Teachers should be aware of the limiting factors of PPT animations and their potentially restrictive impacton pedagogy and deep learning in mathematics.
Evidence from my small scale research of PPT based resources currently widely used by schools, showed examples of the number of ‘clicks’ needed in what was identified as an animated PPT slide deck for a single one hour lesson:
Primary – 148 ‘clicks’ in 17 slides
Secondary – 245 ‘clicks’ in 45 slides
Too frequently these PPT animations lead to direct instruction at the expense of developing children’s mathematical behaviours. The slide deck is set up to ‘flow through’ an idea and does not facilitate any live ‘in the moment’ responses to children’s thinking or questions.
Whereas, using dynamic technology there is every opportunity to respond to children with visuals to help them secure the understanding and even offer alternative representations.
Surely we want teachers to be asking children: “What do you notice?” “What do you think will happen when..?” “What number do you want to try next” as well as children being curiousand asking: “What if……”, “Does it always work” Using dynamic technology is about improved pedagogy where teachers are teaching not presenting, the focus is on the needs of the children and how the teacher can meet their needs, and should be included as a key element fin the DfE funded NCETM Big Ideas.!
Below are 2 approaches to the ‘teaching’ of ‘Perimeter of a rectangle’ one from a published resource and one I have created. Each video is less than 2 minutes, and for some readers, today could be the day you are enlightened to the potential of dynamic technology!
The Animated PPT approach
Children are watching a procedure being modelled but the animation does not embed the conceptual understanding of the perimeter being a measurement of length nor encourage children encouraged to develop their mathematical behaviours.
Slide 1 24 separate red lines appear, which may well be used for choral class chanting/counting, but will children be focusing on the sequence of counting numbers or recognising the red lines are meant to be representing a length?
Slide 2 Again the animated red lines are not showing lengths. Children are led to the fact opposite sides of the rectangle have the same value and sum to 24. The algorithm is correct.
Most importantly the children are not seeing the Perimeter as a measurement of length and evidence of its location on the rectangle, and they are only working with one example.
Now for the Dynamic Technology version.
The dynamic technology can be used Front of Class or on 1:1 devices.
As with any learning environment it is the teacher’s pedagogy that makes the difference to learners in classrooms, but with this dynamic technology there are visuals to support children of low prior attainment in their learning.
I would create the first rectangle to simulate the rectangle of tiles and the child stepping around them in the image, then encourage the children’s curiosity by asking children in the classroom: What do you notice? What rectangles shall we draw next? What can you notice now and can you make any generalisations? Does your generalisation always work?
The classroom experience being
You do, the children are invited to action and respond to the task provided We do, the children and the teacher build up/draw together the finding on the mathematical concept I do, the teacher refines the class findings to develop more sophisticated mathematical generalisations.
Using dynamic technology children can:-
learn from feedback
readily compare and contrast different representations
pattern spot – explore the effects of varying values and look for invariance and covariance
The DfE funded NCETM has 5 Big Ideas at the core of Teaching for Mastery (TfM) in Mathematics for all UK schools. For a 21st Century Mathematics education the place of Digital Dynamic Technology must surely be included and become the 6th Big Idea in TfM.
The JMC report of 2011 highlighted this missing element and in 2023 said little had changed. In 2025 there is still an absence of dynamic technology being promoted.
The current practice of using PPT with single use animation does not offer anything like the potential of dynamic technology, results in children ‘watching’ and not being given the opportunity to see ‘in the moment’ visual responses to questions they ask. The integration of dynamic tools and interactive learning experience creates a more engaging and personalised learning environment for all children to develop the essential Mathematical Behaviours.
Recent evidence from Nottingham University Observatory for mathematical education offers further support with a key finding from the ‘Key Stage 3 teachers of Mathematics Themed report 25/01’ (April 2025):
“The most pressing professional development need reported by KS3 maths teachers is on the use of digital technologies.“
Direct evidence from teachers collated from conference presentations I have delivered and numerous CPD sessions I have led for both Primary and Secondary teachers support my recommendation for Dynamic Technology as the 6th Big Idea for Teaching for Mastery, e.g.:-
“Digital technology in maths is such a powerful learning tool for all learners – our focus on adaptive teaching will need to consider this if we want to truly to ensure all children are included in the lesson.“
“The slide on ppt clicks was incredible and made me reflect on how the children in my class learn – are they really interacting with the maths??“
“Love the teaching ideas, schools need more guidance on this”
“Love the interactive tangible nature of your presentation – you showed what is possible in context!”
Evidence from the neuroscientists adds further support for the use of Dynamic Technology can offer to the learner:
‘Advocates of dual coding theory argue that people retain information best when it is encoded in both visual and verbal codes’ (Byrnes, 2001, p. 51). It is therefore appropriate to surmise that using visualisations improves retention of the mathematics taught.
Schacter’s (2001) research implies that students may ignore symbolic work, if not accompanied by visualisations.
Additionally ‘Any attempt to reduce transience (memory loss over time) should try to seize control of what happens in the early moments of memory formation, when encoding processes powerfully influence the fate of the new memory’ (Schacter 2001)
When a child has a personal stake in the task, he can reason about that issue at a higher level than other issues where there isn’t the personal stake… These emotional stakes enable us all to understand certain concepts more quickly. Greenspan and Shanker (2004)
IMO – Teaching for Mastery must include Dynamic Technology
The use of dynamic technology positively impacts on and connects the other 5 Big Ideas.
It is important to explicitly value the visualising and thinking children engage in and not just focus on the correct final answers.
Far too often children jump into performing a calculation without appreciating the full task or problem and the ‘components’ actually needed.
Gestures and talk are likely to be early demonstrations of children’s visualisation, and this is best achieved by delaying access to recording materials, giving children the opportunity to interact before ‘diving into’ a pool of mathematics.
Children need to have enough time to secure an understanding of the problem and a strategy before they start. It is the need to get ‘a feel’ for the task which I describe as the ‘Build-it’ stage; build a mental image or physically build a representation with manipulatives which enhance the understanding of the problem and helps children consider:
what they do know
what they need to know
what they have enough information to ‘work out’?
what information they need to work towards their solution
what are the options if they don’t have the mathematical knowledge
To demonstrate this approach I gave the task below to a mixed group of secondary school mathematics and science teachers for whom GCSE Mathematics was the common qualification attained but for some it was ‘a quite a while ago’!
Teachers started by using their forearms to indicate the vertical telegraph poles and gesturing/ ‘air drawing’ whilst talking about a cable between the posts – “a straight line between the poles will be 80m and the cable should sag below the horizontal”
Already the shared language is key to supporting visualisation:
straight
vertical
horizontal
sag
Teachers talked of their mental picture of telegraph poles and to appreciating a distance of 80m related to a more commonly recognised distance of 100m track length. When it came to the gesturing the intended sag, the distance between the ends of fingers when pinching the first finger and thumb was an attempt to visualise the ‘smallness’ of 50cm length relative to their poles 80m apart.
Part 2 – using AI
It was at this point the teachers sketched on A3 White Boards (an ideal size for collaborative working) a representation of their visualisations and discussions so far; shared gestures, language and reasoning with explanations of:
midpoint
parabola
symmetrical
approximating lengths to line segments and calculate using Pythagoras Theorem
With the information available the mathematics gets more challenging (beyond GCSE) if you want to calculate the exact length of the cable forming an arc of a parabola, and this is where AI can assist. However, AI needs to be asked clear questions!
Let’s ask for the intended cable with a 50cm sag
What is the approximated length of the cable using the length of the line segments and Pythagoras Theorem – checking our calculation?
What is the calculated length of the parabola passing through the 3 identified points?
What does a graphical representation of the curve look like ( checking our sketches)?
The following includes our questions to Co-Pilot and the AI responses.
Now let’s ask about the ‘mistaken’ cable which has a length of 80.5m
What is the lowest point of the parabola passing through (0,10) and (80,10)?
What is the difference between the ‘intended’ sag of the cable and the ‘mistaken’ sag?
For AI to be useful, students (and teachers) need to
follow a logical argument
Identify and communicate the requirement of the task – can they describe what they want to build, in detail and guide the process?
be curious, collaborative and resourceful
‘guesstimate’, reflect and check reasonableness/accuracy of AI responses
SupportingMetacognition
Visualisation, gestures, collaboration and articulating their ideas help children develop the skills needed for problem solving:
“comparing different students’ approaches to problem solving and decision making; identifying what is known, what needs to be known, and how to produce that knowledge; or having students think aloud while solving problems” (Costa, 1991)
The school as a home for the mind: A collection of articles. Corwin. [Google Scholar]
• Modelling your thinking out loud helps pupils develop their own strategies
• Resilience is built by teaching children strategies for what to do when they do not know what to do.
• Identifying appropriate questions to ask in AI can support children as they work towards a solution
Privileged to have been invited to ‘Make Space – the value of spatial reasoning for Mathematics’ event led by Emily Farran at Surrey University this week.
Some key reflections: 1. Spatial abilities can be trained and increases achievement in mathematics 2. Spatial reasoning is intrinsic to learning in all domains of mathematics 3. Spatial reasoning leads to flexible thinkers 4. Mental maths questions should be include spacial reasoning. 5. Spatial reasoning is for EYFS to adult 6. Spatial reasoning should not be ‘bolt on’ to the curriculum 7. The use of technology for spatial reasoning is currently underdeveloped in UK
CPD will be key to making an awareness of the importance of spatial reasoning and developing strategies with teachers to use in the classroom.
When reviewing the data of the national KS2 SATs 2024 outcomes by question, the eye is always drawn to the pieces of data that ‘buck the trend’. I am not aware that the data is expected to rigidly align with a statistical ‘line of best fit’ but is used here as a tool to assist when reviewing.
My attention was drawn to Question 13 on Paper 2, a mid-paper question and <50% of the cohort submitted a correct answer, approximately 11% less than might be anticipated using the ‘trend line’ of the graph below. Question 13 is on the topic of 3-D shape as is Question 23 on Paper 3, which received 23% of the cohort answering correctly, the lowest percentage and furthest below the trend line for any question on the paper.
Whilst the circled red data points are questions focusing on 3-D shape only, it is worth noting all Geometry questions on Paper 2 (Qu’s 1,13, 21 and 26) and on Paper 3 (Qu’s 8, 10 ,20 and 23) fall below the ‘line of best fit’ in the graphs!
These are the 3-D Shape 2024 SATs questions:
Paper 2 – ReasoningPaper 3 – Reasoning
These two 3-D Shape questions primarily relate to National Curriculum content from Years 1-3 of the Programmes of Study for Mathematics (2013) with the KS2 expectation for children to recall mathematical subject knowledge and reason using the knowledge.
A key requirement for children to answer these questions would be to have a visual recall or mental image of the shapes. Based on the outcomes detailed above, it would suggest a significant proportion of children do not have a working command of this knowledge/skill. Insecure foundations are likely to impact on children when working at KS3/KS4.
The following offers support for teachers as to how this issue may be addressed:
Children need to be provided with the opportunity to develop a visual mental recall of 3-D Shapes
The need for children to ‘play’ and ‘explore’ when learning mathematics is not something to be restricted to EYFS and KS1. Play allows children to observe, make sense of and provide a concrete example to help communicate their thinking and understanding. Play is an essential part of children having the opportunity to develop the desirable mathematical behaviours of young mathematicians:
to conjecture
to predict
to justify
to compare and contrast
to challenge another’s thinking through asking questions and discussion
to generalise
Design created using Napkin.ai
When children have a mental image/visual recall of 3-D shapes they are not reliant on separate memorised facts. The visualisation empowers the child to identify multiple facts, answer questions and reason solutions to problems.
“Talk in mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics… It should extend to high-quality discussion that develops children’s logic, reasoning and deduction skills, and underpins all mathematical learning activity. The ultimate goal is to develop mathematical understanding – comprehension of mathematical ideas and applications.” The Williams Report (2008)
The Role of the teacher is to:
provide learning opportunities/tasks for the children’s mathematical habits to be developed
probe children’s thinking with appropriate questions
introduce and refine mathematical language whilst allowing children to talk freely in a non-scripted manner
3-D Manipulatives
Provide the children with a suitable range of 3-D shapes to touch and hold, connect and separate, compare and sort.
E.g. A set of ten different 3-D shapes; cube, triangular prism, rectangular prism, hexagonal prism, triangular pyramid, square pyramid, sphere, hemisphere, cone and cylinder, each in 4 different colours provide opportunities for children to explore the content required for primary school learning. Note this set unlike many others includes a hexagonal prism encouraging children to think about 3-D shapes with polygons of more than 4 sides.
Source TTS MA03349
Tasks
The following tasks are intended for children to do in pairs or small groups. Each task can be adapted for the age and/or prior knowledge of the children when selecting the 3D shapes to be used. The purpose of the tasks is:-
to encourage children to talk/discuss as they touch and play with the 3-D shapes
to gather an insight into the key features of the shapes
to support the development of visualising shapes – which is hard to achieve from looking at only diagrams
1.Feely bag
This task is for children to develop and use their sensory and oracy skills to describe 3-D shapes.
A selection of 3-D shapes is placed in a non-transparent bag.
One child puts their hand in the bag, selects one shape without removing the shape from the bag or looking inside.
Using touch alone, the child must describe the selected shape to their partner/s, one detail at a time
Partner/s suggest the identity of the shape either by naming it or pointing to what they think is the shape from a separate set of shapes
Once children think they have identified the shape, it can be removed from the bag to check.
Repeat the task with another child making the shape selection
3-D shapes and Opaque Feely Bag
Questions:
What vocabulary/descriptions are most helpful?
How many pieces of information do the children need to identify the shape correctly?
2.Sorting
This task is to help children to identify and categorise the key features of the 3-D shapes
A selection of 3-D shapes is placed on a large piece of card.
Working in pairs/small group children sort the physical shapes into 2 groups, agreeing the sort criteria.
Allow children to describe the criteria using their own description which can be refined to mathematical language.
e.g. Shapes with a ‘Rounded surface’ (curved surface) and shapes without.
Shapes sorted into 2 groups
Questions:
How do you decide which group a shape is to be placed (sorting criteria)?
How can you sort the same selection of shapes in a different way?
How are your sorted groups of shapes the same or different to another pair/groups? What criteria have they used to sort the shapes?
The task could be repeated using shapes with some common elements (Venn Diagram), or shapes sorted into 3 separate groups or 2 dimensional shapes could be included.
3.What’s my shape?
This task is to encourage children to ask questions and in doing so develop, refine and practice their skills in precision of questioning and use of mathematical language.
Two children face each other with a white board or similar acting as a barrier between them and ensuring neither can see what is on the opposite side. Alternatively, children could sit back to back.
A child selects a 3-D shape and hides it from their partner behind the barrier.
The partner must ask questions to identify the hidden shape.
Initially allow questions to be open, however as the task is repeated it can be more challenging if the child with the shape can only respond with Yes or No to questions.
Image generated with Adobe Express
Questions:
What questions could the partner ask the child to help them identify the shape? E.g.
Are all the faces the same shape?
How many faces does the shape have?
Does it have a ‘pointy’ end?
What refinements can be made to a question/answer? (supported by the teacher) e.g.
“What is the mathematical term for a ‘corner’?”
Is the end at the top or the bottom – does it matter, is the orientation important?
Are some questions more helpful/informative than others? – make a list of ‘good’ questions
4. WODB – Which one doesn’t belong
This task is for children to practice and strengthen their visualising skills, critical and creative thinking with reasoning.
The names of different 3-D shapes/objects are placed on the 4 sections of the card.
Children will need to visualise the four shapes/objects and use their knowledge of the shapes to reason which they consider to be the ‘odd one out’ based on the attributes of the shapes.
The choice of shapes/objects should not lead to there being only one correct answer.
Encourage children to think creatively when looking for attributes
A collection of cards can be made for future use and could include landmarks etc which link with a recent humanities topic.
E.g. WODB – with possible reasons for selection
WODB Example Card
Football because
it is made up of hexagons and pentagons
it has a curved surface
Square because
it is 2-D
it has 4 sides (not edges)
Cube because
all faces are equal in area
a regular polyhedron (3-D shape)
Pyramid because
it has triangular faces
it has a point (apex) when its base is on the table
Questions
Do all pyramids have the same shape base?
Are all footballs made from Hexagons and Pentagons?
What’s the difference between a pyramid and a prism?
Which 3-D shapes always have the same shape face at either end?
What other shapes have an apex?
National Curriculum Statements DFE Reference 00180-2013
Pip Huyton is a mathematics consultant working in both the primary and secondary sectors. Her roles involve being a trainer, adviser, facilitator, often in a bespoke school improvement capacity. Interests include curriculum development, the use of manipulatives for supporting children developing conceptual understanding and effective use of dynamic technology for learning.
Authored:
Build-it Say-it Write-it Understanding the concepts of Perimeter and Area using Manipulatives
Curiosity is the one of the most important attributes that you can want for a child. Today was an example of where young children in reception were curious to ‘play’ with the resources I brought with me – footballs from TTS . Yes the first interest of some children was to take the football outside and kick the ball, but whilst standing for the photograph curiosity ‘kicked in’ just looking at the football they held and prompted them to explore and ask questions.
How many black ‘spots’ are there on the ball?
What shape are the black marks on the ball, as they ran a finger along the outline of the shape?
Their questions were developed by the class teacher and the children learnt a new word Pentagon. Memorable moments which can be developed further to recognising the shape in other circumstances, defining other shapes starting from the football – a Hexagon, Sphere. All part of their learning of Geometry and Spacial reasoning.
Having led this 4 day programme it was wonderful to see the increase in their confidence when supporting primary aged children in their schools.
The importance of helping children develop a mastery of the mathematics rather than a rote learnt algorithm which they cannot apply has required TAs to do things differently to that in which they learnt the mathematics themselves.
