수학 교육과 수학의 역사 활용
- The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.
학생들의 사고 방식을 종합적인 것으로 만드는 또 하나의 방법은 수학의 역사를 사용하는 것인데, 그 수학사는 단순한 날짜나 인명의 나열이 아니라, 학습 과제가 되고 있는 각각의 주제를 흥미 있는 대상으로 연구하게 만든 당시의 일반적 사상 조류의 설명이 되도록 꾸며져야 한다.
알프레드 노스 화이트헤드, 교육의 목적 186p
- The Unique Effects of Including History in College Algebraby G. W. Hagerty, S. Smith, D. Goodwin
- Felix Klein,Elementary Mathematics from an Advanced Standpoint, Dover reprint, 1945, Vol. 1, p. 268)
"In concluding this discussion of the theory of assemblages [sets] we must again put the question which accompanies all of our lectures: How much of this can one use in the schools? From the standpoint of mathematical pedagogy, we must of course protest against putting such abstract and difficult things before the pupils too early. In order to give precise expression to my own view on this point, I should like to bring forward the biogenetic fundamental law, according to which the individual in his development goes through, in an abridged series, all the stages in the development of the species. Such thoughts have become today part and parcel of the general culture of everybody. Now, I think that instruction in mathematics, as well as in everything else, should follow this law, at least in general. Taking into account the native ability of youth, instruction should guide it slowly to higher ideas, and finally to abstract formulations, and in doing this it should follow the same road along which the human race has striven from its naive original state to higher forms of knowledge. It is necessary to formulate this principle frequently, for there are always people who, after the fashion of the medieval scholastics, begin their instruction with the most general ideas, defending this method as the only scientific one. And yet this justification is based on anything but truth. To instruct scientifically can only mean to induce the person to think scientifically, but by no means to confront him, from the beginning, with cold scientifically polished systematics".
"An essential obstacle to the spreading of such a natural and truly scientific method of instruction is the lack of historical knowledge which so often makes itself felt. In order to combat this, I have made a point of introducing historical remarks into my presentation. By doing this I trust I have: made it clear to you how slowly all mathematical ideas have come into being, how they have nearly always appeared first in rather precursory form, and only after long development have crystallized into the definitive form so familiar in systematic presentation."