The Maths Pipeline Programme
for the FE and Skills Sector
Post 16 GCSE resit:
A Nuffield funded project developing a
new approach to GCSE resit
Based on Realistic Mathematics
Education
S.HOUGH@MMU.AC.UK
Today’s session
Background to the project
Student responses pre and post
Intervention
Working with the materials
Problem Solving
1 1

4 2
DO YOU THINK YOU HAVE GOT
THIS RIGHT?
EXPLAIN WHY.
Year 11
% correct % Correct
Fractions Target
Target
N=50
grade C Grade
D/E
Project
83%
57%
Control
72%
30%
Pupils may attempt to solve a
problem by
Engaging solely with the numbers
Attempting to make sense of the problem
GCSE resit students
What do these students look like?
GCSE resit cohort - Mathematical issues
Memory of formal methods can be poor
Use of misremembered strategies – ‘doing
something with the numbers’
Desire to use informal methods – these
tend not to have been developed to a more
efficient, ‘of worth’ level
GCSE resit cohort – attitudinal
issues
Repeated failures in the examination
Lack of confidence + belief
‘Oh no not this again’
GCSE resit cohort – Some Teacher
dilemmas
How to cover the syllabus in 9 months (or
less)
How to cope with the variety of methods
students may bring
Realistic Mathematics Education
(RME)- the Dutch approach to
teaching maths
Well researched activities encourage students to move
from informal to formal representations of maths
Use of context is sustained throughout
Use of models to support student development
Progress towards formal notions seen as a long term
process
RME, MMU and Post 16 GCSE
resit
MMU have worked on RME related projects for the
last 13 years
‘Making Sense of Maths’ series published by Hodder,
written by MMU with support from the Dutch
Has the potential to offer students a different
approach to GCSE resit
MAKING SENSE OF MATHS’
SERIES PUBLISHED BY
HODDER
‘
Nuffield Funded GCSE RESIT
Project
4 project and 4 control classes in three sites
Intervention consists of Number and Algebra
modules
Data includes: pre and post tests, attitude data,
post test video interviews, teacher interviews
Post- test script - rates
Post-test - rates
Post-test script- percentage
Examples of the Material
Use of context
Use of models
The Download Bar
This is an image of a download bar on a computer.
1) When did you last see something like this?
2) What information is there in the window?
3) How long has the program been loading so far?
4) How many megabytes (MB) are there left to load?
The Download Bar
On Worksheet N1, work out the total installation time for
each of the 9 bars.
1. Work out the total installation time
for the program below:
0
4
0%
25%
? minutes
100%
Now work out the total installation
time for this program:
2.
0
9
0%10%
? minutes
100%
The Download bar
Reverse Percentage Calculations
Susan sold her car for £6820. This was 20%
less than she paid for it. How much did she
pay for the car?
Draw a bar to represent this information
Pre-test – reverse percentage
Post-test – reverse percentage
Buying ribbon
Louisa is a dress maker. She uses ribbon to edge her
garments as a way of making her designs stand out.
Louisa buys a sample of the ribbon shown below:
a)It costs her £ 1.16 for 80cm of the spotty ribbon. Draw a picture
to represent this information and make it look realistic
b)What else do you know? Mark on your picture some other
quantities of this ribbon, which you would know the cost of.
Sharing Food
The café where Ruby works specialise in making large rectangular pizzas.
These are popular with lunch time diners who often order one of the large
pizzas to share. Masood and Tim are students. They meet for a pizza in the
café once a week. On one occasion they order the rectangular cheese and
tomato pizza shown below costing £10.35.
Tim is not as hungry as Masood, so they cut the pizza into 9 slices, Tim eats 4
slices and Masood eats 5 slices
 Draw a picture to show how they might share out the pizza
 Share out the cost of the pizza between Masood and Tim in the ratio 5 : 4
Post-test- ratio
Post-test - ratio
Can this be true?
I’ve got an 80 waist
How can this be true?
You need to sort that out.
Mine’s only 40
Extending the Number Line
Unlike many countries, in the UK we still use two
different units for measuring length. Both of these can
be seen on a standard tape measure.
The tape shows that 6 inches is roughly the same as 15
cm.
What do you think 12 inches is in centimetres?
The Number bar
Daniel drew the number bar above to represent the tape
measure
1. Make a copy of this bar and mark four other points on it
that you know in both centimetres and inches.
2. Mark is 5 ft and 3 inches. Alexandra is 1 metre and 72
centimetres. Use the 30cm to12 inches rule of thumb to
decide who do you think is the taller of the two?
Recipes – the ratio table
Helen decides to use the ratio
table below to work out the
ingredients needed for different
numbers of pancakes.
Pancakes
Makes 8 pancakes
Ingredients
125 g plain flour, sifted
1 medium size egg, beaten
Copy the table and fill in four more 300 ml milk
columns showing the ingredients
a little oil for frying
needed for different numbers of
pancakes
Best buy – ratio tables
In the supermarket, Helen and Nisha are buying ingredients
for other pancakes and trying to make sure that they get the
‘best buy’
Which do you think is the best buy?
Best Buy
To work out which is the best
buy, they decide to use a ratio
table. They begin by doubling
to see if this helps them to
compare the two buys. After a
few minutes, they both have
exactly the same thing on their
notepads. It looks like this:
Can you decide from here which is the
‘best buy’?
From the original table above, Helen and Nisha then work
in slightly different ways to make a comparison easier.
Below is their working.
Explain carefully what each of them has done and how you can
now see which is the best buy.
Starting the ratio table
For the next questions, draw your ratio table and fill in four other sets of
values that you know to be true.
1) A hare travelling at top speed
can run 260 metres in 12 seconds.
What else do you know? (30 secs)
2) 8 metres of ribbon costs £4.80
What else do you know? (30 metre
3) 5 miles is roughly 8 km. What
else do you know? (120 miles)
4) To make pink paint Joel uses a
ratio of 4 parts red to 10 parts white.
What else do you know? (30 RED)
5) A printing machine can produce
24 copies in 30 seconds. What else
do you know? (95 SECS)
Menu
Back
Forward Cont/d
Idea
Vocabulary Q 1
6) A multipack of crisps contains 15
bags. What else do you know? (12
MULTIPACKS)
Opinion 1 Opinion 2 Answer
Q2
Opinion 1 Opinion 2 Answer
Some early findings
Easier for the adults to take on the approach than the 17 year olds
Time is required to develop the approaches
Students are able to recognise the potential for using the bar and the
ratio table to answer questions in a variety of topics, and do so several
weeks later.
More difficult to have impact in the Algebra module
Some early recommendations
Teachers need support to take on this approach in the way it is intended
Students who narrowly missed a grade C may do as well to be taught
topics in the ‘usual’ way
Students who are at Grade E or below could really benefit from this
approach if it is used over a two year course