Abstract
Not often cited as one of the countries making major contributions to new/modern math movements in school mathematics, the case(s) in Canada may seem of lesser interest to the international community. However, in this chapter, we show how the multiple forces acting on school mathematics curricula across the country led to a slow brew of quiet change. In addition to surveying existing writings on various Canadian contexts, we also examine some book and article publications written in the early 1960s that shed some light on the intricacies of this quiet change. We also highlight some of the significant reasons for Canada’s slow pace.
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Notes
- 1.
This island is very near Kingston, Ontario, home of Queen’s University, about which more later.
- 2.
It might have been better to write “new approaches,” not least that it is unclear to us that the Soviet Union took on the Bourbaki approach.
- 3.
David Wheeler (1925–2000) came from England to North America in 1973 for the rest of his life. He had already had a sabbatical year in New York City with Caleb Gattegno 1969–1970, and returned there in 1973 before moving to Canada in 1976.
- 4.
In the fortieth meeting of CMESG, Bill Higginson (2016) commented, “The rapidly growing tertiary education level of the mid-seventies was open to possibilities which it never had been before, and never has been since. The mathematics/mathematics education spheres were extremely fortunate to have the energies, imaginations, and influences of two outstanding educators, David Wheeler and John Coleman, who worked together very effectively to create an unusual organization. The framework and the Group’s prevailing values were largely due, in my view, to David Wheeler, and these in turn had been very largely formed through his extensive work with the Association of Teachers of Mathematics in the United Kingdom before he immigrated to North America” (p. 87).
- 5.
In a more extensive presentation at CMESG, Higginson (2012) commented in more detail about the origin of CMESG and its originators: “Not so long after the [1976] ICME meeting, we have Wheeler’s delicate letter of inquiry. New person in country, might there be merit in looking at possible ways of increasing communication across provinces, etc.? The letter is sent to a large number of senior mathematicians and mathematics educators across the country. The return rate is not terribly high and most of the responses express contentment with existing arrangements (NCTM, CMS, ...). Among the outliers, two independent responses from Coleman (smarting a bit about the Science Council Study response, committed to education, having some unassigned resources from the Science Council Study) and Higginson (remembering how impressed he had been with Wheeler’s work in the United Kingdom). An invitational meeting followed with [Claude] Gaulin and [Tom] Kieren as keynote speakers and the rest is Study Group history” (p. 41).
- 6.
In a note on the ICMI history, it documents, with regard to PME, that, “Professor Fischbein proposed to members in 1976 that the group be called The International Group for the Psychology of Mathematics Education (IGPME) to distance it from Professor Zoltan Dienes’ group that was called The International Study Group for Mathematics Learning” (https://www.icmihistory.unito.it/pme.php, p. 1). Canada’s CMESG also adopted the term “Study Group.”
- 7.
Hans Freudenthal, a German mathematician who moved to the Netherlands, had become president of ICMI in 1967 and was the first editor of ESM for a decade. He also organized the first ICME conference in 1969. In the first two years of ESM, the only Canadian-placed author was Zoltán Dienes, who published two articles, one in French then a different one in English.
- 8.
There are many significant aspects of this journal which are distinctive. One is that it was created (and edited for the first seventeen years) by David Wheeler, and subsequent editors have all been from Canada or the United Kingdom.
- 9.
But only in 1967, when the founding conference, with representatives from each province, was held in Ottawa on December 8 and 9 (for more details, see Dawson 1968). But CAMT did not survive for long.
- 10.
Professor Tom Kieren (University of Alberta) gave David Pimm an engaging remark twenty years ago, about how he experienced Canada having predominantly local but not global existence, in that when he went abroad he almost never saw any mentions of Canada in newspapers.
- 11.
This is somewhat unsurprising, as Canada contributed relatively little to curriculum development at that time.
- 12.
One could argue that it is part of the national character to focus inward, and perhaps even to refrain from boasting. This became obvious for Nathalie Sinclair when she was invited (along with Chris Suurtamm from the University of Ottawa and Florence Glanfield from the University of Alberta) to a panel discussion organized by Ed Silver from the University of Michigan at the NCTM conference in 2018. Ed wondered why American researchers were not looking more toward Canada for ideas on how to improve their mathematics education system, instead of turning toward Singapore and Finland (which had recently been very successful in PISA levels), countries which were much more culturally different from the US than Canada.
- 13.
Tom O’Shea’s chapter is the last one in the first volume of almost 900 pages. The second volume (of a comparable length) also has a final chapter, written by Carolyn Kieran (2003), entitled, “The twentieth-century emergence of the Canadian mathematics education research community.”
- 14.
In 1999, Nunavut became a new distinct territory, separated out from the Northwest territories.
- 15.
There is also a second chapter about Canada in the second volume of A History of School Mathematics (Stanic and Kilpatrick 2003), entitled, “The Canadian student population,” whose author Catherine Le Maistre of McGill University in Montréal wrote, “Canada shares a long border with the United States, has one-tenth of its population, and is greatly influenced by the activities and reforms that are initiated by its large neighbor. Yet there are many differences between the two countries” (Le Maistre 2003, p. 1186).
- 16.
In 1960, Canada’s population was 17.9 million; in 1970, 21.3 million; in 1980 24.5 million. In 2020, it was 38.0 million and these three provinces now entail 75% of the country’s populace.
- 17.
The quotations marked inside the O’Shea quotation come from Chant et al. (1960).
- 18.
Servais had also been one of the guest speakers at the Royaumont Seminar in 1959.
- 19.
There’s a Dave Allen joke about when asked if everyone in Northern Ireland is either Catholic or Protestant, to which he replied, “No, but they are either Catholic atheists or Protestant atheists.”
- 20.
In 1980, however, Gattegno did give a plenary lecture at CMESG.
- 21.
In Québec, CEGEP stands for Collège d’enseignement general et professionnel [General and professional teaching college], a public school that provides the first level of post-secondary education.
- 22.
In 1973, David Pimm took a mathematics education course in the mathematics department at the University of Warwick taught by David Tall, and this book was its central focus.
- 23.
The title is interesting, in that vector spaces became part of some schools’ new mathematics in the 1960s. For this journal, see Chernoff et al. (2015).
- 24.
This title is also interesting, in that delta-K is a symbol for kinetic energy, a physics notion. For this journal, see Chernoff and Sternberg (2014).
- 25.
Vinculum means “a horizontal line drawn over a group of terms in a mathematical expression to indicate that they are to be operated on as a single entity by the preceding or following operator. In Latin, the meaning is chain, bond, fetter, imprisonment (p. 1).” (https://www.lexico.com/definition/vinculum). For this journal, see Chernoff et al. (2019).
- 26.
Near the end of an article, Coleman (1991) wrote: “Compared with many other jurisdictions, the [mathematics curriculum] change in Ontario was sensible and relatively painless. [In the final paragraph, he added] “Everything useful that can be said is in A. N. Whitehead’s The Aims of Education and other Essays. Read this every second year!” (p. 25).
- 27.
Just to take a recent example, Canada followed (days after) the USA, Britain, and Australia in declaring that it would engage in a diplomatic boycotting of the Beijing Olympics.
- 28.
The ones from Ontario, Saskatchewan, Alberta, and British Columbia, all from the early 1960s.
- 29.
For instance, he certainly did not write a book like the American Morris Kline’s (1973) Why Johnny Can’t Add. Even Wikipedia writes, “Why Johnny Can’t Add: The Failure of the New Math is a 1973 book by Morris Kline, in which the author severely criticized the teaching practices characteristic of the “New Math” fashion for school teaching, which were based on Bourbaki’s approach to mathematical research, and were being pushed into schools in the United States. Reactions were immediate, and the book became a best seller in its genre and was translated into many languages.” And, once again, the Wikipedia entry on “New math” mentions a number of countries, but Canada is not one of them.
- 30.
He was also one of the editors of a series of textbooks for schools published by W. J. Gage and Company, and in this document, he later added a category of “parents struggling with the “New Maths”” (p. 39).
- 31.
R. Scorer (1964), a professor of theoretical mechanics in London, wrote, “The new fashion of teaching the techniques of matrix algebra in sixth forms [the last two years of United Kingdom high school] (often presumptuously called “modern mathematics” when it is century-old) provides an instance worth noting” (p. 23). He proposed “new mechanics” to be taught at school and described, “The present-day obsession with some ‘new’ but rather trite topics in algebra” (p. 25).
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Acknowledgments
We are very grateful for helpful conversations with four senior Canadian academics who had varied involvement with mathematics and mathematics education in the 1960s and beyond: Jean Dionne (Université Laval, QC), Bill Higginson (Queen’s University, ON), Tom O’Shea (Simon Fraser University, BC), and Peter Taylor (Queen’s University, ON). With regret, we are painfully aware there would have been even more attachment with significant figures such as John Coleman, Sandy Dawson, Zoltán Dienes, Caleb Gattegno, Claude Gaulin, John Trivett, and David Wheeler, among others, had they still been alive.
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Pimm, D., Sinclair, N. (2023). Aspects of Canadian Versions of So-Called “Modern” Mathematics and Its Teaching: Another Visit to the Old “New” Math(s). In: De Bock, D. (eds) Modern Mathematics. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-11166-2_18
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