Bite Sized

It is a strange feeling, teaching the new maths syllabus.
 On  the hand one is teaching a course that is actually very worth while - in the sense that the maths that allows one to fill in a tax return or work out a fuel consumption is always good, always useful. More than that it, teaching the kind of methods that one needs to work out real world situation demands one actually teaches thought, rather than simple 'you do this then that, then this.' The philosopher me really revels teaching this syllabus, as it really demands pupils think and presents the teacher with the challenge that we teach the links between topics, rather than the formal topics itself.
 On the other hand, it is very very strange to  teach, if one understands teaching in its old formal sense. That definition of teaching was very class room based, and what it taught reflected the classroom situation. One taught methods inside topics and during formal lessons - one did fractions then percentages, then ratios, and left it to minds of the smartest to work out that these are really the same thing. One could use the connection between the different elements of the syllabus as a signifier for smartness: A's were given to those who link topics, and as teachers we conspired that it was so.
 The strangeness for me, is that while the first stratagem for teaching is for me preferable, it is as a teacher much harder to work out both what you are doing, and what the long terms effect of what teaching be. I mean you are teaching to something that is integral to humans, namely their real understanding. The pupils therefore really comprehend what you are saying, which is just as well as the bite sized  ' you do this then that in this case' approach cannot be formally taught as such. There are no simple methods or internal 'one-size-fits-all written answer calculators (that is very few formal written methods). One is therefore never really sure, until the next week or week after, of the power ones teaching:-  If you like one is always flying blind, as one cannot read another's mind, and there nothing on paper to read. If you like maths teaching has become intuitive! Which for my money is no bad thing....
 The only trouble is, of course that this being blind makes the teaching slightly weird for the teacher as it is (potentially) good for the pupil- and problem is that education is run by adults, as is basically for adults: Teaching is so often an expression of adult anxiety, and not what is good to learn. It is then surely only a matter of time before we turn back to what is easy for adults to teach, asses and so judge both pupils and teachers. A fact that makes teaching the new approach all the more odd. I know even as I really get my teeth into how to teach it, how to think it, that the knowledge will soon be useless, and swept away in the interest of tradition.