Zoltán Pál Dienes


Quick Info

Born
11 September 1916
Budapest, Hungary
Died
11 January 2014
Wolfville, Nova Scotia, Canada

Summary
Zoltan Dienes was born in Hungary but spent much of his life in England and Canada. He was passionate about studying ways to teach mathematics to children and became a leading world expert carrying out numerous experiments in different countries. He was the author on many books on the subject.

Biography

Zoltán Pál Dienes is also known as Zoltan Paul Dienes but often simply as Zoltan Dienes. He was the son of the mathematician Paul Dienes, who has a biography in this archive, and his wife Valéria Anna Geiger (1879-1978). Paul and Valéria Dienes were married in December 1905 and had two children, Gedeon Dienes (born in Budapest on 16 December 1914) and Zoltán Pál Dienes, the subject of this biography. Gedeon Dienes learnt English, French, German, Swedish, Italian and Russian and became a secretary at the Foreign Office. He represented Hungary at the peace conference at the end of World War II. He later worked in the Publishing House of the Hungarian Academy of Sciences, then became interested in dance, writing articles in many languages and founding a Budapest dance company.

Béla Kun was a Hungarian Communist revolutionary and politician who, with Soviet support, led a successful coup d'état and proclaimed the Hungarian Soviet Republic following World War I. Zoltan's father was a strong supporter of Béla Kun and, after the Hungarian Soviet Republic was formed in March 1919, became the head of the committee appointed to run the University of Budapest and also took part in the organisation of the Marx-Engels Workers' University. In mid July 1919, the Romanian army attacked Hungary, and when the Red Army failed to come to their aid, Béla Ku fled the country. Counter-revolutionaries started to hunt down supporters of Béla Kun and execute them and Paul Dienes, Zoltan's father, escaped to Vienna. Zoltan, his mother Valéria, his brother Gedeon and Sari Chylinska, a close friend of Zoltan's father, joined Paul Dienes in Vienna in the autumn of 1920. Gedeon and Zoltan were put into a Montessori children's home where they could stay without paying. Zoltan wrote [14]:-
I distinctly remember my first night in the "Kinderheim". I lay on a small bed and sobbed and sobbed all night, not knowing what was happening, and one of the members of staff stayed with me all night and held my hand and tried to console me, of which I of course understood not a word, as it was all in German. But I did realise that she was trying to be kind, and I am eternally grateful for her patience with me on that first terrifying night.
Zoltan's parents decided to divorce and, after about a year in the Montessori children's home in Vienna, Zoltan, his brother and his mother, went to Nice in France where they lived in a commune run by Raymond Duncan, the brother of the dancer Isadora Duncan. The way the commune was run meant that children were common property of all the adults and Zoltan had to call his mother Valéria. "Mother" could not be used. All the children dressed in the same style ancient Greek clothes and could only go out of the commune as a unit with every child present. He had learnt German while in Vienna but now soon learned French. After several months, the commune moved from Nice to Paris. Zoltan learnt to read and write in the commune and wrote a weekly letter to his father Paul Dienes.

One day Valéria took Zoltan and Gedeon to the train station and they travelled by train to the Bavarian town of Oberammergau where they met Paul Dienes and his new wife Sari. By this time Paul Dienes was employed in Aberystwyth, in Wales, so they could buy things with English pounds while Germans struggled to cope with hyperinflation. When Paul and Sari Dienes went back to Wales, Valéria, Zoltan and Gedeon went to live with their grandmother in Pápa in Hungary. Zoltan attended primary school, first in Pápa and then in Budapest, before continuing his secondary education at the Piarista Gimnazium in Budapest. This Priarist school had been founded in 1717 but between 1913 and 1917 a large-scale construction had taken place, with new buildings housing the grammar school, the convent, the student house, and the provincial headquarters. Zoltan found mathematics easy [32]:-
Mathematics in school was mostly boring for him, he preferred solving differential equations under the desk. Fortunately his teacher did not punish him for his lack of attention, rather he decided to facilitate him through private discussions.
Zoltan would spend the summers with his father Paul and his wife Sari travelling in France, Germany, Hungary, Italy and Transylvania. This gave Zoltan two very different world views. His mother Valéria was a Roman Catholic so he was being educated at the Catholic Priarist school in Budapest. His father Paul, however, was a Communist. Interestingly, Zoltan did not end up as either a Roman Catholic or a Communist but would, for the greater part of his life, be an enthusiastic member of the Quakers.

In 1929 Paul Dienes had become a reader at Birkbeck College in the University of London. Around 1931, Zoltan came to England to join his father looking to continue his education in England. Although he spoke Hungarian, German, French and Italian, Zoltan had little knowledge of English. He recalls in [14] how he managed to overcame this obstacle:-
My father had a long telephone call with Bill Curry, the headmaster [of Dartington Hall School near Totnes in Devon], who said he would come and see me in two weeks' time. My father said to me, 'You have two weeks to learn English! Go to it!' ...

'Have you read anything in English?' asked Mr Curry. 'Yes, I am reading David Copperfield,' I answered in a very thick Hungarian accent. 'I have read about half of the book.' 'Tell me about it,' said Mr Curry. In somewhat broken English, I tried to give him an idea of the plot to the point where I was in the story. 'How long have you been studying English?' was the next query. 'I started two weeks ago,' I replied. At this point he indicated that the interview was at an end and went to talk with my father in another room. After he had departed, my father came towards me smiling, finding me already at work on David Copperfield, and informed me that I could indeed go to Dartington Hall School. So the continuation of my education was assured and I could look forward to some interesting times in one of the most avant-garde schools in the country.
Dartington Hall School had been founded in 1926 and it was a co-educational boarding school. The school was set up to have:-
... no corporal punishment, indeed no punishment at all; no prefects; no uniforms; no Officers' Training Corps; no segregation of the sexes; no compulsory games, compulsory religion or compulsory anything else, no more Latin, no more Greek; no competition; no jingoism.
Zoltan Dienes graduated from Dartington Hall School in 1934 having taken the Oxford and Cambridge Joint Board Examinations. Later that same year he entered University College, London, where he studied Latin, German, Pure Mathematics and Applied Mathematics. He graduated in 1937 with a B.A. with Honours in Pure and Applied Mathematics and continued to study for a Ph.D. He spoke about his early interest in mathematics, saying [9]:-
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.
His research was on the foundations of mathematics and he studied the logical and philosophical difficulties in the foundations of mathematics, mostly from an intuitionist point of view. He was awarded a Ph.D. in 1939 for his thesis Constructivist Foundations of Mathematics According to Borel and Brouwer. His first paper, Canonic Elements in the Higher Classes of Borel Sets, was published in the Journal of the London Mathematical Society. In it he thanks the referee and his father Paul Dienes for simplifying the proof of one of his theorems.

In 1938 Dienes married Mina Joyce Timms (also known as Mina Joyce Cooke) (18 November 1920 - 17 October 2006) who was known to all as Tessa. Dienes had met Tessa soon after arriving in England, Tessa's family being friendly with Paul Dienes. Richard George Cooke (1895-1965) was a mathematician who worked with Paul Dienes, the two writing a joint paper. Richard Cooke married Rosalind Marion Timms in 1920 and then married Gabrielle Sylvia Barnard in 1938. We note that Richard Cooke wrote the London Mathematical Society obituary of Paul Dienes. Zoltan and Tessa Dienes had five children: Corin Ruth Jasmine Dienes (1939-2010), Nigel Anthony Dienes (1942-1992), Jancis Nicola Dienes (born 1944), Sorrel (now Sarah) Dienes and Bruce Dienes. Tessa [37]:-
... loved children, poetry, dance and all things beautiful.
After graduating with his doctorate, Dienes began a career as a teacher at Highgate School in London in 1940. This famous independent school had been founded in the middle of the 16th century. After teaching for a year at Highgate, Dienes was appointed as a mathematics teacher at Dartington Hall School where he had been a pupil. Again he spent a year teaching but felt that he did not want to make a long-term career as a school teacher so began applying for university positions. In 1942 he was appointed to a Mathematics Lectureship at the University of Southampton. After two years at Southampton, he was appointed as an Assistant Lecturer in Mathematics at the University of Sheffield. Again this was a position he held for two years 1944-46, after which he was an Assistant Lecturer in Mathematics at the University of Manchester during 1946-48, before being appointed as a Lecturer in Mathematics at the University College of Leicester (now the University of Leicester) in 1948.

At Leicester, in addition to lecturing in mathematics, he attended courses in the Education Department from 1950 to 1953 and was awarded a Diploma in Education by University College of Leicester in 1953. He explained his thinking in [9]:-
... I tried to put a price tag on mathematical notions and theorems through analysing 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.
The publication that he refers to in this quote is Sulla definizione dei gradi di rigore (1952). After the award of the Diploma in Education, Dienes continued to teach mathematics at Leicester while becoming an external student of University of London in psychology. Supplementary Psychology was added to his existing University of London degree in July 1955. To understand why he moved towards psychology, we quote from [32]:-
In his lectures [at Leicester] he used a structural approach to mathematics: he would tell his students to forget everything they had learned before, so they could rebuild mathematics together. It was his belief, that looking at mathematics from a mathematical perspective is fundamentally different from just memorising complex problem solving strategies. But this message did not spark much enthusiasm then, only years later, when his audience changed to elementary school students did he manage to truly inspire.

Around this time he began to be concerned about the amount of impact he could have as a researcher. More and more he began to feel that he could contribute much more by changing mathematics education. It became increasingly clear to him that the subject was taught in a wrong way: that what he saw as beautiful and exciting was commonly regarded as scary and boring. He began connecting his research to learning processes: he thought there had to be a connection between ideas about the foundations of mathematics and learning the subject. Many look at mathematics as a closed science based on axioms carved into stone. On the other hand, people like Émile Borel, one of the mathematicians Dienes considered to be a role model, saw mathematics much more as a constructive and thus open discipline. This is how he came to recognise that the personality of children and their mathematical conceptualisation may be more closely related. He found proof of this in his experiments at the University of London, where he studied psychology. He came to the conclusion that constructive thinking is much more characteristic of children than analytical thinking, and that children of age ten were much more able in certain types of mathematical problem solving than it was believed at the time.
In 1959 Dienes published the two books Concept Formation and Personality and The growth of mathematical concepts in children through experience where he presented details of his work with 10-year old children. He aimed, as the Introduction to the second of these states, to:-
.... show that there are ways in which mathematical concepts can be caused to develop in children so that the techniques they learn are preceded by an understanding of the corresponding mathematical structures.
For more information on these works, and many other books by Dienes, see THIS LINK.

Dienes spent thirteen years as a mathematics lecturer at Leicester. When he was appointed in 1948, the University College of Leicester could not award degrees, the students sitting examinations for external degrees from the University of London. In 1957, however, it was awarded a Royal Charter and from then became a university in its own right, able to award degrees. The year 1960-61 he spent as a research fellow at the Center for Cognitive Studies at Harvard University. In 1961 he took up a personal chair in Psychology at Adelaide University in Australia, spending four years there. In 1964 he was appointed director of the Centre de Recherche en Psychomathématiques (Psychomathematics Research Centre) in the Université de Sherbrooke in Sherbrooke, Quebec, Canada [9]:-
The Sherbrooke work touched upon different forms of artistic expression. Preliminary field trials were conducted to ascertain the relationships between abstraction, generalisation, representation, symbolisation and formalisation. 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.
The Centre was funded by a grant from the Canadian Government and given the remit to "study learning and thinking about complex mathematical structures." In 1977 the grant ran out and the University of Sherbrooke could not afford to fund the Centre so it was forced to close.

The International Study Group for Mathematics Learning was an organisation which was established in 1962 in order to promote mathematics learning by encouraging the investigation of the processes by which it is achieved and by facilitating exchange and dissemination of teaching techniques and materials. To these ends it provided an information service, it encouraged the pooling of resources and the initiation of cooperative ventures, and it published a quarterly bulletin on recently completed and ongoing work. Dienes was a member of the Advisory Council from the establishment of the Study Group and led work on reviewing researches into the learning of mathematics by pupils between six and twelve years of age, and describing significant classroom and curricular projects of interest to educators, mathematicians and psychologists who are involved in mathematics-learning. Dienes prepared a report and presented it to the first Study Group conference held at Stanford University in December 1964. A modified report by Dienes was presented to the second Study Group conference held in Paris in April 1965. The International Study Group's temporary headquarters became the Psychomathematics Research Centre in Sherbrooke and its aims were set out in 1969 as follows:-
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 Psychomathematics Research Centre in Sherbrooke closed in 1977, the headquarters of the International Study Group for Mathematics Learning moved to London, England.

Dienes was a professor at Brandon University Manitoba, Canada from 1975 to 1978 and during these years, and also during the following two years when he was based in Italy, he visited many countries as a consultant carrying out experiments teaching mathematics. Among these countries, he worked in England, Australia, Papua New Guinea, USA, Canada, Germany, Italy, Chile, Argentina, Brazil, France, Spain, and Greece. He spoke about experimenting with the [9]:-
... 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 programme 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.
In 1980 Dienes and his wife bought a home in Totnes, Devon, England where they spent part of the year. He taught at several different schools in Devon, and was appointed as an honorary researcher at the University of Exeter. After a few years, he retired to Canada, and was given a part-time teaching post in the Faculty of Teacher Education at Acadia University.

Allison Lawlor tells us that he continued to explore his methods of teaching mathematics after he retired to Canada [29]:-
After his retirement, he and his wife moved to Nova Scotia to be closer to family. He taught part time at Acadia University's Department of Education and worked with elementary-school teachers, visiting their classrooms. Ramona Jennex, Nova Scotia's former education minister and an elementary-school teacher, remembers Dr Dienes visiting her class of primary and Grade 1 students. An elderly man at the time, he didn't hesitate to get down on the carpet with the students to play his games. While discussing people's homes (how they are built and shaped), he taught the children about place value, which is the value of digits based on where they are positioned within a multiple-digit number. Children often have difficulty understanding, for example, that the 1 in 1, 10 and 100 mean different things. "He never said to the children, 'You're learning place value.' He let them explore and play the games," Ms Jennex said, "He literally made maths magic." Mixing his teaching with stories and dances, he would captivate the children and get them moving. "He was just so charming," she said. "His research laid the foundation for a shift in the way we do mathematics," Ms Jennex added.
You can learn much more about his teaching methods from the books that he wrote; see THIS LINK.

There are two other aspects of Dienes's life that we should mention. We noted above that as a young boy he saw two different world views from his Roman Catholic mother and Communist father. He became very religious, joining the Quakers in 1952 and took an active part volunteering with the Friends Service Council. He was a member of Ministry and Counsel for the Montreal Quakers and when in Wolfville, he was a member of the Annapolis Valley Quaker Meeting. He also attended the Wolfville Baptist Church and sometimes visited the Third Horton Baptist Church. The second aspect of Dienes's life was his enthusiasm for writing poetry, a book of his poems Calls from the past being published in 2000. We agree with Bernhard Neumann when he writes in a review of the book [36]:-
Dr Dienes is no poet: many of the rhymes are artificial, and the scanning is often awkward. However, the 'poems' are worth reading for their contents.
You will learn much about Dienes's life from these poems and also from his fascinating autobiography Memoirs of a Maverick Mathematician (2003).

Dienes received many honour for his outstanding contributions to teaching mathematics to young children. He was awarded honorary degrees by the University of Caen in France, the University of Siena in Italy, the University of Pécs in Hungary, Mount Allison University in Sackville, Nova Scotia, and the University of Exeter in England.

After suffering a heart attack in 2014 when he was 97 years old, he was taken to Valley Regional Hospital in Kentville, Nova Scotia where he died.


References (show)

  1. J Adkins, Review: Modern Mathematics for Young Children, by Z P Dienes, The Arithmetic Teacher 13 (6) (1966), 509.
  2. W Bart, Mathematics Education: The Views of Zoltan Dienes, The School Review 78 (3) (1970), 355-.
  3. C A R Bailey, Review: Relations and Functions, by Z P Dienes and Peter L Seaborne, The Mathematical Gazette 60 (413) (1976), 227.
  4. A G Benedek, Embodied Conceptions of Mathematical Understanding in the Twentieth Century: the emergence of Zoltan P Dienes's principles and their origin, Repository of the Academy's Library (1 January 2018).
    https://core.ac.uk/download/pdf/159127121.pdf
  5. A G Benedek and A Tuska, Pólya and Dienes: Two men of one mind or one culture?, Repository of the Academy's Library (1 January 2019).
    https://core.ac.uk/reader/200208041
  6. A G Benedek and A Tuska, Synthesizing the legacy of Varga and Dienes, Repository of the Academy's Library (1 January 2020).
    https://core.ac.uk/reader/364708960
  7. J Biggs, Review: The Power of Mathematics, by Z P Dienes, International Review of Education / Internationale Zeitschrift für Erziehungswissenschaft / Revue Internationale de l'Education 13 (1) (1967), 93-96.
  8. J Biggs, Review: An Experimental Study of Mathematics Learning, by Z P Dienes, International Review of Education / Internationale Zeitschrift für Erziehungswissenschaft / Revue Internationale de l'Education 13 (1) (1967), 93-96.
  9. Biography of Zoltán Dienes, Dr, Dienes Family Home Page.
    http://www.dienes.hu/?page_id=50
  10. A Church and N Rescher, Review: On an Implication Function in Many-Valued Systems of Logic, by Z P Dienes, The Journal of Symbolic Logic 15 (1) (1950), 69-70.
  11. H M Cundy, Review: The growth of mathematical concepts in children through experience, by Z P Dienes, The Mathematical Gazette 44 (350) (1960), 301-303.
  12. H M Cundy, Review: Building up Mathematics, by Z P Dienes, The Mathematical Gazette 45 (352) (1961), 147-148.
  13. Dienes, Dr Zoltan Paul, Zoltan Dienes' Web Site (2022).
    https://zoltandienes.com/obituary/
  14. Z P Dienes, Memoirs of a Maverick Mathematician (Upfront Publishing, 2003).
  15. Z P Dienes, Mathematics as an Art form, Zoltan Dienes' Web Site (2002, 2004).
    https://zoltandienes.com/wp-content/uploads/2010/05/Mathematics_as_an_art_form.pdf
  16. Z P Dienes, What is a base?, Zoltan Dienes' Web Site (2002).
    https://zoltandienes.com/wp-content/uploads/2010/05/what_is_a_base.pdf
  17. Z P Dienes, Zoltan Dienes' six-stage theory of learning mathematics, Zoltan Dienes' Web Site (2022).
    https://zoltandienes.com/academic-articles/zoltan-dienes-six-stage-theory-of-learning-mathematics/
  18. Z P Dienes, I Will tell You Algebra Stories You Have Never Heard Before (Upfront Publishing, 2003).
  19. J A Easley Jr, Review: An Experimental Study of Mathematics Learning, by Z P Dienes, Contemporary Psychology 10 (7) (1965), 328-329.
  20. J A Fossa, On the Ancestry of Z P Dienes's Theory of Mathematics Education, Revista Brasileira de História da Matemática 3 (6) (2003-2004), 79-81.
  21. S M Gningue, Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra, International Journal for Mathematics Teaching and Learning 17 (2) (2016).
  22. S Hill, Review: Sets, Numbers and Powers, by Z P Dienes and E W Golding, The Arithmetic Teacher 15 (8) (1968), 740-742.
  23. S Hill, Review: Learning Logic, Logical Games, by Z P Dienes and E W Golding, The Arithmetic Teacher 15 (8) (1968), 740-742.
  24. J Hirstein, The Impact of Zoltan Dienes on Mathematics Teaching in the United States, in B Sriraman (ed.), Mathematics Education and the Legacy of Zoltan Paul Dienes (Information Age Publishing, 2008).
  25. M Holt, Review: Playing with Infinity: Mathematical Explorations and Excursions, by Rózsa Péter and Z P Dienes, Mathematics in School 6 (3) (1977), 35.
  26. M Holt, Review: The Effects of Structural Relations on Transfer, by Z P Dienes and M A Jeeves, The Mathematical Gazette 55 (394) (1971), 471-473.
  27. D St J Jesson, Review: The Six Stages in the Process of Learning Mathematics, by Zoltan P Dienes and P L Seaborne, The Mathematical Gazette 58 (405) (1974), 225.
  28. J Kiss and S Klein, Interview with Zoltan Dienes by Julianna Kiss and Sandor Klein, Zoltan Dienes' Web Site (15 January 2021).
    https://zoltandienes.com/posts/biography/
  29. A Lawlor, For mathematician and teacher Zoltan Dienes, the play was the thing, The Globe and Mail (4 February 2014).
  30. J Matthews, Review: ZOO Books, by Zoltan P Dienes and Michael Holt, Mathematics in School 2 (2) (1973), 35.
  31. E McIver, Zoltan Dienes and teaching mathematics through games, Maths - No problem (10 August 2020).
  32. A Mécs, The Hungarian who taught mathematics to tribal Papuans, Zoltan Dienes' Web Site.
    https://zoltandienes.com/posts/biography/
  33. Memorial Minute for Zoltan Paul Dienes from Annapolis Valley Quaker Meeting, Zoltan Dienes' Web Site (2022).
    https://zoltandienes.com/obituary/memorial-minute/
  34. H F Miller, Review: Building up Mathematics, by Z P Dienes, The Mathematics Teacher 11 (2) (1964) 125-127.
  35. B H Neumann, Review: Memoirs of a Maverick Mathematician, by Zoltan Paul Dienes, The Mathematical Gazette 84 (500) (2000), 348-350.
  36. B H Neumann, Review: Calls from the past, by Zoltan Paul Dienes, The Mathematical Gazette 85 (504) (2001), 534.
  37. Obituary of Tessa Dienes, Serenity Funeral Home (2016).
    https://serenitylindsay.funeraltechweb.com/tribute/details/3846/Tessa-Dienes/obituary.html#tribute-start
  38. E T Paluch, Zoltan Paul Dienes: um interesse histórico-cultural, in José Manuel Matos and Manuel Joaquim Saraiva (eds.), Actas do I Congresso Ibero-Americano de História da Educação Matemática (Caparica, Portugal, 2011), 526-533.
  39. P Peak, Review: The Elements of Mathematics (T_t, P), by Z P Dienes, The Mathematics Teacher 65 (5) (1972), 442.
  40. P Peak, Review: Approach to Modern Mathematics (L, P), by Z P Dienes and E W Golding, The Mathematics Teacher 65 (5) (1972), 440-441.
  41. P Peak, Review: Playing with Infinity: Mathematical Explorations and Excursions, by Rózsa Péter and Z P Dienes, The Mathematics Teacher 70 (3) (1977), 282.
  42. Prof Dr Zoltan Paul Dienes, University of Pécs (2010).
    https://international.pte.hu/honorary-doctors/prof-dr-zoltan-paul-dienes
  43. B Sriraman, A Conversation With Zoltan P Dienes, Mathematical Thinking and Learning 9 (1) (2007), 59-75.
  44. B Sriraman (ed.), Mathematics Education and the Legacy of Zoltan Paul Dienes (Information Age Publishing, 2008).
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  46. B Sriraman, Editorial: The Legacy of Zoltan Paul Dienes, The Montana Mathematics Enthusiast 2 (2007), i-ii.
  47. B Sriraman and L D English, On the teaching and learning of Dienes' principles. International, Reviews in Mathematics Education (ZDM) 37 (3) (2005), 258-262.
  48. B Sriraman and R Lesh, Reflections of Zoltan P Dienes on Mathematics Education, n B Sriraman (ed.), Mathematics Education and the Legacy of Zoltan Paul Dienes (Information Age Publishing, 2008).
  49. B Sriraman and R Lesh, Leaders in Mathematical Thinking & Learning- A conversation with Zoltan P Dienes, Mathematical Thinking and Learning: An International Journal 9 (1) (2007), 59-75.
  50. A G Sillitto, Review: Building up Mathematics, by Z P Dienes, The Mathematical Gazette 49 (369) (1965), 328.
  51. R B Skemp, Review: The Effects of Structural Relations on Transfer, by Z P Dienes and M A Jeeves, Research in Education 0 (6) (1971), 91-92.
  52. W O Storer, Review: The Power of Mathematics, by Z P Dienes, The Mathematical Gazette 50 (372) (1966), 194-197.
  53. W O Storer, Review: An Experimental Study of Mathematics Learning, by Z P Dienes, The Mathematical Gazette 50 (372) (1966), 194-197.
  54. A Tuska, Zoltan Paul Dienes: The life and legacy of a maverick mathematician, in Péter Körtesi (ed.) Proceedings of the History of Mathematics and Teaching of Mathematics (Miskolc, Hungary, 2018).
  55. P E Vernon, Review: Concept Formation and Personality, by Z P Dienes, The British Journal of Sociology 11 (2) (1960), 190-191.
  56. S S Willoughby, Review: Thinking in Structures, by Z P Dienes and M A Jeeves, The Mathematics Teacher 60 (7) (1967), 793-794.
  57. D J Winteridge, Review: Relations and Functions, by Z P Dienes and Peter L Seaborne, Mathematics in School 6 (1) (1977), 36.
  58. J L Wisthoff, Review: Memoirs of a Maverick Mathematician, by Zoltan Paul Dienes, The Mathematics Teacher 94 (7) (2001), 616.
  59. Wolfville's Dr Zoltan Dienes to receive honour from Hungary's Pecs University, Hungarian Presence in Canada.
  60. Zoltán Pál Dienes, Alchetron (15 April 2022).
    https://alchetron.com/Zoltán-Pál-Dienes
  61. Zoltan Paul Dienes (1916-2014), Serenity Funeral Home and Chapels (2014)
    https://serenityfuneralhome.ca/tribute/details/3981/Zoltan-Dienes/obituary.html
  62. Zoltan Paul Dienes, slideshare (26 July 2014).
    https://www.slideshare.net/jhenny31/zoltan-paul-dienes

Additional Resources (show)

Other pages about Zoltán Dienes:

  1. Zoltan Dienes' books

Cross-references (show)


Written by J J O'Connor and E F Robertson
Last Update July 2022