Making Sense of ‘Number Sense’

In today’s post we look at early mathematical ability and consider what is meant by number sense.

Developing Early Mathematical Knowledge

Children learn by having opportunities to actively construct knowledge and link this with their prior learning.  We can support the construction of knowledge by engaging in conversations with children and asking appropriate open-ended questions. 

It is important to be aware of children’s mathematical thinking as shown through their play and to allow them opportunities to represent this knowledge with their own mark-making, symbols, and imagery.

The formal processes and symbols of mathematics are too abstract for young children.  In many settings, there is a reliance on worksheets, but we often fail to examine their utility or to consider to what extent they are mere ‘busy work’.  Young children develop mathematical proficiency by having lots of time to explore mathematics using concrete materials. 

What Influences Mathematical Proficiency?

Yelland, Diezmann, and Butler (2014) consider concepts, processes, and attitudes the key facets to developing mathematical proficiency. 

• The core concepts in mathematics are number, measurement, space (geometry), chance, and data. 
• Problem-solving is the driving process, supported by reasoning, communication, making connections, and representing ideas. 
• A positive attitude influences attainment.

Underpinning the concept of Number is Number Sense.

What is Number Sense?

Number Sense is a broad term for many skills related to a child’s understanding of number and related concepts.  It supports mental mathematical fluidity and is closely linked to later mathematical attainment.   

Well-developed foundational number sense includes:

• Number recognition (identifying and naming a number (up to 20) when shown its symbol);
• Understanding and using number vocabulary;
• Systematic counting (forwards and backwards), ordering of number names, and knowing each number has a fixed place in the number sequence;
• Being able to count on and back from different starting points (not always beginning to count from 1);
• Using cardinal numbers for quantities and knowing the last number in a count represents the total;
• Using ordinal numbers for position and place (1^st, 2^nd, 3^rd etc.);
• Demonstrating one-to-one correspondence between a number and quantity;
• Decomposing and composing numbers (breaking down / building up numbers e.g. knowing 4 + 1 = 5);
• Discriminating quantities and identifying which is bigger / smaller.  This is based on the child’s ability to subitise i.e. to recognise how many are in a small group of objects without having to count them;
• Contrasting magnitudes and identifying which is bigger than / smaller than (without having to count how many are in each set);
• Estimating in different ways (e.g. how many are in a set / where does this number go on an empty number line);
• Conducting simple addition and subtraction operations;
• Identifying number patterns and using this to find missing numbers.

Our next posts will look at elements of number sense and how to promote them using CardEd and other materials.