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Russian Mathematics Education: History and World Significance

Alexander Karp and Bruce R. Vogeli, editors
World Scientific
Publication Date: 
Number of Pages: 
Series on Mathematics Education 4
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Michael Berg
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There is no question that Mathematics Education has in the last decade or two (to assign time-parameters to the event) grown into an industry whose clout all but eclipses that of its ostensible root, Mathematics proper. MathEd faculty are being hired everywhere, majors in teaching (as opposed to doing?!) Mathematics sprout up like mushrooms (and kids flock to them in huge numbers — no surprise!), and cash seems to abound — even now. Additionally, Mathematics departments all across the country, and even beyond our borders, sponsor or subsidize research programs in this pedagogical field, attracting scholars from across the spectrum, both in the time domain (rookies as well as senior people sitting in endowed chairs) and the specialties domain (in my department the pedagogy mavens come from topology and algebra). Agencies at all levels fund this research in Mathematics Education, or, more broadly, the Scholarship of Teaching and Learning (the mot juste in my department, as of a couple of years ago), and they tend to do so rather liberally, as I already indicated, even in these economically dicey times. Therefore, since grants carry so much weight (and granting agencies call the best attended dances) in modern acadème, it is nigh on impossible to remain blissfully ignorant of all things pedagogical, even if you’re a curmudgeonly dinosaur like me, who just wants to spend his days trying to prove theorems and give lectures they way he always has. The times, they are a-changing — well, they have a-changed, really.

So, what if you’re a pedagogy true believer, then, who wishes to figure out how to engineer success in the teaching of Mathematics, or, more narrowly (and perhaps somewhat more legitimately) in the creation of a more mathematically literate and sympathetic base as well as the care and nurturing of mathematically gifted youths? Well, workshops and consortia notwithstanding, the logical thing to do is admit that functioning wheels already exist and there’s no need to try to invent new ones, i.e. study programs that work and try to solve your problem by transfer of structure.

The former Soviets built an educational system that, for all of the horrors and inhumanity of its surrounding totalitarian system, produced a striking record of huge successes and rare achievements, and should accordingly be looked at. Deo gratia, the communist state crumbled, Glasnost set in, Perestroika began, and détente eventually developed into something somewhere between laissez faire coexistence and alliance (and how’s that for dropping foreign political science phrases?). Most importantly for Mathematics world-wide, borders finally opened and something of a diaspora ensued of now free former Soviet scholars, with Israel and the United States as doubtless the primary recipients, ahead of Western Europe. In any case, the entire world can now benefit from the achievements of these Russians.

So the timing is right for a volume of essays and articles devoted to the question of what the Russians did, why they did it, and how they did it. The book under review, Russian Mathematics Education: History and World Significance, edited by Alexander Karp and Bruce R.Vogeli, addresses this question in the form of ten chapters, contributions by various scholars, most of them Russians themselves (of the right age, so that we get a lot of insiders’ views), covering historical, social, political, as well as pedagogical aspects of the matter. The stage is set by a first chapter evaluating Russia’s Mathematical education before 1917, after which the predictable theme of reform (and counter-reform) is addressed. À propos, it is worth noting that much like France, Hungary, and Germany (viz. Felix Klein), Soviet Russia also benefited from the phenomenon of a handful of first-rate scholars (Kolmogorov, Egorov, Tikhonov, Pontryagin, and Dynkin, for example, not to mention the ecumenically minded titan, Gel’fand) taking great interest in the problem — often with battles ensuing: we find out in the book, for example, that Pontryagin and Kolmogorov were on opposite sides on certain pedagogical matters.

Indeed, Kolmogorov is prominently featured in Russian Mathematics Education: History and World Significance; for good reason, of course, but much as a tragic figure. This is movingly conveyed in a speech by Ershov (pp. 135–136): “…if the Kolmogorov reform … [failed], then its failure represents nothing more than the projection onto Mathematics of a more global failure … [namely] the transition to mandatory secondary education with the retention of all of the former rigidity, homogeneity, and authoritarianism in the content and methodology of school-level education …” (I guess we’re dealing with something of a Soviet-style “no child left behind” initiative.) Eshov then goes on to compare Kolmogorov to Boris Pasternak: “The same degree of talent, high professionalism, and capacity for ordinary work. The same incompatibility with many aspects of quotidian reality … The same extreme jealousy and prejudice on the part of his colleagues …”

As the book unfolds we come across discussions of the role played by Mathematics contests, the developments in Russian elementary Mathematics education figuring into what should transpire later, the Russians’ preparation of their Mathematics teachers (then and now), and the influence of the Soviet system on other former communist countries, namely Poland and Hungary, and on a communist hold out, Cuba. Russian Mathematics Education: History and World Significance closes with an apposite chapter tying things together: “Influences of Soviet research in Mathematics Education.”

Thus, the true believer in MathEd will find this book chock-full of relevant and inspirational material, possibly even making for raw material for education reform in this country, at least working locally. There is also a lot of fascinating historical material in the book. Finally, even hide-bound reactionaries like me will also find something for them in Russian Mathematics Education: History and World Significance, seeing that the stories of individual scholars are always evocative and serve to bring out an element of empathy in us: psychologically sound stuff, of course.



Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.


  • Mathematics Education in Russian Before the 1917 Revolution (T Polyakova)
  • Reforms and Counter-Reforms: Schools Between 1917 and the 1950s (A Karp)
  • Toward a History of Mathematics Education Reform in Soviet Schools (1960s–1980s) (A Abramov)
  • Challenges and Issues in Post-Soviet Mathematics Education (M Bashmakov)
  • Mathematicians and Mathematics Education: A Tradition of Involvement (A Sossinsky)
  • Russian Traditions in Mathematics Education and Russian Mathematical Contests (M Saul & D Fomin)
  • The Relevance of Russian Elementary Mathematics Education (J Schmittau)
  • The Preparation of Mathematics Teachers in Russia: Past and Present (N Stefanova)
  • Russian Influence on Mathematics Education in the Socialist Countries:
    • The Traditions and Development of Mathematics Education. Case of Poland (A Pardata)
    • Case of Hungary (K Fried)
    • Case of Cuba (O B Alonso)
  • Influences of Soviet Research in Mathematics Education (J Kilpatrick)