• Bryant, P. (2009) Key understandings in mathematics learning. Paper 5: understanding space and its representation in mathematics. London: Nuffield Foundation

This is one of a series of papers resulting from a review commissioned by the Nuffield Foundation of the available research literature on how children learn mathematics. This paper considers children’s informal knowledge of space and spatial relations and their formal learning of geometry and deals with the connection between these two kinds of knowledge, providing summary headlines and recommendations for teaching and learning, together with the main report and supporting bibliographic references.

Activity A

Create a display with a selection of shapes attached by split pin fasteners; each day, rotate the shapes and talk to the children about the changes.

Activity B - Robotic toys

Allow the children to design and set up a ‘maze’, through which they can direct each other or a floor robot, with clear instructions. Set out cards numbered 1-12 on the floor in a circular arrangement to imitate a clock. A floor robot can be programmed to travel to a specific number on the ‘clock’, e.g. ‘3’. Children can predict where it will end up next, if programmed to make half a turn before travelling forwards for example.

Activity C - Barrier games

Children work in pairs with a ‘barrier’ between them (e.g. a large book standing upright), so that they cannot see what their partner is doing. Both children are provided with a small number of interlocking cubes. Child A has to make a model, explaining verbally exactly how they are doing this; Child B has to try to make the same model, following these instructions. Once the models are completed, the barrier is removed and children compare their models.

Activity D - Treasure hunts

Get the children to hide a ‘treasure’, somewhere in the room or playground, and then ask them to give each other clues as to where to go, to get closer to the treasure.

They could also try to find the treasure on a large floor grid in which each square is marked off – begin with a 5 x 5 square labelled A-E and 1-5. ‘Child A’ steps in the square where s/he thinks the treasure might be hidden. ‘Child B’ (who has hidden the treasure) has to work out how far away this first child is, using only vertical or horizontal steps, or a combination of both. They can be given a whiteboard to record the fact that s/he is ‘2 steps away’. A second child is invited to take up a position of their choice, on this grid, with reference to this information, possibly after discussing the various possibilities. The hunt goes on, and more children join the grid, until the ‘treasure’ is found.

Children can also then make their own treasure maps on paper, using a similar grid system and adding in their own individual illustrations of a ‘treasure island’. This can also be extended to a ‘battleships’ type barrier game, where one child positions their ship on one side of a grid, unseen by the second child and s/he has to decide where to place her/his ship.

Activity E – collection of ideas

‘Movement and Position in Key Stage 1’ is a collection of activities from Nrich, designed to enable the children to explore shapes, movement and position in enjoyable ways.

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

Pupils should be taught to describe position, direction and movement, including whole, half, quarter and three-quarter turns.

Look at the map. Go to start.

Follow this route from there.

Go to the fourth house on the right.

Draw a ring around it.

Look at this map

Desi's house is the 2nd on the left. Tick ( ✔) it.

• Mathematical Development

This video, originally from Teachers TV, shows EYFS children learning about position and direction through play. Some useful ideas that could be integrated into Year 1 classrooms.