Geodesic
Productive education in the mathematical school
Čebyševskij sbornik, Tome 22 (2021) no. 1, pp. 413-446.

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The article examines the reasons why mathematical schools (mathschools) have become an important and very productive phenomenon in Russian education in recent decades. A brief description of the modern model of productive education traced back to the established tradition of teaching in mathschools, which can lead to the construction of a reproducible model of productive education not only for specialized teaching of mathematics, but also for other areas of Russian general education.
Keywords: the tradition of mathschools and mathclasses, the Konstantinov School, school mathematics education in Russia, productive education, solving unexpected problems, recreational mathematics, mathematical circle, mathematical Olympiad, university students as teachers, level differentiation, learning and research activity of students, digital transformation of education. 
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N. N. Konstantinov; A. L. Semenov. Productive education in the mathematical school. Čebyševskij sbornik, Tome 22 (2021) no. 1, pp. 413-446. http://geodesic.mathdoc.fr/item/CHEB_2021_22_1_a28/

[1] Kukulin I., Maiofis M., Safronov P. (red. i sost.), Ostrova utopii. Pedagogicheskoe i sotsialnoe proektirovanie poslevoennoi shkoly (1940–1980-e), Biblioteka zhurnala «Novoe literaturnoe obozrenie», seriya «Neprikosnovennyi zapas», M., 2015, 695 pp.

[2] Asmolov A. G., Shekhter E. D., Chernorizov A. M., “Preadaptatsiya k neopredelennosti kak strategiya navigatsii razvivayuschikhsya sistem: marshruty evolyutsii”, Voprosy psikhologii, 2017, no. 4, 3–26

[3] Lankov A. V., K istorii razvitiya peredovykh idei v russkoi metodike matematiki, Posobie dlya uchitelei, Uchpedgiz, M., 1951, 152 pp.

[4] Kalyagin Yu. M., “Shkolnyi uchebnik matematiki: vchera, segodnya zavtra”, Matematicheskoe obrazovanie, 2006, no. 3(38), 2–8

[5] Gurev P. S. (sost.), Rukovodstvo k prepodavaniyu arifmetiki maloletnim detyam, v. 1–2, Tipografiya K. Vingebera, SPb., 1839–1842 (data obrascheniya 25 yanvarya 2020 g.) https://rusneb.ru/catalog/000199_000009_003823712/

[6] Gurev P. S., Arifmeticheskie listki, postepenno raspolozhennye ot legchaishego k trudneishemu, soderzhaschie v sebe 2523 zadachi s resheniyami onykh i kratkim rukovodstvom k ischisleniyu, Imperat. Akad. nauk, SPb., 1832, 345 pp.; Гурьев П. С., “Арифметические листки”, Матем. обр., 40 (2007), 32–48

[7] Gurev P. S., Klyuch k arifmeticheskim listkam, Imperat. Akad. nauk, SPb., 1832, 74 pp.

[8] Gurev P. S., Prakticheskaya arifmetika, Ya. A. Isakov, SPb., 1861, 336 pp.; Ключ к практической арифметике, 31 с.

[9] Prudnikov V. E., Russkie pedagogi-matematiki XVIII-XIX vekov, Uchpedgiz, M., 1956, 640 pp.

[10] Gurev P. S., Dmitriev A. D., Prakticheskie uprazhneniya v geometrii, ili sobranie geometricheskikh voprosov i zadach s ikh otvetami i resheniyami, v. 1, Voprosy i zadachi, tip. K. Zhernakova, SPb., 1844, 227 pp.

[11] Arnold I. V., “Printsipy otbora i sostavleniya arifmeticheskikh zadach”, Izvestiya APN RSFSR, 1946, no. 6, 8–28 (data obrascheniya 25 yanvarya 2020 g.) https://math.ru/lib/files/iva46.htm

[12] Khinchin A. Ya., “O tak nazyvaemykh «zadachakh na soobrazhenie» v kurse arifmetiki”, Matem. prosv., ser. 2, 1961, no. 6, 29–36

[13] Depman I. Ya., Istoriya arifmetiki, Posobie dlya uchitelei, Uchpedgiz, M., 1959, 424 pp.

[14] Propositiones ad Acuendos Juvenes, , 2020 https://ru.wikipedia.org/wiki/Propositiones_ad_Acuendos_Juvenes

[15] Alcuin Singmaster D., Problems to Sharpen the Young: an Annotated Translation of Propositiones Ad Acuendos Juvenes, the Oldest Mathematical Problem Collection in Latin, South Bank University, 1995

[16] Olekhnik S. N., Nesterenko Yu. V., Potapov M. K., Starinnye zanimatelnye zadachi, Drofa, M., 2006, 176 pp. | MR

[17] Ignatev E. I., V tsarstve smekalki, ili Arifmetika dlya vsekh: opyt matematicheskoi khrestomatii. Kniga dlya semi i shkoly, S.-Peterburg, 1908, 275 pp.

[18] Perelman Ya. I., Zanimatelnaya fizika, v. 1, 2, P. P. Soikin, Sankt-Peterburg, 1913–1916

[19] Perelman Ya. I., Veselye zadachi: 101 golovolomka dlya yunykh matematikov, tip. t-va A. S. Suvorina, Petrograd, 1916, 158 pp.

[20] Lyusternik L. A., “Molodost Moskovskoi matematicheskoi shkoly”, UMN, 22:4(136) (1967), 147–185 | Zbl

[21] Leman A. A. (sost.), Sbornik zadach moskovskikh matematicheskikh olimpiad, ed. V. G. Boltyanskii, Prosveschenie, M., 1965, 384 pp.

[22] Shklyarskii David Osipovich, Sait math.ru, razdel «Istoriya matematiki», (data obrascheniya 25 yanvarya 2020 g.) https://math.ru/history/people/shklyarskiy

[23] Chentsov N. N., Shklyarskii D. O., Yaglom I. M., Izbrannye zadachi i teoremy elementarnoi matematiki. Arifmetika i algebra, Ser. «Biblioteka matematicheskogo kruzhka», 1, Nauka, M., 1976, 384 pp. (6 izdanii: 1950, 1954, 1959, 1965, 1976 i 2001 gg.)

[24] Malyi mekhmat MGU. Arkhiv listkov, (data obrascheniya 25 yanvarya 2020 g.) http://mmmf.msu.ru/archive/

[25] Kenguru. Matematika dlya vsekh. Konkursy dlya shkolnikov, , 2020 (data obrascheniya 25 yanvarya 2020 g.) https://russian-kenguru.ru/konkursy/kenguru

[26] Bashmakov M. I., “U istokov YuMSh”, Iz istorii MatMekha (15 oktyabrya 1996) (data obrascheniya 25 yanvarya 2020 g.) http://dm47.com/sbornik_iimm_bashmakov.html

[27] Shvartsburd S. I., “O matematicheskoi spetsializatsii v srednei shkole”, Uspekhi matematicheskikh nauk, 21:1 (127) (1966), 205–214

[28] Shvartsburd S. I. (sost.), Lineinaya algebra i geometriya, ser. «Problemy matematicheskoi shkoly», APN RSFSR, In-t obsch. i politekhn. obrazovaniya, Prosveschenie, M., 1967, 366 pp.

[29] Landis E. M., Yaglom I. M., “Ob Aleksandre Semenoviche Kronrode”, UMN, 56:5(341) (2001), 191–201 | DOI | MR | Zbl

[30] Kronrod A. S., Besedy o programmirovanii, Predisl. L. A. Kronrod. Poslesl. V. L. Arlazarova, Izd. 2-e, stereotipnoe, Editorial URSS, M., 2004, 248 pp.

[31] Konstantinov N. N., “Rossiiskie matematicheskie klassy”, Tezisy vserossiiskogo s'ezda uchitelei matematiki v moskovskom universitete, 2010 (data obrascheniya 25 yanvarya 2020 g.) https://mccme.ru/teachers/articles/russmath.htm

[32] Dynkin E. B., Molchanov S. A., Rozental A. L., Tolpygo A. K., Matematicheskie zadachi, Seriya «Bibliotechka fiziko-matematicheskoi shkoly. Matematika», 1, Nauka, M., 1965, 80 pp.

[33] Gelfand S. I., Gerver M. L., Kirillov A. A., Konstantinov N. N., Kushnirenko A. G., Zadachi po elementarnoi matematike. Posledovatelnosti. Kombinatorika. Predely, Ser. «Bibliotechka fiziko-matematicheskoi shkoly», 3, Nauka, M., 1965, 176 pp.

[34] Kanel-Belov A. Ya., Kovaldzhi A. K., “Zanyatiya po matematike - listki i dialog”, Matematicheskoe Prosveschenie, 3 seriya, 19, 2015, 206–235 (data obrascheniya 25 yanvarya 2020 g.) https://www.mccme.ru/free-books/matpros/pdf/mp-19-kk.pdf

[35] Golenischeva-Kutuzova T. I., Kazantsev A. D., Kudryashov Yu. G., Kustarev A. A., Merzon G. A., Yaschenko I. V., Elementy matematiki v zadachakh s resheniyami i kommentariyami, v. 1, MTsNMO, M., 2010, 248 pp. (data obrascheniya 25 yanvarya 2020 g.) https://mccme.ru/free-books/yaschenko/v08book-08.pdf

[36] Firsov V. V., “O sovershenstvovanii metodicheskoi sistemy obucheniya matematike”, 1988 g., Uchim matematikoi, Prosveschenie, M., 2012, 136–142 (data obrascheniya 25 yanvarya 2020 g.) https://www.mathedu.ru/text/firsov_uchim_matematikoy_2012/p136/

[37] Firsov V. V., “Metodika obucheniya matematike kak nauchnaya distsiplina”, 2005 g., Uchim matematikoi, Prosveschenie, M., 2012, 160–172 (data obrascheniya 25 yanvarya 2020 g.) https://www.mathedu.ru/text/firsov_uchim_matematikoy_2012/p160/

[38] Firsov V. V., “Edinaya i mnogoobraznaya”, 1989 g., Uchim matematikoi, Prosveschenie, M., 2012, 142–147 (data obrascheniya 25 yanvarya 2020 g.) https://www.mathedu.ru/text/firsov_uchim_matematikoy_2012/p142/

[39] Loginova O. B. (sost.), Urovnevaya differentsiatsiya obucheniya, Sb. statei. Mosk. departament obrazovaniya, Nauch.-ped. ob-nie «Obrazovanie dlya vsekh», M., 1994, 125 pp.

[40] Obukhov A. S., Razvitie issledovatelskoi deyatelnosti uchaschikhsya, 2-e izd., pererab. i dop., Natsionalnyi knizhnyi tsentr, M., 2015, 288 pp.

[41] GBOU goroda Moskvy «Shkola No 1553 imeni V. I. Vernadskogo, (data obrascheniya 25 yanvarya 2020 g.) https://lycu1553.mskobr.ru/

[42] Sodruzhestvo Litseya No 1533 (informatsionnykh tekhnologii), (data obrascheniya 25 yanvarya 2020 g.) https://www.lit.msu.ru/

[43] Galich A., My ne khuzhe Goratsiya, 1966 (data obrascheniya 25 yanvarya 2020 g.) http://www.bards.ru/archives/part.php?id=4132

[44] Konstantinov N. N., “Opyt matklassov shkol No 7, 57, 91 i 179 (1962–1986 gg.) s tochki zreniya VNTK”, Tezisy vystupleniya na seminare VNKT pod ruk. akademika E. P. Velikhova 19 marta 1986 g., Arkhiv akademika A. P. Ershova (data obrascheniya 25 yanvarya 2020 g.) http://ershov-arc.iis.nsk.su/archive/eaimage.asp?fileid=207596

[45] Rudchenko T. A., Semenov A. L., Informatika. 1–4 klassy, Uchebno-metodicheskii komplekt (uchebniki, rabochie tetradi, tetradi proektov, pourochnye razrabotki dlya kazhdogo goda obucheniya) dlya obscheobrazovat. organizatsii, Seriya «Perspektiva», Prosveschenie, INT, M., 2011–2012

[46] Semenov A. L., Positselskaya M. A., Positselskii S. E., Rudchenko T. A. i dr., Matematika i informatika. 1–4 klassy, Uchebno-metodicheskii komplekt (uchebniki i zadachniki) dlya obscheobrazovat. organizatsii, MTsNMO, INT, M., 2012–2019

[47] Semenov A. L., “Simor Papert i my. Konstruktsionizm – obrazovatelnaya filosofiya XXI veka”, Voprosy obrazovaniya, 2017, no. 1, 269–294

[48] Papert S., Pismo akademiku A. P. Ershovu ot 22 iyunya 1988 g., Arkhiv akademika A. P. Ershova (data obrascheniya 25 yanvarya 2020 g.) http://ershov-arc.iis.nsk.su/archive/eaimage.asp?l20ang=1&did=38546&fileid=206979

[49] Startovaya stranitsa proekta «PiktoMir» na saite FGU FNTs NIISI RAN, (data obrascheniya 25 yanvarya 2020 g.) https://www.niisi.ru/piktomir

[50] Betelin V. B., Kushnirenko A. G., Leonov A. G., “Osnovnye ponyatiya programmirovaniya v izlozhenii dlya doshkolnikov”, Informatika i ee primeneniya, 14:3 (2020), 55–61 | MR