Counters, cubes, Cuisenaire rods: mathematical manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). are widely used resources in most primary maths classrooms. But how can we make the most out of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and ensure we’re using them effectively?
Over the past few years at Catton Grove Primary School this has been our focus in maths. We believe the use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). is a crucial strategy for pupils in developing a secure understanding of key mathematical concepts. Effective manipulative use should reveal mathematical structures and enable pupils to understand and use mathematics independently.
Improving Mathematics in the Early Years and Key Stage 1 Guidance Report.
At Catton Grove, we prioritised effective manipulative use as an area for improvement and carved out significant staff meeting time to address this.
PD is the key
Professional Development (PD) can be a highly effective way to develop staff understanding of mathematical concepts and, therefore, their use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and representations. However, for PD to be truly sustainable and effective, it needs to draw on a range of PD mechanisms as detailed by the EEF’s Effective Professional Development Guidance Report.
The mechanisms are split into four groups, and it is recommended that at least one mechanism from each group is featured in any PD.
Revisiting prior learning
Every maths staff meeting at Catton Grove Primary School started with staff retrieving prior learning from their long-term memory. This not only ensured key knowledge was not forgotten but also modelled the key principle of revisiting prior learning with pupils too. For example, we used quiz questions to revisit definitions of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and representations.
Modelling the technique
As part of the PD, implementation leaders demonstrated effective use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). to staff within a live lesson context.
Staff could see the interplay between the physical manipulation of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and the mathematical explanations that went along with them.
It was also far more effective to see manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). being purposefully engaged with by pupils. And it always goes a long way when leaders of PD show that they can not only ‘talk the talk’, but ‘walk the walk’ too!
Instructing teachers on how to perform a technique
Staff were provided with opportunities to engage with the manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). themselves both from a pupil and practitioner perspective. With the pupil in mind, it provided opportunities to consider what misconceptions and challenges could arise. When in role as the practitioner, staff had the opportunity to refine their mathematical explanations alongside the use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods)..
Prompting action planning
Once staff had the opportunity to engage in the maths themselves, and had become inspired by it, they were asked to purposefully plan for and embed this practice. Staff worked together in year group teams to decide how this would look in the context of their year group’s curriculum and context.
Providing affirmation and reinforcement after progress
Cycles of follow-up monitoring, celebration,
and support were then provided in a range of forms including peer support observations, learning walks, and instructional coaching.
Three future considerations for us
- Continue the PD
We want to keep manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and representations a focus for PD this academic year, concentrating on topics like fractions and measure. - Pupil voice
We want to take time to observe and listen to children interacting with the manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). during lessons, as well as learning about their attitudes towards using them. - Keep celebrating successes along the way
We have already noticed an uptake in pupils’ willingness to engage in more unfamiliar mathematical problems, which we believe is in part to their familiarity and use of manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods)..
Find out more: watch this Clip from the Classroom from Unity Research School.