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THIS PAGE is nearly a microcosm of the Internet: it contains nostalgia, mild intellectual elitism, and a sort of call to arms all in one page instead of spread all over the place! But I hope that, at least to some extent, it also embodies that other important theme of the Internet: the lone voice crying out for common sense...

Primary Maths: Where did the spirit of Adventure go?

“Divide fractions? I can’t divide fractions!” wailed Jill.
“You don’t have to,” said Clarence, “you can turn them upside-down and multiply.”

THE presence of Clarence is a giveaway that this is an excerpt from Book 5: Clarence wears glasses, and only crops up in the last book in the Maths Adventure series, where some really tricky concepts are to be explained.
I can’t remember the other “presenters’” names (if anyone can, please email me) but I certainly remember Maths Adventure itself. It was the maths book I used when I was a pupil at Alsager County Primary School on Bankside Court -- not that this means much, as I believe the school has since changed (a) its maths textbook (b) its name and (c) its premises.
Changing premises must have made a lot of sense (the Bankside Court buildings were, er, not great, though the grounds [“Down the Bank”] were brill); expanding the name makes some sense too (there are several other state primaries in Alsager); but I can only think of one reason to change from Maths Adventure. It was too much fun and must have turned a disproportionate number of its followers into mathematicians. Perhaps a concerted outcry was made by the Arts and Applied Science lobbies.
For Maths Adventure lived up to its name. Often (though not universally) primary school textbooks are an Adventure into knowledge for their followers; the best feature of Maths Adventure, though, was that it was an adventure into very genuine Maths.
As the quote at the top of this page shows, it wasn’t afraid to teach core arithmetical skills along the way. (Incidentally, please don’t draw from that one quote the inference that Maths Adventure was sexist. I don’t remember that it was, though surely even if it had been it would be easy to change.) But a lot of its pages were adventures into areas of mathematics which don’t get taught formally until well into secondary school -- and in some cases, far beyond that. I’ll pick two examples of this which I can still remember, but there were many -- and if you don’t believe me, try and get hold of a copy of Book 4 or 5 yourself! I went to a good secondary school, Alsager School, and in the first two years’ maths there encountered no concepts which had not been in Maths Adventure.
One example of very genuine maths was a series of pages about “number machines”, which were devices whereby, say, Jill could heave a large figure 4 into the feed hopper, and if the machine were an Adding Three machine, a figure 7 would emerge from the back end. Other sorts of simple machines performed the other basic arithmetic operations, and multi-stage machines produced by chaining these simple ones together were encountered too. For all the simple machines, pupils were invited to specify machines which would reverse their effects -- the opposite of an Adding Three machine is a Subtracting Three machine, and the opposite of a Subtracting From Ten machine is another Subtracting From Ten machine. And armed with this, pupils could construct “reversers” for the multi-stage machines as well, and work out what must have been heaved into a multi-stage machine to produce a given output.
This is, of course, the solution of linear equations. It’s algebra. But it’s algebra looked at from its theoretical underpinnings of functional theory and inverse functions; it’s algebra with no x’s in; it’s algebra for primary pupils, and it’s algebra that’s fun.
The other example I’ll reminisce about was just one page, on which were drawn three stone columns reaching up into some clouds (the graphic design of these books, incidentally, was as wonderful as the content). On one column was written 1, 4, 7 ... from the ground upwards; on the middle one, 2, 5, 8 ...; and on the third, 3, 6, 9 etc. The columns went about as far as the 50s before disappearing into the clouds. The exercises were actually pretty simple: they were all about taking numbers from two columns, adding or multiplying them, and seeing what column you ended up in.
And what’s this? Well, it’s group theory. It’s about the closure, or not, of infinite groups under certain operators. This is strong stuff! Its “proper place” is university-level maths, but here it is presented so that primary pupils can do it: presented so it’s an adventure.
At the time, of course, I had no sense that it was called group theory; not even any sense that it might be important; quite possibly whoever was teaching me then had no idea what it was about either. But years later, when I encountered group theory, I was able to say to myself, as it were, “Ah! This is all about infinitely tall columns with multiples of three written on them!” and gain an immediate head start over friends who’d never had these concepts seeded into them at that early age.
Which, sadly, was almost all my friends. When I was 14 I moved away from Alsager, and since then I don’t think I’ve ever met anyone who was taught maths from Maths Adventure. I can only wonder why not.
A search on Alta Vista for references to a textbook called Maths Adventure turns up nothing, as does a search for its authors’ names (one of which was so unusual and delicious to me at the time that I can still recall them both: Jan Stanfield and Anna Potworowska). Or rather, the searches turned up nothing before I’d written this page!
Does anyone still use Maths Adventure? And if not, why not? Are there really even better age 7-11 primary maths textbooks out there? Or, as I rather fear, has the prevailing mood become that it’s not worth sowing the seeds of university pure mathematics in a mixed-ability primary class of whom, on average, only one or two will ever need to know about group theory*?
If so, this is a shame, and can only be a decision based on a lingering feeling that mathematics can never be fun in its own right, that it is a tool and there is no beauty or Adventure there. The elegance and finality with which Maths Adventure dismissed this argument is perhaps what has lasted in my mind from it the best.

-- Peter Hartley, 7th March 1996
Alumnus of Alsager County Primary School, 1976-1983


* This proportion was actually a guess. If anyone has real statistics as to what proportion of the English population gets Maths, Computing or Physics degrees, let me know. At least two from my primary school class of 20ish did, and I lost touch with several more who might have, but this may have been an exceptional case. But then again, perhaps it was an exceptional case because of Maths Adventure...

Ten years on

Since I first wrote this page, just over a decade ago, it’s caused me a slow but steady stream of email correspondence. People from all over the UK have written to me to say they too enjoyed the books, and some (homeschoolers and teachers) have asked if I know where they can be found second-hand. I don’t; a web search conducted nowadays using Google shows Amazon listings for some of them, but they’re deeply, deeply out-of-print.
Pleasingly, one primary-school teacher emailed me to reassure me that, even though the books themselves were no longer used at her school, the spirit behind them was very much alive and informed the way they still teach maths there. She also recommended an organisation called the Association of Teachers of Mathematics for those interested in good and inventive teaching of maths.
Several correspondents wrote to say they knew, or had met, the authors, and filled in a bit of the back-story: Jan (the writer) and Anna (the illustrator) were brother and sister, and although Anna has sadly passed away since the days of Maths Adventure, Jan is still around, and, among other things, runs a foundation and web site celebrating the work of his late father, the Polish artist Piotr Potworowski. “I can assure you,” wrote one correspondent, “that life for everyone in Jan and Anna’s world was as delicious and exciting as the books”.
Most pleasingly of all, I recently had an email from Jan (Stanfield) Potworowski himself, with appreciative words for the page (I’m guessing maths textbook authors don’t often get fan-sites) and including the snippet that he’s still keeping his hand in, preparing (at the time of writing) a workshop for maths teachers in his native Poland.

-- Peter Hartley, 24th October 2006

All Rites Reversed -- Copy What You Like