The educator teaches children the connection between number and quantity:

• number words and sets (for example, the spoken word ​‘three’ and a set of 3 objects)
• numerals and sets (for example, the written numeral 4 and a set of 4 objects).
  

The educator teaches children to use counting to find out ​‘how many’ are in a set, by understanding that the last number they say tells them how many there are (referred to as cardinality).

Evidence tells us that this approach can have a positive impact on children’s early mathematical development.

Educators often deliver this approach alongside the Building number fluency approach: the two approaches can reinforce each other.

Based on the evidence, educators should:

• provide opportunities for children to subitiseThe ability to recognise the quantity of a small group of items instantly, without counting them one by one.
• model one-to-one correspondencePairing one number word with one item whilst counting. while counting – evidence suggests that this is particularly helpful
• help children to visualiseHelping children to ​‘see’ numbers and quantity, for example, using manipulatives and representations. numbers and quantity, using manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). and representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs.
• encourage children to match or compare quantities
• focus on exploring number composition The idea that a whole number is made up of two or more smaller numbers. with children (for example, encouraging children to notice that when they see 3 spots on dice, they can see 1 and 2, or 2 and 1, or 1 and 1 and 1).

We suggest some practices educators can use during activities in the ​‘Putting the approach into action’ section below.

Targeted individual or small-group teaching can also be effective. In some studies, this included the use of EdTech​‘EdTech’ includes many different approaches and devices, from robots to interactive apps and games, to support children’s learning..

Most of the studies we found focused on activities rather than the educator’s role in detail. However, they do describe some of the ways educators supported children with visualisingHelping children to ​‘see’ numbers and quantity, for example, using manipulatives and representations. numbers and quantity. For example:

• Using manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods).: incorporating manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). in maths teaching and encouraging children to use objects to represent mathematical concepts in a range of contexts (for example, making different arrangements of 5 with seashells to help children to ​‘see’ a whole number and its parts at the same time)
• Using representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs.: incorporating representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs. in maths teaching and encouraging children to make their own visual representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs. of mathematical concepts (for example, encouraging children to move their finger along a number line as they count aloud)
• Using fingers: encouraging children to use their fingers to represent a quantity (for example, showing 4 fingers whilst saying ​‘four’).

In the evidence, educators used several different resources to do this. This included using EdTech​‘EdTech’ includes many different approaches and devices, from robots to interactive apps and games, to support children’s learning. to help children visualiseHelping children to ​‘see’ numbers and quantity, for example, using manipulatives and representations. numbers and symbols, and to provide opportunities for repeated practice.

We spoke with educators, who described a range of additional practices they use while delivering this approach. These include:

• Naming and labelling: giving a name or label to a quantity using a:
  • word (for example, ​‘you’ve scored two goals’)
  • symbol (for example, writing the numeral 2 on the scoreboard)
  • visual (for example, drawing two short lines on a tally chart)

• Estimating: encouraging children to make a guess or estimate (for example, ​‘how many cars do you think we have in the box?’)
• Emphasis: highlighting key information through:
  • comments (for example, ​‘you’ve found four pieces of treasure’)
  • intonation (for example, ​‘let’s see how many shells we’ve got: one, two, three, four’)
  • gesture (for example, making a circular gesture around the pieces of treasure when saying ​‘four’, to highlight that the last number counted represents the total number in the set)
• Thinking aloud: verbally expressing thought processes to make them explicitThe direct and intentional teaching of new words and their meanings. (for example, ​‘I’m going to touch each duck as I count them to make sure I don’t miss any out’).
  

It is more important for young children to be enthusiastic counters who enjoy counting, rather than worry so much about errors that they become reluctant to count.

For example, a child might have only recently shown they understand that they should say one number word for one object. As they count, they might mix up the counting sequence and say ​‘one, two, four,’ and the educator might decide to ignore the error on this occasion.

Sometimes it is appropriate to let errors go, if children are trying hard – as long as they understand that correct counting requires one word for each object and they are trying to do that. Educators will need to give children further practice opportunities in the future to ensure that they learn the correct sequence, in line with the Building number fluency approach.