Abstract
As part of a large reciprocal learning partnership project between Canada and China, this study explored Canadian teachers’ perceptions of mathematics teaching in elementary schools in China. Using reciprocal learning and Activity Theory as the theoretical lens, we collected data, i.e., classroom observations, group discussion, and informal exchanges from teachers in a pair of research sister-schools in Canada and China. Qualitative data analyses revealed four themes in Canadian teachers’ perceptions of the characteristics of Chinese mathematics teaching: an active teacher-student interaction model of questioning-responding, a mathematical knowledge-package summary at the end of each lesson, integration of the history of mathematics into teaching, and the development and implementation of well-structured lessons. Contributions, implications, and limitations of the study in mathematics education and research are discussed.
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References
An, S. H. (2008). Outsiders’ views on Chinese mathematics education: A case study on the United States teachers’ teaching experience in China. Journal of Mathematics Education, 1(1), 1–27.
Arthur, L. (2010, November 2). Insider-outsider perspectives in comparative education. Seminar presentation at the Research Center for International and Comparative Studies, University of Bristol, Bristol, UK.
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). American Educational Research Association.
Biggs, J. B. (1994). What are effective schools? Lessons from East and West. Australian Educational Researcher, 21, 19–39. https://doi.org/10.1007/BF03219558
Cai, J. F., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: Perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education, 13(3), 265–287. https://doi.org/10.1007/s10857-009-9132-1
Cao, Y. M., & Leung, F. K. S. (Eds.). (2018). The 21st century mathematics education in China. Springer.
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258–277.
Connelly, F. M., & Clandinin, D. J. (1990). Stories of experience and narrative inquiry. Educational Researcher, 19(5), 2–14. https://doi.org/10.3102/0013189X019005002
Connelly, F. M., & Clandinin, D. J. (2006). Narrative inquiry. In J. Green, G. Camilli, & P. Elmore (Eds.), Handbook of complementary methods in education research (pp. 375–385). Lawrence Erlbaum.
Connelly, F. M., & Xu, S. J. (2019). Reciprocal learning in the partnership project: From knowing to doing in comparative research models. Teachers and Teaching: Theory and Practice, 25(6), 627–646. https://doi.org/10.1080/13540602.2019.1601077
Dooley, T. (2012). Constructing and consolidating mathematical entities in the context of whole class discussion. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: Expanding horizons. Proceedings of the 35th conference of the Mathematics Education Group of Australasia (pp. 234–241). MERGA.
Engeström, Y., & Cole, M. (1997). Situated cognition in search of an agenda. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 301–309). Lawrence Erlbaum.
Fan, L. H., Wong, N.-Y., Cai, J. F., & Li, S. Q. (Eds.). (2004). How Chinese learn mathematics: Perspectives from insiders. World Scientific.
Fan, L. H., Wong, N.-Y., Cai, J. F., & Li, S. Q. (Eds.). (2015). How Chinese teach mathematics: Perspectives from insiders. World Scientific.
Givvin, K. B., Hiebert, J., Jacobs, J. K., Hollingsworth, H., & Gallimore, R. (2005). Are there national patterns of teaching? Evidence from the TIMSS 1999 video study. Comparative Education Review, 49(3), 311–343. https://doi.org/10.1086/430260
Hasan, H., & Kazlauskas, A. (2014). Activity Theory: Who is doing what, why and how. In H. Hasan (Ed.), Being practical with theory: A window into business research (pp. 9–14). The THEORI Business Research Group. http://eurekaconnection.files.wordpress.com/2014/02/p-09-14-activity-theory-theori-ebook-2014.pdf
Howitt, C. (2019). Building a bridge between Western and Eastern worlds: Reciprocal learning programmes that create reflective practice, hope, and prosperity in education. Teachers and Teaching: Theory and Practice, 25(6), 743–751. https://doi.org/10.1080/13540602.2019.1680358
Hu, X., Leung, F. K. S., & Teng, Y. (2018). The influence of culture on students’ mathematics achievement across 51 countries. International Journal of Science and Mathematics Education, 16, 7–24. https://doi.org/10.1007/s10763-018-9899-6
Huang, L. H., Doorman, M., & van Joolingen, W. (2020). Inquiry-based learning practices in lower-secondary mathematics education reported by students from China and the Netherlands. International Journal of Science and Mathematics Education, 1–17. https://doi.org/10.1007/s10763-020-10122-5
Huang, R., & Leung, F. K. S. (2004). Cracking the paradox of the Chinese learners: Looking into the mathematics classrooms in Hong Kong and Shanghai. In L. H. Fan, N.-Y. Wong, J. F. Cai, & S. Q. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 348–381). World Scientific.
Huang, R. J., & Li, Y. P. (Eds.) (2017). Teaching and learning mathematics through variation: Confucian heritage meets Western theories. Sense Publishers.
Iserbyt, P. (2011). Reciprocal learning. In N. M. Seel (Ed.), Encyclopedia of the sciences of learning (pp. 2785–2786). Springer.
Jaworski, B., & Potari, D. (2009). Bridging the macro- and micro-divide: Using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. Educational Studies in Mathematics, 72, 219–236. https://doi.org/10.1007/s10649-009-9190-4
Jin, X. Y. (2012). Chinese middle school mathematics teachers’ practices and perspectives viewed through a Western lens [Unpublished doctoral dissertation]. Monash University, Melbourne, Australia.
Leung, F. K. S. (1995). The mathematics classroom in Beijing, Hong Kong, and London. Educational Studies in Mathematics, 29, 297–325. https://doi.org/10.1007/BF01273909
Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51. https://doi.org/10.1023/A:1017936429620
Leung, F. K. S., Park, K., Holton, D., & Clarke, D. (Eds.). (2014). Algebra teaching around the world. Springer.
Lê, F. (2016). Reflections on the notion of culture in the history of mathematics: The example of “geometrical equations.” Science in Context, 29(3), 273–304. https://doi.org/10.1017/S0269889716000089
Li, Y. P., & Huang, R. J. (Eds.). (2013). How Chinese teach mathematics and improve teaching. Routledge.
Lim, C. S. (2007). Characteristics of mathematics teaching in Shanghai, China: Through the lens of a Malaysian. Mathematics Education Research Journal, 19(1), 77–88. https://doi.org/10.1007/BF03217450
Liu, P.H. (2009). History as a platform for developing college students’ epistemological beliefs of mathematics. International Journal of Science and Mathematics Education, 7(2), 473–499. https://doi.org/10.1007/s10763-008-9127-x
McAvinia, C. (2016). Activity theory. In C. McAvinia (Ed.), Online learning and its users: Lessons for higher education (pp. 59–100). Chandos Publishing.
McGrath, S. (2017). Book review: “Revisiting insider-outsider research in comparative and international education.” Educational Review, 69(1), 134–135. https://doi.org/10.1080/00131911.2016.1205275
McNess, E., Arthur, L., & Crossley, M. (2015). “Ethnographic dazzle” and the construction of the “other”: Revisiting dimensions of insider and outsider research for international and comparative education. Compare: A Journal of Comparative and International Education, 45(2), 295–316. https://doi.org/10.1080/03057925.2013.854616
Miao, Z. Z., Reynolds, D., Harris, A., & Jones, M. (2015). Comparing performance: A cross-national investigation into the teaching of mathematics in primary classrooms in England and China. Asia Pacific Journal of Education, 35(3), 392–403. https://doi.org/10.1080/02188791.2015.1056593
Milligan, L. (2016). Insider-outsider-inbetweener? Researcher positioning, participative methods and cross-cultural educational research. Compare: A Journal of Comparative and International Education, 46(2), 235–250. https://doi.org/10.1080/03057925.2014.928510
Ministry of Education of the People’s Republic of China. (MoE). (2020). 普通高中数学课程标准(2020修订版) [High school mathematics curriculum standards (2020 ed.)]. 人民教育出版社 [People’s Education Press].
Morris, P. (1985). Teachers’ perceptions of the barriers to the implementation of a pedagogic innovation: A South East Asian case study. International Review of Education, 31, 3–18. https://doi.org/10.1007/BF02262565
Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers’ beliefs of students’ algebra development. Cognition and Instruction, 18(2), 209–237. https://doi.org/10.1207/S1532690XCI1802_03
OECD. (2010). PISA 2009 results: Executive summary. http://www.oecd.org/pisa/pisaproducts/46619703.pdf
OECD. (2013). PISA 2012 results: What students know and can do. Student performance in reading, mathematics, and science (Vol. I). http://www.oecd.org/pisa/keyfindings/pisa-2012-results-volume-I.pdf
OECD. (2016). PISA 2015 assessment and analytical framework: Science, reading, mathematics, and financial literacy. OECD.
OECD. (2017). PISA 2015 technical report. http://www.oecd.org/pisa/data/2015-technical-report/
Palinscar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension fostering and comprehension monitoring activities. Cognition and Instruction, 1(2), 117–175. https://doi.org/10.1207/s1532690xci0102_1
Peng, A., & Nyroos, M. (2012). Values in effective mathematics lessons in Sweden: What do they tell us? The Mathematics Enthusiast, 9(3), 409–430.
Peng, A., Ezeife, A. N., & Yu, B. (2018). Reciprocal learning in mathematics education: An interactive study between two Canadian and Chinese elementary schools. Comparative and International Education/Éducation Comparée et Internationale, 47(1), 1–14.
Peng, A., Cao, L., & Yu, B. (2020). Reciprocal learning in mathematics problem posing and problem solving: An interactive study between Canadian and Chinese elementary school students. EURASIA Journal of Mathematics, Science and Technology Education, 16(12), 1–13. https://doi.org/10.29333/ejmste/9130
Perry, B., Wong, N.-Y., & Howard, P. (2006). Comparing primary and secondary mathematics teachers’ beliefs about mathematics, mathematics learning, and mathematics teaching in Hong Kong and Australia. In F. K. S. Leung, K.-D. Graf, & F. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West (pp. 435–448). Springer.
Rocher, G. (1968). Introduction à la sociologie générale (Introduction to general sociology). Hurtubise.
Skott, J. (2001). The emerging practices of a novice teacher: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4, 3–28. https://doi.org/10.1023/A:1009978831627
Star, J., & Chang, K.-L. (2008). A review of “how Chinese learn mathematics: Perspectives from insiders.” Journal for Research in Mathematics Education, 39(2), 213–216.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. https://doi.org/10.1080/10986060802229675
Tweed, R. G., & Lehman, D. R. (2002). Learning considered within a cultural context: Confucian and Socratic approaches. American Psychologist, 57(2), 89–99. 10.1037/0003-066X.57.2.89
Wang, K., Wang, X.-Q., Li, Y. P., & Rugh, M. S. (2018). A framework for integrating the history of mathematics into teaching in Shanghai. Educational Studies in Mathematics, 98, 135–155. https://doi.org/10.1007/s10649-018-9811-x
Watkins, D. A., & Biggs, J. B. (2001). The paradox of the Chinese learner and beyond. In D. A. Watkins & J. B. Biggs (Eds.), Teaching the Chinese learner: Psychological and pedagogical perspectives (pp. 3–26). The Comparative Education Research Center (CERC) and the Australian Council of Educational Research (ACER).
Xu, B. Y. (2010). Research on mathematics education in China in the last decade: A review of journal articles. Frontiers of Education in China, 5(1), 130–155. https://doi.org/10.1007/s11516-010-0009-y
Xu, S. J. (2019). Reciprocal learning in teacher education between Canada and China. Teachers and Teaching: Theory and Practice, 25(6), 703–729. https://doi.org/10.1080/13540602.2019.1659766
Xu, S. J., & Connelly, F. M. (2014). Partnership grant: Reciprocal learning in teacher education and school education between Canada and China. http://www.reciprocal-learning.ca/pages.php
Xu, S. J., & Connelly, F. M. (2017). Reciprocal learning between Canada and China in teacher education and school education: Partnership studies of practice in cultural context. Frontiers of Education in China, 12(2), 135–150. https://doi.org/10.1007/s11516-017-0013-6
Yang, Y. D. (2009). How a Chinese teacher improved classroom teaching in Teaching Research Group: A case study on Pythagoras theorem teaching in Shanghai. ZDM, 41, 279–296. https://doi.org/10.1007/s11858-009-0171-y
Yuan, Z. Q., & Matney, G. (2018). Searching for the middle zone of Chinese and American mathematics teaching through math camps. Journal of Mathematics Education, 11(2), 1–16. https://doi.org/10.26711/007577152790024
Zou, H. (2014). U.S. and Chinese middle school mathematics teachers’ pedagogical content knowledge: The case of functions [Unpublished doctoral dissertation]. Arizona State University, Tempe, AZ.
Acknowledgments
We would like to express our sincere gratitude to the two anonymous reviewers for their valuable comments and suggestions which led to substantial improvement of the manuscript. We also gratefully acknowledge Dr. Ruth Hayhoe for her insightful suggestions to improve the paper. Furthermore, we acknowledge the grant from the National Social Science Foundation of China (No. 17XMZ032), Chongqing Association of Higher Education (No. CQGJ19A02), and Ideological and Political Course at Southwest University (No. 20190711) for providing funds to the study. We greatly appreciate the Social Sciences and Humanities Research Council (SSHRC) of Canada which funds the larger Reciprocal Learning Canada-China Partnership Project (898-2021-1011). Last but not least, we appreciate the support and contributions of the graduate students, mathematics students, teachers, and school administrators in Canada and China for their participation in this project. Of course, any remaining errors are the responsibility of the authors.
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Peng, A., Cao, L. How Chinese Teach Mathematics: Canadian Teachers’ Perspectives. Front Educ China 16, 31–59 (2021). https://doi.org/10.1007/s11516-021-0002-7
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DOI: https://doi.org/10.1007/s11516-021-0002-7