Today's maths PISA results are predictable in the successes that many Asian countries show and the mediocrity of many of the traditional Western countries--like the UK.
I believe PISA is meticulous in conducting its tests and reflects a good evaluation of standards of today's maths education. And yet I think if countries like the UK simply try to climb up today's PISA assessment, they'd be doing the wrong thing.
The playing field of today's maths education is restricted to manual calculating procedures allied to the limited problem-solving that they can support. Today's mainstream real-world maths is much broader: applying the process of maths--using the best computational mechanisation--to much harder problems. The skills it requires are rather different, but if anything more conceptual, more intellectual and definitely more creative.
That's a playing field on which Brits and the like could do relatively much better than on the playing field of procedural hand-calculating. It's a playing field on which drilling kids for hours a day on their algebra isn't going to win.
Now let's be clear. I'm not saying that that's universally what's happening in Asia. In fact there's great innovation in the process of schooling and particularly the learning of maths in the region (famously Singapore). Nor am I in any way writing off Asian problem-solving ability which I think, correctly and creatively trained, could be top-notch too. What I am saying is that if Brits really put their minds to modern computer-based maths, they are just as able to compete with their Asian counterparts--whereas I don't think culturally we will do so well at drilling the needlessly pre-abstracted and often irrelevant current subject. I think that non-conformity, creativeness and looking around the rules is key to British (and many other Western) cultures and a great competitive strength if tethered appropriately, opposite to the cultural imperatives present in many of the countries performing well in today's maths PISA test, countries that may struggle to imbue such charactertistics.
And crucially, it's many of these abilities and the computer-based maths subject we desperately need in the workplace, and in life--not for the most part the subject we're largely failing to succeed at of hand-calculating procedures. (My recent talk opening the CBM summit at UNICEF details the argument).
A central question in all this is precisely what outcomes we wish for our students after their years of maths study? This is a question which we have been addressing from first principles in formulating CBM, unencumbered by constraints PISA necessarily has of not going too far ahead of today's curriculum and needing accurate quantitative assessment of it. For the brave, here is an early (hard to digest) draft which spans 10 dimensions. I won't detail all the ideas here but point out the importance of confidence, knowing how to operationally manage the application of maths, and understanding the separation between maths concepts (like significance) and use of a wide variety of specific tools (like a hypothesis test).
Intelligently ranking countries as PISA does is very helpful in pushing progress in education because succeeding at today's maths education or tomorrow's computer-based variety needs well-directed effort and focus and competition. But in the end, however well education is delivered, it must deliver the right subject.
Notice that our first CBM country Estonia is already high on PISA. They recognise that despite their achievements, they need to lead the change to maths. Actually, many of the countries near the top of today's rankings have been most active in pursuing the CBM approach.
Now the UK is doing well with Estonia in leading the coding education agenda. But why oh why does the UK government choose to separate coding in primary education from maths with which it should be so intertwined (as has the US)? They need to be closely associated as I pointed out last year. And it's particularly galling that they're not in the country where a mathematician invented the computer...
Playing badly on the wrong field is hardly smart. As the playing field shifts, let's lead the change, not be laggards at a game we can succeed well in.