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The Further Mathematics
Support Programme
Working with students and teachers
to promote, enrich and support
mathematics in schools and colleges
To find out more please visit
www.furthermaths.org.uk
Our aim is to increase the uptake of AS and
A level Mathematics and Further
Mathematics to ensure that more students
reach their potential in mathematics.
New Maths and Further Maths A-levels
2017
KS4-5 Transition
New funding structure for sixth forms
…?
KS5 Issues
2017 A Levels
in
Mathematics
Handouts - http://www.furthermaths.org.uk/2017-support
Area of FMSP website dedicated to 2017 A-Levels
http://www.furthermaths.org.uk/2017
MEI Sample SOW (not board specific and will be freely
available next year) http://www.mei.org.uk/2017-sow
Useful links for this session
All of the A level content will be examined at the end of
the course.
AS and A levels have been de-coupled so that, while
students can sit an AS level halfway through the two-
year course the grade awarded at AS will not be counted
towards the full A level grade.
AS level qualification will carry UCAS points as long as
the full A level is not awarded (40% of an A Level)
Linear Course
The subject content for both A level Mathematics and AS
level Mathematics is 100% prescribed by the DfE.
All students will be assessed on their knowledge of Pure
Mathematics, Mechanics and Statistics.
Decision mathematics will no longer be an option at A
level.
The assessment objectives include a greater emphasis
on modelling, problem-solving and reasoning, so some
questions are likely to be longer with less scaffolding.
AS/A level Mathematics content
A level Further Mathematics has 50% of the content
prescribed by the DfE.
Awarding organisations have decided on the topics
included in the remaining 50% of the content.
AS level Further Mathematics has 30% prescribed
content with 70% decided by the awarding
organisations.
It will still be possible to teach AS and A level Further
Mathematics alongside A level Mathematics.
See http://www.furthermaths.org.uk/2017-fm for detail of
the different options
Further Mathematics content
There are 2 handouts that detail the change to content:
For both the Core Pure and Applied content.
Content Changes to A Level
The awarding bodies submitted their draft specifications
and sample assessment materials to Ofqual on June 9th.
All the specs and sams can be downloaded from the
appropriate websites or here..
https://www.dropbox.com/sh/r5p24gda83q7jr1/AAAjRUr
OLxkhOexq-tGkp5eHa?dl=0
Specifications
The FMSP has produced a guide to help departments:
“What to consider when choosing a new specification for A
level Mathematics and Further Mathematics”
It is not necessary to make a decision in the summer or
autumn 2016 on which specification(s) to follow. Although
the draft specifications and SAMs are available these have
not been accredited and may well change.
Guidance for Choosing a Spec
Teacher events organised by the FMSP, MEI, the
awarding organisations and others will provide further
information and support.
In particular, you could consider your choice of AS/A
level Mathematics specifications separately from your
choice of AS/A level Further Mathematics.
We advise that departments take time to reach their
decision.
Guidance for Choosing a Spec
For AS/A level Mathematics, as the content is the same
for all specifications, you could delay your decision about
which specification to follow until as late as January
2018 for AS level, or January 2019 for A level
Mathematics.
Hence you could begin teaching A level Mathematics in
September 2017 without making a final decision about
your choice of specification.
Guidance for Choosing a Spec
Both the AS and A Level will be examined in summer
2018.
This is to accommodate schools who teach the A Level
in one year and then do Further in year 13.
First Examination
Board Paper 1 Paper 2 Paper 3
AQA Pure Pure & Mech Pure & Stats
Edexcel Pure Pure (some
different topics to
Paper 1)
Mech & Stats
MEI Pure & Mech
(36.4%)
Pure & Stats
(36.4%)
Pure & Comp
(27.3%)
OCR Pure Pure & Stats Pure & Mech
A-Level Assessment
All 2 hour exam papers
All equally weighted except MEI
Board Paper 1 Paper 2
AQA Pure & Mech
(90min 50%)
Pure & Stats
(90min 50%)
Edexcel Pure
(2 hours, 66.66% [sic])
Mech & Stats
(1 hour, 33.33%)
MEI Pure & Mech
(90min 50%)
Pure & Stats
(90min 50%)
OCR Pure & Stats
(90min 50%)
Pure & Mech
(90min 50%)
AS-Level Assessment
Binomial Expansion & Distribution
OCR AS-Level, Paper 1
Edexcel A-Level, Paper 2
First Principles & Small Angle
“Real life” situations!
AQA AS-Level, Paper 1
Linking Topics
AQA A-Level, Paper 3
Use of technology
MEI A-Level, Paper 1
Data Sets - requirementsStudents should
become familiar with one or more specific large data
set(s) in advance of the final assessment (these data
must be real and sufficiently rich to enable the concepts
and skills of data presentation and interpretation in the
specification to be explored)
use technology such as spreadsheets or specialist
statistical packages to explore the data set(s)
interpret real data presented in summary or graphical
form
use data to investigate questions arising in real contexts
Mathematical modelling
represent situations mathematically and understand the
relationship between problems in context and
mathematical models that may be applied to solve them
Problem solving
use their mathematical skills and techniques to solve
challenging problems which require them to decide on
the solution strategy; recognise when mathematics can
be used to analyse and solve a problem in context
Modelling and Problem Solving
read and comprehend mathematical arguments,
including justifications of methods and formulae, and
communicate their understanding
read and comprehend articles concerning applications of
mathematics and communicate their understanding
Comprehension
Data Sets
explore the data set(s), and associated contexts, during
their course of study to enable them to perform tasks
that assume familiarity with the contexts, the main
features of the data and the ways in which technology
can help explore the data
demonstrate the ability to analyse a subset or features of
the data using a calculator with standard statistical
functions
Data Sets Consist of real data – the data may be reorganised into a
standard format but should not be cleansed
Include the source of the data (including URLs) so that
learners can understand how it was collected;
Include a short piece of text and/or a glossary to help
learners understand the data and associated
terminology;
Make clear to learners whether the whole data set is
(essentially) a population, or a sample from a larger
population;
.
A data set for A level could include some data where the
Normal distribution could be considered as a model.
A data set for AS level should support questions related
to the binomial – these could be based on proportions of
the data that have some characteristic.
Models
Students should be expected to interpret output from a
spreadsheet or statistical software.
Students should be expected to interpret and explain
terminology which has been introduced via the data set.
Students should be asked to explain what effect missing
data would have on a model that has been derived.
In the exam:
Students should be asked to explain how they would
collect data and to describe the drawbacks and
advantages of particular sampling methods. They
should understand the kinds of methods that were used
to collect the data set(s) they have been working with.
Students might be presented with a reasonably small
selection of data within a question and be required to
process these data, for example to produce and interpret
summary statistics.
In the exam:
Short questions requiring brief
comments/interpretation.
Questions requiring deep interpretation of the
data, using given graphs and summaries.
Questions which require students to select from
given graphs and summary data to solve a
statistical problem.
Modelling with trend lines for bivariate data (can
include quadratic or exponential trend lines
where appropriate).
Types of Questions
Modelling with distributions.
Hypothesis testing
Describing a situation where data needed to be
collected and how it might be done.
Types of Questions
Body Format Description of data Comment Lifetime
AQA PDF gives links
to 40+
datasheets on
gov.uk site
Family Food datasets Most have no
categorical
fields
Until further
notice
Edexcel 2 sets of 5
spreadsheets
Met Office weather
for 5 different stations
over 2 different time
periods
No categorical
fields and
nothing to
explain the
data
Until further
notice
MEI Single sheet
spreadsheet
2012 Olympics
Medals and
demographic data by
country
2 categorical
fields
New data set
for each
cohort
OCR Spreadsheet
with 4 sheets
Methods of Travel by
Local Authority
2 categorical
fields
Until further
notice
Data Sets
Example large data set question AQA
A level
Example large data set question
Edexcel A level
MEI large data set question
MEI large data set question
MEI large data set question
The use of technology, in particular mathematical
and statistical graphing tools and spreadsheets,
must permeate the study of AS and A level
mathematics
Use of technology
Calculators used must include the following features:
an iterative function
the ability to compute summary statistics and access
probabilities from standard statistical distributions
the ability to perform calculations with matrices up to at
least order 3 x 3 (FM only)
Use of technology
Calculator FunctionsFeature Mathematics or
Further
Mathematics?
What calculators have this feature?
Iteration Both Any calculator with an Ans key – most
modern scientific calculators have this
Summary statistics Both Most scientific and graphical calculators
produce summary statistics for lists of
data. Check whether it is also possible to
enter frequencies as well as raw data.
Probabilities for standard
statistical distributions
Both Modern graphical calculators have this
feature; so do some scientific
calculators. The Casio fx-991ES plus
has standard N(0, 1) probabilities. The
Texas TI-30X pro has general Normal
probabilities and cumulative binomial
probabilities.
Calculations with
matrices up to 3 x 3
Further
Mathematics
Modern graphical calculators have this
feature; so do some scientific
calculators. The Casio fx-991ES plus
and the Texas TI-30X pro both have this
feature.
MEI are providing a scheme of work which can be
downloaded free from http://www.mei.org.uk/2017-sow
It supports all the specifications.
It can be customised by schools.
Each section includes:
Assessment Objectives
Commentary
Links to (free) resources
Use of technology
Schemes of Work
With the new linear structure, it will important to access
progress on a regular basis
It is likely that textbooks and awarding bodies may
produce some materials
An example is the MEI Binomial Section Test
Assessing Progress
What aspects of teaching the new
A level might require PD?
Problem solving; modelling.
Working with Large data sets
Use of Technology
Mechanics for non-specialists
Stats for non-specialists
Integration of pure with mechanics and statistics
What skills do staff in your department have?
Where might there be gaps?
Which areas of the new A levels are you least confident
about?
What PD do you are your department need in order to be
ready to deliver the new A levels?
Existing skills and needs
What CPD is available? FMSP provision
MEI
Awarding Bodies
Other Providers
In autumn 2016 free one-day courses on planning and
preparing for the new A levels looking at the big ideas and
themes that run through the new specifications
problem solving and use of technology;
how to plan a scheme of work for a linear A Level,
a departmental skills audit;
deciding on CPD priorities;
and finding the best resources and support for teaching
the new specifications.
Preparing to teach the linear A levels in
Mathematics and FM courses
A level subject knowledge courses for Mathematics and
Further Mathematics content. These will continue to
ensure that teachers are prepared for teaching the
content in the new A levels.
FMSP Developing Subject
Knowledge Courses
Live Online Professional Development (LOPD) is a
programme of innovative online courses delivered using
a web-based http://www.furthermaths.org.uk/lopd
FMSP Live Online PD
The FMSP offers a range of extended professional
development courses which are designed to develop
subject knowledge and classroom practice.
Teaching Mechanics (TM)
TM1 covers the compulsory mechanics content in the new
A level Mathematics and TM2 covers topics in Further
Mathematics.
Teaching Statistics (TS) includes the use of large data
sets, hypothesis testing and use of technology. TS1 covers
the compulsory statistics content in the new A level
Mathematics and TS2 covers topics in Further
Mathematics.
FMSP Extended Courses
Teaching Further Mathematics (TFM) , from 2017, will
cover all of the compulsory Pure Mathematics content for
the new AS level and A level Further Mathematics
specifications.
Teaching Advanced Mathematics (TAM) , from 2017,
will cover the all of the compulsory Pure Mathematics
content for the new A level Mathematics specifications.
FMSP Extended Courses
MEI Get Set courses: four one day courses focussing on
specific aspects of the new A levels
(www.mei.org.uk/2017-pd)
Awarding Bodies: your chosen awarding body will be
offering support and PD for their specification
Your local teacher network or Maths Hub
Other Support available
Conferences in 2017 (like 2016) will probably have a
number of sessions devoted to the aspects of teaching the
new A Level.
MEI http://conference.mei.org.uk/
ATM www.atm.org.uk
MA www.m-a.org.uk
Conferences
Support for students
Promoting the further study and appreciation of mathematics
Helping to develop deeper problem-solving skills in mathematics
Ensuring opportunities to study Further Mathematics, online or face to face
Providing guidance relating to university and career choices
Support for teachers
Providing professional development for mathematics teaching at Key Stage 4
and Post -16, including support for problem-solving and extension
Advising on mathematics provision at Key Stage 4 and Post-16
Coordinating teacher networking opportunities
Providing high-quality teaching and enrichment materials for mathematics
The FMSP provides . . .
www.furthermaths.org.uk
