Posted by: Alexandre Borovik | May 7, 2011

Some random thoughts about ICT in mathematics teaching

Here are some random thoughts prepared for discussion in some mailing list but never used. I forgot, and have no time to check what was the igniting post of the discussion, so simply publish my stuff here.

It is a number of questions to proponents of unrestrained  use of Information and Communication Technology in teaching mathematics.

  1. I heard on BBC that there are now more mobile phones in the world than toothbrushes. Each of these phones contains more mathematics, in form of various algorithms implemented at hardware and software level, than graduates of a British universities learn in 3 years of the study for a BSc in mathematics — and in many case, mathematics involved is too complex to be part of a  BSc degree. In some sense, 2 billion mobile phone users in the world use very sophisticated mathematics — but why should they learn it?
  2. In particular, most mobile phones have a calculator, and most users are not aware of its existence. If a mobile phone has Internet connection, the user can go to http://integrals.wolfram.com and evaluate, in seconds, any integral which can be evaluated in elementary functions, and much beyond that — I just tried integral of (1+x^2)^(1/3) and got, as I inspected, an answer involving hypergeometric functions.
  3. I remember using this simile at least 15 years ago: ICT in mathematics teaching can be best compared with a computer simulation of a slide rule: it could be sleek, efficient — and absolutely pointless. Have a look at http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html — it is fully functional interactive online slide rule. If interconnected with a grading module, how useful this Javascript applet would be in 1950-s!
  4. Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without a human’s participation?
  5. Would you agree that ICT is very good indeed at “teaching to test”, and in that sense its efficiency could and should be measured? But would you also agree that “teaching to test” is the cancer of mathematics education?
  6. But you would of course agree that the core content of mathematics, its heart and soul, cannot be done by a computer. How would you teach THIS mathematics?
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Responses

  1. But you would of course agree that the core content of music, its heart and soul, cannot be done by a computer. How would you teach THIS music?

    What you say seems to contradict your earlier post “Counterintuitive outcomes of technology”.

    Replace ‘mathematics’ with ‘music’, and see that all your arguments collapse:
    of course computers cannot do music as humans do, and
    of course computers can teach a human a lot about music. Computers can do so
    by providing musically rich, interactive environment, training one’s ear and voice, e.g.
    by presenting a child with slightly modified interpretations, graphical representations
    of sound, comparing your singing with that of a recorded tune, etc.
    (and, by the way, teaching of music, e.g. beats, teaches fractions;
    this has been done).

    Computers can be used to teach mathematics in a similar way, by providing
    a mathematically rich environment. This is perhaps harder to do, but I think
    this can be done. Take a football match and record the speeds
    of all the players, their derivatives etc. Let children develop their intuition by
    playing with examples of finite groups and movements of R3 bodies.
    Explain ‘length’, ‘area’ and ‘volume’ and their additivity and interaction
    by a computer game where these are important, etc.

    Unfortunately, I would guess that way is very different from what ICT
    proponents propose.

    Computers

    Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without a human’s participation?
    Would you agree that ICT is very good indeed at “teaching to test”, and in that sense its efficiency could and should be measured? But would you also agree that “teaching to test” is the cancer of mathematics education?
    But you would of course agree that the core content of mathematics, its heart and soul, cannot be done by a computer. How would you teach THIS mathematics?

  2. As a response, I strongly recommend to take the book The Art of Piano Playing by Heinrich Neuhaus and substitute in it “music” by “mathematics”. In my opinion, the book should be compulsory reading for every researcher in mathematics educations. And perhaps even for every teacher of mathematics.


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