Integrating maths into everyday routines

Plan daily activities targeting specific maths concepts and skills

Practitioners should dedicate time each day for purposeful mathematics activity.¹ This should focus on supporting children to develop specific mathematical ideas and skills, taking into account developmental progressions. Practitioners can use whole-class, large and small groups to tailor instruction for children who need support on different aspects of content. Approaches will look different for children at different developmental stages, and in the early years activities are likely to be short and active.

Mathematics can be explored through different contexts, including books, puzzles, songs, rhymes, puppet play and games. Using storybooks to teach mathematics can be particularly effective, through providing an opportunity for mathematical talk and questioning. Much of this evidence comes from studies where practitioners were explicitly supported in promoting mathematical discussion from the story, for example, by being provided with notecards displaying prompting questions and discussion points that they could use.³ Practitioners should therefore plan how they will use storybook resources to discuss mathematical concepts.

^{From Development and Research in Early Math Education.}

^{Mathematics Through Stories, a U.K. organisation that promotes the teaching of mathematics through stories, is another useful source for stories and resources.}

Games can be an engaging way to practise and extend skills. They can build on children’s mathematics knowledge, generate repeated practice in a motivating context, and give children and practitioners an opportunity to discuss strategies and ideas. Practitioners should select specific games to suit current objectives to provide appropriate challenge.

There is some evidence that board games with linearly arranged, consecutively numbered, and equal-sized spaces may be particularly beneficial to numerical understanding, by providing opportunities for developing strategies such as ‘counting on’.³ Snakes and Ladders is an example of a commercial board game that may support this, or practitioners may produce their own versions based on the research. An example from the Mathematical Reasoning project, evaluated by the EEF,⁴ is the caterpillar game (see Box 3).

The EEF conducted a randomised controlled trial of Mathematical Reasoning in Year 2 with 55 schools,⁵ where teachers were trained in the approach and provided with classroom exercises and training materials. Children who experienced the Mathematical Reasoning approach made an additional three months’ progress in mathematics compared to the control group. The EEF then funded a scaled-up evaluation⁶ in partnership with the National Centre for Excellence in Teaching Mathematics. In this second, larger trial, pupils who experienced Mathematical Reasoning made one month of additional progress compared to the control group. Mathematical Reasoning is an EEF Promising Project.

Reinforce mathematical vocabulary and create opportunities for discussion of mathematics

Practitioners should seize chances to reinforce mathematical vocabulary—for example by making a comment about which child is standing ‘first’, ‘second’, or ‘fourth’ in line, which child has ‘more than’ or ‘fewer’ objects than another child, or helping children rephrase statements that use ambiguous, non-mathematical language, such as refining ‘big’ when the child means ‘tall’.

It is important that children are supported to use informal language to describe mathematical ideas for example ‘more than’, ‘smaller than’, ‘pointy’, ‘curved’. Once children are comfortable with using informal language, practitioners can introduce more formal mathematical vocabulary.³ Practitioners need to consider how formal vocabulary is introduced. For example, it may be more beneficial to introduce formal names of shapes gradually rather than all at once then reinforce this as part of an ongoing routine. Practitioners in a setting could plan their use of mathematical language to ensure a consistent approach.

Practitioners should create opportunities for extended discussion of mathematical ideas with individuals or small groups of children in order to extend their thinking. This can be
particularly effective when a child is showing an interest in a certain problem or activity. A number of different frameworks exist to support high quality interactions, such as guided interaction⁸ and sustained shared thinking.⁹

Being highly tuned-in to the child’s behaviour and motivations, responsive to what children are saying and using a variety of techniques to help develop and extend children’s thinking are central to these approaches, which can be used while children engage in a variety of everyday activities.

Features of such approaches include:

• the use of open-ended questions:
• ‘How did you…?’, ‘Why does this…?’;
• asking children to elaborate: ‘I really want to know more about this…’;
• recapping: ‘So you think that…’; and
• clarifying ideas: ‘So you think we should…?’.

Highlight mathematics across the day

Throughout the day there will be meaningful ways to use mathematics. Mathematics can be highlighted through daily routines, during play, and in other curriculum areas.

Everyday routines such as registration time, snack time, and tidying up provide opportunities for counting and comparison as well as addition, subtraction, sharing, and time problems. Practitioners should take advantage of such time to support mathematical development, for example, by engaging in mathematical conversations, singing a song, or playing a number game.

Practitioners should provide a variety of tools to allow children to explore all areas of mathematics, and opportunities for outdoor provision should be maximised, where this is possible, for the development and reinforcement of mathematical ideas. Appropriate tools include 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)., measuring items, scales, construction materials, puzzles, sorting and pattern materials.¹⁰ Building blocks may be especially important for developing children’s spatial awareness and knowledge of shapes.² Children should have experiences with a wide variety of shapes. For example, exposure to a variety of triangles, rather than limited to certain types, such as equilateral or isosceles.¹

Practitioners have an important role in scaffolding opportunities for learning and extending the learning during play. Through observing children’s play, practitioners will identify ‘teachable moments’ in which they can join the play to add to the discussion, reinforce mathematical vocabulary, and encourage problem-solving. Practitioners may find it useful to think about mathematics concepts, discussion points, and vocabulary related to the different play areas and activities so they can use them when appropriate moments arise.¹¹

Practitioners can provide extra opportunities to explore mathematics by highlighting where mathematics exists elsewhere in the curriculum.³ However, practitioners should carefully consider how to embed purposeful mathematical learning opportunities at an appropriately challenging level. Physical education can be a particularly fruitful area for reinforcing and exploring the mathematical concepts of number, shape, and measure (see Box 7).

As the term progressed, the recording extended to estimating and measuring activities, such as lengths of long jumps and timing how long it took to run round a circuit with a digital timer (which led to discussion about the numerals after the decimal point, which the children decided to ignore). The teacher also set up a class graph of how long it took them to get changed for PE.