Making Maths Visible
A DfE Shared Learning Project
Introduction
Making Maths Visible was a Natspec led, DfE funded project that aimed to increase the
confidence of students with learning difficulties and disabilities and their teachers to feel
positive about maths and understand its importance to the achievement of good outcomes.
All students on Study Programmes must follow some form of maths/numeracy (and
English), whether GCSE, functional skills or non-accredited.
Research question
Best practice in the delivery of maths for learners with disabilities or difficulties is that in
which the teaching and support staff clearly understand the concepts, processes and
elements of mathematical principles and can relate them to the learners’ experiences. We
asked, ‘How are you designing and delivering maths within your curriculum?’ We aimed to
answer this by using a range of approaches and reaching as wide an audience as
possible.
Programme
The wide ranging and comprehensive reach of the programme drew evidence from those
providers who took part. This indicated that there is a great deal of good practice in the
sector, with examples of resources, practice, approaches and student work shared by a
variety of means.
The programme comprised three phases:
1. Workshops with providers to investigate current practice, share ideas and
approaches. These incorporated a pre-event questionnaire to inform the team of
the level and format of maths being delivered in the providers taking part.
2. Maths week comprising:
a. A webinar introducing a competition and the idea of visible maths
b. Website presence on the Natspec site providing up to date and relevant
information
c. A twitter hashtag - #visiblemaths encouraging providers to share their maths
stories
d. An ethos of sharing and celebrating the maths that is part of everyday life,
learning and work.
3. A competition to gather data and then represent the data set in a way that is
creative and appropriate for the relevant student cohort
a. A survey form available for download from the Natspec site for groups to
complete as appropriate
b. Publication of the results on the Natspec site
c. Collection of competition entries
Resources and materials from each of these phases were analysed and reviewed in order
to answer the research question and to determine possible ways to improve the process.
Workshops
Recruitment
We recruited 38 delegates for the workshops that were held in London, Birmingham and
Sheffield. Of these 13 were from mainstream FE colleges, one from a school and 22 from
specialist colleges.
Pre-event questionnaire
We provided each with a pre-event questionnaire asking for details of their current maths
provision, attached as Appendix A.
All providers were working with students who had either Learning Difficulty Assessments
or Education Health and Care Plans. Numbers from individual providers varied from 9 in
one small specialist provider to over 200 in a mainstream FE college. They were almost
all delivering some accredited courses, ranging from functional skills at Entry level to level
1or 2. There were also other qualifications being offered, including personal progress,
independent living, employability and others.
Just under half of the returns indicated that they were using RARPA or a similar system to
track and support the progress of their students on non-accredited programmes.
Often those not using RARPA indicated that this was not applicable. This may indicate a
lack of understanding of the RARPA process and ethos, which can be applied to both nonaccredited and accredited learning. Respondents provided a wide range of suggestions
for using maths in the Preparing for Adulthood outcomes of employment, independent
living, community participation and good health and well-being, see Appendix B
Resource Sharing
All delegates attending the workshops were subject specialists and were delivering maths
as a discrete subject within their own organisation.
Each participant was asked to bring both a suggested resource and a maths joke. There
is a collection of the maths jokes in Appendix C
Resources shared with other delegates included links for online content such as game
based mathematics sites, apps that support everyday maths problems and other examples
of maths support that are available. The National Centre for Excellence in the Teaching of
Mathematics https://www.ncetm.org.uk/ is one site that has a wealth of support materials
and resources for wide levels of achievement.
Workshop discussions
The workshops provided an opportunity for delegates and facilitators to raise wide ranging
subjects for discussion. These provided information for the programme and some
excellent examples of good practice.
All providers were delivering maths as discrete sessions for all students. However there
were numerous times across the curriculum that maths activities were taking place, but the
maths specialists were not always aware of or able to support them.
The inclusion of maths in other curriculum activities was an intended outcome for all
delegates. Most providers did not have a designated option to identify maths opportunities
in their planning documents, either ‘schemes of work’ or session plans. The activities were
all embedded in activities such as weighing ingredients, shopping, using public transport or
planting out seedlings. So maths is being used, even if not explicitly in many sessions, and
the workshop programme provided opportunities to highlight how to establish the
crossover.
Delegates also highlighted the difficulty of transferring mathematical opportunities and
processes from the education environment to both the residential and the home situation.
Although there can be some excellent work done within the college or education
environment, for the maths skills to become really functional they need to be used in
everyday life and work. Identifying and solving maths problems in these situations needs
to be done in a way that supports the previous learning. Providing this support to both
teaching and support staff is crucial in enabling the students to progress.
Much time was spent discussing ways of addressing some of these common maths
problems. For example, telling the time and the difficulty in explaining an analogue clock,
or deciding if ‘10.35’ is ‘ten thirty five’ or ‘twenty five to eleven’, as students with cognitive
impairment may find it very challenging to view the same concept in different ways.
Anomalies such as this occur all the time with maths teaching and emphasise the need for
professional development for all teachers and support staff to ensure a consistent and
uniform approach for each individual.
Every workshop included comments and discussion on the difficulties that learners on the
autistic spectrum find with scenario based assessment questions, such as those used in
functional skills assessments. It was agreed that contextual evidence based functional
skills assessment would be more appropriate for this cohort of students.
Webinar
We held a webinar at lunchtime on Monday 9 February. The webinar was widely
publicised and 67 people registered to attend. It was recorded and a simplified version
was uploaded to YouTube and embedded into the Natspec website. The video has had
over 80 views so far.
The webinar introduced both the pizza survey competition and the suggested activities for
Maths Week that was due to take place between the 23 and 27 February.
Data Survey and Competition
Delegates at the workshops discussed on how we might collect data and on what subject.
It was decided that a short and simple survey on pizza toppings would be easy to
administer and relevant and interesting to students. A simple form was made available on
the website – see Appendix D.
Providers were asked to provide details on how they administered the survey along with
their results. This produced the first set of resources from colleges.
Forms were to be returned by Monday 23 February and the collated data set was
published on the Natspec website on Tuesday 24 February. There were over 1,000
responses to the survey with Pepperoni being the outstanding favourite. See the table
below for the results.
Margherita
Chicken
Tandoori
Pepperoni
Hawaiian
Roast
Vegetable
166
98
232
150
158
Providers had until Friday 6 March to send in their interpretation of the data in a form that
was relevant to their learners. Colleges provided a wide range of creative and innovative
ways of representing the data. Many produced pie charts in the form of pizzas; others
provided a wealth of additional material showcasing how they had delivered the survey,
and what the results meant. We had a number of videos and even one song written about
pizza toppings.
Examples of competition entries and winners are available on the Natspec website.
Maths Week
Maths week itself ran from the 23 to the 27 February. Our twitter hashtag #visiblemaths
meant that we could easily search and collate for content. We had over 100 tweets or retweets over the course of the week and reached a potential audience of over 42,000 twitter
accounts.
Content was shared by a number of colleges and covered subjects such as innovative
ways of doing maths (toilet paper geometry), activities that students were taking part in
such as making chocolate éclairs, measuring a wide range of objects and even scoring a
dance performance.
Outside agencies also took part with seven members of Jisc staff either posting or retweeting other content. The Natspec social media team provided additional content on
twitter and the Natspec Facebook page. Other agencies including XTLearn also posted
examples of online maths resources. Since then the hashtag has continued to be used
with some colleges using it to showcase work. For example one college tweeted their
students working together to view the partial eclipse in March.
In addition to the social media presence many colleges documented the work they were
doing by sending it direct to the project director. Examples of these resources are
available on the Natspec website. They include whole college work highlighting the
presence of opportunities to do maths work in many areas. Some colleges held a whole
day themed around making maths visible and included posters, signs around the building
and maths incorporated into all their subjects. One college produced 3 videos around
supporting and working at maths.
One example of collaboration was between a specialist college and their local FE College.
This involved the Maths AS level students from the mainstream college visiting and
working with the learners in the specialist college to make pizzas and discuss the maths
that they were using as part of the task. Both colleges provided excellent competition
entries with video and images from the day.
Answering the Research Question
Resources from the maths visible programme indicate that there is a lot of very good
practice happening in specialist provision across the country. Almost all maths teaching is
delivered as discrete sessions, but the skills of the maths specialists are incorporated
across the curriculum with varied success. The identification of maths opportunities in
planning documents for ‘non-maths’ sessions is sporadic, although it is clearly happening,
and the problem of the transfer of maths processes from educational provision to both
residential and home is a continued issue that needs to be addressed.
One of the overwhelming responses to the programme from functional skills staff was that
‘it was easy to do’ and that it enabled them to focus all their curriculum staff on maths for a
whole week. The importance of maths subject specialists was emphasised in all the
contact we had. Many maths co-ordinators used the programme to integrate maths into
simple visual displays for staff and students. An example from one college was to include
the figures for times tables above coat hangers.
The resources from both the pizza competition and the maths week activities provide
examples of good practice in the teaching and support of maths across the curriculum that
would be relevant to many providers in all sectors.
One example of the work done in maths week is provided in the case studies, and
concludes that the programme provided “the beginnings of what we see as an ongoing and never ending process of
identifying, encouraging and supporting maths throughout college life.“
Feedback
The social media campaign provided some instant feedback both on the work that colleges
were doing and how they addressed the questions.
In March we held a workshop at the Natspec annual conference; we reviewed the project
and used the opportunity for more in depth feedback. Once again the simplicity and ease
of implementing the programme was highlighted by all delegates. The timing of the project
just after the half term was felt by some to be a difficulty and communications to providers
may have been an issue for some.
All delegates both in the initial workshops and in the feedback session at the conference
felt that an online forum to continue the conversation would be beneficial for all those that
took part.
They also agreed that it would be beneficial to provide this sort of co-ordinated and
focussed opportunity as a regular annual event. This would allow providers and their
students to share and celebrate their work and in the process provide resources for others.
Recommendations
For providers:
 To enable the maths specialist to work across the curriculum, ensuring that
teachers become more confident about the place of maths in their own subject
areas
 To ensure that maths opportunities are clearly identified in schemes of work and
session planning.
 To acknowledge and record maths opportunities and activities which take place in
the residential setting.
For Department for Education:
 To acknowledge the complications of assessment of achievement for learners with
learning difficulty or disability, and ensure that DfE guidance and other
documentation reflects this
General recommendation:
 We believe that a further maths week should be held next year and know there is
an appetite and support for this. We have some early indications that Jisc may be
interested in supporting this in the future.
Lisa Featherstone
Project Director
Alison Boulton
Project Manager
Appendix A
Making Maths Visible: pre-event questionnaire
1. College:
2. How many students do you have with LDAs (or EHCPs)?
3. Please complete the following information:
Approximate
percentage of
students following
accredited maths
programmes
Qualifications being taken
a) What percentage of
your students with
LDAs (or EHCPs) is
following accredited
courses?
b) What percentage is
doing GCSE?
c) What percentage is
doing stepping stone
qualifications from
the approved list?
d) What percentage is
doing other
qualifications?
4. For students following non-accredited maths, do you have Rarpa or a similar
system to record their progress?
5. Please indicate how you apply maths to the following outcomes under the Children
and Families Act (give a couple of examples for every area)
Outcome
a) employment
b) living more independently
c) participating in the community
d) good health and well-being
Activity
Appendix B
Table showing examples of Maths opportunities identified by workshop delegates
Preparing for
Adulthood
Outcomes
Maths opportunities
Employment
Timekeeping: students learn about being on time for work, how long
tasks take (by timing them) to improve time management, the importance
of following the daily timetable, daily/weekly/monthly/annual/seasonal
tasks in the workplace, etc.
Specific vocational tasks: students learn about water & capacity, taking &
recording temperature/pulse/respiration, making feeds (involves
measuring in fractions, extracting information from charts, weighing,
ratios, etc.), measuring heights/lengths/weights
Living more
independently
Measuring accurately in workshop activities in a wide range of processes
including catering, horticulture, metal work and agriculture.
Money management: students learn to work with their own money and
bank accounts in order to manage their weekly budget according to their
ability
Cookery: students learn to plan, shop for and prepare meals for a small
group which includes calculating quantities, weighing ingredients,
working within an allocated budget, timings, etc.
Participating in the
community
Independent travel: students learn to plan and complete journeys
involving walking, buses and trains which includes reading timetables,
calculating timings, budgeting for the journey
Organising events: students learn to check dates, manage money (using
a float and calculating profit/loss), calculate quantities, etc.
Good health and
well-being
Participation in community events: summer or Christmas fairs, producing
and selling hampers and other goods.
Fitness: students learn about healthy eating & weight (by looking at
quantities & ingredients & healthy options, monitoring their weight),
increase physical fitness (by timing themselves completing physical
activities), etc.
Managing medical appointments: students learn to make appointments at
appropriate times, check medication quantities (daily to take and in order
to process repeat prescriptions to prevent running out), etc.
In sport: students can keep score as well as timing for activities, how long
can you hold a position, how many jumps/squats and length of time for
sporting activities, running, swimming etc.
Appendix C
Maths Jokes
The Making Maths visible also included a strong element of Maths is fun. We collected a
number of maths jokes in the process and thought they were worth sharing.
1. I hired an odd job man to do 8 jobs for me. When I got back he'd done jobs 1, 3, 5,
and 7.
2. What did the zero say to the eight? Nice belt.
3. Why was the ten frightened of seven – because seven, eight, nine (you have to say
it out loud).
4. How do you make the number seven even – remove the S.
5. There were three French cats on thin ice – Un, deux, trois, quatre cinq! (you have to
say this one out loud too)
6. A talking sheepdog gets all the sheep in a pen for the farmer. He goes back to the
farmer and says,
'Right that's all 40 sheep accounted for'.
The farmer replies ' But I've only got 36 sheep'. The dog replied - 'I know, but I
rounded them up'
7. There are 10 types of people who understand binary – those who do and those who
don’t.
Appendix D – Pizza Survey form
Pizza survey and competition
The survey
One way for everyone to get involved in Maths Week is to take part in our survey. Almost
everybody loves pizza, but what is the favourite topping?
♡ Margherita - cheese and tomato
♡ Chicken Tandoori
♡ Pepperoni
♡ Hawaiian - Ham and Pineapple
♡ Mushroom and vegetables
During Maths Week, we aim to find out and to let you know
Find out from as many people as possible - students and staff - their favourite topping from
the list above. Please circulate this document within your college and choose how you are
going to discover the results. It may be from a show of hands in a classroom or putting
voting boxes around the college. Then collate the results.
Fill in the results below and send this form to Lisa Featherstone by 4 pm on Monday 23rd
February
Margherita
(cheese)
Chicken
Tandoori
Pepperoni
Hawaiian
(Ham and
Pineapple)
Roast
Vegetables
and
Mushrooms
Please indicate here how you collected and collated your results. How did the
students take part in the count or the collection of the figures?
The competition
Once we have the overall figures, we will put the information on
http://www.natspec.org.uk/information-for-professionals/making-maths-visible/ on Tuesday
February 24th. Then we want you to come up with a really great way to present the data
– pictorially, a video, a song – whatever you can think of to make it easy to understand for
everyone. Students can work on their own or with a team
Send your ideas along with your name(s), college and email to Lisa Featherstone by noon
on Friday 6th March. We will put as many ideas we can on the site, and announce a
winner on Monday 16th March. Winners will receive a pizza apron.
You can take part in just the survey and use the results yourself, or just enter the
competition, but we hope you will do both!