Monday, April 21, 2014

Teaching Simple Addition

I hold engineering degrees and am able to solve complex mathematical equations. But when it came to teaching my almost 4 year old son to do simple addition, I was stumped. It is something that I knew how to do, and could do it in an instant, but how do I teach my child the concept of addition and impart the skill of doing simple mental sums to him? After some trial and error, I've figured it out. If teaching 1+2 has stumped you, the following might be useful.

1. Rote counting
Most children are able to rote count when they are about 2 years old. Singing songs like 12345 Once I caught a fish alive and Counting Bananas helps them to learn rote counting.

Rote counting backwards (i.e. from 10 to 1) will come in useful for subtraction, but not necessary at this time. 

2. Recognising numbers and using manipulatives to represent numbers.
My boys love working with manipulatives. I like how they think they are 'playing' but I am actually fulfilling my lesson objectives for the day. For counting, we use our bear counters. Lego bricks or bread tags work as well. I lay out numbers and get them to lay out the correct number of bears. Then I introduce 'more than' and 'less than' as well. 

This things about boys... they like lining the bears up in neat rows and pretending that the bears are soldiers in an army parade.

3. Use fingers to represent numbers.
Other than using manipulatives, children should be comfortable holding out the correct number of fingers to represent any number within 10. I find Nathan struggling with this initially, but as he 'practises' more, he was able to hold out the correct number of fingers in an instant.

4. Which is bigger?
Being able to identify the bigger number will help them to add quickly, especially when they are first starting out. There is a dizzying array of pre-school math books available in the bookshops, but they might not contain enough of certain type of exercises that I'd like my kids to work on. As such, I just buy one or two math assessment books and plug the gaps by writing out the ones that I would like more work on.

These are two pre-school math books that we have / are using. They are not necessarily the best around (since I haven't tried all of them), but I chose these two based on layout and breath of topics covered.

Having covered the "basics" above, one should have the skills required to do simple addition.

Method 1: Counting on
When faced with a sum like 8 + 3, we first identify the larger number. In this case, Nathan will determine that 8 is the larger number, and actually say out loud, "8 in my head", then he'd hold out 3 fingers, and count up from 8 as he folds down each finger one at a time... "9, 10, 11". 11 is the correct answer. When he first started out, he tended to start counting from 1 all the time... so he'd go... "8 in my head... 1, 2, 3, 4, 5, 6, 7, 8..." and then proceed to count up. With more practise, he's now able to start counting from any number without starting from 1 all the time.

Method 2: Number line
The number line method is more visual. Kids start from 8 and draw arcs jumping from 8 to 9 to 10 to 11. Nathan is not quite able to visualise the arcs without actually drawing them out. So this means that he actually has to redraw the line each time he has a new sum, which is rather time consuming. Anyhow, the number line is useful for more complex sums, so it is good to know how to use it.

I had a look thru Singapore's Primary 1 Math syllabus, and also flipped thru two popular Primary 1 math assessment books. Much of what is done in the first six months (in Primary 1) requires a child to be able to add well. So it is important to get the basics right at pre-school.

Find opportunities for the child to use his skills in a meaningful way... When making lunch, I'd get Nathan to find out many slices of pizza each person in the family wants, then work his sums and tell me the total so have enough for everyone. Some restaurants have ordering chits at the table, so we write our orders down instead of having a waiter take down our orders. Most of the time, it involves writing the item code and quantity. I'll let Nathan take the orders. He's delighted that he's able to help, and it motivates him to improve. 

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