Yijie He, Xintao Shen
Zhejiang Normal University, Jinhua 321004, China
The three core elements of abstraction, reasoning and model constitute the basic idea of mathematics. The basic idea of mathematics has the following two principles: one is the ideas that mathematics must rely on for its production and development; the second is the basic thinking characteristics that people who have studied mathematics should have. Mathematical education that embodies the basic ideas of mathematics should at least have the following characteristics: pay attention to the degree of consistency between school mathematics tasks and real situations outside school; pay attention to students' emotional fields; pay attention to students' individual socialization; provide adaptive thinking guidance.
Basic idea of mathematics, Mathematics education
Yijie He, Xintao Shen. Reflecting the Basic Idea of Mathematics in Mathematics Education. Frontiers in Educational Research (2022) Vol. 5, Issue 17: 48-51. https://doi.org/10.25236/FER.2022.051709.
 Shi Ningzhong. 18 Lectures on Basic Ideas of Mathematics [M]. Beijing: Beijing Normal University Press, 2016
 Freudenthal H. Why to teach mathematics so as to be useful [J]. Educational studies in mathematics, 1968: 3-8.
 John Dewey. The school and society [M]. Communication University of China Press, 2018.
 Vos P. “How real people really need mathematics in the real world”—Authenticity in mathematics education [J]. Education Sciences, 2018, 8(4): 195.
 Borromeo Ferri R. Modelling problems from a cognitive perspective[J]. Mathematical modeling:
Education, engineering, and economics, 2007: 260-270.
 Bergman Ärlebäck J, Bergsten C. On the use of realistic Fermi problems in introducing mathematical modelling in upper secondary mathematics [M]. //Modeling Students' Mathematical Modeling Competencies. Springer, Boston, MA, 2010: 597-609.
 Dong Lianchun, Wu Libao, Wang Lidong. A Review of PISA2021 Mathematical Literacy Assessment Framework [J]. Journal of Mathematics Education, 2019, 28(04): 6-11+60.
 Boaler J. The Role of Contexts in the Mathematics Classroom: Do they Make Mathematics More" Real"? [J]. For the learning of mathematics, 1993, 13(2): 12-17. Palm T. Word problems as simulations of real-world situations: A proposed framework [J]. For the learning of mathematics, 2006, 26(1): 42-47.
 McLeod D B. Research on affect in mathematics education: A reconceptualization [J]. Handbook of research on mathematics teaching and learning, 1992, 1: 575-596.
 Wiggins G. A true test: Toward more authentic and equitable assessment [J]. Phi Delta Kappan, 2011, 92(7): 81-93.
 Hidi S, Renninger K A. The four-phase model of interest development [J]. Educational psychologist, 2006, 41(2): 111-127.
 Surya E, Putri F A. Improving mathematical problem-solving ability and self-confidence of high school students through contextual learning model [J]. Journal on Mathematics Education, 2017, 8(1): 85-94.
 Yildiz E P. Analysis of the Last 10 Years of Articles and Theses on Authentic Learning: A Meta Analysis Study [J]. African Educational Research Journal, 2021, 9(2): 505-514.
 Skovsmose O. Research, practice and responsibility [J]. 2004.
 Xu Jun. Educational Mission in an Individualized Society [J]. Educational Development Research, 2014, 33(Z2): 35-41.
 Wood D, Bruner J S, Ross G. The role of tutoring in problem solving [J]. Child Psychology & Psychiatry & Allied Disciplines, 1976.
 Van de Pol J, Volman M, Beishuizen J. Scaffolding in teacher–student interaction: A decade of research [J]. Educational psychology review, 2010, 22(3): 271-296.
 Stender P, Kaiser G. Scaffolding in complex modelling situations [J]. ZDM, 2015, 47(7):1255-1267.
 Smit J, AA van Eerde H, Bakker A. A conceptualisation of whole‐class scaffolding [J]. British Educational Research Journal, 2013, 39(5): 817-834.