We brought together maths education experts from around the world for a series of online expert panels and webinars to consider how we can equip maths learners for the future – whatever that future looks like. This series of blog posts aim to highlight the key takeaways to help you empower today’s learners to embark on a lifelong adventure with maths through resilience, connection, curiosity, and creativity.
In this blog we summarise David Lyttle’s webinar on how manipulatives allow for strong communication in both teaching and learning by enabling children to identify patterns and to physically show their understanding while their maths vocabulary is growing.
David Lyttle is an Elementary Maths and Numicon Accredited trainer and consultant. He is currently employed as a Support for Learning teacher and Instructional Coach for Elementary Mathematics at the International School of Düsseldorf. David has authored various curriculum mapping works that link math programs to the IB PYP.
Mathematics: The science of patterns
Pattern is at the heart of mathematics (Sousa, 2015).1 The goal of any maths learning is to see through the situation to an underlying conceptual pattern, and it is this that uncovers meaning and connects us to the world. Patterns make numbers more accessible and tangible, and once we have a pattern we can calculate rather than count. Using manipulatives is one of the best ways to aid the transference from counting to calculating.
What are manipulatives?
Manipulatives are objects that can be touched or moved, to develop meaningful comprehension, allowing learners to review different ideas. There are four types of manipulatives:
Formal: Bought for the classroom for use when creating specific mathematical patterns and to uncover underlying big conceptual ideas. For example: Cuisenaire rods, Numicon, pattern blocks.
Informal: Readily available items that can be used to represent patterns. For example: pasta, buttons, straws.
Environmental: Things around the house, or that can be found nearby, used to explore patterns in nature and the world. For example: kitchen tiles for exploring geometrical patterns, leaves for symmetry.
Digital: Digital versions of formal manipulatives. Although these allow the creation of a visual representation of a pattern, they don’t stimulate all of the senses in order to best activate working memory and then long-term memory in the same way as a physical manipulative in a child’s hands.
Why use manipulatives?
Manipulatives help uncover the underlying patterns of mathematics:
Number sense
Manipulatives help model why procedures work and why algorithms exist. They offer an opportunity to bridge the gap between understanding and the abstract symbols, thereby uncovering deeper number sense.
Visualisation
Manipulatives show underlying part-whole patterns, allowing students to observe, model and internalise concepts.
Communication
Manipulatives help educators communicate specific maths ideas, illustrating what they are and link these ideas to the relevant vocabulary. The power of manipulatives means that even if children don’t understand a term, they can show their understanding while they build up the vocabulary required. They develop this vocabulary in context, so that it becomes ingrained and they are able to communicate these ideas with confidence.
Metacognition
Body, movement and perception are all essential to cognition. Manipulatives give the structure needed for working memory to build on. Monitoring your steps, noticing how you think, checking for errors, and proving answers is shown much more clearly when children have manipulatives.
Generalisation
Manipulatives create the template from which students can reflect, explain abstract ideas and access much more complex maths later on.
Making connections
Manipulatives facilitate following a Concrete-Pictorial-Abstract approach, helping children feel it, do it, change it, express it, and reflect on it, all the while building their mathematical language and making bigger connections.
To make maths meaningful, to understand abstract concepts, and to become confident and competent mathematicians, students need to touch, see, feel and use it. But manipulatives are only as good as the practitioner. Professional Development is essential to ensure that the right manipulative is chosen for the right course or concept.
You can watch the full webinar ‘How can the use of manipulatives improve both mathematical understanding and mathematical language skills?’ here. (Note: you will be taken to a sign-up page and asked to enter your details in order to access the recording).
For the next blog in this series, ‘Five top tips for transforming your primary maths teaching’ by Professor Anne Watson click here
Effective teaching with Numicon apparatus
Manipulatives are a great way to make your teaching more effective – including using the concrete-pictorial-abstract approach, teaching for understanding, generalisation and assessment. Apparatus and shapes are an integral part of Numicon. Discover our cost-effective kits, starter packs, and boxes of shapes which contain key manipulatives to support mastery teaching at home or in the classroom – whatever the existing programme.
1 Sousa, D. (2015) How the Brain Learns Mathematics (2nd Ed.) London, Corwin