Using Models and Images in Play to Support the Understanding of Number Facts with
Special Educational Needs Children in Year 2.
Sarah Hughes attended Edge Hill University, Ormskirk, where she completed the two year
Mathematics Specialist Teacher (MaST) programme. The programme is designed to help
teachers develop a deep understanding of a range of approaches to the teaching and
learning of mathematics across key stages, helping them to become "champions of
mathematics" who will work to change attitudes towards the subject, making it more
accessible and relevant to children. The following article, written with the support of tutor
Vicki Grinyer, discusses the use of models and images in play to support the understanding
of number facts with pupils with SEN in Year 2.
Introduction
The following article investigates the use of models and images and explores how such
resources can contribute to ‘playful teaching’ (Pound, 2008:53). Playful teaching is described
as a style of engagement, where the practitioner interacts with the learner through play
(Pound, 2008). The article reflects on the impact these play opportunities had on the
understanding of number facts with a group of Year 2 children with Special Educational
Needs (SEN).
Class based research was undertaken to develop this project, using questioning,
observations and teacher assessments to assess the impact this pedagogical approach had
on the children’s learning.
School X is a larger than average primary school, with 320 children currently on roll. In Key
Stage One there is a two form intake and children are taught in single year group classes.
The catchment for the school is mixed, 40% of children living in a deprived area of the town.
Baseline on entry to school is below age expected attainment, and as a consequence end of
Key Stage 1 attainment is also below the national average despite the progress made being
classed as ‘good’. Currently, average point scores at the end of Year 2 are low, which reflects
a high percentage of learners either below age appropriate or ‘stuck’ at level 2c.
The percentage of children registered as having Special Educational Needs is in line with
national averages and currently stands at 21%. Rigorous internal monitoring and tracking
systems have identified SEN as an area of concern in terms of progress. The progress made
by SEN children, therefore features heavily in our School Development Plan.
The class based research will focus on the learning of four children, all of whom have SEN to
varying degrees. Child C is currently registered as a class concern, due to a lack of progress
in her learning. Children G and J are registered at School Action and both children have
moderate learning difficulties. Finally, child M is on the SEN register at School Action Plus.
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Her needs are more complex; however a recent Learning Support Advisory Teacher reported
that her current level of learning did not match her potential and capacity for further
learning. All of these children are working significantly below level 1 as they enter Year 2.
Planned Approach
It is my personal opinion, based on my professional experience, that using models and
images to teach mathematics is synonymous with effective teaching. I always use a wide
range of models and images to teach concepts in mathematics and I also encourage children
to choose and use their own models and images, so that they can support their own
learning and develop decision making and independence.
Piaget (1952 cited in Lindon, 2001:23) proposed that younger children do not have the
mental maturity to grasp abstract mathematical concepts, therefore suggesting that
experience of concrete materials are important for learning. Furthermore, Skemp (1987)
suggests that children’s early experiences with physical objects form the foundations for
later learning at a more abstract level.
Panhuizen (2003: 9) suggests that models are often attributed the role of bridging the gap
‘between the informal understanding connected to the real and imagined reality on the one
side and the understanding of formal systems on the other’. Throughout my research I
hoped to develop the use of models and images further, considering how play, or ‘playful
teaching’ (Pound, 2008:53) can be used to make the link between the world of mathematics
and the world we live in (Tucker, 2010:13).
I believe that through play, children will engage more fully with the world around them and
the progress made will be greater because the children will see a purpose for their learning.
Throughout the project, the role play area was used as a way of creating ‘real-life’
mathematical situations within the classroom. The role play area was developed as a toy
museum shop, which linked to the wider curriculum. The area provided the children with
lots of models and images to support their learning. Jarman (2008:32) makes the point that
‘worthwhile mathematical experiences replicate mathematical situations in the outside
world’. Pound (2008) also suggests that although we understand the importance of
contextualised learning, all too often we expect children to practise mathematical ideas
without purpose. She asserts that ‘making it real makes all the difference’ (Pound 2008:41).
Throughout the study, the children involved were supported in their play as part of the
teacher focus group once a week. My involvement and interaction was integral to the
learning experience. The children were prompted to use models and images and engage in
play that supported the development of key mathematical concepts and the learning of
number facts at level 1.
Some research suggests that children should play and engage with models and images
before they are scaffolded by a practitioner (Andrews and Andrews, 2007). This view implies
that playing should take place before the adult is involved. Other writers consider a balance
between child-initiated and practitioner-initiated play to be appropriate (Pound, 1999;
Fisher 2002). I personally believe that to be most effective the play experience needs to be
teacher led, particularly with the children involved in this study. If the play was wholly child
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initiated with these particular children, then the learning would be likely to have social
outcomes, but mathematical development would be less likely to take place.
Through my questioning and interaction with the children, I hoped to adequately scaffold
their learning. I wanted the children to make greater gains from what they could do without
assistance to what they could do with the assistance of an adult. This is what Vygotsky
(1978), referred to as moving through the Zone of Proximal Development (ZPD).
The teaching sessions took place over a four week period. During each session I deliberately
undertook a leading role in the play experience as and when it seemed appropriate in order
to move their mathematical learning forward. By the end of the sessions I wanted the
children to be able to count and write numbers to 10, calculate addition number facts up to
10, and grasp an understanding of ‘one more’ and ‘one less’. Each of these objectives has
previously been assessed as insecure by the children’s previous teacher. I hoped that
through ‘playful teaching’, learning will be accelerated and the children would begin to work
within level 1.
The Play Sessions
During the play sessions I observed that children were more motivated to learn in the play
context. During the first play session I was able to observe the children’s conservation of
number, as well as their ability to count using a one to one correspondence. Throughout this
first session my input was minimal because I was surprised by what the learners were
achieving. Through play they were displaying what they knew and practising what they were
beginning to understand (Tucker, 2010). This far exceeded my expectation based on
professional conversations I had had with their previous teacher.
In the next three sessions, my role involved scaffolding the learners to a much greater
extent. I asked questions and prompted the children to work mathematically, observing
their responses. For example, before the play session began I explained to the children that
we needed to keep the toy museum shop in good order and count the toys to make sure
that as the shopkeeper they would know what stock they have. They were very excited to
pretend to be the shop staff and put the badges on.
An example of how the meaningful context enhanced their mathematical learning came
when the children were encouraged to count the jacks, marbles, and other toys in the toy
museum shop to work out one more. I produced marbles from the floor and deliberately
said ‘I have found one more, what is one more than 8?’ The children then looked back to the
marbles and counted them and one child amended the number on the stock list. Another
child said ‘I knew one more was 9 because it is the next number’. At this point I deliberately
used a mini bead string and showed the children 8. I said ‘There were 8 small marbles and
then one more makes 9’. This was demonstrated by moving one more marble along.
Another child then moved another bead along the string and laughed ‘and one more will
make 10’.
After a while working on one more, I intervened in order to move the children on to
understanding ‘one less’ using yo-yos and the bead bar.
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During the session the children worked well and remained on task throughout. This is not
always the case when they are asked to record work in books. The group counted efficiently
and my engagement and interaction prompted them to consider one more and one less,
which they managed well, using the models and manipulatives they had access to.
Importantly, I feel that without my intervention they would have been unlikely to have
extended their thinking into one more and one less and they would have merely counted.
Two children continued to use the models and images to support their learning, whereas
the other two used the models for a short time and then continued in their heads. When
asked why they did not use the bead string for long, one said ‘because I could see it in my
head’. The resource had become an image she could apply to different contexts, rather than
needing to physically manipulate the concrete model. The children observed and used
different models and images from the museum toy shop to support their understanding of
more and less, whilst still maintaining the freedoms that play offered
In addition to the mathematical learning, by this point in the research it was very apparent
that the children were remaining engaged in the learning experience for much longer than
they would had there been an activity to complete at their table. The children were enjoying
maths, their attitudes were changing and they were beginning to see the connections
between the maths world and the real world, between ‘work’ and ‘play’ (Jarman, 2003:13).
Another example, of using the role play toy museum to extend mathematical thinking came
when the group were prompted to use coins to support addition facts up to 10. They were
encouraged to practically find totals with penny coins for toys with price labels on them and
they identified number facts that they knew e.g. 5 + 5 =10. This number fact seemed to be
rooted in the visual image of our two hands because all children knew this number fact and
they used their hands when reciting it. This was a good example of the children having a
visual representation upon which to ‘hang’ a particular known fact.
During this session I was most surprised by two children who demonstrated their recall of
number facts and they were able to share the methods that they used. This is something
they would have found challenging had they not had an observer to share their work with,
or to prompt them to think about what to do. Had there been no adult involvement I doubt
whether any of the children would have counted out the correct value in coins, and certainly
would not have found totals to 10.
The children also found other addition facts during the session, including totals that bridge
ten. This placed them securely at level 1, a great achievement particularly for Child M and
Child J. I believe that without the interaction and scaffolding of the adult the children would
not have even paid the correct value for one item, let alone find the sum of two. The role of
the adult therefore supported the transition of the children through their ‘zone of proximal
development (Vygotsky, 1978), supporting them to move from their previous level of
understanding to their current learning with support from an adult.
During the final session, the children chose a shop keeper and customers to come into the
shop. At this point, the children used models and images to support them with subtraction
facts. The children used the physical objects, applying context to the problem, for example,
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one child knew that he had to take 3 away from 7, if another child wanted to buy 3 of his 7
marbles. Child J also provided evidence of known facts when asked to sell another three
marbles, he stated ‘then I’ll only have 1 left. In addition to this, Child M applied learning
from a previous session, when demonstrating that she knew one more.
Findings
Using models and images was a powerful way of supporting the children’s understanding of
mathematical concepts, so that the children could apply their learning more widely, across a
greater range of contexts. Through seeing and manipulating the models that supported
mathematical concepts, the children understood the concept rather than copying it. This
observation supports the suggestion that ‘children must understand what they are learning
for it to be permanent’ (Moyer, 2001:175).
As a result of the success of these playful sessions, the children are able to count and write
numbers to 10, calculate addition number facts up to 10, and they have developed an
understanding of ‘one more’ and ‘one less’. Interestingly, the children have continued to
use the role play area as part of their numeracy, and even use the area when other
opportunities arise (for example, indoor lunch times). When engaging in child initiated play
I have noticed that these children increasingly make the transition to mathematical play.
The progress made by this group of children has continued across the half term, including
when they are not working in the role play area. The children are increasingly seeing the
connections in their mathematical learning and the principles of collaborative play are being
transferred to group work and work alongside peers (Gura, 1992). Moreover, whereas
previously the children relied heavily on the support of an adult, they have been more able
to complete work independently to a much greater degree this half term, and have been
successful when doing so.
Taking into consideration the children’s achievements during the research sessions and the
progress made in the period since, the end of autumn term data for these children has
highlighted that all children involved in this work are now working securely at Level 1.
Conclusions
The children thoroughly enjoyed the play sessions and they offered me an incredible insight
into the learning of each of the children. In a short period of time, the children developed an
understanding of certain mathematical concepts, which I feel has been, in part, due to the
emphasis on models and images, through the context of ‘playful teaching’. My increased
understanding of play, as a tool for mathematical teaching and indeed learning, has
positively impacted on this particular group of children with Special Educational Needs.
The play experience offered the children the opportunity to engage with a range of models
and images, in a context that was purposeful and reflected ‘real-life’. I would suggest that
the play experience made the use of these models and images more engaging, motivating
and meaningful.
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The provision of carefully selected models and images triggered curiosity in the children and
helped to develop their understanding of number facts as well as other mathematical
concepts.
I think it is important to stress at this point, that play, or ‘playful teaching’, cannot merely be
a gesture, it needs to be embedded in a curriculum with context and purpose at the heart.
The next step in my own personal learning journey will be to consider how these principles,
the pedagogy of play and the use of models and images can be applied to mathematical
learning throughout my primary school, from the Early Years Foundation Stage up to Year 6.
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