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Do the children you teach have problems with money?
When first introduced to money in the classroom, many children find it difficult to distinguish between the value of a pile of coins and the number of coins in the pile. These children may go on to find the concepts of equivalent amounts of money and giving change difficult to grasp.
Let's look at the skills we need to enable us to understand money.
By the time children are introduced to 'money' in Year 1 most will have the first two skills, at least up to ten. Some may have acquired the third skill, the fourth skill will be being taught to them, and the fifth skill will probably be the last they comprehend.
Digits and values
In the course of research* carried out in the 1980s with children aged between three and eight, it was discovered that although the children could accurately count small numbers of bricks, recording the information in the form of figures was not universally understood. Many children would prefer to record the numbers iconically (e.g. by tallies), or pictorially (e.g. one square to represent one brick) but few chose to record the numbers by writing digits. The use of digits was not widely used until about the age of seven or eight.
Addition and subtraction
It was also found that even very young children could accurately combine small groups of bricks and say how many there were altogether without recounting them, (two bricks and three more bricks - there are five bricks). However their ability to manipulate figures and to make sense of addition and subtraction signs in order to record the 'transactions' they had performed was poor, if it existed at all. (Not one child in the study spontaneously used a plus or minus sign to represent addition or subtraction.) In other words, although they could completely comprehend what they had been doing, they had no way of storing the information on paper, or 'reading' what another person may have 'written' to explain the 'transactions'.
Value
In everyday situations children will generally have come across things having a 'one-to-one' correspondence; dots on the dice equal jumps on the game board, one plate for each person at the table, etc. The concept of a monetary value of an object is not one with which most young children are familiar. If a child wants a new toy, for example, the depth of desire for the toy is of much greater importance than its cost.
The mechanics of money
In these days of increasing use of credit/debit cards and supermarket shopping, few young children have experience of even watching, let alone taking part in, a monetary transaction which involves the use of cash and coins. Some children may have exchanged a five or ten pound note for a toy in a toy shop, but the reason for their receiving 'a penny change' will be beyond the scope of their mathematical ability and would probably pass as an insignificant puzzle.
With luck some children will have been allowed to buy sweets or a comic in the local newsagents, and will have been able to hand over the coins themselves. Here, providing the amount of money is at about the 10p level, the arithmetic may well be within the scope of the child and can provide a very valuable 'lesson in money'. However, this is likely to be the limit of a child's use of money.
A class shop can be seen as an opportunity for children to use money, and buy and sell objects. However, unless play in the class shop is supervised by the teacher or a classroom helper, the accuracy of any monetary exchanges is likely to be nil.
The use of vocabulary relating to money will also be very limited. The words 'coin' and 'change' are rarely used or understood by young children. Vocabulary may even be used ambiguously by adults talking to children. An adult might say, 'I've brought you some pennies.' but mean 'Here is some pocket money.' as he hands over 10p pieces or a pound coin.
To understand exactly what a 2p coin represents we have to have mastered two of the skills in the list above (connecting digits with the value they represent, and understanding that value may be independent of physical properties). We have to understand that the '2' on the coin means two pennies and that this is the same as having two single penny coins, or two coins with '1' on them. When we introduce 2p coins to Year 1 children we are making the assumption that these skills have been acquired. If they have not (as the research would suggest) we are most probably about to introduce confusion to the child as well.
Avoiding confusion
How can we avoid the confusion? Well, if one problem is that a 2p coin has no intrinsic 'twoness' about it, why don't we start with something that does? It is true that a 2p is larger than a 1p and may 'reveal' its greater value in that way, but a 5p coin is smaller than both of these so the analogy cannot be carried very far.
Suppose we start children off with 'pre-money coins' or tokens that indicate their value in a way more acceptable to young children than by putting digits on them. Simply use tokens that are marked with one dot if it stands for a value of one, two dots for a value of two, five dots for a value of five, etc. In this way we will be able to talk about holding a number of dots (something the children can see and quantify), rather than a number of pence (which is an unfamiliar and abstract quantity).
Further, we should be able to combine and separate groups of dots, and be able to compare their 'value' by physically counting the dots displayed on the tokens. In other words a group of tokens will be worth ten dots whether they are arranged.
![[4 x 2 dots + 2 x 1 dot] or [2 x 2 dots + 4 x 1 dot + 1 x 2 dots]](/content/id/2586/pict1.gif)
Building on knowledge
Most children, even at the age of five or six, have a concept of 'fairness', and it is on this basis that an understanding of money can be built. After all, all monetary transactions should be based on 'a fair swap'.
Communicating an understanding of 'value' is certainly not easy. Our understanding probably results as much from continued exposure to 'real life', and values we put on things as we interact with other people, as it does from anything we can be taught.
If children have a problem with understanding the meanings of operation symbols (skill 4) we should ensure that we give them every chance to show they have understood what is happening 'in a shopping situation' without use of these symbols. This can be done by oral recording of problems and their solutions, or by the invention of a more meaningful way of recording transactions on paper, such as using pictures.
Putting theory into practice
Early last year I was able to do some research with Year 1 children. I took a group of children for a few weeks before they were introduced to money in their maths lessons. I gave them an introduction to 'fair exchanges' and 'pre-money' tokens as mentioned above. They were then taught 'money' along with their classmates and I compared the understanding of the 'experimental' group against the rest of the class. The results were encouraging and seemed to show that the children benefited from practising 'fair exchanges' and from dealing with counters which could have a value of one, two or five, before they were formally taught about money. Their regular teacher noticed that the skills of the 'experimental' group were greater than she would have usually expected, and most encouraging of all, the low ability children amongst the group were able to join in with the rest of the class, when normally they would have been left behind at a much earlier stage. In fact, all the low ability children in the experimental group could find the value of sets of 1p and 2p coins (something the teacher would not have expected), while three children in higher groups, but not included in the experimental group, could not confidently do so.
Preparing the equipment
Counters
The counters or 'pre-coins' used have to show their value in a clear way. Size, shape, colour, etc. should not be relevant to the value of the counter. Stick paper dots on plastic counters, all the same size, and all the same colour. (This prevents children being more interested in the colour of the counter than its value.) The only way to tell the value of a counter is to count the number of dots on it. Stick the dots on one side only to avoid the confusion of 'Does one dot on each side mean one dot or two dots?'
The National Numeracy Strategy says Year 1 children should be able to recognise all coins. However these 'pre-money' tokens are to be an introduction to money, so you only need counters with one, two or five dots on them.
Cards
Make five sets of cards carrying a value of one to five dots with a meaningful object pictured on each, plus a card with no dots. (The cards might show a ship, a football, a teddy, a cake or a toy train.)
Using the equipment
If we think about why money developed, we quickly realise it was as a consequence of barter and exchange. Coins merely provide a convenient way of carrying something of value to exchange for the goods you desire.
Using the equipment provides a natural way to use money vocabulary, such as 'buying' cards, giving 'change', etc. When the children are eventually introduced to 'real' money, you should find that they are confident at handling coins and using money vocabulary.
*Reference: Martin Hughes (Children and number. Difficulties in Learning Mathematics Oxford: Basil Blackwell(1987))
Money Problems?
Do the children you teach have problems with money?
When first introduced to money in the classroom, many children find it difficult to distinguish between the value of a pile of coins and the number of coins in the pile. These children may go on to find the concepts of equivalent amounts of money and giving change difficult to grasp.
Let's look at the skills we need to enable us to understand money.
- We have to know the names of the numbers, in the correct order.
- We have to be able to count objects accurately.
- We have to understand the connection between digits (symbols) and the value they represent.
- We have to understand the concepts of addition (grouping things together) and subtraction (splitting things apart).
- We have to understand that objects can have a value, which is irrespective of their colour, shape, size, mass, etc.
By the time children are introduced to 'money' in Year 1 most will have the first two skills, at least up to ten. Some may have acquired the third skill, the fourth skill will be being taught to them, and the fifth skill will probably be the last they comprehend.
Digits and values
In the course of research* carried out in the 1980s with children aged between three and eight, it was discovered that although the children could accurately count small numbers of bricks, recording the information in the form of figures was not universally understood. Many children would prefer to record the numbers iconically (e.g. by tallies), or pictorially (e.g. one square to represent one brick) but few chose to record the numbers by writing digits. The use of digits was not widely used until about the age of seven or eight.
Addition and subtraction
It was also found that even very young children could accurately combine small groups of bricks and say how many there were altogether without recounting them, (two bricks and three more bricks - there are five bricks). However their ability to manipulate figures and to make sense of addition and subtraction signs in order to record the 'transactions' they had performed was poor, if it existed at all. (Not one child in the study spontaneously used a plus or minus sign to represent addition or subtraction.) In other words, although they could completely comprehend what they had been doing, they had no way of storing the information on paper, or 'reading' what another person may have 'written' to explain the 'transactions'.
Value
In everyday situations children will generally have come across things having a 'one-to-one' correspondence; dots on the dice equal jumps on the game board, one plate for each person at the table, etc. The concept of a monetary value of an object is not one with which most young children are familiar. If a child wants a new toy, for example, the depth of desire for the toy is of much greater importance than its cost.
The mechanics of money
In these days of increasing use of credit/debit cards and supermarket shopping, few young children have experience of even watching, let alone taking part in, a monetary transaction which involves the use of cash and coins. Some children may have exchanged a five or ten pound note for a toy in a toy shop, but the reason for their receiving 'a penny change' will be beyond the scope of their mathematical ability and would probably pass as an insignificant puzzle.
With luck some children will have been allowed to buy sweets or a comic in the local newsagents, and will have been able to hand over the coins themselves. Here, providing the amount of money is at about the 10p level, the arithmetic may well be within the scope of the child and can provide a very valuable 'lesson in money'. However, this is likely to be the limit of a child's use of money.
A class shop can be seen as an opportunity for children to use money, and buy and sell objects. However, unless play in the class shop is supervised by the teacher or a classroom helper, the accuracy of any monetary exchanges is likely to be nil.
The use of vocabulary relating to money will also be very limited. The words 'coin' and 'change' are rarely used or understood by young children. Vocabulary may even be used ambiguously by adults talking to children. An adult might say, 'I've brought you some pennies.' but mean 'Here is some pocket money.' as he hands over 10p pieces or a pound coin.
To understand exactly what a 2p coin represents we have to have mastered two of the skills in the list above (connecting digits with the value they represent, and understanding that value may be independent of physical properties). We have to understand that the '2' on the coin means two pennies and that this is the same as having two single penny coins, or two coins with '1' on them. When we introduce 2p coins to Year 1 children we are making the assumption that these skills have been acquired. If they have not (as the research would suggest) we are most probably about to introduce confusion to the child as well.
Avoiding confusion
How can we avoid the confusion? Well, if one problem is that a 2p coin has no intrinsic 'twoness' about it, why don't we start with something that does? It is true that a 2p is larger than a 1p and may 'reveal' its greater value in that way, but a 5p coin is smaller than both of these so the analogy cannot be carried very far.
Suppose we start children off with 'pre-money coins' or tokens that indicate their value in a way more acceptable to young children than by putting digits on them. Simply use tokens that are marked with one dot if it stands for a value of one, two dots for a value of two, five dots for a value of five, etc. In this way we will be able to talk about holding a number of dots (something the children can see and quantify), rather than a number of pence (which is an unfamiliar and abstract quantity).
Further, we should be able to combine and separate groups of dots, and be able to compare their 'value' by physically counting the dots displayed on the tokens. In other words a group of tokens will be worth ten dots whether they are arranged.
Building on knowledge
Most children, even at the age of five or six, have a concept of 'fairness', and it is on this basis that an understanding of money can be built. After all, all monetary transactions should be based on 'a fair swap'.
Communicating an understanding of 'value' is certainly not easy. Our understanding probably results as much from continued exposure to 'real life', and values we put on things as we interact with other people, as it does from anything we can be taught.
If children have a problem with understanding the meanings of operation symbols (skill 4) we should ensure that we give them every chance to show they have understood what is happening 'in a shopping situation' without use of these symbols. This can be done by oral recording of problems and their solutions, or by the invention of a more meaningful way of recording transactions on paper, such as using pictures.
Putting theory into practice
Early last year I was able to do some research with Year 1 children. I took a group of children for a few weeks before they were introduced to money in their maths lessons. I gave them an introduction to 'fair exchanges' and 'pre-money' tokens as mentioned above. They were then taught 'money' along with their classmates and I compared the understanding of the 'experimental' group against the rest of the class. The results were encouraging and seemed to show that the children benefited from practising 'fair exchanges' and from dealing with counters which could have a value of one, two or five, before they were formally taught about money. Their regular teacher noticed that the skills of the 'experimental' group were greater than she would have usually expected, and most encouraging of all, the low ability children amongst the group were able to join in with the rest of the class, when normally they would have been left behind at a much earlier stage. In fact, all the low ability children in the experimental group could find the value of sets of 1p and 2p coins (something the teacher would not have expected), while three children in higher groups, but not included in the experimental group, could not confidently do so.
Preparing the equipment
Counters
The counters or 'pre-coins' used have to show their value in a clear way. Size, shape, colour, etc. should not be relevant to the value of the counter. Stick paper dots on plastic counters, all the same size, and all the same colour. (This prevents children being more interested in the colour of the counter than its value.) The only way to tell the value of a counter is to count the number of dots on it. Stick the dots on one side only to avoid the confusion of 'Does one dot on each side mean one dot or two dots?'
The National Numeracy Strategy says Year 1 children should be able to recognise all coins. However these 'pre-money' tokens are to be an introduction to money, so you only need counters with one, two or five dots on them.
Cards
Make five sets of cards carrying a value of one to five dots with a meaningful object pictured on each, plus a card with no dots. (The cards might show a ship, a football, a teddy, a cake or a toy train.)
Using the equipment
If we think about why money developed, we quickly realise it was as a consequence of barter and exchange. Coins merely provide a convenient way of carrying something of value to exchange for the goods you desire.
- Introduce the 'pre-money' counters. Spend some time counting a number of counters and counting the value of the counters. Although this may seem trivial it is very important that the children understand the difference.
- Play games where the children swap counters with a partner, making sure they always hold the same value.
- Use the 'shopping cards' as something else the children can swap and exchange, something which has a recognisable value or price. Play a 'Happy family' type game where each child collects a set with a certain picture and may only exchange a card for one which has the same value.
- After a while the counters can be used to 'buy' desired cards by simple exchanging of counters for cards.
- As the children's ability grows, the cards and counters can be used in shopping situations, where 'change' has to be given.
- As a final step before real (or facsimile) coins are introduced, use a second set of counters which has the dots on one side and the appropriate number 1, 2 or 5 stuck or painted on the reverse. This means the value of the counter may be seen whichever way up the counter is, and provides an opportunity for the children to link the digit symbol to its value.
Using the equipment provides a natural way to use money vocabulary, such as 'buying' cards, giving 'change', etc. When the children are eventually introduced to 'real' money, you should find that they are confident at handling coins and using money vocabulary.
*Reference: Martin Hughes (Children and number. Difficulties in Learning Mathematics Oxford: Basil Blackwell(1987))