Educators teach and model mathematical problem-solving skills so that children can apply logical thinking in purposeful ways. This includes supporting children to 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 answer maths problems and communicate their mathematical thinking. As children’s understanding and confidence grows, educators teach and model the use of representationsA visual that presents a mathematical concept, including drawings, marks, symbols, number lines and charts or graphs. when problem-solving.

Teaching problem-solving skills for maths has a positive impact on children’s mathematical progress in the early years.

Based on the evidence, educators should support children by:

• modelling problem-solving strategies
• sequencing and breaking tasks down
• providing prompts or cues to help children approach problems strategically.

Educators should teach problem-solving skills for maths at the same time as other evidence-informed early maths approaches. In most studies, it was one part of a broader maths curriculum or programme, although it was the central focus in some studies that found positive effects.

Research has identified several practices which are associated with improved outcomes. Educators can use these in combination – they were often evaluated alongside one another. These practices include:

• Breaking tasks down: breaking a task into smaller steps that children can follow to solve a problem (for example, to work out how many are left when 2 are taken away from 5, the educator counts out 5 apples, removes 2, and then counts the remaining apples to answer the question, ​‘how many are left?’)
• Providing prompts or cues: using verbal or physical cues to remind children of relevant information (for example, the educator makes a circle in the air with their finger to remind a child of the strategy of rotating a jigsaw piece to fit it into the puzzle)
• Modelling problem-solving strategies: demonstrating and explaining different ways to solve a problem (for example, the educator narrates how they are going to solve a problem, ​‘I’m going to use the rekenrekA calculating frame with two rows of 10 beads, 5 red and 5 white. to find out how many are left if I take 2 away from 5. So, I’m going to partition the 5 beads by moving 2 away. Now I can count how many are left: 1, 2, 3’).
• 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, providing cubes that connect and break apart for children to use while comparing lengths)
• 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 in a range of contexts (for example, suggesting that children use a tally chart to keep track of the score in a football game).

The practices above were associated with improved outcomes, so educators might choose to prioritise them. Additionally, there are several other practices in the studies we found. These include:

• Thinking aloud: verbally expressing thought processes to make them explicitThe direct and intentional teaching of new words and their meanings. (for example, telling children how you plan to share eight cars between four children, or prompting children to share their own thinking)
• Using signs, gestures and other visual aids to support understanding (for example, using your hand to indicate the height of a tower, while describing it as ​‘tall’ or ​‘short,’ or clapping whilst counting)
• Using mistakes as learning opportunities: providing feedback to help children see where they have gone wrong, so they learn from mistakes (for example, noticing that a child is counting some milk cartons in a set more than once and saying ​‘I noticed that you touched some of the milk cartons twice. If you put them in a line, it might help you count each carton only once.’)

In the evidence, educators discussed maths tasks with children (for example, an educator might ask ​‘how can we use these blocks to make as big a house as possible for the 3 bears?’). They also worked with children – or supported children to work together – to solve mathematical problems. An important part of this approach is encouraging children to explain and show their thinking, for example, while 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..

Many of the practices described within this approach can be used to scaffoldProviding temporary support for a child during a task, to adjust the level of challenge. children’s learning. Find out more about the STAIRS model for scaffoldingProviding temporary support for a child during a task, to adjust the level of challenge. children’s learning scaffoldingProviding temporary support for a child during a task, to adjust the level of challenge.” style=“border:0px solid rgb(229,231,235);color:rgb(51,151,255);text-decoration:inherit;”>here.