Building Blocks For Maths

Dr Deborah Cameron-Flitcroft, Educational Psychologist with a passion for maths. Deborah is currently developing a new EdPsychEd online CPD course - Maths: Making EPs Count. In this blog, Deborah considers the essential building blocks of mathematics education, exploring how they shape children's mathematical understanding.

Laying the Groundwork: The Essential Building Blocks of Math

When considering the building blocks of mathematics, counting from one to ten often springs to mind. We take pride in our children's ability to count from an early age. However, counting, akin to reciting a nursery rhyme, is merely a learned sequence of words lacking meaning for children. This begs the question: Are we missing early signs of children struggling with maths, if we rush ahead without considering what the building blocks of the subject are.

The National Centre for Excellence in the Teaching of Mathematics outlines six fundamental building blocks for mathematics, serving as a cornerstone for primary school education and beyond:

Cardinality and Counting: Cardinality involves quantifying and understanding the number of objects present. It's the ability to count three objects and understand that there are indeed three. Counting serves as the method to grasp the cardinality of items.

Comparison: This skill revolves around comparing sets of objects and understanding their relative numerical values. It lays the groundwork for comprehending number lines and the concept that each successive number represents one more than the previous—a critical transition from concrete tools to abstract representations, which highlights the necessity for a phase where these methods are utilised together, such as incorporating counters into activities involving the number line.

Composition: Composition involves understanding that a single number can be composed of two or more smaller numbers, establishing a part-whole relationship. For instance, realising that 10 comprises 7 and 3. The concept of partitioning is pivotal for comprehending addition and subtraction as inverse operations.

Pattern: Patterns are considered the heart of mathematics (Schoenfeld, 1992). They evolve from simple alternating patterns to increasingly complex repeating ones. This understanding extends beyond objects to encompass music and dance, laying the foundation for algebraic thinking and problem-solving skills and gives children the opportunity to problem solve rules and generalise them to situations (Clements and Sarama, 2007).

Shape and Space: This building block focuses on developing spatial skills, such as understanding transformations and combinations of shapes. Rather than merely labelling shapes, emphasis should be on actively exploring spatial relations and properties.

Measures: Measures involve comparing different attributes like length, weight, and volume—a precursor to understanding units in the curriculum. While children may easily engage in measuring activities, accurately interpreting measurements from tools requires a grasp of conservation—the understanding that the amount remains constant despite changes in appearance.

Strengthening the Building Blocks

In conclusion, these building blocks are indispensable for children's mathematical development, serving as a foundation necessary for engaging with more advanced concepts in the national curriculum. Early mastery of mathematical concepts correlates with later reading ability and overall educational and social progress (Duncan et al., 2007). Should a child encounter difficulties despite intervention, it's imperative to consider underlying learning difficulties and adapt teaching strategies accordingly.

For more detailed information and progression charts on these concepts, I highly recommend visiting the National Centre for Excellence in the Teaching of Mathematics website.