I Know I Am, But What Are You?

A while ago we had cause to meet with a school principal. The principal happened to have a PhD in mathematics education, and it was on that basis that they began the conversation: “As a fellow mathematician …”. It will come as no great surprise that our association with the principal ended soon after.

The principal was doubly wrong: no, of course they are not remotely a mathematician; but, neither are we. Once upon a time, yes, but not now. We are no longer seriously engaged in mathematical research, in trying to discover the facts and the nature of mathematical truth.

But, to the principal and the principle. Of course it doesn’t matter whatsoever if a principal is not a mathematician. What matters a great deal, however, is if a principal falsely imagines that they are. If a school principal does not understand what it means to be a mathematician then they cannot possibly understand what a mathematician might offer to their school, or to education in general.

Such a lack of understanding, an ignorance of what it means to think deeply about mathematics, is now endemic in Australian mathematics education. The consequence is that mathematicians are treated as inferior teachers and education academics, merely as weirdos with relevant training a proper subset of that of the education pros. The consequence is that clear and informed and deep mathematical thought is marginalised to the point of non-existence. The consequence is a pointless mathematics curriculum taught using painfully bad textbooks by poorly trained teachers and administered by organisations with no respect for or understanding of the nature of mathematical thought.

Mathematicians can be arrogant and annoying, and wrong. But mathematics education without the deep and continued involvement of good and serious mathematicians is pure insanity.

11 Replies to “I Know I Am, But What Are You?”

  1. In answer to “I know what I am, what are you” ~ You – Marty – might like this topical response…
    Well, “Aye” personally consider myself very definitely NOT to be a mathematician, yet…
    Not having a Ph.D, nor a background of teaching ~ has (“Aye” think) actually led me to insights that can only be deemed down to my ignorance of modern mathematical thinking…
    Your recent posting on BODMAS Versus USBB did tickle my own (very well developed) use of acronyms…
    In a soon to be published (planned for 23/9/2019, or more realistically ~ the likely date of 23/9/2020), “Aye” shall publish substantive analyses on the following subjects ~ all earnestly researched and pulled together under the nifty little acronym of ~ GO APE A CRAFTY FIRST…
    Goldbach’s Conjecture “snakily” ladderised…
    Origami’s linear roots empirically realised…
    Archimedes Cattle Problem actually visualised…
    Plimpton 322 tablet “summarily” exercised…
    Euler’s perfect cuboid unwisely publicised…
    ABC Conjecture logarithmically parameterised…
    Collatz Conjecture synthetically “tree-o-lised”…
    Reimann-Descartes line tangibly normalised…
    Apollonian Circles “Roundly” criticised…
    Four Colour Theorem fractionally “Pascalised”…
    Twin Primes Conjecture asymptotically synchronised…
    YBC 7289 tablet belatedly sexagesimalised…
    Fermat’s Last Theorem famously marginalised…
    Invertible 3-Sat Logic ~ intractability theorised…
    RSA Algorithm 2B immediately excised…
    Susa tablet “T.H.I.C.K.O” analysed…
    Tell Dhiyabi immeasurably lionised..
    Such an acronym might seem to be just a contrivance ~ merely a clever play on words ~ but to me, it is much, much more…
    For any “anglophiles” out there – the odd one out is the one where what looks like an adverb, is actually a noun…Shall let you work that little puzzler for yourselves…
    This confirms my direction ~ the next step in my rather surreal world of Number Theory ~ to be to produce the modern equivalent (via computer) of Pascal’s Pascaline…
    Yup, “Aye” have to build a mechanism to mimic the mechanical “digit dial” of the Pascaline..
    Only this version has to enable very large numbers to be multiplied – of the order of 200 digits plus – and it has to be invertible, truly, it has to be able to factor numbers of 500 digits plus…
    “Aye” only learnt of the Pascaline quite recently – on 21/05/2019 to be precise – but ~ as a fataliste, “Aye” have to “go with the flow”…
    Now, what would you think your purpose in life is – waking up to the fact that you have (unplanned) – pursued the many and varied areas of Number Theory detailed by this very odd acronym…
    Having also been the owner of a completely “Off the shelf” Limited Company since 1988 – called Digitdial – you might (like me) just think of a simple word called destiny…
    Answers on a Postcard…

  2. I would like to start a disagreement on one and only one point Marty – namely that Mathematicians are treated as inferior teachers. I really don’t think they are; perhaps on the technicality that most high school students will never actually be taught by a Mathematician and therefore never form the belief.

    I was once taught by a number of really great Mathematicians who were excellent teachers:

    Hyam Rubenstein
    Kris Wysocki
    Tim Brown
    John Groves
    Derek Chan
    Plus several other “Mathematicians in training” who ran tutorials while completing their PhD.

    Are teachers on the whole poor Mathematicians? Yes, of course. Are Mathematicians bad teachers? My limited sample so far suggests not.

    As to everything else in your post… I’m free for a vodka whenever you are.

    1. Number 8, I wasn’t arguing that mathematicians are inferior teachers. I was arguing that they are *treated* as, regarded as, inferior teachers. And, although I was thinking of the school context, it is also commonly true in the university context you discuss. The guys you mention were/are strong mathematicians (at minimum) and great teachers, and I am very pleased you appreciated them. But not all academics are that strong, and your opinion is the minority.

      In current production line universities, there’s no shortage of 5th rate academics, and they are typically praised for their teaching exactly because they’re 5th rate academics. Most students like the way these lecturers dumb down, not realising such lecturers are too dumb to dumb up. Most students have no idea that they’re missing anything.

      In the school context, this is much, much worse. The ignorance of and the knee-jerk belief in the inferiority of mathematicians is standard. It was unquestionably true of the principal mentioned, but that principal is of no consequence (except to the ignorant parents who have expressed their pleasure that the school is being led by a “mathematician”.) The trouble is, the principal is exactly typical, entirely predictable.

      1. I’m not sure any students or parents have expressed such pleasure knowingly. Many things get said; some are based in fact, some are a convenient story. We both know this.

        I also know I never was, nor will be a Mathematician, but I do like to think I can appreciate good Mathematics (usually found online or in old textbooks – certainly not the prescribed VCE texts, some of the old HSC ones have some reasonable stuff) and the Mathematicians who came up with it.

        I’m sure my students grow tired of hearing me wax lyrical about Ramanujan, Euclid, Polya, Liebniz and others – I don’t care. Their contribution and perhaps more importantly, the “need” which their Mathematics satisfied, is essential if we are to have any hope that one day one or more of our students will venture a bit further down the Mathematics path than we did.

        Principals come and go, as do teachers (and sometimes schools). Mathematics tends to hang around a bit longer, on the whole. So I choose the side of Mathematics.

        And after speaking with some current university staff (not in the Education department) I do tend to agree to a large extent about the dumbing down, except for slightly different reasons.

        1. Number 8, there are mathematics teachers who have a sense of and appreciation of mathematics, and many will bring some such sense to the classroom. Even among such teachers, however, the sense of what a mathematician is and what he does, and thus what he can offer, can be limited. And, there is no shortage of mathematics teachers with no such sense.

          My reference above to pleased parents was not a hypothetical.

          1. It annoys me that someone with a Ph.D. in mathematics education would claim to be a mathematician. In my experience, that Ph.D. is usually based on research into the use of [insert technology] for teaching and learning mathematics, and this research is typically driven by an agenda ….

            I doubt that someone who has a Ph.D. in science education (physics, for example) would say that they were a physicist.

            But I have a question: Do you see a distinction between a professional mathematician (which I think is what your post is about) and an amateur mathematician? Is it possible that the Principal was the latter, but made the mistake of identifying themselves as the former (not understanding the distinction, if there is one)? (Or maybe the Principal was neither).

  3. Number 8, the answer is “no”. The familiarity of the expression “fellow mathematician” suggested much more than merely a shared interest.

  4. A group of grade 4 children on a school outing to a commercial tv network and was asked by the American host shortly after the Apollo 11 moon landing what they wanted to be when they ‘grew up’ . There were plenty of astronauts , train engineers and movie stars etc but only one of their party wanted to become a mathematician…

    When asked to define a mathematician I usually quote ‘ the black sheep in a Scottish field ‘ scenario when given to a physicist,engineer,mathematician…

    SteveR

    https://www-users.cs.york.ac.uk/susan/joke/3.htm

    1. Thanks, Steve. I’m not fussed that so few young children want to be mathematicians. Until one gets some sense of abstraction and generalisation, it’s hard to have any sense of what mathematicians might do. On the other hand, the fact that older children are taught such a warped form of mathematics is very depressing.

      The black sheep joke is very funny, even if mathematicians are usually too smug in the telling.

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