Number Sense

Fluency with numbers  is IMPOSSIBLE without NUMBER SENSE.  Fluency with Numbers begins with NUMBER SENSE. 

Number sense is important because "developing a strong grounding in number is essential...to excel mathematically." (Development Matters, Department for Education 2021). 

Number sense is a DEEP and FLEXIBLE understanding of numbers and involves the ability to perceive numbers, how they relate to each other and how they can be manipulated. Number sense underpins most other mathematical learning, so it is vital that children develop a strong understanding of numbers in the early years of their education. Research has shown that characteristics for number sense correlates with later mathematical achievement, so all young children can benefit from acquiring a strong sense of number.

Number sense does not only involve the ability to count, compare and perform operations on numbers, but also requires understanding and flexible manipulation of numbers. Number sense can be improved by encouraging children to make links, reason, giving children opportunities to explore numbers in different ways and move between representations.

Read more:
Cambridge Mathematics
NRICH
Jo Boaler

The phrase 'number sense' is often used to mean conceptual fluency - understanding place value and the relationships between operations.

Children need to be both procedurally and conceptually fluent - they need to know both HOW and WHY. Children who engage in a lot of practice without understanding what they are doing often forget, or remember incorrectly, those procedures. Further, there is growing evidence that once students have memorised and practised procedures without understanding, they have difficulty learning later to bring meaning to their work (Hiebert, 1999).

Research evidence points in one direction: The best way to develop FLUENCY with NUMBERS is to give children many opportunities to:

  • Construct relationships among numbers, 
  • Work with numbers in different ways, 
  • Make sense of basic facts and to be able to retrieve them.

From the earliest stages of learning about numbers, children can be making connections that will establish flexibility in their thinking - that is characteristic in developing number sense and ultimately fluency.

 

HOW DO I HELP MY LEARNER BUILD NUMBER SENSE?

NUMBER SENSE is not a set of skills that learners can develop in a short period of time. It is something that grows and develops over time.  

Van de Walle and others (2018) suggest Four Early Numeracy Concepts 

Early Number Concepts

  • Verbal Counting – to say the numerals in the correct order
  • Object Counting – 1 to 1 correspondence
  • Cardinality – the last object counted in a set tells how many
  • Subitising – the ability to see how many without having to count

OUR NUMBER LOVING LEARNING RESOURCES support these concepts. 

Van de Walle and others (2018) suggest Four Number Sense Relationships necessary for the development of Number Sense: 

 

Our Subitising Spots were designed to help children develop these number relationships. Heres how:

 

  A more common definition of NUMBER SENSE comes from Howden, 1989.

For more activity ideas to help children develop NUMBER FLUENCY, take a look at our FLUENCY TOOLKITS, SUBITISING SPOTS and MULTIPLICATION CONCEPT CARDS