On Simplicity, Silk Purses and Bad Teachers

What can one say in a teacher PD that can possibly make a difference? After having given about a thousand of these, we think the answer is obvious: bugger all.

Even if a teacher has a mind to get something from a PD session, a FIFO “expert” can offer little that won’t immediately get lost in the jungle chaos of real live teaching. And of course many teachers, either through exhaustion or lethargy or not-really-being-a-maths-teacher or all three, will not be very interested in the little of value that might be on offer. So, over the years, we have tried to adapt to this grim reality. We look to offer very little, while trying to make that very little offering as loud and as unignorable as possible. We yell. A lot.

Does this work? Probably not, not much. But at least the teachers may remember that we were there. And we’re comfortable that we have honestly tried to do what we could, to convey a very few clear and simple truths, and to indicate how important we regard those truths. And we get to yell.

This all came back to mind when preparing for our recent school visit. For the PD, our teacher host wanted us to focus upon the early secondary years, as the basis for later study at the senior years. Hence the title: Platform or Cliff? As to our message, it boiled down to delivering three truths, and a fourth, implicit truth:

1. Algebra is all

It goes without saying, says the man who has said it a thousand times, that the Australian mathematics curriculum contains a heavy surplus of swill, directed to be taught with swillish priorities, using swillish methods. All of this should and must be ignored. But the message here goes way beyond ignoring the swill. The important stuff is not of equal importance, and algebra is the most important by miles.

In the end, in modern mathematics, everything is an application of algebra. You need to know geometry to do geometry, and you need to know trig to do trig, and you need to know Y to do Y, but for all of them you also need, front and centre, algebra. For every Y, you also need x.

It follows that, first and foremost, Year 7 kids must be properly instructed and practised in the truths and techniques of algebra. Everything else can wait, and everything else must wait. Except, …

2. Year 7 students are already screwed

Well, not all of them. Those with Chinese mothers and those who did their primary years at Polo Grammar are typically OK. And there are a few other primary classrooms scattered around, which are bucking the trend, in which something of substance is presented and expected, rather than the endemic numeracy twaddle. But the norm is mathematical abnormality, meaning a sizeable fraction of incoming Year 7 students have already fallen off the cliff, or are barely holding on by their fingertips. All secondary maths teachers know this. They will not tell the parents, they will not write the stark truth in school reports, because they are instructed to lie and because they are scared to tell the truth. But they all know it.

Students haven’t a hope of mastering algebra if they do not begin with a solid grounding in arithmetic and, in particular, the mechanics and meaning of fractions. Many, many Year 7 students have no such grounding, implying they are primed and ready for the plummet ahead. This brutal truth tells secondary schools everything they need to know.

Nothing in Year 7 mathematics is remotely as important as repairing the damage of neglect done by primary schools,  rescuing as many of the kids as possible. Which means dragging the kids and their parents, kicking and screaming if required, into the world of proper, solid arithmetic. They must learn their friggin’ tables. They must learn the operations and how they work. Their calculators must be smashed and they must learn to compute in their head, quickly and accurately. They must learn to factorise and to to find common denominators. They must do hundreds of exercises, until all this arithmetic is natural and mechanical and painless. And if no one teaches or learns anything else for six months, so be it. It does not matter. Schools have a choice, to save the kids or to let them fall, and schools must accept what that choice implies.

3. Follow a solid, sensible textbook

Things must be simple. It is maddening for teachers to hunt for resources and it is maddening for other teachers to follow. Individually such resources are almost invariably second rate and collectively they are ill-fitting and confusing, with no consistent message or a manner of delivering it. What is required, almost all that is required, is a single solid sensible textbook.

Of course, short of buying a time machine and traveling back to 1980, how one obtains such a text is a difficult question. Obviously, the technicolour trash produced by the major publishers is entirely irrelevant. Are there sane alternatives? Possibly. The Catholics, who seem to be doing things better these days, are going with Ochre. There are texts from other countries and other eras. There is ICE-EM, which is snotty and boring, but solid.  No such outside-the-box solution is perfect, of course, and we’ll let readers debate the merits and drawbacks of the various possibilities. The principle, however, is clear: stick as much as possible as closely as possible to the single best possible resource.

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Silk purses

Those were the three messages of our PD, but there was a fourth, implicit message, left unsaid. All of the above is hard enough, if not impossible, but there is an obvious reason why this is so much harder than hard, less possible than impossible: lots of teachers really suck. Even with a clear goal and a clear plan and a solid text and plenty of allotted time, it is all doomed unless the teachers are there, in body and spirit, to make it work. Many teachers are not.

What to do? One can whine AMSI-like about out of field teachers, of course. Which does as much good as most of AMSI’s grandstanding. Sure, when you’re lumped with a know-nothing phys ed teacher or, worse, a knows-much-less-than-he-thinks science teacher, then yelling at the Principal is entirely appropriate. But she will have no magic wand to wave, to make mathematics teachers spontaneously appear. Moreover, it is not just OOF teachers. Many, many “qualified” mathematics teachers have little sense of what mathematics is, of what approach and ideas one should be trying to get across, or how. Every school, even Polo Grammar, has bad mathematics teachers. This is the reality and it will remain the reality for a long time.

It seems to us there are two natural and important things one can do about this reality. First, place the very bad teachers where they can do the least amount of damage. Which means, above all and always, keep bad teachers away from Year 7. No exceptions. Year 7 is where the school must be doing everything they can to save the students, to give as many as is humanly possible the opportunity to do serious mathematics in the years ahead. One must have the very best teachers assigned to the task.

Secondly, make it as easy as possible for the Year 7 teachers, and all teachers. One must keep in mind that “very best teachers available” may still not be the greatest teachers on the planet. The more planned and programmatic the syllabus and the lessons and the homework and the everything, the better everyone will do. Even the greatest teachers on the planet appreciate and benefit from coherent schemes, and for the mere mortal teachers it is absolutely essential. Which brings us back to having a solid textbook, or a solid electronic semi-text. It is essential.

That’s it. Those are the three plus one messages. And there is one final overarching principle: simplify.

One must make it all simple, in design and and in execution. The world is too complicated, education is too perverted, the idiots are too plentiful for anything else to have a shot at working.