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All entries for Thursday 28 October 2010

## October 28, 2010

### The wrong way or just not your way?

This is something that bothered me during my observations of a few weeks ago. Also, I'm not enjoying writing my SCT2 based on said observations. In 2 of the 6 lessons I observed, pupils were told that their method (ie a method they'd invented to do something, rather than following the teacher's method) was wrong or wouldn't work. One of those observations I only saw because I was stood nearby, so I'm willing to bet there are others I missed in the other 4 lessons.

The first was in a lesson on compound interest. Pupils had to calculate what £1000 plus 5% interest was by typing "1000x1.05=" into their calculators, and got £1050. They then had to work out what another 5% of interest on that was like by doing "1050x1.05=". One boy put up his hand and offered a different method:

We already know 1000x1.05=1050.

Lets do 50x1.05=52.5.

Then the total is 1050+52.5= 1102.5.

He was told a simple "no, you must do..". In the teacher's defense, she may not have realised he had a valid method, as when he explained it he got a figure wrong early on and so gave an incorrect answer. He gave an answer at the start "Miss, I got something else!" and the teacher asked for the calculation, presumably looking to find an incorrect figure in the calculation she suggested, and so not expected a different method. A "listening for" rather than "listening to", I think my books class that as!

The second was in a lesson finding the sum of interior angles in polygons. They were to find these by drawing lines from vertex to vertex to split the polygon into triangles, then use the fact that angles in a triangle sum to 180 degrees. While the class were working individually on a worksheet, one girl put her hand up to ask if you could do it a different way:

Draw a dot at the centre of the polygon.

Draw a line from the dot to each of the vertex of the polygon.

Use these triangles to find the interior angle.

The teacher told her "no *that doesn't work*". I'm sure I heard "that doesn't work". It got to me, since I can understand that sometimes it's learning a certain method that is important, and the teachers professional judgement and knowledge of the class trumps mine any day. But...it does work. An n-gon will be split into n triangles. Total of 180n degrees so far. Some of that is used to go around the centre point of the polygon, not to fill the interior angles, so we need to take away 360 degrees. That's just as neat as the other method. It doesn't work as generally, but they were given convex polygons on the worksheet so the method was fine for that. It's not just the stifling of creativity that got to me, it was the plain incorrectness of what the girl had now learnt. How could she trust her internal logic and mathematical thinking when it lead her to this idea she saw no problem with, but now thinks is incorrect?