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.
- 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?
- 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.
- 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?