Abstract :
The paper focuses on the synergy between mathematical thinking and solving trigonometric problems within Mason’s cognitive framework. It presents and analyzes concepts related to mathematical thinking, especially Mason’s definition of the thinking process into three stages: input, impact, and evaluation. Applying this framework to solving trigonometric equations, the paper illustrates how mathematical thinking can help approach problems in an organized and rigorous manner, while opening opportunities for creativity and exploration.
Discussing mathematical thinking, the paper defines it as a creative process involving prediction, induction, interpretation, description, abstraction, and reasoning. Aligned with Mason’s definition of mathematical thinking, the paper describes how this thinking aids students in understanding complex structures and solving problems quickly and flexibly.
Keywords :
development of mathematical thinking, Mason's thinking, Mason's thinking process, Mathematical thinking, Thinking, Trigonometry.References :
- Phan Dung (2013), Reflections on thinking, Center for Science and Technology Creativity (TSK), University of Sciences – National University Ho Chi Minh City.
- Nguyen Van Doc, Nguyen Thi Hoai Nam, Ngo Tu Thanh, Nguyen Minh Giam (2023). Teaching Mathematics with the Assistance of an AI Chatbot to Enhance Mathematical Thinking Skills for High School Students. International Journal of Current Science Research and Review, 6(12), 8574-8580. DOI: https://doi.org/10.47191/ijcsrr/V6-i12-102
- Edgar Morin (2009), Introduction to complex thinking, Tri thức Publishing House, Hanoi.
- Freudenthal, H. (1973). Mathematics as an educational task. Reidel.
- Henderson, P. B., Hichtner, L., Fritz, S. J., Marion, B., Scharff, C., Hamer, J., & Riedesel, C. (2002). Materials development in support of mathematical thinking. ACM SIGCSE Bulletin, 35(2), 185–190. Doi: 10.1145/782941.783001
- Liu, P. H. (2003). Do teachers need to incorporate the history of mathematics in their teaching?. The Mathematics Teacher, 96(6), 416.
- Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (Second edition). Harlow England: Pearson Education Limited
- MOET (2018). New General Education Program: Understanding the Mathematics Curriculum. Retrieved from https://moet.gov.vn/Pages/home.aspx
- Schoenfeld, A. H. (1992). Learning to think mathematically : Problem solving, metacognition and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 334–370). MacMillan.