a) Choose a topic in measurement, and design two activities in your context to help your pupils explore and learn the concept.
b) Try these activities out on a few children, and write down the ways in which they promote children's mathematical thinking.
A very important aspect of mathematical thinking is the ability to recognise patterns and links. How can you as a teacher foster this ability in a child? Let's see how Anna's teacher did this.
10-year-old Anna was busy with problems of mental arithmetic. While calculating 2 x 74 she arrived at 432. She was asked to do it again, and again she said 432. The teacher realised that Anna had calculated 72 x 6 rather than 76 x 2. She describes how she helped Anna to arrive at the correct answer. She asked her the following questions in the given order:
What is 2 x 100? Anna replied 200.
2 x 90? 180
2 x 80? 160
2 x 76? (After a slight pause) 432
2 x 70? 140
2 x 80? 160
2 x 76? 432
2 x 100? 200
2 x 200? 400
2 x 76? 432
Suddenly Anna stopped, thought a bit and said, "Wait. I think something's wrong.
Let me work it out. "She got her paper and pencil, and worked out that 2 x 76 equals 152, and felt very pleased with herself
What is striking about the situation above is what the teacher did not do.
- She did not give Anna the correct answer immediately.
- She did not tell her that she had made a mistake.
- She did not call her a fool and try to hurt her ego.
- She did not threaten her.
- She did not get the class to snigger at her.
What the teacher did do was:
- She talked to Anna.
- She thought about and realised why the error was being made.
- She thought of a method which, according to her, would help Anna realise her error.
- She was patient and gave more than one opportunity to Anna to help her realise that something was wrong with her way of solving the problem.
- She encouraged Anna to observe, think, recognise patterns and make connections.
In short, the teacher was trying to create a meaningful learning environment. Unfortunately, a lot of teachers do not do this. As-was discussed ,previously most children are compelled to mechanically use the algorithms taught, rather than helped to understand the process.