With maths teaching it seems to me there are two main approaches. The first, the traditional approach, really has Maths down as the great initiation rite of our country. It is the Bar we put up to stop just anyone being anything. You have to be able to solve these random puzzles, some with some relevance to here and how, some dating from Ancient Greece, some from even older than that.... - no matter- to prove you are one of us.
This method is good for elites, as pupils very quickly work out whether they are one of us or not. It is good for universities, who ensure that only pupils who can think in a very certain very prescribed way come into to the institutions. It is good for politicians who get an exam they can claim is difficult. It is good for Maths teachers (and tutors), who get an exam that is easy to teach (or next to impossible for the uninitiated). The people it lets down of course are the pupils -most of whom are not able to get those grades, and have to rest content with the fact they somehow it is all their fault.
The exam then is then very much a passion play, in which a social order based on an arbitrary selection and partial (if highly obscure) merit is re-enacted, and enforced in the same moment. What is lacks any notion is maths as we live as adults with all richness, and complexities (from filling in tax forms, to guess measurements - its all maths). Rather than any of this richness we are presented, as a necessary truth, a maths exam that is the stale, sterile exam. the product of empire and tradition, and utterly valueless in itself.
The other approach, the one we have just moved to sacrifices the obscurities of mathematical rigour and the elegancies of of a single exam, for continued modular assessment, using questions that are based on real life adult experience. Now there is a real sacrifice here, if you understand maths only in terms of a tradition exam, where a certain number of universally acknowledged truths must be imparted (or else some one somewhere has failed). The modern exam, with its emphasis of reading and actually thinking, will not have space for such truths. But instead it teaches the really very valuable skills of how one reads different maths questions, how one thinks about them, and one one is reflex about what one is writing.
The importance (and uniqueness) of this reflexive complex method of reading and thinking is difficult to over emphasize. You see maths needs to be read and written in a way utterly different to the way you read english. Is so many many ways maths reading and writing is unique and different: In maths one reads and reads questions, as one is solving it (and as it starts to make sense); one does not necessarily start at the beginning; one plays with meaning, resolving it careful, part by part, and only at the end creating a whole (which makes sense); one checks the links of algebra and grammar, finding different ways thought can be described; one creates accords between drawing, writing, thinking and reading, accords that are hard to express, but easy to grasp.
In short this is an exam where one must really think and one reads and writes, and do so without let up. What is more one thinks about thins one has a handle on, that one can see are useful, and do matter. In In addition to this the unit version of some of the exams allow pupils to really get the bit between their teeth. They do well in one part of the exam, and suddenly wake up and work. Pupils in such circumstances will start to feel that the exam is for them, and that is enough to make them think differently. It gives them an impetus to engage. It is not then that unit exams are easier, they are not; they merely inspire people to work, people the old exam would necessarily fail....
Now the exam is messy. It does not produce simple 'product'. Pupils with 'A' might excel at different parts of the rich exam, and so universities (and politicians) can not guarantee what a grade 'means'. Likewise the rest of europe, which has kept the initiation approach, looks on in amazement at the sheer 'wierdness' of our exams (I actually teach European students, who have done very well in the Baccs, but cannot get their head round exams that make you think). It goes without saying that the exam is hard to teach, and so does maths tutors at least no favours.
But the people who respond well to it are the pupils (and their parents), for them the exam opens out endless new possibilities and new worlds. Is that not the point?
No of course not.
The exam is bad for the social repression element of a maths exam, - for lots of people, from many different backgrounds, might do well in it, and we no longer have the select brotherhood of 'mathematicians' (Good I say even as a member of that group). But it is of course this last element, the role of maths in the social institution and enforcement of a particular kind of meritocracy, that really matters. Which is probably why the power that be, when they wake up to the change, need to suppress it. Maths is our initiation rite. The idea that 'standards have slipped', and the maths of Ancient Greece is going by the board, feels significant, feels like a diminution in some manner, and lessoning of the magic of the old exam, and the power of the initial initiation. And therefore, to defend the status quo, we need to destroy this new exam, and do so even as we deny the reasons why we must do so. Our system of exam-ocracy masquerades as a more open meritocracy, and we would defend it as that.
The real problem for me at least, is not the defence of a social order, but the clear political (and anthropological) hypocrisy, that this defence involves. To undermine kids in the interests of a social order is common place (that is what societies do), but we ought at least to be honest about it - and accept the choice between different ways to teach and think about maths, is nothing to do with quality, or merit.
No comments:
Post a Comment