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The role of the computer in school mathematics

  • Address of the First International Congress on Mathematical Education
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References

  1. For an account of the effects on the training of engineers, see: ThwaitesB.: 1968, ‘The Second Century Papers: Looking Ahead in Aeronautics-3’, J.R.Ae. S. 72, 688, 275–284.

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  2. For a review of the probable impact of computers on the discipline of mathematics, see: Thwaites B.: 1967, ‘1984: Mathematics ⇔ Computers?’,Bull. Inst. Maths. Applics. 3, 6, 133–159.

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  3. The best book I know of, which looks into the relationship between the continuous and the discrete, is: LanczosC. 1961, Linear differential operators, Van Nostrand, London.

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  4. The London Mathematical Society held a conference in 1967 which startled many people by its revelations of how computers can help even the ‘purest’ of mathematics. The proceedings were written up as: Leach, J. (ed.): 1968, Computational problems in abstract algebra, Pergamon, Oxford.

  5. The two books Machine Intelligence I, 1967 (eds. Collins, N. L. and Mickie, D.), Machine Intelligence II, 1968 (eds. Dale, E. and Mickie, D.), Oliver and Boyd, Edinburgh, are compulsory reading for those who wish to glimpse the heuristic potentialities of computers.

  6. Much of the work on mathematical manipulation by computer is being done in the U.S.A. See, for example: (i) Gelernter, H.: 1959, ‘Realisation of a geometry-theorem proving machine’, in Proc. Int. Conf. on Information Processing 1959, UNESCO House, Paris, pp. 273–282. (ii) Martin, W.A.: 1964, Hash-coding functions of a complex variable. Massachusetts Institute of Technology Memor. MAC-M-165. (iii) Slagle, J. R.: 1961, A heuristic program that solves symbolic integration problems on freshman calculus, Symbolic Automatic Integrator (SAINT). Ph.D. Thesis, Massachusetts Institute of Technology. (iv) Moses, J.: 1966, Symbolic integration. Massachusetts Institute of Technology Memors. MAC-M-310 and MAC-M-327.

  7. I guess that the symbolism which is bound eventually to be agreed on a world-wide scale will be strongly influenced by the ideas of: IversonK. E.: 1962, A programming language, Wiley and Sons, New York. I heartily recommend another book by him which indicates a computer-approach to elementary mathematics: Iverson, K. E.: 1966, Elementary functions: an algorithmic treatment, Science Research Associates, Chicago.

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  8. An account of Russian developments is given in: ThwaitesB.: 1968, ‘Mathematical Education in Russian Schools’, Math. Gaz. 52, 382, 319–327.

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  9. Leaflets outlining the Project, and further details, may be obtained from the present author at Westfield College, London, N.W.3., England.

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  1. Bryan Thwaites
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Summary of address delivered to the First International Congress of Mathematical Education.

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Thwaites, B. The role of the computer in school mathematics. Educ Stud Math 2, 346–359 (1969). https://doi.org/10.1007/BF00303468

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