Number sense forms the foundation of all mathematical work. It refers to ‘a person’s understanding of number concepts, operations, and applications of numbers and operations. It includes the ability and inclination to use this understanding in flexible ways to make mathematical judgements and to develop useful strategies for handling numbers and operations’ (McIntosh, Reys and Reys, 1997, p. v). Talking about and exploring numbers, numerical relations, symbolic and non-symbolic representations and patterns all help build strong foundations and connections.
Number sense upholds mathematics as a sense-making endeavour and reveals the flexibility inherent within numbers and mathematical thinking.
‘Successful math users have an approach to math, as well as mathematical understanding, that sets them apart from less successful users. They approach maths with the desire to understand it and to think about it, and with the confidence to make sense of it’ (Boaler, 2016, p.34).
Number sense is developed through discussing, debating and analysing various experiences over extended periods of time. It involves knowing, describing, using and generalising:
- Multiple relationships between numbers;
- the number before and after
- 2 more/less
- relationships to benchmark or landmark numbers
- relationships to other numbers
- Decomposition and composition of numbers;
- Magnitude and relative size;
- Cardinality (linking the quantity to the word/symbol); and
- Numeral identification.
Students demonstrate number sense when they can do things such as:
- Count with understanding;
- Explain the counting principles;
- Small, random and structured collections
- Larger, structured collections using spatial relationships
- Identify, describe and use relationships between numbers (including the relationship to benchmark/landmark numbers);
- Identify, describe and use part-part-whole knowledge;
- Represent numbers in a vast range of ways;
- Identify which number is bigger/smaller (e.g. 7 or 5);
- Make reasonable estimations;
- Explain more, less and equivalent to;
- Look to the context of a problem to decide which strategies they may use to find a solution;
- Explain the reasonableness of a solution using words, symbols and visuals;
- Use known facts to derive unknown facts; and
- Visualise quantities in a range of ways.
The acquisition of number sense begins before children begin school and requires constant, meaningful nurturing. Teachers should invest time in developing strong number sense in all years of schooling, supporting students to be able to make meaning from the mathematics they encounter. Number sense is never ‘complete’ – there is always something more to know, another relationship that can be found, another way of representing, etc.