As a supply teacher, I always realised when pupils had not been taught maths well when they asked me "what do those 3 dots mean". When demonstrating to them how to do some routine or other I would invariably start subsequent lines of my maths with 3 dots arranged as an equilateral triangle, the symbol for "therefore". The fact that the pupils did not recognise this symbol showed me that they did not use it. If they did not use it, then they were not reasoning their way through the calculation.
This is not to say that they were not using mathematical routines. They might well have been following the rules of mathematics and rearranging their expressions in a manner that would eventually lead them to the desired solution, but they were not reasoning their way through. Maths should be about reasoning. At Puppet Maths we stress the use of logical reason within maths problems.
Instead of using "therefore" to start each line of their calculations pupils would often use the equals sign at the start of the line. They would do this even when the new line of working was not the same as the preceeding one. They might divide all the expressions on the previous line by 2, for example, and write it out again starting with the "=" sign. This is not true, and shows a lack of proper understanding of what "=" means. When challenged the pupils would say "you know what I mean", indeed I did (they meant "therefore", but that is no compensation for the lack of precision in the pupils' work. This lack of precision is indicative of pupils regurgitation maths routines rather than engaging in logical thinking on their own part. They do this... then do this... then do that, because that's what they've been taught to do, and they are not reasoning their way through the problem. At Puppet Maths we want our pupils to reason their way through their problems, as this will make maths easier for them, it will turn problems into puzzles, and it will make maths fun.
Wednesday, 22 September 2010
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