Junior staff and students recently experienced two days of inspiring professional development, thanks to a visit from Liz Gibbs, a highly experienced Maths Adviser.

Liz, who is based in the UK, shared valuable insights on mental maths and the use of manipulatives to foster deep and sustained learning. For those who might not be familiar with the term, manipulatives are physical objects that help students visualise and interact with mathematical concepts. Examples are base-ten blocks, place value counters, number lines, and simply folding paper. This is the ‘C’ in the Concrete-Pictorial-Abstract (CPA) approach developed by American psychologist Jerome Bruner. These materials transform abstract symbols and problems into something tangible and relatable for students. A wealth of research and evidence shows that when used skilfully, this method results in a deep and sustainable understanding of concepts in maths. 

During a hands-on workshop, class visits, and meetings with teachers, Liz shared new ideas that can make a significant difference in how our students understand and engage with maths. For example, using Cuisenaire rods to expose the concept of area, bead strings to make the connection between tenths and hundredths clearer, double-sided counters to deepen understanding when finding fractions of amounts, and Numicon to see and express number patterns algebraically. 

The excitement in a Year 3 class was evident as children solved problems involving partitioning numbers. Place value counters helped break numbers down before they drew diagrams of their different solutions, exposing the mathematical relationships. Using number cards scaffolded the reasoning of some Year 6 children who were tasked with spotting patterns to solve a problem. Having the cards aided them in identifying the pattern, applying it to solve similar challenges, including negative numbers, and moving towards generalising. Children’s responses revealed how the cards assisted their deep thinking, leading to enhanced learning. 

Liz also demonstrated mental maths techniques. These routines are valuable in helping children perform calculations in their heads rather than relying on pencil and paper or calculators. They teach students to break down numbers, spot patterns, and estimate answers, which are crucial skills for everyday life and future mathematical challenges. 

In a Year 4 class, Liz modelled a choral counting strategy, which can be applied across various concepts such as fractions and measures. With Liz conducting, children counted forwards and backwards in different steps and from different starting numbers, having to notice and respond quickly to her cues. The goal of this activity is not just to practise rote counting but to engage children in reasoning, predicting, and justifying. To do this, teachers may record the count so that patterns within the numbers are readily noticeable and ask questions such as, “What do you think will come next? How do you know?”. Regular practice helps build these fundamental skills for all students, ensures they are kept sharp, and increases efficiency and accuracy with calculations. 

The role of talk in maths was highlighted through Liz’s demonstration of a Number Talk in Year 5. Children were asked to think of strategies to solve 42 + 29. After the answer was quickly agreed upon, a rich discussion followed, with children explaining their different approaches and Liz guiding them to consider how they connected, why they worked, and the technical language involved. Number talks are now being introduced in all our classes to broaden students’ repertoire of strategies, conceptual understanding and their ability to reason mathematically.

In summary, Liz’s visit prompted reflection on the potential impact of manipulatives and mental maths. By purposefully incorporating these strategies more regularly in lessons, teachers are better positioned to foster a deeper understanding of mathematics for all children. As they advance in their educational journey, the skills and insights gained from these practices will serve as a strong foundation for our students’ continued success in mathematics.