The educator teaches and models how to:

• make comparisons
• make connections
• identify sequences and patterns.

This supports children’s understanding of mathematical relationships. The educator develops children’s spatial reasoning through a range of experiences and by using mathematical language.

This section presents key messages supported by research, providing evidence-based insights about the approach.

Evidence tells us that this approach can positively impact children’s understanding of mathematical relationships. There is also evidence that incorporating this approach into mathematics teaching is effective in improving outcomes for children from lower income families or children at risk of falling behind. However, it is important to note that evidence about this approach through systematic reviewsSystematic reviews collect and analyse multiple research studies on a specific question, using a structured and transparent method to summarise the evidence. is currently limited: we need more research.

Based on the evidence, educators should:

• ScaffoldProviding temporary support for a child during a task, to adjust the level of challenge. children’s learning effectively, ensuring that the opportunities they provide build on what children already know
• Break tasks down into simple steps.

Researchers also comment that early years settings should find ways to encourage parental involvement in these kinds of mathematical activities at home.

It is important for educators to use lots of representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs. (for example, pictures) and 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). to teach this approach. Using a wide range of examples and 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). for classificationGrouping objects according to properties, such as size or length., seriationArranging objects in order according to properties such as size or position., and related activities helps children to generalise their learning to new contexts.

The evidence indicates that educators should provide opportunities for children to:

• understand and use ordinal numbersNumbers such as ​‘first’, ​‘second’, ​‘15^th’ or ​‘22^nd’ which describe the order or position of something. to describe order and position
• compare sets of objects
• spot the ​‘odd one out’ from a group of objects
  group objects according to properties such as size or length (classificationGrouping objects according to properties, such as size or length.) – for example, creating a group of small objects
• arrange objects in order according to properties such as size or position (seriationArranging objects in order according to properties such as size or position.) – for example, from smallest to largest
• notice when an object is added to a series, changing the pattern
• add an item into the correct place in a sequence – for example, if blocks are ordered by height, the child identifies where a new block belongs in the series (insertion)
• use 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). to make comparisons or connections, such as noticing how weighing scales move when more or fewer objects are added, or through block-play.

In the evidence, some of the practices educators used to put this approach into action included:

• Emphasis: highlighting key information through:
  • comments (for example, ​‘the square and the rectangle both have four corners’)
  • intonation (for example, ​‘There is a repeating pattern here – red, blue, red, blue, red, blue)
  • gesture (for example, pointing to numerals to highlight a pattern on a number line, such as 2−4−6−8)
    
• Thinking aloud: verbally expressing thought processes to make them explicitThe direct and intentional teaching of new words and their meanings. (for example, the educator says ​‘I want to arrange these blocks in order of length. First, I need to work out which block is the longest;’ or asks the children to share their own thinking)
• Completion: leaving a blank or gap for the child to fill in (for example, setting out circles and squares in an alternating pattern, with a gap at the end for children to fill in)
• Composing and decomposing: combining smaller parts to form a whole or breaking the whole down into smaller parts (for example, helping children to see how a large triangle can be created by combining smaller triangles, and vice versa).

Many of the studies describe educators working with small groups of children, using games and other playful ways of learning.