RESEARCH AND DEVELOPMENT PROCESS OF PENETRATE CORE LITERACY-THE ROTATION AND TRANSFORMATION OF GRAPHICS AS AN EXAMPLE
Keywords:
Rotation transformation, core literacy in mathematics, junior high school mathematics
Abstract
This paper focuses on solving problems from line and difference problems, proving angle problems and common vertex problems using rotational transformation ideas to expand the problem-solving process and develop students' core literacy. After analyzing the mathematics test questions, it is not difficult to find that the rotation of a figure is often tested in a comprehensive expansion. The test questions focused on the problems related to angles or line segments when the figure is rotated to a particular position, integrating the dynamic geometry of change and invariance, geometric conjecture, drawing, reasoning, proof and calculation ability, as well as innovation and practical abilityof students' experience of the operation activities related to the transformation of a figure. The solution of such problems requires intuitive imagination, logical reasoning and mathematical literacy. After rotation, the figure and the original figure are congruent, therefore, the method of rotational change becomes a new way of thinking in solving mixed problems with complex figures, and it is easier for students to understand the idea of doing the problem by rotating and transforming the figure to construct auxiliary lines.
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References
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Chen, C. S. (2019). Teaching strategies and reflections of "graphical transformation" in junior high school based on core literacy in mathematics. New Curriculum (Next), 10, 116-117.
Chen, Xiaofang. (2016). Analysis of the three major types of special graph rotation problems in the Chinese examination categorized and dissected. Secondary Mathematics: Middle School Edition, 1, 2.
Cheng, C. N. (2022). Modeling originates from the need of problem solving into exploring the nature of graphs--a micro-teaching design of problem solving based on the idea of allometric transformation from the perspective of rotation. Science Examination Research, 18, 26-31.
Jiang, Y. (2019). Introduction to proving geometry problems by using rotation method as auxiliary lines. Mathematics for Middle School Students: Middle School Edition, 4, 2.
Jinlu, Q. (2023). The solution of "Hand-in-Hand Model". Mathematical World (Junior High School Edition), 07, 23-24.
Li, G. (2023). The essence of multiple solutions of one problem and multiple questions to find the general method--Example of the finale of the 2022 Shenzhen Chinese examination. Science Examination Research, 10, 24-28.
Li, N., Mok, I., & Cao, Y. (2019). The Evolution of Mathematical Thinking in Chinese Mathematics Education. Mathematics, 7(3), 297. http://dx.doi.org/10.3390/math7030297.
Miao, Y-Y. (2023). Constructing the "co-vertex rotation" model when solving similar triangle problems. Modern Middle School Students (Junior High School Edition), 02, 27-28.
Ministry of Education of the People's Republic of China. (2011). Curriculum standards for compulsory education in mathematics. Beijing: Beijing Normal University Press.
Ministry of Education of the People's Republic of China. (2022). Curriculum Standards for Compulsory Education in Mathematics. Beijing: Beijing Normal University Press.
Pereira, J., Tang, J., Soares, B., Prihandini, R. M., & Wijaya, T.T. (2023). Exploring the Accuracy of Mathematics Students on the Final Semester Assessment Based on Racsh Model Analysis in Timor-Leste. In: Al-Sharafi, M.A., Al-Emran, M., Al-Kabi, M.N., Shaalan, K. (eds) Proceedings of the 2nd International Conference on Emerging Technologies and Intelligent Systems ICETIS 2022. Lecture Notes in Networks and Systems, 573, 416–425. Springer, Cham. https://doi.org/10.1007/978-3-031-20429-6_38
Qiang-Hua, L. (2022). Using rotational transformations to solve the most value problem of line(s) (sums). Teaching and Learning of Middle School Mathematics, 17, 31-32+11.
Shijian, Y., & Chufang, H. (2012). Compulsory Education Textbook of Mathematics, Grade 7, Lower Book. Hunan Education Publishing House.
Tang, J., Pereira, J., Tan, S., & Wijaya, T. T. (2023). The Research on Design and Application of Dynamic Mathematics Integrable Ware Design Model in Junior High School. In: Al-Sharafi, M.A., Al-Emran, M., Al-Kabi, M.N., Shaalan, K. (eds) Proceedings of the 2nd International Conference on Emerging Technologies and Intelligent Systems ICETIS 2022. Lecture Notes in Networks and Systems, 573, 402–415. Springer, Cham. https://doi.org/10.1007/978-3-031-20429-6_37
Tian, J-J. (2023). The Pythagorean theorem and its converse theorem - Important properties and determination of right triangles. Mathematics and Chemistry for Secondary School Students (8th grade mathematics) (with the textbook of Human Education Society), 03, 3-4.
Tran, D., Reys, B. J., Teuscher, D., Dingman, S., & Kasmer, L. (2016). Research Commentary: Analysis of Curriculum Standards: An Important Research Area. Journal for Research in Mathematics Education JRME, 47(2), 118-133. https://doi.org/10.5951/jresematheduc.47.2.0118
Wang, C. (2023). The application of auxiliary lines in plane geometry problem solving. Math and Science World (Middle School Edition), 05, 28-29.
Wang, F. L. (2009). Strengthening the teaching in math problem-solving to raise the efficiency of review for middle school entrance examination. Journal of Ningbo Institute of Education.
Wang, L., Cao, C., Zhou, X., & Qi, C. (2022). Spatial abilities associated with open math problem solving. Applied Cognitive Psychology, (2), 36.
Wu, Y. (2021). An investigation on the solution method of the topic of rotational transformation of graphs. Mathematical and Physical Problem-Solving Research, 29, 48+60.
Zhang, M. H. (2023). Reflections on the application of the new curriculum concept to junior high school mathematics teaching. New Education, 14,23-25.
Zhiyan, R. (2019). A study on the penetration of graphical transformation ideas in junior high school mathematics teaching. Mathematics Teaching Newsletter, 11, 79-80+85.
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