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Colin Foster describes a practical way of assessing pupils' confidence in their mathematical answers.
'Negative' marking, in which marks are deducted for wrong answers, may strike you as a bad idea. Why would you want to inflict something 'negative' on pupils (Foster, 2007)? It is often said that tests should be about being rewarded for what you know and can do, not being punished for your mistakes. So it is hard to see how 'negative marking' could contribute to a positive classroom ethos. Surely this would just be discouraging for pupils?
The problem with positive marking is that it rewards guessing, which can have some undesirable consequences. In high-stakes school assessments pupils may be told to guess if they are not sure. Teachers may say, "There's nothi ng worse than leaving a blank answer. That will definitely be marked wrong! Always put something, even if it's a complete guess. It might be right!" But if pupils carry this advice into the classroom and react to uncertainty by guessing, this can create problems. I once observed a pair of pupils working through a sheet of 10 questions, thinking hard about them and getting the correct answers to the first few. After they had completed the first four the teacher said to the class: "You've got 10 more seconds to finish off." One of the pupils said, "Quick, just put anything for the last ones," and the other pupil quickly wrote in some numbers. The class then marked their answers and this pair got 4/10, the first four correct and the last six wrong. I wondered how the teacher would interpret this when they collected in the sheets. Would they realise what had happened or would they spend time wondering what made the last six questions harder than the first four? Might they try to work out how the pupils had obtained those wrong answers and look for what misconceptions might lay behind them?
There may be times in a mathematics lesson when you might want pupils to use their intuition and guess or 'guesstimate' an answer. But this would be a starting point rather than an end point. You might ask them to conjecture something and then work on reasoning it out and deciding...