Area of maths How manipulatives support this
The science of patterns The goal of any maths learning is to see through a situation to an
underlying conceptual pattern. Once learners identify a pattern, they can
calculate rather than count, and using manipulatives is a highly effective
way to help them with this.
Number sense Manipulatives can be used to model why procedures work and why
algorithms exist. They provide an opportunity to bridge the gap between
understanding and abstract symbols,14 allowing learners to experience
number grouping, combining, wholes and parts etc.
Visualisation Manipulatives allow learners to picture maths problems in their minds,
showing underlying part-whole patterns and the properties of operations.
Learners observe, model and internalize concepts, and thereby improve
their understanding15.
Communication Manipulatives help to illustrate specific maths ideas and link them to
maths vocabulary. Even when learners don't understand a term, they can
use manipulatives to demonstrate their understanding and build the
required vocabulary alongside this.
Metacognition The body, movement and perception are essential to cognition, and in
this way, manipulatives support active learning16. Manipulatives provide
structure for learners to monitor their steps, note how they think, check
for errors and prove answers.
Application Manipulatives create a template, e.g. part + part = whole, from which
learners can reflect, explain abstract ideas and apply to access more
complicated maths.
Making connections Manipulatives facilitate the Concrete-Pictorial-Abstract (CPA)17
approach to teaching, whereby learners connect concrete experience
using manipulatives (Feel it/Do it) with visual representations (Draw it),
language (Say it) and symbols (Write it)18.
15
" Manipulatives are effective when the teachers help guide
connections between them and the underlying concepts"13
David Lyttle, 2021
Example
Display an arrangement of differently coloured
manipulatives and use these to model mathematical
language, by encouraging statements like: "There is more
yellow than green", "The ratio of red to black is…"
13Ruzic, R. & O'Conell, K. (2001) "Manipulatives' Enhancement" Literature Review
14Marley, S & Carbonneau, K (2014) "Theoretical Perspectives and Empirical Evidence Relevant to Classroom Instruction with Manipulatives"
15Bruner, J (1960) "On Learning Mathematics'"
16Haylock, D. & Cockburn, A. (2008) "Understanding Mathematics for Young Children: A guide for foundation stage and Lower Primary Teachers"
17
Oxford University Press, (2021) "Maths and the impact of Covid-19 survey of international teachers"
18
Oxford University Press (2021) Expert Panel: The future of maths in the Primary classroom practitioner perspective