Having been a mathematics educator for almost three decades, I have had the privilege of meeting many parents and fellow educators.
One topic that arises frequently is the concern over mathematics learning. Most parents find that helping their children with their maths homework can be quite daunting.
But my experience with many children shows that keeping a maths journal is a very effective way to track and chart a child's mathematical reasoning and progress. It records maths problems, thinking processes, and strategies used to work out the solution, whether through words, pictures or symbols.
We may like to think of it as a form of mathematical conversation.
The journal is a place where children can show how well they understand maths concepts, and share their mathematical reasoning with teachers, classmates and anyone else who may be interested.
It could also be where children reflect on what they had been taught.
For instance, you can ask children to write on the difficulties encountered when learning about the area and perimeter of circles, or ask them to describe the three key points they remember after a lesson on volume.
The journal can provide a useful insight into how he or she approaches ideas and whether the child is under any misconception. Once identified, the child's misconception needs to be corrected.
An example of a Primary 5 pupil's maths journal entry illustrates how a parent can help a child with a new concept, identify and correct a misconception and move on to tackle more challenging problems.
Question: Kelly has $2,000. Kelly has 25 per cent more money than Elsie. How much money does Elsie have?
As Kelly has 25 per cent more than Elsie, Elsie has 25 per cent less than Kelly.
•Elsie has 100%-25% = 75%
•Amount Elsie has = 75% x $2,000 = $1,500
The child's explanation clearly reflects his misunderstanding of percentages and the use of 100 per cent as the base.
When we say Kelly has 25 per cent more money than Elsie, we are comparing the amount of money Kelly has against the amount of money Elsie has. In this case, Elsie's money is the base - the 100 per cent.
Therefore, the amount of money Kelly has is 125 per cent that of Elsie's .
Child's new reasoning
•Base = 100% = Elsie's money
•Kelly's money = 100% + 25% = 125%
Child's new working
•125% of Elsie's money = $2,000
•1% of Elsie's money = $2,000/125 = $16
•100% of Elsie's money = $16 x 100 = $1,600
Once we have identified the problem area or misconception and corrected it, we move on to work through a variety of examples to help the child learn how to identify the base.
Question: Joy sells soft toys. She has 120 panda bears in her shop. There are 75% fewer panda bears than teddy bears in Joy's shop. How many teddy bears does Joy have in her shop?
Penning down thinking processes, strategies and workings, means the child has to organise what he or she knows, be clear about the concepts and reflect that on his or her level of understanding.
And that is why the journal can be such a great tool. But lots of support and encouragement will be needed in the initial stage of keeping a maths journal as children are not adept at thinking clearly and communicating their ideas on paper.
As with any skill, the more they practise, the easier it will become.
•The writer is Mathematics Expert at Marshall Cavendish Education, a leading provider of educational solutions here, having pioneered the use of Singapore Maths materials locally and around the world.