Masterclass: Take Action Issue 4 - Staffordshire Learning Net

Issue 4
Spring 2012
MaSTerclass
Take action!
Early
counting
Case studies:
Mathematics
Specialist Teacher
programme
gets results
Dot to dot:
Developing the skill
of subitising
Join in:
Test your class with
our puzzles page
Maths teachers move
from excellent to outstanding

Issue 4, Spring 2012
Masterclass – Take action
Welcome
As I reflect on the past few years of the MaST
programme, I can’t help but be impressed and
inspired by teachers who have participated. Not
only have they seen an improvement in their
own mathematics teaching, but there is clear
demonstration that their work is making a big
impact across the school. It is clear that these
teachers are bringing their vision and leadership
skills together to improve schools.
So what makes this so successful There is
no doubt in our minds (or in the minds of head
teachers who have seen these benefits), that
commitment from the head teacher, support for
MaSTs attending meetings during school time,
and support and resources to undertake inschool
activities linked to a school improvement
plan, are key factors. Despite changes
in funding, registration to the programme
continues to rise. The fact that head teachers
are willing to pay this and support their teachers
on the programme (even allowing them to be
away from their classrooms for short periods of
time), shows their very real commitment to the
programme, and their conviction that there will
be a good return on their investment. Each and
every one of those head teachers who has a
member of staff signed up to MaST is giving a
massive vote of confidence to both the MaST
team here at Edge Hill University and to our
local authority partners.
We are now actively recruiting for Cohort 4.
Once again, schools will have the opportunity to
invest in outstanding professional development
which is linked directly to school improvement
plans and which has been demonstrated
to make a huge difference to teaching and
learning, leadership development and
children’s achievement.
If this is the first time you have seen a
MaSTerclass magazine, I extend a very warm
welcome. In this issue we focus on early
counting, with views from two experts in the
field and case studies of MaST in action. Do
get in touch with us if you have comments or
questions. You are a vital part of the three way
partnership – Edge Hill, local authorities and
schools – that is making MaST so successful.
One last word. You may have noticed that
we are using the NCETM logo, indicating
that we, the Edge Hill MaST team, have met
their standard for Continuing Professional
Development provision. This is another
valuable endorsement of the MaST
programme at Edge Hill.
Dr Mary McAteer
MaST Project Director
Edge Hill University
A unique
view of maths
improvement
Senior lecturer Sue Bailey has a unique view of the MaST programme. She
is seconded to the programme at Edge Hill for three days a week, but is still
also a primary maths consultant for Lancashire, which means she gets to see
things from both sides of the fence.
Sue takes an active role in advising teachers currently on the MaST programme, in
supporting them with their assignments, developing teaching material and helping to
organise the Saturday lectures and workshops.
She says: “Having both roles is interesting and gives me a complete picture of the
MaST programme and the impact it is having on mathematics teaching and practice.
I find my involvement in the local meetings particularly useful. I’m there with my
Lancashire hat on; but can take the teachers’ ideas and feed them back into the
central MaST team, and I can see how my local teachers are building up their
subject knowledge.
The two things complement each other. The local meetings are all about cohort
members sharing ideas and knowledge, but then at the workshops and study
days I see them unpicking the deeper theories and rethinking aspects of their own
mathematics teaching.
It is really good, getting to know the students in my local group and seeing them
develop. One particularly encouraging thing is that one group now coming to the end
of its formal local network meetings plans to carry on. The teachers are hoping to
keep meeting up – and that must mean that they find the whole process valuable.”
Having two distinct roles means spinning lots of plates sometimes, but Sue says she
enjoys the constant challenge.
“I really like the student support aspect on MaST, answering questions and making
the whole process clearer for them. I get a lot out of the one-to-one email support
too, and I also enjoy the visiting lecturers and workshops. Getting to know individual
teachers on the programme is really great.
Obviously, there are cost implications when it comes to joining MaST, but I think
most schools see it as an investment in the whole team, not just one member
of staff.
From the teachers’ point of view, it does call for a high level of commitment – there is
work to be done outside of school hours, and it can be challenging – but feedback to
MaST and the positive impact it can have in the classroom has been really good.”
Sue Bailey
Calling all new recruits
to MaST
We are now recruiting for a new MaST cohort, so why not sign up for a unique
programme of professional development leading to lasting school improvement
It’s a win-win. One teacher
takes part in MaST, but
every member of a school’s
teaching staff can benefit
from the programme because
as they grow into their role,
a Mathematic Specialist
Teacher works closely with
colleagues to identify needs
and support professional
development opportunities
in mathematics.
Jan Jackson
Schools taking part in MaST
get a new tool for lasting
classroom improvement as
well as a positive impact on the quality of teaching and learning
in school and a reinvigorated attitude towards maths for teachers,
children and parents.
Numbers are increasing with each Edge Hill MaST cohort, as
head teachers begin to see the wider benefits of the programme,
and feedback clearly shows that MaST can lead to improvements
in pupil attainment .
Teachers who successfully complete the MaST programme
are awarded a Postgraduate Certificate in Specialist Primary
Mathematics (worth 60 credits at Masters Level) and Mathematics
Specialist Teacher status.
Case study
MaST has transformed
my career
The MaST programme not only
boosted Rachel Burns’ confidence –
it also transformed her teaching day.
Rachel is now teaching mathematics full time at Moor Green
Primary School in Birmingham; something she says could
never have happened without MaST.
She says: “I have got my dream job. I have gone from being a
classic maths phobic to a fully fledged maths geek – and proud
of it. Seriously, the programme made me much more aware of
the massive range of resources on offer and put me in touch
with a group of people who have taught me so much. The
interaction with other teachers on the programme was really
important and helped give me good ideas.
I have been able to transfer the learning straight into the
classroom. I have now taught maths to every year group,
Sounds like a great opportunity It is – but it also calls for
commitment, with some events and personal study at weekends
and ‘out of hours’.
Jan Jackson, MaST Project Manager says: “MaST is evolving
from an excellent professional development and school
improvement programme into an outstanding one.
When I speak to teachers taking part it is quite clear that their
view of mathematics changes – and so does the methods they
use. MaST gives them the benefit of expert opinion and new
thinking, and an opportunity to hear from fellow teachers in
other settings. This sharing of knowledge is fundamental to
the programme’s success.
MaST isn’t something you devote the occasional hour to; it tends
to become all consuming, which is great, because that can only
be down to the enthusiasm and vigour of the teachers involved.”
Remember:
This is your last chance to get partial funding from DfE
(they pay half of the first year).
It’s great value for money – the whole school benefits, and
MaST provides 12 half days of Local Consultant time, plus
keynote speakers who are leaders in the field. To find out
more call 01695 650774 or email mast@edgehill.ac.uk.
even Reception, and am also working with small groups of
gifted and talented pupils.
I have also contributed to a maths training day for NQTs run
by the local authority maths adviser. I would not have had
the confidence to do something like that before. Maths was
a subject I did not enjoy at school and I would never have
believed I could end up doing this.
MaST has given me a deeper subject knowledge and
pedagogy and real enthusiasm for the subject which has
been transferred to the children. We run a maths club at
school, and the children are so keen to learn.
I think the programme was excellent; probably the best
professional development I have come across. I was one
of the first to take part and it’s no exaggeration to say
that MaST has transformed my outlook, my teaching
and my career.”
2
jacksonj@edgehill.ac.uk
jacksonj@edgehill.ac.uk
3

Issue 4, Spring 2012
Masterclass – Take action
Look and learn:
join the
subitising set
When you play a board game using dice you are probably subitising. It’s the
same with dominoes. As any mathematics teacher will know, subitising is the
ability to recognise the number of objects (dots, in the example of dice) without
actually counting them.
Ian Sugarman
This method of knowing a number simply by looking at a grouping
is something most adults take for granted, but it is a skill that is
developed at a very young age.
Pre-school children can quickly learn to recognise small groups
of dots, or lines (or just about any object) without having to count
them individually, and their ability to do this is a fundamental
building block in the teaching of number to Reception and Year
One pupils.
Primary Mathematics Consultant Ian Sugarman is a visiting
lecturer on the Edge Hill University MaST programme and has
focused on this subitising skill, helping teachers to see the
benefits of actively developing it in their pupils and showing
how it can lead to a better understanding of number and early
strategies of calculating.
Ian explains: “Often in the teaching of four and five year olds the
emphasis is on mechanically counting small quantities of things.
But children can ‘see’ these numbers as a group from an early
age, and if a teacher can draw a child’s attention to his or her
ability to visualise numbers in this way, it helps give the child a
deeper understanding of how numbers relate to each other and
it can have a big impact when children move on to calculating
numbers mentally.”
Benefit
“By encouraging subitising a teacher is getting a child to use
both sides of the brain: it is not just about memory or mechanical
counting; it is about recognising shapes and patterns, which is a
different skill and of huge benefit in early number work.
Often children can see groupings very quickly, and this is
something Ian demonstrates by quickly flashing an image onto a
screen and asking children to reproduce it. Some children may
need to look up two or three times, but most can hold the image
in their mind and reproduce it perfectly after seeing it fleetingly
for just a couple of seconds.
He explains: “You put a simple line drawing on the screen and
ask the children to copy it using a pile of sticks on a table in front
of them. If there is a pattern or a symmetrical element to the shape,
children can hold onto that image and reproduce it easily. Crucially,
they know how many sticks are needed to recreate the shape.
I encourage teachers on MaST to introduce this sort of activity into
the classroom. It is fun of course, but it develops and enhances
this subitising skill, which is a way of getting children to slow
down and explore numbers, examining them in a way that simple
mechanical counting does not.”
Skills
The ability to see groups instead of counting separate items leads
to other important skills when children move onto more complex
number work. For example, if a child can see a group of sticks,
and identify how many triangles could be made from those sticks,
they can also see how many ‘threes’ they need.
Ian says: “There are lots of ways to engage children. It used to
be a case of using flash cards, which were then replaced by a
series of Powerpoint slides. But now I’ve been able to offer this
as a ready-made software activity. It’s the sort of activity that
should be done little and often in the classroom because it is not
a maths technique that can be compartmentalised – it flows into
many aspects of number work.
I had one teacher in a previous lecture who told me that these
ideas on subitising had completely transformed the way she and
her colleagues approached counting with Early Years pupils.
At her setting they had reorganised and given a fresh priority to
this skill, and I don’t think that’s unusual.
Adults can forget that their ability to ‘see’ groups of things without
counting is a skill that underpins their understanding. Getting
back to basics and building these activities into lessons for the
youngest learners can have a big impact.”
More about Ian…
Ian Sugarman has many years experience as a Primary
practitioner, advisory teacher in Shropshire and trainer of
Primary teachers at Manchester Metropolitan University.
He has produced an extensive range of mathematics
curriculum materials, served on QCA committees producing
guidance on the teaching of mental and written calculation
strategies and the writing and reviewing of SATs.
He is a well established author of journal articles and
curriculum booklets and has served on UK Government
committees for the production of national assessment
packs and guidance. With 25 years experience as a
training provider for Primary teachers he is still very much
classroom-based, and since retiring from MMU has been
working with both gifted and talented and under-attaining
pupils at several schools.
He is co-author of Numbergym software, designed for
non-specialist teachers and parents from Foundation
stage to GCSE.
For more information and ideas see his website at
www.sugarmaths.net
Case study
Putting Ian’s
ideas into
action
Ian Sugarman’s lecture on subitising
led to a change of practice in the
Reception class at Aspull Church
Primary School near Wigan.
Teacher Alison Moore was a member of the first MaST
cohort and says that introducing some of Ian’s techniques
for number recognition has made a big difference to pupils.
She says: “I had gone from being a Year 6 teacher to
Reception, and of course the younger children had very
different needs when it came to learning maths.
After hearing Ian’s lecture I decided to try out some of the
ideas and the children did really well as a result. We used
dice games and looked at patterns and somehow it just
‘clicked’ with them – it made a tangible difference.”
Training
“I have been able to incorporate other elements of the
MaST programme into our teaching, and we are just starting
to include some things into staff training too, which means
my colleagues also get the benefit of the learning.
MaST enables you to look more closely at how young
children learn maths and helps you to deal with some of
the most common problems they can face.
The local meetings on the programme were very useful
as a way of sharing ideas, and getting together with other
teachers helps you see that the same ‘problems’ in teaching
and learning maths occur at many other schools.
My colleagues on the cohort were a very important source
of support, and even though I finished the programme at
Christmas, I still keep in touch with them.
Being part of the first MaST cohort meant that I wasn’t
exactly sure what to expect. Although it’s true that MaST
demands considerable personal commitment and
can be time consuming when you already have a
full time job, I would recommend it to others.”
4
jacksonj@edgehill.ac.uk
jacksonj@edgehill.ac.uk
5

Issue 4, Spring 2012
Masterclass – Take action
One, two, three steps
to success in
early counting
Early number expert Professor Effie MacLellan, Research Professor of Education
at the University of Strathclyde, is a visiting lecturer on the MaST programme. A
former primary school teacher, she advocates the use of simple classroom-based
counting techniques to help young children understand both the concept and its
importance. Here she answers some questions frequently asked by teachers.
She says: “What does it mean to say
that someone can count For adults,
counting is a seemingly straightforward
activity: they notice the set of items to
be counted, assign a number name to
each item and recognise that the last
number name used defines the total
number of items in the set.
That adults are skilled in counting
is not surprising – most of us have
Effie MacLellan been practising since the age of
two. Of course two year olds cannot
count with the same level of skill as
adults, but research shows that the rudiments of counting can be
observed in many two year olds. Counting is both a very complex
process and a very important process.”
How long does it take for a child to
learn the number names
How long is a piece of string Most children will have learned the
sequence up to 100 by about six or seven years of age. Typically,
two to three year olds can reliably produce the string ‘one, two,
three’, though after ‘three’ may become confused. The hardest
part of learning the number names is learning the sequence from
‘one’ to ‘thirteen’, because all the names are so very different from
each other. By the time the child has learned the number name
sequence to ‘twenty’, they may have spotted part of the repeating
one to nine pattern: four and fourteen, six and sixteen and so
on. Once children have mastered the number name sequence to
twenty and have grasped the repeating pattern, all that is left is for
them to learn the decade names: thirty, forty, and so on. It takes
most young children four or five years to learn the number name
sequence up to one hundred.
Can children count when they know
the number names
Categorically no. Counting involves much more than the rehearsal
of strings of number names. Counting involves three procedures.
First, there has to be a pairing of each item with a number name.
Someone counting has to mentally ‘move’ (and possibly physically
move) each item from a to-be-counted category to an alreadycounted
category and, at the same time, must assign a different
number name to each item. This pairing is open to error. One is
when the person counting either counts an item twice or misses
one out. Another error is when there is a mistake made in using
the number names (perhaps using the same number name twice).
A third is when the person counting fails to ‘move’ and name the
items in a synchronised fashion: for example the number naming
may be in advance of the ‘moving’ of items; the naming may
continue after the ‘moving’ is complete; or during the procedure
there may be a failure to maintain one-to-one correspondence so
that although the procedure begins and ends in synchrony, there
has been some confusion in between.
Second, while assigning a number name once, and only once, to
each item in the array is important, it is not enough. Additionally,
the sequence of number names generated must be reliably
produced from one count to another. We have to learn a stable
list of counting words and use this list consistently.
The third procedure is the recognition that the final number name
used has a special significance. This final number name defines
the total number of items which were counted. This is later in
developing than the first two procedures and is dependent upon
the first two. A child may be able to pair number names and
items-to-be-counted and may assign the number names in a
fixed order but may not further know that the last number name
assigned represents the numerosity of the items.
I was taught that before children can
really learn to count, they must be able
to sort objects into groups
Yes, but this is only a bit of the story. Actually children will count
elephants, bananas and toys or girls and lollipops and refer
to such collections as “things”. This means that the ‘sorting’
activities, often used in early education, are not as important
to understanding counting as was once thought.
So if ‘sorting’ activities are not essential,
what about ‘matching’ Don’t children
need one-to-one correspondence before
they can count
Yes, children do need one-to-one correspondence in order to
count, but what is questionable is whether children need to
engage in the ‘matching’ activities of assigning straws to cups of
juice or eggs to egg cups. If the child can pair a number name with
an item and continue pairing a different number name to each new
item in the set, the child already has one-to-one correspondence.
Remember that one-to-one correspondence is an abstract notion;
it is not something we can see.
Is counting important
Yes. Counting is a pre-requisite for many other mathematical
activities such as telling the time and multiplying. And counting
is the means by which young children penetrate the concepts
of addition and subtraction. When a set of items has been
transformed either through some items being
added or removed, the only strategy which the
young child has for defining the outcome of the
transformation is counting. When children
start school, they may have informal knowledge
of addition and subtraction.
Case study
Looking at practice
in the Pacific
Big changes could be on the cards
for Katie Hebden, a Year 3 teacher
from Millfields CE Primary on the
Wirral. She is hoping that involvement
in MaST will help her secure a
teaching role in New Zealand.
She says: “I think the programme is really good at developing
your understanding of the child as a mathematical learner.
You would not get that in everyday teaching.
I teach Year 3, but since MaST have been doing some
intervention work with small groups and also some one-to-one,
helping children overcome their maths misconceptions.
The programme was very useful. I now know where to
find good resources and the pedagogy was excellent.
It was certainly more than just an investment in me;
What can I do to promote the young
child’s counting
Good readers are the people who do a lot of reading; young
children who are good at counting tend to have done lots of
counting. Many children count when there is nothing in the
immediate environment which demands it: they get intrinsic
satisfaction from counting.
• For children who have not developed the conventional list of
number words, there is nothing to be lost by some rote counting:
rehearsing the sequence of number names, perhaps to ten.
• The pairing of a number name with an item can be better
managed by children if they point to each item in the set.
Pointing, while saying the number names, is a cue to the
child that each item is counted once and only once.
• Be ready to show the children the observable behaviour you
wish them to demonstrate. If you want the children to touch
the items as they are being counted, show them clearly what
you want. Check and correct, with further demonstration, those
who are having problems in synchronising the touching and
the naming. Similarly, be ready to make explicit what children
seem to know, but do not articulate clearly. For example, having
executed a count correctly, the children can be reminded that
the last number name used tells how many are in the set.
• Don’t worry if children use their fingers to make sense of
counting more easily. Traditionally there has been a fear that
children would become over dependent by a reliance on
fingers for counting but there is no evidence to suggest that
by using their fingers to support their counting, children are
handicapping themselves, either short or long term.
it is about sharing the ideas and activities with other teachers
and TAs in my school.
Whilst researching for my initial assignment on language
within mathematics I was interested in how this was widely
developed and focused on in the Pacific region, especially
New Zealand education. It appeared that the children
progressed a lot quicker at an earlier stage with only the
key concepts being taught.
When it was time to do my second assignment I looked again
at their Maths Curriculum and really liked the emphasis they
gave to their teachers’ pedagogy and wanted to be part of it.
So at Easter I am travelling to New Zealand where I hope to
gain a teaching position, and after speaking to a few Head
Teachers already it seems that a Primary maths specialist is
something they are very interested in having.
I would recommend MaST; but it does represent a lot of work
and so demands a big personal commitment. I would say that,
having now completed MaST, I feel one step ahead.”
6
jacksonj@edgehill.ac.uk
jacksonj@edgehill.ac.uk
7

The classic ‘6801
to 1089 trick’
Dr Mark
Effect:
You predict the 4-digit number
your victim will calculate from
a 3-digit number they choose
What
you
need:
A victim... er... I mean volunteer
A pencil (or pen) and paper for writing down calculations
Maybe a calculator to help with the calculations
A blank sheet of paper
L
What L
to do:
Without letting anyone see what you are writing,
write the number ‘680I’ on a blank sheet of paper.
NOTE: Make sure you write the number ‘one’ at the end using just
a single vertical line, and don’t insert a comma between the ‘6’
and ‘8’ as some people do – you’ll see why later!
Choose your victim... er... volunteer and ask them to carry out the
following instructions:
1. Think of any 3-digit number and write it down, making
sure that the first and last digits of your 3-digit number
are different, or, perhaps a simpler instruction, just
choose a 3-digit number without any repeated digits.
This is your FIRST 3-digit number.
- Worked example: Your volunteer might choose their FIRST
number as ‘123’.
2. Now write down a SECOND 3-digit number, whose digits
are the exact reverse of your FIRST 3-digit number.
- Worked example: If their FIRST number is ‘123’, then their
SECOND number will be ‘321’.
3. Using a calculator if you like, now subtract the smaller
3-digit number from the larger 3-digit number, to
produce a THIRD 3-digit number. Note that if you
should end up with a 2-digit answer number, then
you should simply insert a ‘0’ in front of it to make it a
3-digit number that now starts with the digit ‘0’ in the
hundreds column.
For example, suppose your volunteer had instead chosen their
first 3-digit number as ‘201’; then their second 3-digit number
would have been ‘102’. Subtracting ‘102’ from ‘201’ produces
the 2-digit answer ‘99’. To make this a 3-digit number they
would simply insert a ‘0’ in front of the ‘99’ to make the 3-digit
number ‘099’.
- Worked example: Subtracting ‘123’ from ‘321’ equals ‘198’
(THIRD 3-digit number).
4. Now write down a FOURTH 3-digit number, whose digits
are the exact reverse of your THIRD 3-digit number.
- Worked example: Their THIRD number is ‘198’, so their
FOURTH number will be ‘891’.
5. Finally, ADD together your THIRD and FOURTH 3-digit
numbers to get a final 4-digit number answer, and write
it down.
- Worked example: Adding ‘198’ to ‘891’ equals ‘1089’
Now reveal your sheet of paper to your volunteer with the
number ‘680I’ you wrote on it earlier, and say:
“This is your final 4-digit number!”
Your volunteer will now no doubt sneer that you are
TOTALLY WRONG!
Look a little downcast and confused, pause for thought and then
look at your sheet of paper with the number ‘680I’ written on it, and
say, “A-ha! I see what I’ve done wrong.” Then simply turn your
sheet of paper around upside-down, where the original ‘680I’ now
reads as ‘I089’ – your volunteer’s final 4-digit number!
Take a bow!
What’s going on:
This is a ‘classic’ number trick and usually amazes those who have not come across it before and can still confuse even those who have!
As you’ve no doubt realised by now, it works with any 3-digit number at the start, provided the first and last digits are different. This trick is a
good source for problem solving, reasoning and further investigation, not least by repeating the trick with different starting 3-digit numbers,
which will give further practice with adding and subtracting, paper arithmetic, place value and calculator work.
For another ‘magical’ version of this trick, along with a detailed mathematical explanation of how it actually works – including the algebra
(ARRRRGH!) – enter the following URL into your favourite browser: www.dr-mark.co.uk/monthlyMaths/monthlyMathsJan2012.pdf
For details of Dr Mark’s range of science and maths in-school pupil shows, in-school teachers’ CPD, his teachers’ resources books,
CDROMs and DVDs, and FREE RESOURCES NEWSLETTER, visit his website at: www.dr-mark.co.uk
© Dr Mark Biddiss 2012. Dr Mark’s INSPIREducation: INSPIREmathsTM Web: www.Dr-Mark.co.uk
We are happy to share, but please ask before reproducing stories and photographs
from MaSTerclass magazine. Contact: jacksonj@edgehill.ac.uk
© Edge Hill University 2012. The publisher, authors and printers cannot accept
liability for errors or omissions. Designed and produced by Epigram 0161 237 9660