Abstract
Russian culture developed under the burden of a series of totalitarian governments, a circumstance that, oddly, supported mathematics education. The Soviet period in particular saw a flowering of mathematical culture, the seeds of which have, since the collapse of the Soviet Union, been carried to the rest of Europe and America. A trickle of ideas, materials—and émigrés—has swollen to a powerful stream. Some of the heaviest influences have occurred in the field of extra-curricular education. We explore some of the ways that Russian and Soviet mathematical culture has fertilized this field. In particular, we look closely at the pivotal role of the professional mathematical communities, both in Russia and in America.
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Notes
The account of the ARML Power Contest is largely from personal recollection. The author was the president of ARML at the time, conceived of the program, and arranged for the funding of the Russian visit.
Much of this paragraph is based on the author's personal communication with Ross.
The writer's own grandfather was educated in an Odessa gymnasia, and S.O. Shatunovsky was one of his teachers. He recalled that Shatunovsky’s pedagogical style was engaging and exacting. “It was easy to get a 1 or 5 [the lowest and highest possible grade],” he told me. “But if you were on the edge you had to really work, to prove to him that you understood the material.” An examination of notebooks he has left me from Shatunovsky’s classes show advanced work in Euclidean geometry and theory of equations, areas that were covered only in the most specialized classes in the English-speaking world.
This information is from the writer's personal communication with Hal Abelson in 1992. Other information in this paragraph is likewise from personal communication with other individuals mentioned.
By 'mathematical circles' we mean here any informal environment where students (or sometimes teachers) meet with a mathematical professional or mathematically sophisticated leader to discuss mathematics outside of a formal school structure.
Information in this paragraph from the author's personal experience.
References
American Mathematical Society (n.d.). Bookstore. https://bookstore.ams.org/mcl.
American Mathematical Society (n.d.). Summer math camps and programs for students. http://www.ams.org/programs/students/emp-mathcamps.
American Regions Mathematics League (2019). https://www.arml.com/ARML/arml_2019/page/index.php. Accessed June 2021.
Australian Mathematics Trust (1988). c. Mathematics competitions 1.1. https://sites.google.com/site/pjt154/home/a4-life-tributes/greitzer. Accessed June 2021.
Beilinson, A. (2016). I.M. Gelfand and his Seminar—a presence. Notices of the American Mathematical Society, 63(3), 295–298. https://doi.org/10.1090/noti1337
Blalock, J.T. (2011). The impact of Singapore math on student knowledge and enjoyment in mathematics. Louisiana Tech University. https://core.ac.uk/download/pdf/236621565.pdf. Accessed June 2021.
Blau, A. (2016). The exodus equation: Study shows Russian math geniuses excelling in west. Radio Free Europe, Radio Liberty. https://www.rferl.org/a/russian-math-geniuses-excelling-in-west/27507561.html. Accessed June 2021.
Brisckoe Center for American History (n.d.). A guide to the new mathematical library records, ca. 1929, 1957–1997. https://www.maa.org/archives-spotlight-the-new-mathematical-library-records. Accessed June 2021.
Brousseau, G. (2002). Theory of didactical situations in mathematics. Kluwer Academy Publishers.
Buck, R. C., Kovanko, A. S., & Churikove, F. S. (1959). A look at mathematical competitions. The American Mathematical Monthly, 66(3), 201–212. https://doi.org/10.1080/00029890.1959.11989270
Chan, C.L. (2015). Fallen behind: Science, technology, and Soviet Statism. Intersect, 8(3), 1–11. http://ojs.stanford.edu/ojs/index.php/intersect/article/view/691. Accessed June 2021.
Conrad, S, R. (1977). The widening circle of mathematics competitions. The Mathematics Teacher, 70(5), 442–447. http://www.jstor.org/stable/27960879
Dion, P. (n.d.) I collect soviet books. https://sovietbooks.wordpress.com/about/. Accessed June 2021.
Fedorov, R., Belov, A., Kovaldzhi, A., & Yashchenko, I. (Eds.). (2011). Moscow mathematical Olympiads, 2000–2005. American Mathematical Society.
Fomin, D., Genkin, S., & Ittenberg, I. (1996). Mathematical circles: Russian experience (translated by M. Saul). American Mathematical Society.
Fomin, D., & Kirichenko, A. (1994). Leningrad mathematical Olympiads, 1987–1991. MathPro Press.
Frank, T. (2007). The social construction of Hungarian Genius (1867–1930). https://studylib.net/doc/8525154/tibor-frank. Accessed June 2021.
Freudenthal, H. (1969). ICMI report on mathematical contests in secondary education (Olympiads) I. Educational Studies in Mathematics, 2(1), 80–114. www.jstor.org/stable/3482114.
Gelfand, I.M., Glagoleva, E.G., & Shnol, E.E. (1968). Funktsii i grafiki. Moscow: Nauka. English translation: Functions and Graphs. The MIT Press, 1969, Birkhäuser: Boston, 1990 and 1998.
Gelfand, I.M., Glagoleva, E.G., & Kirillov, A.A. (1973). Metod Koordinat. Moscow: Nauka, English Translation: The Method of Coordinates. The MIT Press, 1967; Birkhäuser: Boston, 1990.
Gelfand, I.M. and Shen, A. Kh. (1998/2009). Algebra. Moskow: MTsNMO. English translation: Algebra. Birkhäuser: Boston, four editions, 1993–2003.
Gelfand, I. M., & Retakh, V. S. (Eds.). (2000). The Gelfand mathematical seminars. Birkhauser.
Gelfand, I. M., & Saul, M. (2001). Trigonometry. Birkhauser.
Gelfand, I. M., & Alekseevskaya, T. (2020). Geometry. Birkhauser.
Gerovitch, S, (2013). Parallel worlds: Formal structure and informal mechanisms of postwar soviet mathematics. Historia Scientiarum, 22(3),181–200. https://www.academia.edu/5366902/
Ginsburg, A., Leinwand, S., Anstrom, T., Pollock, E. (2005). What the United States
Can Learn From Singapore’s World-Class Mathematics System (and what Singapore can learn from the United States): An Exploratory Study, Prepared for US Department of Education Policy and Program Studies Service by The American Institutes for Research https://files.eric.ed.gov/fulltext/ED491632.pdf
Givental, L., Nemirovskaya, M., & Zakharevich, I. (2018). Math circles by the bay. American Mathematical Society.
Glagoleva, E. (2013). Matematika s chelovecheskim litsom (Mathematics with a Human Face). Nauka i zhizn, 12, 40–46. https://www.google.com/books/edition/_/g_1QAgAAQBAJ?hl=en&gbpv=1&pg=PA46&dq=%D0%B3%D0%B5%D0%BB%D1%8C%D1%84%D0%B0%D0%BD%D0%B4+%D0%B7%D0%B0%D0%BE%D1%87%D0%BD%D0%B0%D1%8F+%D1%88%D0%BA%D0%BE%D0%BB%D0%B0. Accessed June 2021.
Gnedenko, B. V. (1957). Mathematical education in the USSR. American Mathematical Monthly, 64(6), 389–408. https://doi.org/10.2307/2310164
Govtrak (1958) HR 13247. https://www.govtrack.us/congress/bills/85/hr13247/text. Accessed June 2021.
Grove, J. (2016). Russia's math Diaspora. Inside Higher Ed. https://www.insidehighered.com/news/2016/01/14/study-analyzes-impact-russian-diaspora-mathematics. Accessed June 2021.
Gruver, H. L. (1968). School mathematics contests: A report. National Council of Teachers of Mathematics.
International Mathematical Olympiad (2020). https://www.imo-official.org/year_statistics.aspx?year=1959, https://www.imo-official.org/country_info.aspx?code=FIN, https://www.imo-official.org/country_info.aspx?code=USA. Accessed June 2021.
Jackson, A. (1998). The demise of the young scholars program. Notices of the American Mathematical Society, March, 381–387. https://www.ams.org/notices/199803/scholars.pdf
Jackson, A. (2001). Interview with Arnold Ross. Notices of the AMS, 691–698. http://www.ams.org/notices/200107/fea-ross.pdf. Accessed June 2021.
Kaplan, R. (1995). The Math Circle. Notices of the American Mathematical Society, 42(9), 976–978. https://www.ams.org/notices/199509/kaplan.pdf. Accessed June 2021.
Karp, A. (2010). Reforms and counter-reforms: Schools between 1917 and the 1950s. In A. Karp & B. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 43–86). World Scientific Publishing Co.
Kilkelly, T. (2014). The ARML Power Contest, 1994–2013. Berkeley California: Mathematical Sciences Research Institute and Providence RI: American Mathematical Society.
Kilpatrick, J. (2010). Influences of soviet research in mathematics education. In A. Karp & B. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 359–368). World Scientific Publishing Co.
Kvant. (n.d.). http://www.kvant.info/.
Kvant (1996–2002). http://www.kvant.info/, http://kvant.mccme.ru/, http://kvant.mccme.ru/1985/01/p02.htm. Accessed June 2021.
Leung, F.K.S., Graf, K-D., Lopez-Real, F.J. (eds.) (2006). Mathematics education in different cultural traditions—a comparative study of East Asia and the West. (The 13th ICMI Study) New York: Springer Science and Business Media. https://www.google.com/books/edition/Mathematics_Education_in_Different_Cultu/dGxQ7aHnWXAC?hl=en&gbpv=1&dq=mathematics+education+icmi+study&pg=PR10&printsec=frontcover. Accessed June 2021.
Lloyd, D. B. (1956). The National Status of Mathematics Contests. The Mathematics Teacher, 49(6), 458–463. http://www.jstor.org/stable/27955216
Marshall, J. (2003). Math wars: Taking sides. Phi Delta Kappan, 85(3), 193–200. https://doi.org/10.1177/003172170308500306 249.
Marushina, A., & Pratusevich, M. (2011). Extracurricular work in Mathematics. In A. Karp & B. R. Vogeli (Eds.), Russian mathematics education: Programs and practices (pp. 375–410). World Scientific.
Mathematical Association of America. (1950). Mathematics contest of the metropolitan New York section of the mathematical association of America. American Mathematical Monthy, LVII, 657.
Mathematical Sciences Research Institute (2015). Final report national math circle. https://www.msri.org/system/cms/files/196/files/original/H98230-14-1-0269_Final-Report_webversion.pdf. Accessed June 2021.
Maugh, T.A. (2009) Widely influential Russian mathematician. Los Angeles Times, Oct. 11, 2009 www.latimes.com/archives/la-xpm-2009-oct-11-me-israel-gelfand11-story.html. Accessed June 2021.
Maurer, S., & Mientka, W. (1982). AHSME, AIME, USAMO: The examinations of the committee on high school contests. The Mathematics Teacher, 75(7), 548–557. www.jstor.org/stable/27963084.
National Science Foundation (1988) Award Abstract #8850177, https://www.nsf.gov/awardsearch/showAward?AWD_ID=8850177. Accessed June 2021.
O'Connor, J.J. & Robertson E.F. (2010). Samuil Osipovich Shatunovsky. https://mathshistory.st-andrews.ac.uk/Biographies/Shatunovsky/. Accessed June 2021.
Periodico Quantum (in Greek) (n.d.). https://ph403.edu.physics.uoc.gr/quantum.php. Accessed June 2021.
Polyakova, T. (2010). Mathematics education in Russia before the 1917 Revolution. In A. Karp & B. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 1–42). World Scientific Publishing Co.
Polya, G. (1945). How to solve it. Princeton University Press.
PROMYS (2020). Program in mathematics for young scientists: History. https://www.promys.org/about-promys/history. Accessed June 2021.
Saul, M. (1992). Love among the Ruins. Focus, 12(1),(1, 6, 7) https://www.maa.org/sites/default/files/pdf/pubs/focus/past_issues/FOCUS_12_1.pdf. Accessed June 2021.
Saul, M. (2001). It all fits together. Notices of the American Mathematical Society, December, 1333–1337. https://www.ams.org/notices/200111/comm-saul.pdf. Accessed June 2021.
Saul, M. (2003). Mathematics in a small place: Notes on the mathematics of Romania and Bulgaria. Notices of the American Mathematical Society, 50(5), 561–565. https://www.ams.org/notices/200305/comm-saul.pdf. Accessed June 2021.
Saul, M., & Fomin, D. (2010). Russian traditions in mathematics education and Russian mathematical contests. In A. Karp & B. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 223–252). World Scientific Publishing Co.
Schoenfeld, A. (2003). "Math Wars" http://pi.math.cornell.edu/~henderson/courses/EdMath-F04/MathWars.pdf. Accessed June 2021.
Shapiro, D. (n.d.). The History of Arnold Ross and his Program. https://rossprogram.org/alumni/history/. Accessed June 2021.
Sharp, L., Carey, N., Frechtling, J. A. & Burgdorf, K. (1994). Short-term impact study of the national science foundation's young scholars program. https://www.nsf.gov/pubs/1996/nsf9551/nsf9551.pdf. Accessed June 2021.
Shkolnaya Pressa, (n.d). Matematika v Shkole, http://www.schoolpress.ru/products/magazines/index.php?SECTION_ID=42&MAGAZINE_ID=34945.
Sinkevich, G. (2015). The Fate of Russian Translations of Cantor. Notices of the International Congress of Chinese Mathematicians, 3(2), 74–83, https://www.intlpress.com/site/pub/files/_fulltext/journals/iccm/2015/0003/0002/ICCM-2015-0003-0002-a006.pdf.
Sossinsky, A. (2010). Mathematicians and mathematics education: A tradition of involvement. In A. Karp & B. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 187–222). World Scientific Publishing Co.
Texas State Mathworks (n.d.). Honors summer math camp. https://www.txstate.edu/mathworks/camps/Summer-Math-Camps-Information/hsmc.html
Timorin, V. (2015). Reasons for the success of the soviet mathematical school. Higher Education in Russia and Beyond, 4(6), (9) https://herb.hse.ru/data/2015/12/14/1134503138/HERB_06_view.pdf#page=9. Accessed June 2021.
Timorin, V. & Sterligov, I. (2015). A metric view on Russian mathematics and Russian mathematical diaspora. Higher Education in Russia and Beyond, 4(6), (10). https://herb.hse.ru/data/2015/12/14/1134503138/HERB_06_view.pdf#page=10. Accessed June 2021.
Turner, N. D. (1971). Why can’t we have a USA mathematical Olympiad? The American Mathematical Monthly, 78(2), 192–195. https://doi.org/10.2307/2317636
Turner, N. D. (1985). A Historical sketch of Olympiads: U.S.A. and International. The College Mathematics Journal, 16(5), 330–335.
Tyre, P. (2016). The math revolution. The Atlantic, https://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/. Accessed June 2021.
United States Senate (1957). Sputnik spurs passage of the national defense education act. https://www.senate.gov/artandhistory/history/minute/Sputnik_Spurs_Passage_of_National_Defense_Education_Act.htm.
US House of Representatives. (1958). National defense education act. https://history.house.gov/Records-and-Research/Listing/lfp_006/. Accessed June 2021.
Valcarce, M. (2012). Russian mathematical pedagogy in reasoning mind. HMC Senior Theses. 30. https://scholarship.claremont.edu/hmc_theses/30.
Van Dalen, D. (2005). Mystic, geometer, and intuitionist: The life of L.E.J. Brouwer, Vol 2 (pp. 555–556). Oxford: Clarendon Press. https://www.maths.ed.ac.uk/~v1ranick/papers/brouwerbio2.pdf. Accessed June 2021.
Vershik, A.M. (2009). Notes of talks at the I.M.Gelfand seminar. Clay Mathematics Institute. https://www.claymath.org/publications/notes-talks-imgelfand-seminar. Accessed June 2021.
Walker, E. N. (2011). Supporting giftedness: historical and contemporary contexts for mentoring within black mathematicians’ academic communities. Canadian Journal of Science, Mathematics, and Technology, 11, 19–28. https://doi.org/10.1080/14926156.2011.548899
Walker, E.N. (2012). Cultivating mathematics identities in and out of school and in between. Journal of Urban Mathematics Education, 5(1), 66–83. https://www.tc.columbia.edu/faculty/walker/Cultivating.pdf. Accessed June 2021.
Wirszup, I. (1963). The school mathematics circle and Olympiads at Moscow state university. The Mathematics Teacher, 56(4), 194–210.
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Saul, M. Russian influences on American mathematics education after 1991: historical roots of changes in extracurricular programs. ZDM Mathematics Education 53, 1605–1616 (2021). https://doi.org/10.1007/s11858-021-01293-8
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DOI: https://doi.org/10.1007/s11858-021-01293-8