Mathematicians’, mathematics educators’, and mathematics teachers’ professional conceptions of the school learning of mathematical modelling in China
Tóm tắt
Mathematical modelling has been included in many mathematics curricula worldwide, and China’s curricula are no exception. The development of modelling competencies has recently been listed among the Chinese mathematics curriculum’s six key objectives. However, the manner in which nationwide learning and teaching of modelling should be conducted presents a key challenge to China’s schools, most of which are wholly lacking in experience of this practice. In this study we present a thematic analysis of the conceptions of four mathematicians, five mathematics educators and seven mathematics teachers, with regard to the learning and teaching of modelling. The results show that the participants’ views of modelling can be categorised and linked to the following theoretical perspectives of modelling: applied, epistemological, educational, pedagogical and conceptual perspectives. Interestingly, the mathematicians and mathematics educators tended towards the atomistic approach to the learning and teaching of modelling, while the mathematics teachers placed greater emphasis on the holistic approach. The mathematicians and mathematics educators stressed student autonomy, while the teachers emphasised teacher demonstration. All participants considered group work to be an appropriate means of conducting modelling learning and teaching. Additionally, some teachers were concerned that modelling could not be incorporated into mathematical teaching and learning if it could not be included in high-stakes examinations. The paper concludes with a discussion on the rationale behind the existence of the various conceptions and the potential insights that may be drawn from these conceptions.
Tài liệu tham khảo
Altman, D. G. (1991). Practical statistics for medical research. Chapman and Hall.
Beswick, K. (2005). The beliefs-practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68.
Blomhøj, M., & Højgaard Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139.
Blum, W. (2011). Can modeling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 15–30). Springer.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of the 12th international congress on mathematical education (pp. 73–96). Springer.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222–231). Horwood.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modeling, applications, and links to other subjects—state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37–68.
Borromeo Ferri, R. (2013). Mathematical modelling in European education. Journal of Mathematics Education at Teachers College, 4(2), 18–24.
Borromeo Ferri, R. (2018). Learning how to teach mathematical modelling in school and teacher education. Springer.
Borromeo Ferri, R., et al. (2021). Mandatory mathematical modelling in school: What do we want the teachers to know? In F. K. S. Leung (Ed.), Mathematical modelling education in East and West (pp. 103–117). Springer.
Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’ modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 185–192). PME.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3, 77–101.
Frejd, P. (2012). Teachers’ conceptions of mathematical modelling at Swedish upper secondary school. Journal of Mathematical Modelling and Application, 17(1), 17–40.
Frejd, P., & Bergsten, C. (2018). Professional modellers’ conceptions of the notion of mathematical modelling: Ideas for education. ZDM – Mathematics Education, 50(1–2), 117–127.
Gainsburg, J. (2013). Learning to model in engineering. Mathematical Thinking and Learning, 15(4), 259–290.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt Für Didaktik Der Mathematik, 38(2), 143–162.
Hankeln, C. (2020). Mathematical modelling in Germany and France: A comparison of students’ modelling process. Educational Studies in Mathematics, 103, 209–229.
Hernandez-Martinez, P., & Vos, P. (2018). “Why do I have to learn this?” A case study on students’ experiences of the relevance of mathematical modelling activities. ZDM – Mathematics Education, 50(1–2), 245–257.
Jung, H., & Lee, K., et al. (2021). How mathematical modelling can be promoted by facilitating group creativity. In F. K. S. Leung (Ed.), Mathematical modelling education in East and West (pp. 377–387). Springer.
Kaiser, G. (1995). Realitätsbezüge im Mathematikunterricht—Ein Überblick über die aktuelle und historische Diskussion. In G. Graumann, T. Jahnke, G. Kaiser, & J. Meyer (Eds.), Materialien für einen realitätsbezogenen Mathematikunterricht (pp. 66–84). Franzbecker.
Kaiser, G. (2007). Modeling and modeling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110–119). Horwood.
Kaiser, G. (2017). The teaching and learning of mathematical modelling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267–291). National Council of Teachers of Mathematics.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM – Mathematics Education, 38(3), 302–310.
Kuckartz, U. (2014). Qualitative text analysis: A guide to methods, practice and using software. Sage.
Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.
Li, D. (2002). Shuxue jianmo yu sushi jiaoyu [Mathematical modelling and quality education]. Zhongguo Daxue Jiaoxue, 10, 41–43.
Li, D. (2020). Shuxue jianmo shi kaiqi shuxue damen de jinyaoshi [Mathematical modelling is the golden key to open the door of mathematics]. Shuxue Jianmo Jiqi Yingyong, 9(1), 1–8.
Lu, X., Cheng, J., Xu, B., & Wang, Y. (2019). Xuesheng shuxue jianmo suyang de pingjia gongju yanjiu [The research of the assessment tool of students’ mathematical modeling competency]. Kecheng Jiaocai Jiaofa, 39(2), 100–106.
Lu, X., & Huang, J. (2021). Mathematical modelling in China: How it is described and required in mathematical curricula and what is the status of students’ performance on modelling tasks. In B. Xu, Y. Zhu, & X. Lu (Eds.), Beyond Shanghai and PISA: Cognitive and non-cognitive competencies of Chinese students in mathematics (pp. 209–233). Springer.
Lu, X., & Kaiser, G. (2021). Creativity in students’ modelling competencies: Conceptualisation and measurement. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-021-10055-y Advance online publication.
Lu, X., Leung, F. K. S., & Li, N. (2021). Teacher agency for integrating history into teaching mathematics in a performance-driven context: A case study of a beginning teacher in China. Educational Studies in Mathematics, 106(1), 25–44.
Manouchehri, A. (2017). Implementing mathematical modelling: The challenge of teacher educating. In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 421–432). Springer.
Ministry of Education of China. (2018). Putong gaozhong shuxue kecheng biaozhun (2017 nian ban) [Mathematics curriculum standards for high schools (2017 version)]. People’s Education Press.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education: The 14th ICMI study (pp. 3–32). Springer.
Patton, M. Q. (2002). Qualitative research and evaluation methods. Sage.
Schmidt, B. (2011). Modelling in the classroom: Obstacles from the teacher’s perspective. In G. Kaiser, W. Blum, R. BorromeoFerri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 641–651). Springer.
Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modeling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling: ICTMA1 (pp. 165–180). Springer.
Tan, L. S., & Ang, K. C. (2013). Pre-service secondary school teachers’ knowledge in mathematical modelling—a case study. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 405–415). Springer.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 127–146). Macmillan.
Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: Empirical verification of theoretical assumptions. ZDM – Mathematics Education, 50(1–2), 343–354.
Vorhölter, K. (2019). Enhancing metacognitive group strategies for modelling. ZDM – Mathematics Education, 51(2), 703–716.
Wang, Z., & Xie, J. (2016). Shuxue jianmo jingsai de fazhan yu shuxue jianmo jiaoshi de zuoyong [The development of mathematical contest in modeling and the role of mathematical modeling teachers]. Shuxue Jianmo Jiqi Yingyong, 5(4), 8–13.
Xie, J., et al. (2013). An introduction to CUMCM: China/contemporary undergraduate mathematical contest in modeling. In A. Damlamian (Ed.), Educational interfaces between mathematics and industry (Vol. 16, pp. 435–443). Springer.
Zhu, Y. (2021). Chinese eighth graders’ self-related beliefs during mathematical modelling. In B. Xu, Y. Zhu, & X. Lu (Eds.), Beyond Shanghai and PISA: Cognitive and non-cognitive competencies of Chinese students in mathematics (pp. 275–288). Springer.
Zubi, A., Peled, I., & Yarden, M. (2019). Modelling tasks and students with mathematical difficulties. In G. A. Stillman & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 213–230). Springer.