A Rational Review of Geometric Reasoning
DOI:
https://doi.org/10.53469/wjimt.2025.08(07).17Keywords:
Geometric Reasoning, Literature Review, Mathematics EducationAbstract
This paper analyzes the necessity of geometric reasoning thinking for students' development by discussing the junior high school mathematics geometry course as an important carrier for the development of students' reasoning ability, summarizing relevant studies on geometric reasoning, and proposing the necessity and measures for the cultivation of geometric reasoning thinking.
References
Liu Xiaomei, Yang Yuqian. Some thoughts on reasoning ability [J]. Journal of Mathematics Education, 2002, (02): 54-56.
Ministry of Education of the People's Republic of China. General high school mathematics curriculum standard (2017 edition revised in 2022) [S]. Beijing: People's Education Publishing House, 2022.
Hu X.P., Li Y. D. Connotation and cultivation of logical reasoning core literacy [J]. Teacher Education Forum, 2018, 31(08):74-76.
Bao Jiansheng. A look back at the century: The rise and fall of the secondary school geometry program [J]. Secondary Mathematics Monthly, 2005, (07):1-3.
Bao Jiansheng, Zhou Chao. The psychological basis and process of math learning [M]. Shanghai: Shanghai Education Press, 2009:4-6.
Xie Meiyun. A preliminary study on improving geometric reasoning ability [J]. Yinshan Journal, 1998, (S2):105-107.
Fuys D. The van Hiele Model of Thinking in Geometry among Adolescents [J]. Journal for Research in Mathematics Education Monograph Number 3. 1988.
Chang K E, Sung Y T, Lin S Y. Developing geometry thinking through multimedia learning activities [J]. Computers in Human Behavior, 2007, 23(5): 2212-2229.
Seah R, Horne M. A learning progression for geometric reasoning [M]. Researching and using progressions (trajectories) in mathematics education. Brill Sense, 2019: 157-180.
Arnal-Bailera A, Manero V. A characterization of Van Hiele’s level 5 of geometric reasoning using the Delphi methodology [J]. International Journal of Science and Mathematics Education, 2024, 22(3): 537-560.
Lowrie T, Logan T, Patahuddin S M. A learning design for developing mathematics understanding: The ELPSA framework [J]. Australian Mathematics Teacher, The, 2018, 74(4): 26-31.
Adams J, Resnick I, Lowrie T. Supporting senior high-school students’ measurement and geometry performance: Does spatial training transfer to mathematics achievement? [J]. Mathematics Education Research Journal, 2023, 35(4): 879-900.
Downton A, Livy S. Insights into students’ geometric reasoning relating to prisms [J]. International Journal of Science and Mathematics Education, 2022, 20(7): 1543-1571.
Wilson R H. Geometric reasoning about assembly tools [J]. Artificial Intelligence, 1998, 98(1-2): 237-279.
Miragliotta E. Geometric prediction: A framework to gain insight into solvers’ geometrical reasoning [J]. The Journal of Mathematical Behavior, 2022, 65: 100927.
Hohol M, Miłkowski M. Cognitive artifacts for geometric reasoning [J]. Foundations of Science, 2019, 24(4): 657-680.
Hamami Y, Mumma J, Amalric M. Counterexample Search in Diagram‐Based Geometric Reasoning [J]. Cognitive Science, 2021, 45(4): e12959.
Ma Yingqiu, Cao Yiming. An international comparative study of geometric reasoning in junior high school mathematics textbooks [J]. Basic Education, 2018, 15(03):52-65.
He Shengqing, Qi Chunxia. An empirical study on the geometric reasoning ability of eighth grade students in China - based on a large-scale test in City Z [J]. Journal of Ningbo University (Education Science Edition), 2017, 39(06):118-123.
Li Hongting. Research on the development of middle school students' geometric reasoning ability [J]. Educational Research and Experimentation, 2009, (06):81-85.
Wang Kuanming. Research on the correlation between eighth grade students' geometric reasoning ability and geometric thinking level [J]. Teaching and Management, 2013, (27):101-103.
Guan Hongyan, Zhou Chao. A test of geometric thinking level for math teachers in Fanhir [J]. Journal of Mathematics Education, 2014, 23(02):83-85.