Session 2 [23 August 2011] - Reasoning and Making Sense

Today, I learnt a new word “subitize”. It is a way of manipulating numbers through visualization. When we look at the things, we do not count them individually but in groups. We recognize and know the amount. For example, when we roll the dice in game and we know what the number is without counting each dot on the dice, we are subitizing.

Another example is the game “Pick up Sticks” we played in class. It’s a game for 2 players and they have to take turns to take away 1 or 2 sticks from her partner. The winner is the one with 1 or 2 sticks. In the process of playing, children learn :

1. To count – how many sticks
2. To look for patterns – number sequence
3. To problem solve – how many stick do I need to remove to be the winner
4. To subitize – visualize the things and know how many

Other games such as Dominos or games that involve the rolling of dice will also help the children to visualize the numbers on the dots and gradually to have a better understanding of mathematics and its relationships.

The dice game that Dr Yeap conducted with the Primary 1 children stirred up my interest in finding the ‘hidden’ answer. Using 2 dice, and with each end joined together, he asked the children to guess the sum of the 2 hidden numbers. The children were asked to reason, to look for pattern and to communicate their ideas to find the answer to the question. Similarly, when children are face with word problem, they are at a loss of what to do. Teachers need to guide them by providing opportunities for them to:

1. Talk about what the answer might look like
2. Think about the problem and what it is about
3. Think of the answer before solving the problem

In the process, teacher has to ask the children to focus on the problem and the meaning of the answer, and to focus on the structure of the problem. Eventually, the thinking will lead to a rough estimate of the answer. The most important approach to solving any contextual problem is to analyze it and make sense of it. We can see that at the end, mathematics is about reasoning and making sense of situations.