A
model for accelerated learning in Secondary
Mathematics
School: Cottenham Village
College, Cambridge
Fellow: Chris Dale
Email: cjdale25@yahoo.com
Final report
Introduction:
This report will consist
of a brief discussion of key points throughout
the year followed by the development and description
of a ‘working’ model.
Key Points:
In September of last year
I attended a very high profile Mathematical
Association Course at the Royal Society in
London entitled ‘Acceleration vs. Enrichment’.
It proved to be a personal disappointment
as I felt that a true cross-section of the
countries’ schools were not represented
and that there was not enough focus upon specific
classroom practice. The one overriding thought
that I took from the conference was the need
to clarify what acceleration and enrichment
exactly mean. There seems to be an obsession
with a polarised argument that acceleration
is a blind fixation on early exam entry and
little else and that enrichment develops ‘real’
understanding and solid mathematical foundations.
Using these definitions there can be little
doubt which is the most effective policy.
There was also a strong feeling that the two
approaches are mutually exclusive and could
not be combined. All this information further
highlighted the need for my approach to be
more flexible and open-minded.
I have observed top set
lessons in all five years at Cottenham and
have been observed myself. I have also had
discussions with other Village Colleges around
Cambridge and have linked up with my PGCE
block practice school in Bradford. These observations
and discussions have highlighted these main
points –
The enthusiasm of High
Ability Lower School pupils to tackle
‘open ended’ tasks
That there are a diverse range of
styles when teaching such pupils
That early exam entry (Year 10) raises
the profile of the subject in terms
of pupils, parents and staff
That there are some problems with
lack of motivation (particularly in
Year 9 and 10) due to lack of challenging
work
There is an adoption of a more formal
teaching style with Upper School pupils
I feel strongly that a great
deal can be learnt from discussion with past
pupils about their experiences at Cottenham.
I have also noticed the obvious effect that
the presence of these students have on the
younger pupils. From this came three main
points –
That Year 10 entry was
thoroughly endorsed particularly as
it helped with the development of study
skills and made maths a ‘special’
subject
The need for a more structured approach
to the content of work in Year 11
The value of supportive older students
and the possible peer mentoring role
In April of this year I
gave a lecture about the project to the secondary
mathematics PGCE students at Hertfordshire
University. I took two students from Cottenham
and ran a highly interactive session involving
a pupil presentation and some group work.
I found this greatly rewarding and the feedback
has been excellent. I have written a scheme
of work and a set of resources suitable for
Year 7/8 pupils. These have an open-ended
problem solving focus and there is real emphasis
on the appropriate use of ICT. I have also
trialled these with some groups this year
and generally the students find them challenging
and motivating. I have also rewritten the
Year 11 post GCSE syllabus concentrating on
making it more diverse and demanding. I have
taken a modular approach to this and have
tried to balance the skills of pure and applied
mathematics. I have taught this since Christmas
but am looking forward to developing it over
the course of a whole year. With part of my
funding I purchased a set of graphical calculators
and have taught lessons to Year 9, 10 and
11 using these. I have found the purchase
very valuable as they are portable! I am looking
to further their use and will be running some
Maths Department Inset with regards to this.
I am also running a Most Able Summer School
this year which is entitled, ‘The Anatomy
of Mathematics’ and will focus on the
links between maths and the living world.
This is going to be targetted at the top 25
pupils coming up to Cottenham next year.
Development of Model:
In developing the model
there were some underlying principles that
were applied-
The need for flexibility
That acceleration and enrichment
could be combined
That the decision about which to implement
was largely age dependent
That Year 10 entry can help with avoiding
the KS3 plateau
The need for a structured curriculum
in Year 11
The Cotterham Model
School
Year
Initiatives and
Approach
5 and
6
Workshops at Primary Schools
Identification of top 25 mathematicians
at the end of Year 6 and invitation
to Most Able Summer School
7 and
8
Pupils set early in Year 7
Top 5 pupils in each year half are
withdrawn from maths lessons approximately
once every 2 weeks to work on problem
solving activities based on standard
schemes of work
These activities place
heavy emphasis on discussion and the
use of ICT
9 and
10
An ‘accelerated’ group
of 20 pupils is identified for Year
10 GCSE entry
Pupils follow rigorous syllabus led
scheme of work
Post
GCSE 10 and 11
Diverse module based scheme of work
involving GCSE Statistics and ‘A’
Level Introduction
2 Pure Modules
2 Statistics Modules
1 Mechanics Module
1 ICT Module
Pupils provide mathematical support
for lower school students (peer mentoring)
12 and
13 (and beyond!)
A’ Level Workshops
Past pupils to be employed as LSAs
to run withdrawal sessions and revision
classes
Peer mentoring
Project Summary:
Aims:
To develop a working
model intended to challenge and motivate
talented young mathematicians and raise
the general profile of the subject
Key points:
Lower school pupils’
enthusiasm for the subject
Raising of subject profile through
early exam entry
The value of older students in a
peer mentoring role
Development of Model:
The need for flexibility
That acceleration and enrichment could
be combined
That the decision about which to implement
was largely age dependent
That Year 10 entry can help with avoiding
the KS3 plateau
The need for a structured curriculum
in Year 11
The ‘Cottenham
Model’:
Summer School at end of
Year 6
Regular withdrawal ‘problem
solving’ sessions in Year 7/8
Accelerated Group in Year 9/10 (Year
10 GCSE Entry)
Diverse curriculum in Year 11
Employment of Past pupils as LSAs
to run withdrawal/revision sessions
