Zoltán Dienes, Dr.

Born in Budapest, Hungary in 1916 from Hungarian parents: Paul Dienes and Valeria Geiger, the brother of Gedeon Dienes. Schooling in Hungary, Paris and England, matriculating from Dartington Hall School, Devon, England in 1934. Studied Latin, German, Pure and Applied Mathematics 1934-37 Obtained B.A. degree with Honours in 1937 from the University of London, Ph.D. degree from the University of London in 1939, thesis on "Constructivist Foundations of Mathematics According to Borel and Brouwer."
He married a very young Tessa...Mina Joyce Cooke as registered at birth, They had five children: Corin - now Jasmine, Nigel, Jancis, Sorrel - now Sarah, Bruce and a great number of grandchildren and great-grandchildren.

After school teaching experience at Highgate School and Dartington Hall School and after teaching at the Universities of Southampton, Sheffield, Manchester and Leicester he became research fellow at the Center for Cognitive Studies at Harvard University 1960-61, associate professor in Psychology at Adelaide University (Australia)1961-64 after which he was appointed director of the Psychomathematics Research Centre in Sherbrooke Quebec 1964 - 1975. After the Centre was closed down for political reasons, he worked for native education as Professor at Brandon University 1975-78.

During this time as well as in later years (1978-80) he acted as mathematics consultant in several countries (Italy, Germany, Hungary, New Guinea, United States) and for different organizations (OEEC,Unesco) all over the world. He also founded the International Study Group for Mathematics Learning (ISGML) in 1964 (Please refer to Bulletin, Vol. 1, No. 1, December 1962, describing the initial ISGML objectives). The objectives of the ISGML, as stated for its 1969 official incorporation, are the following:
A: To investigate and research the processes of learning mathematics, languages, art and allied disciplines;
B: To apply the results of this research to the educational process in these respective fields;
C: To hold international conferences to discuss, plan and promote the above research and their educational applications.
When the Sherbrooke Research Centre was closed, the temporary headquarters of the ISGML were moved to London, England, and the Vice-President, John Williams, of Ealing Technical College, St. Mary's Road, London, W.5. became acting president.
In the 1980s and at the start of the 1990s beside working in Italy, Spain USA,Hawai Greece and Hungary he returned to Canada and later he was associated with Acadia University in Wolfville, Nova Scotia, being elected a Research Associate by the Psychology Department. He lives now in Wolfville with his daughter Sarah.....

Here is what he says, in his own words, of the main essence of his life's work:
My interest in mathematics goes back to childhood and early youth. Along with most mathematicians, I felt, quite early, the fascination of the purely abstract. At quite an early stage, a fascinating problem seemed to me why mathematicians were divided, if rather unevenly, between formalists and intuitionists. This interest found expression in my doctoral thesis in which I tried to compare Borel's mathematical realism with Brouwer's intuitionism.

Later, in a more objective mood, I tried to put a price tag on mathematical notions and theorems through analyzing the assumptions in terms of quantifiers and their uses which had to be made to define these notions or to prove these theorems. I spoke about this work at Turin University in 1951 and published my considerations in the reports of the Turin Mathematical Seminar.

Some time after this, as I became interested in the problem of why mathematics was found difficult by most people, I wondered whether the difficulties in the foundations of mathematics had not something to do with the difficulties that children experienced in understanding mathematics.
I chose the age of ten as a reasonable stable period of childhood and ran a concept formation experiment on a representative sample. I first reported the results of this experiment at the Psychology Institute in Florence, Italy, and published my preliminary findings in the article, Sulla Relazione Fra Ia Formazione dei Concelti Astratti e Ia Struttura Della Personalitd, 1957, Bollettino de Psicologia e Sociologia Applicata, Firenze, Italy. I tried, in a small way, to reorganize mathematical work in some classrooms, turning the classrooms into laboratories of discovery and construction, using specially designed materials which later developed into the now well-known multi-base and algebraic materials. It was impossible to contain the experiment as a psychological one because of its immediate and unqualified success. The experiment turned into a mathematics project throughout the County of Leicester, England. During this time, 1958-59, I worked out, through practical ways, some principles which should account for the success observed. These were written up and published in the article, The Formation of Mathematical Concepts in Children Through Experience, 1959, Educational Research, London, England. With the results of previous experimental work done in England, I proceeded to Australia to work in the psychology department of Malcolm Jeeves. This time we tried to dissect our problem into some of its identifiable component parts. We observed the learning of structure both in classroom situations and individually. The individual experiments were designed so that subjects were obliged to externalize their thinking behavior so that it could be accurately observed and noted. The Report of the first round of this work is contained in the book, Thinking in Structures, 1965.

Other experiments followed on a larger scale largely confirming the results of the first round and generating further hypotheses for further experiments. The work is reported in, The Effects of Structural Relations on Transfer, 1966.

Another very interesting chapter in these attempts is the introduction of mathematics learning to the native schools in Papua New Guinea. The first attempts were sketchy but soon there was a team of about a dozen enthusiastic operators, coordinated by myself as chief consultant, whose job was to bring insightful mathematics learning to the bush.

The eventual result of these efforts was the formation of a group, comprising teachers from Government as well as Mission schools, with whom I met regularly, eventually several times a year, to work out a mathematics program suitably adapted to the needs of the native children. During these investigations it transpired that in all cases real mathematics learning, as opposed to drill whose purpose is the reproduction of certain responses, given certain stimulus situations, involves the use of creativity. The Sherbrooke work touched upon different forms of artistic expression. Preliminary field trials were conducted to ascertain the relationships between abstraction, generalization, representation, symbolization and formalization. Some tests were developed to test the important side-effects of mathematics learning, such as increased learning ability, tendency toward structuring, performance in structural thinking, preference for complexity and the like. In my old age I have also contributed to a family anthology of poems, in which there are poems written by three generations of my family, including my wife Tessa and some of my grandchildren. I also published a whole cycle of poems written by myself: "Calls from the past" in which I touch on the problems of mathematics learning, as well as use the medium of poetry to describe some salient events in my past.

Finally, in the May 1999 number of the Canadian Friend I have an article in the form of an open letter entitled: "To be or not to be a Christian" in which I raise some fundamental questions about life and of what there might be afterwards.

Z.P. Dienes published several books and many articles in many languages in the field of teaching mathematics, in psychology and in pedagogy and made also films about his method.
We just mention his most interesting and epoch-making work, introduced by Hewrbert Read, Building up Mathematics, Hutchinson & Co., London,
French: Construction des mathematiques, Presses Universitaires de France, 108 Boulevard Saint¬Germain, Paris,
German: Aufbau der Mathematik, Herder Verlag.
Italian: Constuiamo Ia matematica, O.S.1970 Also available now in Spanish, Portuguese
Hungarian: Épitsük fel a matematikát by Segitünk Ha Lehet publisher.

Ha managed to put together an autobiography Memoires of a Mawerick mathematician Zoltan Paul Dienes. in 1999 Upfront Publishing, Leicestershire, England Játék az életem in Hungarian, SHL, Hungary A French version is in preparation

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