The Beauty of Number

The  Treehorn  Express

Treehorn, immortalised by Florence Parry Heidi in The Shrinking of Treehorn, continues to be treated badly, together with his present-day school friends, to satisfy the greed of mega-rich test-publishers, the election prospects of compliant hench-pollies; and the ambitions of sycophantic, sciolist educators who provide immoral, destructive testing devices,  through sad, unfortunate, obedient schoolies, to small children who also do as they are told. Treehorn understands the shape of what they do, but not why they do it. He’d like to learn properly, but nobody cares about him.


Is it the End of the Beauty of Number?

A recent email from a primary-principal friend was composed upon his return from a meeting with fellow principals where modifications were being suggested for the administration of the national blanket testing scheme [called ‘Naplan’ in Australia, ‘National Standards’ in N.Z, ‘National Testing’ in the U.K.; and ‘NCLB’ in the U.S.A.] for mathematics. He seemed so disappointed, sad and angry that his fellow principals were working on ways to dilute the poison instead of planning to throw it out.  Stakeholders from academia trying to sanctify the measurement of ‘standards’ were there to lead the instruct/assess/analyse discussion ….and many principals co-operated.

Amongst other things in his lengthy letter, he said, “I’m left with this uneasy feeling that this pattern of instruction/assessment does not have its roots in established learning theories and that it reflects some other kind of approach that is akin to the ‘standards movement’ with its origins in the economic supply side of education ideology.

It sure doesn’t feel like anything I would consider examples of quality mathematics programs (carefully avoiding the jargon of ‘best practice’). I guess that I’ve developed my own feel and vision for mathematics over the 35+ years of my teaching career, and the things I heard today are clashing with this mindset. For the life of me, as a teacher who really enjoyed teaching mathematics, I can not see why in-depth ‘assessment’, and the like, is necessary for every area of mathematics. Exposing children to genuine real life [avoiding ‘authentic’ –ugh] opportunities to explore and use mathematics is much better.

The source of my irritation is the relentless talk about assessment being necessary as a lead-in to learning. The phrase ‘assessment to learn’ is a good example. It is a very deficit-focussed model indeed, and the underlying philosophy is that ‘achievement’ [how I hate that word] is measured and ‘deficiencies’ corrected.

To me, that is the wrong end of the horse. We should be feeding the horse with the highest quality nutrition, in the best possible living conditions and not waste our time ‘assessing’ what comes out. The tendency of principals to buy into this approach, regardless of their attitudes towards national blanket testing, suggests that they do not have an underlying knowledge of learning itself, on which to base their school’s teaching and learning. Alternatively, or equally, their view of education is very didactic and dependent on tight school control and class programs. I can think of no other reason why they would ask their teachers to spend so many hours of their valuable time ‘processing data’……

I’ve started reading a book I ordered from Amazon “A Measure of Failure: The Political Origins of Standardised Testing” by Mark J Garrison. I’m only as far as chapter 3, but already it is crystal clear that ‘standards’ serves a political purpose, and in Garrison’s opinion, the idea is to prove that schools are “failing” so that, in turn, ‘reform’ can be justified. By passively going along with ‘standards’ at any level, we are agreeing to this by default.

That’s my sound-off for today.”


Appreciating the analogy of the horse’s end, I replied: It’s such a shame that teachers, especially principals should get together to help duncanise the measurement of numeracy by revamping it instead of ceasing it… which they can arrange in a wink in Auustralia.   [You may have heard that U.S. Secretary Arne Duncan is softening things up in the US]

Why couldn’t we have entered the 21st century by treating Mathematics for what it is….a search for beauty and challenge through numbers and space; a journey of exploration; a conversation about  the wonder of number; the fun of solving exciting and challenging problems; a chance to calculate; a chance to learn. Mathematics is, after all, the essential element of so many other things, especially art, music, space, architecture, almost everything. Maths is one of the most beautiful of things we do.

Isn’t it sad that those civilisations that invented and developed base ten, because we had ten fingers, into the world of wonderment should go and invent papyrus as well; and ruin it all?

I reckon that your Vancouver mate David Wees [ ] has the right idea pleading for the ‘real world’ to be at the centre of it all mathematics curricula. It   must. surely!…Amen. Whoever invented the first written test of mathematics and its parts should be resurrected and charged with extreme cruelty and perverse destruction of social enjoyment. This doofus needs to be treated to very slow, excruciating, painful, special treatment. His legacy over the years has caused eras of enormous pain, stress and social destruction of children’s lives. which societies have had to wear as a consequence.

There is so much joy and excitement in number that it needs to be shared even more widely than it is; not used as a disgusting kill-joy instrument.

Ever wondered how Fibonacci must have felt to discover what he did ?  He needs…as do other mathematicians of his ilk … to be venerated in the same way that great saints are. The history of maths, its heroes and the details of the discoveries is so remarkable, so exciting….so neglected.  Moon landings and the like are almost non-events by comparison with  such discoveries.

What would we do to some-one who destroyed all the works of art in The Louvre, British, Guggenheim, Tate, Vatican, Smithsonian art galleries and museums ?  Our test mongers are doing something far worse to a beautiful thing –mathematics. Disagree?


 Yes, we are well on the way to ruining the challenges and progress of the 21st century, thanks to our political masters in at least four different countries. As Fred asks, “Who would have thought that, behind the brash, bullying, domineering managerial attitude of the 1990s,  were brash, bullying, domineering dictators?”



[Drop the ‘s’ if you are American]

*A surgeon, mathematician and a politician were discussing the origin of the human race. The surgeon claimed that his profession created the species, “Who else could have created Eve from Adam’s ribs?”  The mathematician, however, maintained that, before Adam and Eve, there was chaos; and God needed a mathematician to explain how to use chaos theory. “Ha!” said the politician, “Who do you think are the only ones who can create chaos?’”

* The Daily News printed an article suggesting that, following a maths test, half of the government members had been shown to be stupid. The government was incensed and  called for a retraction. The Daily News willingly printed an apology and retraction, stating that half of the government members were not stupid.

* The MySchool site, revealing the results of a Naplan maths test, showed that 5 out of 4 pupils had trouble with fractions.

* A tee-shirt at the Ekka [Brisbane Show] this week showed : “SUPPORT NAPLAN. It’s hot.” . On the reverse side it showed. “It’s NAPALM incorrectly spelt!”


‘The Treehorn Express” is sent to 131 friends and colleagues in the U.K., U.S.A., N.Z. and Australia.  If you have a contact who might like to receive it, please send the email address to me.

Phil Cullen

41 Cominan Avenue

Banora Point

Australia 2486

07 5524 6443

Please pass this message along to as many as possible. Give our Aussie children a fair go. Give them the freedom to learn.

Stop Naplan.


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