Maths is Magic, Let's Make it Easy! - Happy Lesson 7
"I was never any good at Maths!"
As a teacher I have often heard parents say "I was never any good at Maths!" and the question is why this subject more than any other bought this response?
At school young children love to play around with hands on maths activities and these experiences are vitally important to enable them to really understanding basic mathematical concepts. The reason so many people feel insecure about maths is that they did not have enough of these opportunities and instead just learnt to follow a process. If you understand a concept rather than just follow them by rote you are able to apply this understanding to a variety of settings, however if you learnt it as a process, then you may become easily confused if it is not in a familiar format.
Why is Maths Play so Important?
Every subject has a developmental process but probably none more so than Maths. If the early concepts are not completely mastered it becomes progressively more difficult to develop understanding and master future concepts. Think of it as trying to build a tall tower with weak foundations, at some point it will fall down. If you understand the developmental structure you can help your child to master the transferable skills needed to become a good mathematician. Time spent reinforcing the early concepts is always time well spent and leads to confidence in the future. Unfortunately because of the many pressures on teachers they are often the first to recognise that children do not have enough time to just play with numbers in the school environment and that is why what you can do at home is so important.
What is Maths?
Maths skills and concepts can be divided into 2 areas, those developing the understanding of Number (Numeracy) and those developing the understanding of Shape and Measure. This week I want to explore Early Numerical Concepts and next week I will look at how to develop an understanding of Shape and Measure.
Early Numerical Concepts
Your child’s experience and understanding of number will start long before they enter formal schooling. I have separated it into 5 steps.
The role of Number Rhymes and Counting by Rote
Your child’s first introduction to number will probably be through Nursery Rhymes such as “1,2,3,4,5 Once I Caught a Fish Alive” and “1 Man Went to Mow”. The words combined with the actions (raising 1 more finger as you count) will help to introduce the concept of number but in a rote format, the same as learning the lyrics of the song. Although this is fun it should not be confused with 1:1 correspondence, when a child can consistently touch 1 object in response to each number counted. Your child can start to experience 1:1 correspondence if you count fruit into a bag when shopping or even counting the stairs when climbing them. However learning to count by rote to 10 and back combined with number songs and rhymes at this very early stage will help to develop an initial idea of number.
The next skill your child will need to master is number recognition, initially to 6, then 10 and then 20. Number recognition is when your child can say a number's name when shown the numerical symbol randomly, by this I mean not in order. The best way to achieve this is to provide lots of opportunities to see, feel and count a number. Here are some fun ideas to do this:
? Draw the shape of a number in the air/sand while saying the number name.
? You can make or buy some number flash cards. The top half has the number in big writing and the bottom half has a number of objects to match. You show them the card and ask them to tell you the number. If they do not recognise it you can count the objects together and then repeat the exercise.
? You can lightly draw in pencil the shape of a number and they can draw over it in paint, felt tip, pencil or crayon. Then say the number together
? Play number bingo.
? Get your child to throw a die with dots on, not numbers. Then they have to find the number card to match the number they have thrown. The one with the most cards after 5 minutes wins.
So what do they need to know next? The next numerical skill is to be able to put their number cards in the correct order (sequence) to 6, then 10 and then 20. Initially they will need assistance with this but with practice they will master it.
A good game to play is for you to put the number cards in in order together and then ask your child to shut their eyes. Now you remove 1 or more cards and they have to tell to which ones have been removed and then replace them in the correct space. Remember to let them do it to you too, children love to ‘play teacher’’.
1:1 Correspondence in Counting
1:1 Correspondence in Counting is when a child can consistently touch one object in response to each number they say. To develop this they need lots of experience in counting objects around the house and when they are out. Here are some ideas.
? Count together pieces of dried pasta, buttons or bricks. Start with a small amount and then increase it as they master the concept. Show them how to put them in a straight line and then say only one more number as they touch each new object, or one less number if they are counting backward,
Make sure they understand that the last number they say is the total (how many they have altogether)
? When you are in the supermarket, count together the pieces of fruit or vegetables as you put them into bags.
? When you lay the table count the knives, forks and spoons together
? As you climb each step count them together.
? If you make a jigsaw or build a construction model, count together the number of pieces as you put them away.
? Write some numbers clearly on paper plates and put some matching dots to help them read the number if they get stuck. Now give them random plates and they have to find the correct amount of objects to match the number.
Now your child can recognise and order numbers, and is able to count accurately, you need to ensure that they have Number Conservation. This is the conceptual understanding that a number or group does not change, however you split it up, unless you add to or take away from the group.
To test your child’s understanding of ‘Number Conservation’ you need to count out a set of objects, say 5 pieces of pasta. Ask your child to count them and tell you how many they have got. Now shuffle them around and repeat the question. After a few attempts a child who has number conservation will no longer recount the group but will just say the total. These children realise the total has not changed as you have not added to or taken away from the group. If they continue to count each time you will need to keep repeating the experience until they do understand the concept. This can be almost immediate or take up to several months.
More and Less
Once your child has mastered number conservation they will be ready to understand more and less. You can now show them that to change the total (the last number they counted) they will need to add to or take away from the group. If they add one or more to a group, the group will have more, if they take way one or more from the group, it will have less. They should also be able to compare 2 obviously different groups by stating which group has more and which group has less. From this they can go on to comparing 3 or more groups using the terms, more than and less than. These are the basic skills that lead to understanding addition and subtraction.
Understanding Addition and Subtraction
Your child can now start to combine two groups of real objects together and to understand that the last number counted is the total of these two groups. They also need to understand combining groups is known as addition and the total will be the largest number.
After this your child can take a smaller group of real objects from a larger group and to understand that the last number is the new total number of objects.They also need to understand that this process is known as take away or subtraction and the new total should always be less than the original group.
It is really important to initially do these activities with physical objects so they can see the mechanical process behind these concepts, the more practical work the better for later understanding.
Using a Numberline
Once they have become confident with adding and taking away real objects then you can introduce a number line to help bridge the gap from a fully practical approach to the written formal method. You will need to talk to your your child about how when we add using the line that we jump up the number line, towards the greater numbers and when we take away using the number line, we jump back down the number line, towards 0, the smallest number. It is key that your child understands that when we add to a number it always becomes more (increases/larger) and when we take away from a number it always becomes less (decreases/smaller)
By truly mastering an understanding of addition and subtraction concepts your child will develop the tools to be able to gain an understanding of multiplication and division. As multiplication is purely repeated addition, 3 x 2 is the same as (=) 2+2+2 and division is purely repeated subtraction: 6 divided by 3 is the same as (=) 6 -2 -2 -2. The children who later have problems with multiplication and division are the same children who never truly developed conceptual understanding of addition and subtraction, but instead learnt it as a simply mechanical process.
The key to happy mathematicians is do not underestimate the impact of understanding these early numerical concepts.
Have fun with Maths