Copyright © University of Cambridge. All rights reserved.
Last time (Uncertain Beginnings) we looked at how the learning of mathematics can be compared with following a meandering path of crazy paving. There are many stones, each providing its own perspective on the maths we have already learnt, and enabling us to make varied routes through the wealth of knowledge that
lies before us.
A path of crazy paving doesn't start with one particular stone, and our knowledge of the mathematical world doesn't start with one particular activity. Children explore shape and space from their very first days. They learn to recognise the shape of their parents' faces. They learn where the edge of the buggy is so they can drop things to be picked up. And they learn which gaps are wide enough to crawl through, and which aren't. They explore their world with all their senses, to find out about the objects around them. Gradually they encounter the vocabulary of mathematics, through nursery rhymes and songs, as well as by hearing words like 'round', 'square', 'longer', 'smaller', etc., etc. in everyday conversation.
Children learn and consolidate what they know through play. This article will take a closer look at some of the toys and games that can enhance a child's mathematical learning. Scroll down to find more detailed explanations of each one.
The range of toys and games which use mathematical processes increases all the time. Whether you use modern board games or traditional toys, they all provide opportunities for children to learn about mathematics in a natural and enjoyable way.
The counting frame: Often regarded as a 'baby toy', the counting frame is a powerful teacher of number. It can be used for simple counting, visualising numbers and number bonds.
Shapes and building blocks: Simple geometric shapes and blocks promote an understanding of shape, and the properties of certain shapes. Being able to handle the shapes also helps the children to learn about balance and improve their fine motor skills.
Dominoes: Dominoes can be used for simple matching games, and can be an aid in the learning of number and recognition of numerals.
Board games: Board games involving the use of dice help with the understanding of number, counting, and begin the development of mental arithmetic.
Card games: An ordinary pack of cards or commercial card games can be used to enhance matching, number recognition, counting and arithmetic.
Jigsaws and puzzles: From very simple shape sorters to complicated three-dimensional puzzles, jigsaws and puzzles provide a wealth of opportunities to practise and improve spatial awareness.
There is one more bonus that follows from playing these games: children learn that winning is fun but that losing is part of life as well. If you can show them that you can 'cope' with bad luck, or that you made a silly mistake which ultimately lost you the game, they too will accept a game for what it is, and not get upset if they aren't always the winner.
As well as learning about the mathematical world through play, children encounter mathematical concepts through everyday activities. By involving children as we do things, we can demonstrate what words like 'more', 'fewer' 'too long', 'how many?', 'cost', 'half', 'heavy', etc., etc. mean.
All through the day, adults are making decisions, and taking actions based upon some kind of mathematical knowledge. The action may seem too trivial to even be talked about. For example, why cut off the end of a piece of paper?, why lay five knives and forks on the table?, why give the shop assistant two pound coins?. If, however, time and patience can be employed in allowing children to be aware of these simple tasks and decisions, the vocabulary of mathematics and science becomes a natural part of every child's life. By enabling children to hear and use such vocabulary, it is less likely to hold any mystique or create any anxiety when it is used in a mathematics lesson.
Playing games with children starts at a very early age, but the toys and games mentioned here could be used by practitioners in Early Years classrooms as well as by parents at home. Enjoyment of playing games continues beyond these first years, and teachers of older children will also find the games useful. They could be used in small group situations, or as ideas to include in clubs and activities used to cultivate a home-school partnership in the promotion of mathematics.
The counting frame
Firstly, of course, the children can just count the beads on a row.
Alternatively the beads can be arranged in steps, increasing from one on the first row, two on the second, etc.
And, although they probably won't consciously use these facts for several years, the five/five split of the beads on each row has subtly shown, for example, when you separate four beads from the ten, you are left with five and one more at the other end, that seven beads is made from five and two and leaves three at the other end, etc., etc.
Pretty high-powered stuff for just a 'baby toy'!
Shapes and building blocks
With a set of blocks made from simple geometric shapes, children can explore balance and the possibilities of building, either intricate facades or more simple towers.
And they can practise tessellation by getting the shapes to fit neatly back into the box!
Traditionally dominoes have patterns of spots on each end. While there is no reason why the spots cannot be treated as patterns in their own right, and not necessarily related to number at the outset, many adults prefer to introduce children to dominoes through picture matching.
A complete set of dominoes may make the game too long for very young children, so start off by using just a few of the set, and gradually build up the number of dominoes used in the game.
To be sure the game is playable choose dominoes that can be arranged in a ring. Then, no matter which domino is played first, someone will have a domino which can be attached. As the ability and attention span of the child/children increases, more dominoes can be used in a game. It is preferable that a very short game is played through with enjoyment, than a full game is started and then left unfinished.
Pictures and colours can be used to introduce the idea of matching. Domino sets with pictures and spots allow you to introduce the idea of numbers and matching numbers.
Sets which include figures (numerals) are in fact taking the matching game one step further, as they use symbols for the amounts shown, rather than a simple representation in the form of spots. No reason not to use them, but remember, although the numerals are second nature to you, they are unfamiliar to the child and he is still learning to relate a certain squiggle to a certain number of objects.
You may also find our Dominoes Environment useful.
A game may have rules which are too difficult for very young children to cope with. Make up your own rules and play a simple race game until the children are ready and able to make the game more interesting with tactics, penalties, etc.
Snakes and ladders is often quoted as a game for young children, but it can get very frustrating and with a run of bad luck, may go on for too long. Ludo , which is often thought of as a simple game can get quite intense if the rules for barriers and double barriers are employed. Again this can be a long game, so reduce the number of counters each player has. Some of the games which we have found particularly enjoyable, for adults and children are: Splat! , Mouse Trap and Ghost Castle by MB Games , Tower of Terror and Open the Bridge by Spears , and Road Safety Game by Early Learning Centre . These games can be played as simple races until the children are ready to understand more complicated rules. The mixture of chance and tactics keeps the games interesting for all levels of ability, and ensures the games are used over and over again.
There are many children's games that can be played with a normal pack of cards.
Sevens (or Donkey)
As with the counting frame, plastic shape sorters shouldn't be regarded as 'merely' baby toys. If we take the example of a sorter with a square, a circular and a triangular hole, the children are learning that the circle has an infinite number of axes of rotation (it doesn't matter 'which way up' the circle is, it will still go through the hole), while the square and the triangle have to placed more carefully to get them to fit through their holes.
As the children progress to more difficult puzzles it is useful to provide ones where whole pieces fit into a rigid outline, as then each piece completes a picture without being reliant on the correct positioning of other pieces.
Gradually the children can progress to more conventional puzzles. At first provide puzzles with very few pieces so that the task can be completed before the concentration runs out. Or get the children to complete a larger puzzle in which you have left a few holes to fill.