  equivalent representations
• can unpack maths routines (the opposite of
  procedural fluency) - profound mathematical
  knowledge

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Designing tasks
The task is to put four decimal numbers in order.
Which set of four numbers would you choose to use
in class and why? .5 7 .01
11.4 .61 2.53 3.12 .45 .6 4.25
.565 2.5
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Unpacking maths procedures
Explain why when you divide one fraction by
another you turn the second fraction upside down
and multiply
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Embedding effective mathematics in practice
Key ingredient is the opportunity and time for
teachers to work together in small communities
and networks to reflect on their practice with
the support of specialists and experts when
required
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issues to increase numbers
high quality maths teaching in all phases and at
transitions building webs of connections for
students stimulate supply of opportunities for
maths engagement and demand for them among the
top 25 set out to increase the diversity of
students ( teachers?)
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Raising the expectations in mathematics of all,
and in particular the top 25 so continue on to
GCE mathematics beyond

• Supply
• Enrichment not acceleration
• fragile confidence
• superficial coverage
• increase assessment load teach for tests
• enrichment opportunities
• extension curriculum for KS3 4
• extra-curricula Mathematics
• out of school clubs, master classes, UKMT, NRICH
  etcetc
• sustained support encouragement over time
• mentoring f2f online in problem solving
• teaching!

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Raising the expectations in mathematics of all,
and in particular the top 25 so continue on to
GCE mathematics beyond

• Demand
• Motivation
• ICT maths
• Career information (website)
• collaborative work
• using the theorems or knowledge
• Focus on transitions
• cross-phase ambassadors school/university
  dialogue links and with workplace SAS/UAS and
  teachers going to university etc
• financial incentives
• Set targets for post-16 take up?
• Work with learn from Specialist Schools

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barriers to participation

• Maths seen as hard and boring
• Difficulty is double edged
• difficult but prepared and can cope ....... or
  not
• Easy is double edged
• Relative difficulty harder than other subjects

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barriers to participation

• Pace coverage
• superfical rather than in depth appreciation
• too many jumps
• Not seen as useful (for jobs, HE)
• Need to enjoy and see maths as something students
  can engage with and personalise, share explain
  why need maths maths results
• computer
• collaborative and communicative

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the underlying challenges

• importance of identity, (alongside coping)
• re-think what it means to be involved in maths
• the identity of people who can understand and
  can do mathematics
• no longer brag about it or hide it
• tackle the image of mathematics mathematicians
  

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Analysis of Further Maths uptake

• AS level 32 increase
• A level 1.8 increase.
• What lessons can we learn from an analysis of
  these data?

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Wanted engineers who are civil Top grades in
maths or physics no longer the essential
requirements to study engineering November 1,
2005 The Guardian

• They are top-quality graduates, brilliant at
  maths, but unable to communicate with anyone at
  all.
• UCL, Prof Nick Tyler wonders what contribution
  they will make to the world. "Our output may be
  fantastic civil engineers, but if they cannot
  explain to their employers and politicians what
  they are doing and, more importantly, why, they
  are going to struggle to find and then keep a
  job.
• for October 2006 degree courses will modify entry
  requirements so high grades at maths and physics
  at A-level no longer required. "We want to turn
  out the world's greatest civil engineers, but we
  want them to be engineers with judgmen-- vision
  -- idealism?

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The department also plans to change the
male-dominated world of civil engineering by
aiming for a 50 female intake, compared with
national average of 15 have more women staff
"We were overwhelmed with applicants from all
over the world. We did not deliberately pick
women eight of the outstanding candidates
happened to be women. But I think it will help
change the whole culture for the better and help
us think about the broader questions about how
civil engineering relates to the world in the
21st century.
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Tyler believes students need to learn to
communicateAsks exam questions in 2 parts
First complex equation to test comprehension of
civil engineering skillsSecond asks what the
answer means and what further questions might
arise"They always seem to get the maths right,
but the second half of the answer is often blank.
They are quite unable to write down the
consequences of the answer.
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Top of his current intake of postgraduate
students is female philosophy graduate from
Oxford. Hardly a typical civil engineer by
background, but it was her ability that
counted."I feel all this is slightly
subversive. We will place this new breed of civil
engineersinto society and see what happens.
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can we design maths to be
? more engaging human ? more self evidently
useful ? more accessible (challenging yes but can
be coped with) ? less ritual ? less
schoolish authoritarian ? less
anxiety-provoking engagement with rigour