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<\/a><\/p>\nIn my visits abroad, working with mathematicians and educators, I have had to both adapt to and learn from these different mathematical cultures.\u00a0 Here I write about three of them, from which I have learned the most.\u00a0\u00a0 These three cultures are:<\/p>\n
\u00a0>East Asia, with its strong ability to bring large numbers of students up to a high level of mathematical competence
\n>The US, where students are urged to develop and use their creativity;
\n>East Europe, where the mathematical community inspires passion for the subject in its students.<\/p>\n
Disclaimer: one of these is my own culture, of the United States of America.\u00a0 I include it because I find it to be a strong influence on others.\u00a0 The reader can decide whether this portion of my account is sufficiently objective.<\/p>\n
The cultures of \u00a0East Asia \u00a0are well-known for providing a solid mathematical foundation for masses of people.\u00a0 Countries such as Taiwan, Singapore, Korea, and Japan shine in results reported by TIMSS and PISA (Mullis et al., 2020, 7ff, 147ff). \u00a0These results have been well studied (see for example\u00a0 Leung, 2020) and the cultures that produced them analyzed.\u00a0 In a nutshell, these largely Confucian cultures revere learning.\u00a0 The Chinese imperial examinations sometimes offered a path through the feudal economy from a rural village to the bureaucracy and splendor of the capital.\u00a0 There are, to this day, local deities who receive offerings at their temples for success in examinations.\u00a0 And the Chinese Empire, like the Roman Empire in the West, had a tremendous influence on nearby cultures.\u00a0 These attitudes, and even some of these practices, persist.<\/p>\n
The profession of teaching is revered in those cultures.\u00a0 The teacher is respected as a source of knowledge.\u00a0 In Taiwan, I saw students bow en masse<\/em> to the teacher at the start of the lesson, and again at the end, thanking him or her .\u00a0 Classes of 50 or 60 are not unusual on the high school level.\u00a0 \u201cClassroom management\u201d is rarely an issue.\u00a0 The student automatically respects and trusts the teacher, and the respect and trust is generally returned.\u00a0 I have returned to Taiwan often over the years, and have observed as pedagogical methods there have opened up to include work by groups of students and project-based learning.\u00a0 While the methods of teaching have changed and developed, the respect between the student and the teacher abides.\u00a0 The public education outcomes of these societies are the envy of the world.\u00a0 But in the countries themselves, something is often perceived to be lacking.\u00a0 The Japanese call it \u2018zest for life \u2018 (see for example Mori, or Ministry of Culture, both 2023) and have been struggling to restore to students their childhood.\u00a0 This quest is on an emotional level, but of course it has its intellectual ramifications.\u00a0 The Japanese seek to balance their children\u2019s intellectual achievement with an emotional goal.<\/p>\n Other cultures have goals that are more directly intellectual.\u00a0 Often one of them is a quest for creativity.\u00a0 In many countries of this region, learning is seen as mastering a body of knowledge which has been well worked out and enshrined in the literature.\u00a0 Teachers and educators\u2014and even politicians\u2014in those countries complain that there is little room for students to create their own knowledge or to invent new ways to reorganize the knowledge.<\/p>\n And in fact they often look to the US for models of \u2018creativity\u2019.\u00a0 This kept coming up, for example, on a tour of China by a group of educators in 2010.\u00a0 In a series of fascinating meetings, the question aroseup: \u201cHow do you encourage creativity in your students?\u201d\u00a0 It turned out that the Ministry of Education had disseminated a memorandum about creativity.\u00a0 Unfortunately, what I often found was that people asking that question would expect an algorithm for creativity: institute practices A, B, and C, and you will get creative thinking.<\/p>\n The question stymied me.\u00a0 It doesn\u2019t work that way. \u00a0\u00a0How could I even begin to answer it?\u00a0\u00a0 My own view, from inside the culture, is clouded.<\/p>\n One of the strengths of Confucian societies is the great respect for teachers and mentors.\u00a0 Many have pointed out that the TIMSS and PISA data are a reflection of this deep and strong tradition. But this very strength, which allows these cultures success in mass education, at the same time hamstrings them in getting students to think for themselves. \u00a0How can the student know something the teacher doesn\u2019t?\u00a0\u00a0 This question did not come up from people working in, say, China.\u00a0 But many Chinese scientists who work in other countries have pointed out that this is the crux of the problem.<\/p>\n It is difficult for us to see this from within America, but we are very good at just this goal.\u00a0 It is difficult partly because \u2018thinking for oneself\u2019 is hard to measure.\u00a0 Only careful, sensitive, and intensive observation, considering the student\u2019s immediate history and relationship to the teacher, can uncover the creative act.<\/p>\n But when it happens in the classroom, the moment is magical.\u00a0 That look on a student\u2019s face, that turn of phrase that you as a teacher have never heard, but which matches exactly the necessary intuitions\u2014including the teacher\u2019s pedagogical intuitions\u2014are hard to forget.<\/p>\n So what is it that unleashes the minds of US students?\u00a0 As with most cultural phenomena, this question is difficult to answer from within the culture.\u00a0 The fundamental levels of culture, of ethnicity, are unconscious, and it is hard for someone participating in them to dig them out.\u00a0 Too, the wellsprings of creativity are also in the unconscious mind, which adds another level of mystery to the question.<\/p>\n So as an American educator I am uniquely unqualified to say more about this phenomenon.\u00a0 I know about it only because my hosts describe it when I travel abroad.\u00a0 But it is true that Americans value creativity in ways that other cultures often overlook.\u00a0 A recent Gallup poll (Gallup, 2019; Saad, 2019) found that teachers who promote creativity see results in achievement.\u00a0 I don\u2019t think this finding is particularly shocking.\u00a0 The point is that an American institution (Gallup, funded partly by Apple Computers) thought to ask the question and seek the answer.\u00a0 This happens less often in other cultures.<\/p>\n Credit in this development must be given to the European legacy in America.\u00a0 British, Dutch, and Scandinavian schools have valued and encouraged independent thinking for a while.\u00a0 Perhaps this is another example of the historical commonplace that America has played the role for European culture that Rome played for Greece.\u00a0 In each case, the one extended and spread the innovations of the other.\u00a0 Maybe.<\/p>\n Credit must also be given to more recent borrowings from Eastern Europe.\u00a0 An extraordinary mathematical culture has developed in these countries, whose strength is not simply creativity, but passion.<\/p>\n The end of the Cold War gave Americans greater access to these countries, and more inter-cultural exchange.\u00a0\u00a0 A form of mathematical engagement new to Americans, the math circle, was largely a borrowing from these cultures.<\/p>\n The cultures of Eastern Europe have been strong in mathematics since their industrial revolution opened up education to their middle classes.\u00a0 I have elsewhere (Saul, 1992,2003, 2017, 2022) chronicled these developments in Bulgaria, Romania, and Russia (or the USSR).\u00a0 Tibor Frank (2007) has written about his native country, Hungary, which followed a slightly different path.<\/p>\n In brief, there are two forces at work here, neither of which apply directly to the American situation.\u00a0\u00a0 One is that of a small nation struggling to assert itself and consolidate its own progress.\u00a0 This is a large part of the Hungarian experience.\u00a0 Hungary underwent an industrialization in the late 1800s as part of the Hapsburg Empire.\u00a0 There was a national resolve to make the most of the nation\u2019s young minds, a tradition which persists to the present.\u00a0 High school teachers knew, and still know, members of the mathematical research community, and would inform them of students with noticeable talent in mathematics.\u00a0 \u00a0A group of research mathematicians and physicists began the journal K\u00f6MaL (see MATFUND, n.d.) which to this day binds together the mathematical community.\u00a0 The result is that this tiny nation of less than 10 million has become famous for producing mathematicians and scientists.<\/p>\n The other force, best exemplified by the USSR, is totalitarianism, which tended to push active minds into mathematics as a refuge.\u00a0 In brief, Soviet totalitarianism pervaded (by definition) its citizens\u2019 entire lives.\u00a0 Thinking was dangerous.\u00a0 Artists and writers worked under strict controls.\u00a0 Biologists were not allowed to study evolution.\u00a0 Psychologists and educators could not mention Piaget.\u00a0 Researchers in the physical sciences, dependent on laboratory resources, generally had to work for the military.\u00a0 Computer science was neglected, even after the Second World War.<\/p>\n But mathematicians were relatively free.\u00a0 They needed little or no equipment, and the applications of their work were sufficiently distant from the work itself to obviate any political \u2018channeling\u2019.<\/p>\n So active minds, people who might otherwise have become chemists, economists, even poets, gravitated to mathematics.\u00a0 Mathematics departments and classrooms became centers for a silent rejection of totalitarian values.\u00a0 The social lives of mathematicians, math educators, and math students, were also their professional lives, a\u00a0 subculture within the Soviet system.\u00a0 And like any subculture, it strove to reproduce itself.\u00a0 Research mathematicians and graduate students found common cause with teacher and pre-college students, in math circles, summer camps, and competitions.\u00a0 A rich literature of advanced mathematics from an elementary standpoint developed, authored by some of the country\u2019s most prominent researchers.\u00a0 The Anneli Lax New Mathematical Library is an example of American borrowings from this culture, as is the more recent flourishing of math circles in the US.\u00a0\u00a0 This passion for mathematics, a love of thinking about the subject, is a strong aspect of East European culture.<\/p>\n I have left out here many more mathematical cultures.\u00a0 The venerable mathematical traditions of South India, the current stirrings in Latin America, the vibrant mathematical culture of Western Europe, all deserve more note than this margin will allow.\u00a0 And the continent of Africa is a giant just beginning to feel its strength.\u00a0 In my work there, I find active young minds, and programs just starting to develop them.\u00a0 This second most populous continent has only begun to offer the benefits to mankind that it surely will in future.<\/p>\n This description of \u2018three cultures\u2019 can be read as a set of stereotypes.\u00a0 Like all stereotypes, they contain some truth.\u00a0 But like all stereotypes, they cannot be applied to individual cases.\u00a0 There are certainly creative Asians, passionate Americans, and schools in Eastern Europe that reach all their students with deep and important mathematics.\u00a0 The point is that each of these stereotypes describes a strength of the culture, an area from with others can learn.\u00a0 I hope we continue to learn.<\/p>\n WORKS CITED<\/p>\n Frank, Tibor. (2007). The social construction of Hungarian genius (1867-1930)<\/em>. Background paper for the conference on John von Neumann, organized by the Princeton Institute for International & Regional Studies and the John Templeton Foundation, The Witherspoon Institute, Princeton, NJ. October 5-6, 2007.<\/p>\n https:\/\/www.researchgate.net\/publication\/242572746_The_Social_Construction_of_Hungarian_Genius<\/p>\n Gallup (2019) Creativity in Learning. <\/em>https:\/\/www.gallup.com\/education\/267449\/creativity-learning-transformative-technology-gallup-report-2019.aspx<\/a><\/p>\n MATFUND Foundation (n.d.) What is K<\/em>\u00f6<\/em>MaL?\u00a0<\/em> http:\/\/www.komal.hu\/info\/miazakomal.e.shtml<\/p>\n Mori, Lynsey Helen (2023) \u201cHaving a Zest for Life: SEL in Japan\u201d, in Exploring Social Emotional Learning in Diverse Academic Settings<\/em><\/a>, Regina Rahimi, Delores Liston, Eds., 102-125. https:\/\/www.igi-global.com\/chapter\/having-a-zest-for-life\/321384<\/a><\/p>\n Mullis, Ina V. S., Martin, Michael O., Foy, Pierre, Kelly, Dana L., Fishbein, Bethany. (2020) Timss 2019 International Results in Mathematics And Science<\/em>, Lynch School of Eucation and Human Deelopmnet, Boston College and International Assiciation for the Evaluation of Educational Achievement, Boston,\u00a0chrome-extension:\/\/efaidnbmnnnibpcajpcglclefindmkaj\/https:\/\/www.iea.nl\/sites\/default\/files\/2020-12\/TIMSS-2019-International-Results-in-Mathematics-and-Science_0.pdf<\/p>\n Saad, Lydia (2019). \u201cTeachers Who Promote Creativity See Educational Results\u201d, in Gallup Blog<\/em>, October 28, 2019.\u00a0 https:\/\/news.gallup.com\/opinion\/gallup\/245600\/teachers-promote-creativity-educational-results.aspx<\/p>\n Saul, Mark (1992) “Love Among the Ruins: The Education of High-Ability Mathematics Students in the USSR,” in Focus<\/em>, Vol. 12, No. 1, February, 1992.<\/p>\n _______ (2003) \u201cMathematics in a Small Place: Notes on the Mathematics of Romania and Bulgaria\u201d, in AMS Notices, <\/em>May, 2003, 561-565;<\/p>\n _______ and Fomin, Dmitri (2017) \u201cRussian Traditions in Mathematics Education and Russian Mathematical Contests\u201d (with D. Fomin), in Russian Mathematics Education: History and World Significance.<\/em> Edited by Alexander Karp and Bruce R Vogeli.\u00a0 Singapore: World Scientific, 2010.\u00a0 Translated into Russian as \u0440\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0438\u0435 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438 \u0438 \u0440\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0438\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441 \u043a\u0438\u0435 \u0441\u043e\u0440\u0435\u0432\u043d\u043e\u0432\u0430\u043d\u0438\u0438, in \u0440\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u043e\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435, \u041c\u043e\u0441\u043a\u0432\u0430, \u043c\u0433\u043f\u0443, 2017, p. 209;<\/p>\n _______ (2022) \u201cRussian influences on American mathematics education after 1991: historical roots of changes in extracurricular programs\u201d in Zeitschrift fur Didaktik in Mathematics<\/em>, 53(7), 1605-1616, DOI 10.1007\/s11858-021-01293-8;<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n<\/a><\/p>\nLeung, Frederick K.S. (2017) \u201cMaking Sense of Mathematics Achievement in East Asia: Does Culture Really Matter?<\/a>\u201d, in Gabriele Kaiser (ed.), Proceedings of the 13th International Congress on Mathematical Education, ICME-13, 201-218.\u00a0 https:\/\/link.springer.com\/book\/10.1007\/978-3-319-62597-3#author-1-0<\/a><\/h4>\n
Ministry of Education, Culture, Sports, Science and Technology (2023) \u201cEncouraging Zest for Living\u201d, in Priorities and Prospects for a Lifelong Learning Society: Increasing Diversification and Sophistication, Chapter 3, Section 3, Notice from the Ministry of Education, Culture, Sports, Science and Technology, May 25, 2023 (in Japanese).\u00a0 \u00a0https:\/\/www.mext.go.jp\/b_menu\/hakusho\/html\/hpae199601\/hpae199601_2_042.html<\/a><\/h4>\n