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    Búrigo, Elisabete Zardo 2018. Researching the History of Mathematics Education. p. 23.

    Tichá, Marie 2018. Modernizace vyučování matematice v letech 1965−1985. ORBIS SCHOLAE, Vol. 7, Issue. 1, p. 119.

    Simeonov, Emil 2016. Mathematical Cultures. p. 439.

    Vohns, Andreas 2016. Fundamental Ideas as a Guiding Category in Mathematics Education—Early Understandings, Developments in German-Speaking Countries and Relations to Subject Matter Didactics. Journal für Mathematik-Didaktik, Vol. 37, Issue. S1, p. 193.

    Solares, Armando and Kieran, Carolyn 2013. Articulating syntactic and numeric perspectives on equivalence: the case of rational expressions. Educational Studies in Mathematics, Vol. 84, Issue. 1, p. 115.

    Roscoe, Matt and Sriraman, Bharath 2011. A quantitative study of the effects of informal mathematics activities on the beliefs of preservice elementary school teachers. ZDM, Vol. 43, Issue. 4, p. 601.

    Nemirovsky, Ricardo Borba, Marcelo Dimattia, Cara Arzarello, Ferdinando Robutti, Ornella Schnepp, Marty Chazan, Daniel Rasmussen, Chris Olszewski, Jennifer Dost, Kevin Johnson, James L. Borba, Marcelo C. and Scheffer, Nilce Fatima 2004. PME Special Issue: Bodily Activity and Imagination in Mathematics Learning. Educational Studies in Mathematics, Vol. 57, Issue. 3, p. 303.

    Schweiger, Fritz 1992. Fundamentale Ideen. Eine geistesgeschichtliche Studie zur Mathematikdidaktik. Journal für Mathematik-Didaktik, Vol. 13, Issue. 2-3, p. 199.

    Ernest, Paul 1989. The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: a model. Journal of Education for Teaching, Vol. 15, Issue. 1, p. 13.

    Steinbring, Heinz 1985. Mathematische Begriffe in didaktischen Situationen: Das Beispiel der Wahrscheinlichkeit. Journal für Mathematik-Didaktik, Vol. 6, Issue. 2, p. 85.

  • Print publication year: 1973
  • Online publication date: September 2011

Modern mathematics: does it exist?


The future historian of mathematics will not fail to be amazed by the extent of the movement of the 1960s known as Modern Mathematics. This movement now appears to have reached its zenith, and the first signs of waning, a justifiably healthy reaction, are beginning to make themselves apparent. I should like, perhaps somewhat prematurely, to set forth in the manner of a balance sheet those things associated with this movement which should be retained, put in their proper place, or purely and simply eliminated. It is useless in such an issue to conceal the existence of preconceptions and of personal bias which cannot avoid influencing one's judgement. It is a question, not of knowledge nor of pedagogical technique, but of a field where the personal feelings of the mathematician cannot fail to play an essential role. Only dogmatic spirits (and they are not lacking among ‘modernists’) can believe that there is in these questions a truth capable of being logically established and before which one needs must bow. Consequently, I see this article as a ‘speech for the defence’ to be contributed to the debate and not a proof which one knows very well to be non-existent.

‘Modern Mathematics’ has a very complex origin and composition. One can say, broadly speaking, that it seeks the two fundamental objectives:

The pedagogical renewal of mathematics teaching

Exception is taken to the didacticism of traditional teaching, even its dogmatism, which is particularly evident – so one is assured – in the teaching of Euclidean geometry.

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Developments in Mathematical Education
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