‘Universal Responsiveness’ or ‘Splendid Isolation?’ Episodes From the History of Mathematics Education in Russia

Abstract

This article investigates the prevalent attitudes toward foreign influences and methodologies in Russian mathematics education at different periods in Russian history. The words ‘universal responsiveness’ belong to Dostoevsky, who, in his famous speech on Pushkin, used them to characterize Pushkin’s openness to the genius of all other nations. Moreover, Dostoevsky considered universal responsiveness to be typical of Russians in general. However, the isolationist tradition in Russia has been no less influential. At times this tradition has prevailed, at times it has retreated. It has expressed itself openly in political life – Stalin’s campaign against ‘cosmopolites’ was an especially striking example – and its impact on the development of literature and science has been the object of extensive research. Mathematics education, however, has rarely been looked at from this perspective. This paper will focus on a few select episodes from the history of mathematics education in Russia. These episodes, however, clearly demonstrate that a conflict between the isolationist and the internationalist traditions has taken place in this field as well. The paper contains a discussion of Leo Tolstoy’s article ‘On the People’s Education’, little‐known in the West, in which Russian mathematics education is aggressively and favorably contrasted with German methodologies. It also examines a methodological work from 1951, which includes a chapter entitled ‘From the History of the Struggle against Foreign Influences in Russian Mathematics’. On the other hand, the article also looks at materials from Russian mathematics teachers’ congresses from before the Russian Revolution, which illustrate Russian involvement and participation in processes taking place abroad. It also analyzes correspondence between the well‐known Russian and American mathematics educators Dmitriy Sintsov and David Eugene Smith, discovered by the author, which facilitates a deeper understanding of certain aspects of the issues under investigation.

Notes

¹ The author wishes to express his gratitude to Dr Gert Schubring for useful discussions and for help with the bibliography.

² Dostoevsky, F. M. Collected Works [Polnoe sobranie sochinenii v 30‐ti t.]. Leningrad: Nauka, Leningr. otd‐nie, 1972–1990. Vol. 26: 136–49.

³ Ibid., 145. Here and below, all translations are by the author.

⁴ Uspenskii, Boris. Studies In Russian History [Etiudy o russkoy istorii]. St Petersburg: Azbuka, 2002.

⁵ See Vucinich, Alexander. Science in Russian Culture: A History to 1860. Stanford, CA: Stanford University Press, 1963.

⁶ Quoted in Poliakova, T. S. The History of Russian Mathematics Education [Istoria otechestvennogo shkol’nogo matematicheskogo obrasovania]. Rostov: RPI., 1997: 83.

⁷ See Vucinich, Science in Russian Culture; Poliakova, The History of Russian Mathematics Education. Here and in what follows, our discussion addresses western influences without examining distinctions between the various countries of Western Europe, and later the United States as well. In this respect, we follow the Russian tradition, which typically perceived the process of ‘westernization’ as a unified whole. However, differences between influences from different countries, as well as changes in the relative dominance of these influences, represent an interesting topic for investigation.

⁸ See Poliakova. The History of Russian Mathematics Education: 93–94.

⁹ Nikol’zeva, N. F., ed. Primary and Secondary School Education in St Petersburg in the Nineteenth and Early Twentieth Centuries: Collection of Primary Sources [Nachal’noe i srednee obrasovanie v Sankt‐Peterburge. XIX – nachalo XX veka. Sbornik dokumentov]. Saint‐Petersburg: Liki Rossii, 2000: 38–39.

¹⁰ Ibid., 98.

¹¹ See Ganelin, Sch. I. Survey of the History of Secondary Schools in Russia in the Second Half of the Nineteenth Century [Ocherki po istorii sredney schkoly v Rossii vtoroi poloviny XIX veka]. Moskva: UchPedGis, 1954.

¹² See for example Mazing, K. “Notes on Teaching Mathematics in Our Gymnasiums” [Zametki o prepodavanii matematiki v nashih gimnasiah]. Zhurnal Ministerstva narodnogo prosveschenia 2 (1872): 162–73.

¹³ Vucinich, Science in Russian Culture.

¹⁴ See, for example, Drobyschev, Iu. A. On History of Russian Geometry Textbooks. [Is istorii russkogo uchebnika geometri]). Kaluga: KGU, 2001.

¹⁵ Prudnikov, V. E., P. L. Chebyshev – Scientist and Teacher [P. L. Chebyshev – uchenyi i pedagog]. Moscow: UchPedGiz, 1950: 92.

¹⁶ Ibid., 92; Legendre, A. M. Éléments de géométrie avec des notes. Paris: Firmin Didot, 1842; Mayer‐d’Almbert, Mathias, and Charles Choquet. Traité élémentaire d’algèbre, Paris: Bachelier, 1841; Wöckel, Lorenz. Die Geometrie der Alten in einer Sammlung von 824 Aufgaben. Nürnberg: Bauer und Raspe, 1847.

¹⁷ Tolstoy, Lev “On the People’s Education” [O narodnom obrasovanii]. Collected Works [Polnoe Sobranie sochninenii v 90 t.]. Moscow, 1928–58, vol. XVII: 71–132.

²⁰ Tolstoy, “On the People’s Education,” 82.

¹⁸ See Mossman, Eliott. “Tolstoi and Peasant Learning in the Era of the Great Reforms.” In School and Society in Tsarist and Soviet Russia, edited by Ben Eklof. New York: St Martin’s Press, 1992: 36–69; Prudnikov, V. E. Russian Mathematics Educators of the XVIII–XIX Centuries [Russkie pedagogi matematiki XVIII‐XIX vekov]. Moscow, 1956. Mossman analyzes aspects of this debate that pertain to the teaching of reading; Prudnikov deals with points that concern mathematics education.

¹⁹ August Wilhelm Grube (1816–1884), German pedagogue and teacher educator; author of numerous textbooks for teacher education, for elementary schools. Highly influential was his “Leitfaden für das Rechnen in der Elementarschule, nach den Grundsitzen einer heuristischen Methode,” 1842, 1852.

²² Ibid., 95.

²¹ Ibid., 93.

²³ Evtushevsky, V. Response to Count L. Tolstoy’s Article, ‘On the People’s Education’ [Otvet na stat’iu grafa L. Tolstogo ‘O narodnom obrasovanii’]. St Petersburg: v tipografii Besobrazova, 1874: 32.

²⁴ Ibid., 52.

²⁵ Ibid., 56.

²⁶ Tolstoy, “On the People’s Education,” 107.

²⁷ Ibid., 117.

²⁸ Karp, A. P. A Classic of Real Education: On the 150th Anniversary of the Birth of A. P. Kiselev [Klassik real’nogo obrazovania. K stopiatidesiatiletiu so dnia rogdenia A.P. Kiseleva]. St Petersburg: SMIO Press, 2002.

²⁹ Morduhai‐Boltovskoy, D. On the First Russian Congress of Mathematics Teachers [O pervom vserossiiskom s’esde prepodavateley matematiki]. Warsaw: Tipografia uchebnogo okruga, 1912: 4.

³⁰ Reports of the First Russian Congress of Mathematics Teachers [Trudy I‐go Vserossiiskogo S’esda prepodavateley matematiki]. Vol. I–III. St. Petersburg: Sever, 1913.

³¹ See Guschel’, R. Z. “On International Reform Movement in Mathematics Education at the Beginning of the 20th century” [O megdunarodnom dvigenii po reformirovaniu matematicheskogo obrasovania v nachale XX stoletia], Mathematicheskoe Prosveschenie Series 3, no. 7 (2003): 39–44.

³² Minutes of the Second Russian Congress of Mathematics Teachers [Dnevniki Vtorogo Vserossiiskogo s’esda prepodavateley matematiki]. Moskva: Orgkomitet S’esda, 1913–1914: 94.

³³ Karp, A Classic of Real Education: On the 150th Anniversary of the Birth of A.P. Kiselev.

³⁴ Novoselov. “Stable Mathematics Textbooks (Secondary School)” [Stabil’nye uchebniki po matematike (sredniaya shkola]. Matematika v shkole 4 (1938): 66–68.

³⁵ See, for example, Fitzpatrick, S. “Culture and Politics under Stalin: A Reappraisal.” Slavic Review 35, no. 2 (1976): 211–31.

³⁶ N. V. Kiselev, personal communication.

³⁷ See Levin, Aleksey E. “Anatomy of a Public Campaign: ‘Academician Luzin’s Case’ in Soviet Political History.” Slavic Review 49, no. 1 (1990): 90–108; Demidov, S. S., and B.V. Levshin, eds. The N. N. Luzin Affair [Delo akademika N.N. Lusina]. St Petersburg: RHGI, 1999.

³⁸ Quoted in Demidov and Levshin, The N.N. Luzin Affair, 270.

³⁹ Loc. cit.

⁴⁰ Ibid., 254.

⁴¹ Alexandrov, D. “Why Soviet Scientists Ceased to Publish Abroad: The Development of Self‐Sufficiency and Isolation of Russian Science, 1914–1940” [Pochemu sovetskie uchenye perestali pechatat’sia sa rubegom: stanovlenie samodostatochnosti i isolirovannosti otechestvennoy nauki, 1914–1940]. Voprosy istorii estestvosnania i tehniki 3 (1996): 3–24.

⁴² See Demidov and Levshin, The N.N. Luzin affair, 257.

⁴³ See Berezanskaya, E. “Brief Report on the Conference of Mathematics Teachers” (Kratkii otchet o soveschanii prepodavateley matematiki). Matematika i fisika 4 (1935): 49–52.

⁴⁴ Lankov, A. V. Toward a History of the Development of Progressive Ideas in Russian Mathematics Methodology [K istorii rasvitia peredovyh idey v russkoy metodike matematiki]. Moscow, 1951: 111.

⁴⁵ Ravitch, Diane. Left Back: A Century of Failed School Reforms. New York: Simon & Schuster, 2000: 130.

⁴⁶ Karp, A. P. Algebra Graduation Exams in Russia over the last 100 years [Pis’mennye vypusknye eksameny po algebra v Rossii sa 100 let]. St. Petersburg: SPbGUPM, 1998.

⁴⁷ Pontriagin, L. S. “On Mathematics and the Quality of Mathematics Education” (O matematike i kachestve ee prepodavania). Kommunist, 14 (1980): 99–112.