B is for Building Blocks
Dr Deborah Cameron-Flitcroft
When we think about the building blocks for maths we quickly think about counting one to 10 and we speak with pride when our children can count to a certain number from an early age. However, what we often don't think about is that counting one to 10 is similar to singing a nursery rhyme; it is a learnt sequence of words and it does not necessarily hold meaning for children. Therefore I sometimes wonder if we miss early signs of children struggling with maths and if we too often rush ahead without considering what the building blocks of the subject are.
The National Centre for Excellence in the Teaching of Mathematics (NCETM) proposes 6 building blocks for maths and these provide a platform for all areas of maths for primary school and beyond.
Cardinality refers to being able to quantify and understand the number of objects in front of you. For example being able to count 3 objects and understand that there are three objects in front of you. Counting is the method we use in order to understand cardinality of items and I will talk about this area further in my next blog C is for Counting.
2. Comparison
This skill is about being able to compare sets of objects and understand which numbers are worth more or less than one another. This skill underpins the use of a number line as the child will develop the understanding that the last number they count is always one more than the previous number and therefore worth more. This demonstrates the importance of bridging from concrete tools to the number line and how there should be a period where they are used activity together, such as placing counters on the number line.
3. Composition
Composition is about understanding that one number can be made-up from 2 or more smaller numbers and involves an understanding of a part whole relationship. For example, the number 10 can be made up of 4 and 6. The scale of partitioning numbers is the building block for understanding addition and subtraction are inverse operations.
4. Pattern
This building block is thought to be at the heart of mathematics (Schoenfeld, 1992). Patterns will initially start as simple alternating patterns to gradually more difficult repeating patterns. This understanding can be developed not just through objects, but also through music and dance. This building block is thought it to be the foundation for algebraic thinking and gives children the opportunity to problem solve rules and generalise them to situations (Clements and Sarama, 2007).
This building block is about the development of spatial skills for example understanding what happens when a shape is moved or combined with other shapes. Here the focus should be on actively exploring spatial relations and the properties of different shapes rather than being able to label what the shape is.
6. Measures
The final building block is measures which is being able to compare different aspects such as length, weight and volume and this is the preliminary building block to understanding units later on in the curriculum. Children often find it easy to engage with measuring items, such as rulers, but often struggle with how to accurately measure and read off the value from the tool. The idea of conservation is important for this building block which is the understanding that the amount will stay the same even if the appearance is altered.
To conclude there are a number of building blocks for the development of mathematical understanding for children and it is important to be mindful that these areas are understood and embedded before we continue on with the national curriculum. I appreciate there are pressures to “get through” everything in the national curriculum but without these building blocks you will find that children will struggle to engage with more difficult concepts. Research shows that early mathematical knowledge predicts later reading ability and general education and social progress (Duncan et al, 2007)thus showing the importance of building blocks.
If a child struggles to develop one of these building blocks despite intervention then it is important to consider what underlying learning difficulties they may be experiencing and therefore what bypass strategies they may require later on in the curriculum.
For more information I would highly recommend going on to the NCETM where each of these concepts are broken down even further and a progression chart for each of these concepts are also provided.
