Use estimation and patterns to rivet reluctant mathematicians
Improving the numeracy and basic calculation skills of children who lack confidence is often one of the trickiest jobs for maths teachers. But after some trial and error, I have found that using estimation and patterns can be highly effective. So, each week, I challenge my pupils with an estimation task and a pattern task.
For the former, students must come up with a numerical estimation based on a picture that I project on to the board. I do not give them any additional information, such as the measurements or dimensions that they should use. I simply leave the picture up there and ask them to make their best guess of the number of sweets in the jar or people on the train, or the amount of water in the bath. All I insist on is that the children justify their estimate with a calculation.
To add a "fun factor" to this activity, I have set up a league with a fixture list. Just as in football, students play a "match" each lesson and they get three points for a win (coming closest to the right answer), one point for a draw and nothing for a loss. I act as referee.
Perhaps it's the competitive instinct, or maybe it's because we all like to take a gamble now and then, but whatever the reason, pupils really enjoy the challenge and I encourage them to share their guesses before I reveal the answer. There are often big differences between the estimates - suddenly I have a class of reluctant maths students discussing the solidity of their mathematical calculations.
The weekly pattern task is similar. I project a pattern on to the board and ask the pupils a simple question: "How do you see the pattern growing?" It might be a series of squares, each one larger than the last, or a line that is in a different position in every iteration. Then I ask the students why the pattern is growing in that way.
Most pupils can instinctively see how the pattern is growing but struggle to explain why. I encourage them to come up with a numerical pattern that is linked to the visual pattern, to see if they can explain mathematically how it is growing.
As with the weekly estimation task, I ask pupils to share their explanations; they are curious to hear different points of view. When I reveal the result, the class talk about why and how they were right or wrong. In this way, topics such as nth-term rules and substitution can be introduced.
The pupils find the tasks interesting and often want to devote full lessons to them. Their explanation skills and confidence with calculations improve quickly. But by how much? Perhaps I will set that task as next week's estimate activity.
Gareth Fairclough is a maths teacher at Thornleigh Salesian College in Bolton
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