Tuesday, December 03, 2013

Maths curriculum: full of howlers & schoolboy errors

Anthony Gardiner has rightly exposed the new maths curriculum, in a 56 page critique, as being so flawed and full of schoolboy errors, that many of the same mistakes, and some extras, will once again lead to poor teaching and low performance. It is ‘doomed to succeed’ in the sense that it dresses up rigour as rote learning and repetition.
Roman Numerals howler
Gardiner ridicules the inclusion of Roman Numerals as having ‘no role to play in school mathematics’. He's right. More importantly, he shows that the authors claim that the Roman numeral system came to include ‘0”. It did not. That was introduced through the ‘Hindu-Arabic’ numeral system. Like the ridiculous imperative to include Latin in the Ebacc, this is pure ideology and snobbery at work. As Gardiner points out, you won't find this nonsense in the curricula of high performing countries.
Too much too early
This is the big one, the mistake that continues to plague the teaching of maths. To introduce concepts and, easy but unsophisticated, methods of calculation too early, may gives the impression of progress but it simply halts progression further down the line. This is Gardiner’s main criticism, that poorly defined ideas and methods are foisted upon the learner without adequate understanding. For Gardiner, some Key Stage 1 and 2 is badly specified with items listed “unnecessarily and unrealistically early”. This has fatal consequences, as their premature introduction will not be understood, badly taught and could be left until later without causing problems. Rigour in this sense is merely a rush to failure.
Too vague
In Key stage 3 “too many things are left implicit”. This is a point he makes time and time again in his 56 page critique. The lack of structure and detail will mean inadequate teaching and the rote learning of concepts that need to be ‘understood’ for later progress. This lack of clarity and guidance is what leads to learners’ failing to cross the many conceptual chasms that await them in early maths.
Practical work
One of the greatest failings of our system is the abject failure to teach using practical work and physical apparatus. It leads to often dry, repetitive teaching and failure by learners to grasp ideas and methods. Gardiner points to an “eerie silence about practical work relating to volume and capacity, and activities designed to establish an internal yardstick that would allow pupils to estimate everyday weights with tolerable accuracy”. I couldn’t agree more. Here we go again – chalk, talk and fail.
Maths howler
He repeatedly points to the unfortunate requirement for pupils to “calculate mathematical statements”. This is a fundamental error, often seen in maths content, where formulae are wrongly assumed to be ‘solved’ and statements ‘calculated'. The bottom line is that the document has “clearly not been proof-read, uses key words incorrectly, or includes avoidable howlers”.

I could go on... but the task is a little depressing.
Don’t imagine for one minute that this is purely about maths, it’s about ideology, stubbornness and a belief that if only young people were taught as I was taught, all would be well with the world. What’s sad is that we’re condemning yet another generation to premature ideas and poor teaching, where learners will either fail to cross the many cognitive chasms that Gardiner outlines or have to learn stuff that is quite simply irrelevant. In my view this has to be solved, not by leaving it to the vagaries of variable teaching but to acpture good maths teaching in a rigorous adaptive learning system, that implicitly knows and tracks the learner's progress using smart software. As we can see from this attempt at a curriclum definition, maths is too important to be left to error-prone humans!

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