The Non-Constant Gardner

Recent events – the bastardisation of Roald Dahl and the burning of history – reminded me of a post I had planned long ago, on Martin Gardner and school libraries. It is often said that Martin Gardner is responsible for creating more mathematicians than anybody else. As the fable goes, a bright-eyed teenager stumbles upon a collection of Gardner’s mathematical writing in the school library, they read away on weird topologies and the Game of Life and so on, they are entranced and another mathematician is born. The fable is not true, but it is true enough.

Gardner’s Mathematical Games column,  which ran for decades in Scientific American, is undeniably great. A collection of Gardner columns is still the default present for a young mathsy person. (Go for the Colossal, which is incredible value.) But what of the fable? It sort of happened to me.

I remember, when 15 or something, stumbling upon a collection of Gardner’s columns in the Macleod High School library. I remember spending a week-end making hexaflexagons, and reading other columns about things I’d never heard of or imagined. It was great stuff. But did it turn me into a mathematician? Nah. I’d long ago figured out that maths was the one thing I didn’t suck at. Gardner showed me where I was going, and perhaps got me moving there a little quicker, but he didn’t change my direction.

I am sure my experience is much more common than the storybook fable. Kids who are open to the mathematical wonders that Gardner offers are already well on their way to being mathematicians. But of course that doesn’t diminish the value of Gardner to these kids. Which is why the disappearance of Gardner is so depressing.

About a decade ago, the Evil Mathologer and I were invited to talk to teachers at a little maths day, for seven schools in inner Melbourne. It was around that time that I was beginning my transition from Jekyll to Hyde, and I decided to engage in some gentle stirring.

Before the talk, I contacted the seven school libraries to find out how many books by Gardner each library held. In total, there were eleven; not too bad. Except, one library had six Gardners.

That left five Gardners for six libraries. Thus, by the Not-Enough-Pigeons Principle, one of the libraries possessed no Gardners. (Nervous laughter.) As it turned out, there were two:

Undoubtedly, things have only gotten worse. The mathematics teachers a decade ago were at least accepting that their school library should hold such books. The teachers could have argued, correctly, that few of their students read anything, let alone on mathematics. But still, the feeling then was that such books should at least be on offer. But now? More and more, the issue is not that the students don’t read but that the teachers don’t read. It is a fair bet that the majority of current mathematics teachers have never heard of Martin Gardner. The percentage who have read anything by Gardner would be small, and is vanishing.

Of course Gardner is not everything, other things are available now, and they might be better. Except, they are not. Whenever I am at a school, I make an effort to check out the library to see what mathematics is on offer. Except for throwback schools such as Our Ladies for Perpetual Properness, the results are almost always depressing. There might be a decent or semi-decent popularisation or two, but rarely a Gardner, and the majority are glossy nothings: books designed for people who don’t want to read.

And yes, there is more than reading now, with the many videos from the Evil Mathologer and his friends. Which is the point: kids are no longer reading, they are watching. And the teachers who no longer read are encouraging the kids to watch rather than read. And watching is not the same: it is way, way worse. Kids are watching amazing things but, even when the videos are done very well, the kids are almost never understanding these amazing things in any solid manner. Worse, it is anti-teaching because the kids are tricked into thinking they understand when they do not: to then teach them means first undoing what they “know” so they can pay attention and learn. That’s not even counting when the video gang get things horribly wrong and then refuse to take responsibility for it.

Of course one can argue that it’s better now, because we have both Gardner and (non-horrible) Mathologer: kids can choose. The argument is bad, and wrong. The argument is bad because it doesn’t negate the fact that for many kids the maths videos are doing more harm than good. The argument is wrong because, as Neil Postman kept hammering, every technology has winners and losers. Here, videos are not companioning books, they are supplanting books. Gardner is the loser. We are the losers.

19 Replies to “The Non-Constant Gardner”

  1. A quick comment and a question:

    Library books are purchased (and sometimes discarded) by librarians. In schools, these are never (show me an example and I will change “never” to “rarely”) people who care about Mathematics.

    So what can Mathematics teachers do about this? I’m being serious. If we buy books on our own budgets, they pretty quickly get given back to us to make room for the new books. All ideas welcome.

        1. It will almost certainly do a lot of good. Librarians may be stupid enough to think they know when to throw out a history book, but they are very unlikely to claim any expertise on maths books.

    1. Hi Red Five – in my government/state school we can ask for books to be purchased (from the maths budget). I even got a copy of Oliver Byrnes’ version of Euclid purchased – just because it’s so pretty. And before my arrival there were nice books like Godel Escher Bach on the shelves too – and it is still there! Although, I just noticed that Martin Garnder is not on the shelves at school…
      In my experience at this school, the maths team gets asked before maths books get removed from the shelves

  2. When I was defending my PhD, the examiner pointed out that I have several old references from 1928, 1934, 1936, 1939 and even 1901. He said he was surprised to see those while many new articles and books were written. I mentioned to him that many contemporary authors take too many things for granted without explaining the context that led to the development of mathematical methods. I told him learning from the development context is important for better understanding and providing insight leading to further improvements. He actually agreed with me, and I passed my viva 🙂 Yes, Gardner’s books are very good.

  3. It seems like a good idiot detector question particularly for a librarian or any teacher – Do you think kids need to be encouraged to read more or to watch more videos?

    Any waffling on possible merits of better videos indicates an idiot who doesn’t understand the problem of our lazy brains and the merits of being able to control the pace when reading.

  4. At my school, which is a government 7-10 school in an area that is not at all prosperous, the staff in the library are very keen to get more books on mathematics. In response to their requests, I donated a fair number of suitable books this year on mathematics and chess; some came from my own collection, others I bought specifically for the library. The library staff collect statistics on borrowing patterns – I assisted with the analysis of last year’s data – and, in light of last year’s data, they are keen to promote reading books. For example, there is a book club that meets every week in the library and there are additional incentives. The library seems to be well used at lunch time. Good collaboration with the library staff seems to help the cause.

  5. Marty,

    I have managed to get Borondoora library Hawthorn to try to purchase a copy of a couple of reasonable texts aimed at engaging secondary students into mathematics

    They use Readings as a book buyer but have had difficulty sourcing the texts?!

    Do you have any spares in your collection To fast track their order?

    Steve R

    1. That’s very funny, and flattering, and a little silly. Burkard’s and my books are hardly in the same league. But if you email me I’m happy to discuss.

      1. Marti

        Engaging for todays students nevertheless IMO

        We used to get mathematical pi 4 times a year in England in the 70s which was not as good as Martin Gardner’s scientific American articles either but still readable

        Steve R

      1. Thanks, Dr. M. I know Rademacher was interested in such issues (and I know Rademacher’s Theorem …), but I haven’t looked at that book.

    2. SteveR: You might check whether the library accepts donations. Many libraries no longer accept donations.

      1. SteveR: I now occurs to me that you were just after a source rather than offering to donate the books. bookdepository works for me.

      2. TM,

        The library agreed to acquire the texts 6 months ago from AMS but their supplier has let them down.

        Steve R

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