BỒI DƯỠNG NĂNG LỰC GIẢI QUYẾT VẤN ĐỀ TOÁN HỌC CHO HỌC SINH LỚP 9 THÔNG QUA PHÂN TÍCH ĐỘ DỐC BẬC CẦU THANG
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Tóm tắt
This study investigates the effectiveness of experiential learning through real-world staircase slope analysis in enhancing ninth-grade students' mathematical problem-solving competency, specifically within the context of trigonometric ratios of acute angles. The research addresses the pedagogical challenge of transforming abstract trigonometric concepts into embodied understanding through authentic measurement tasks. Thirty-nine ninth-grade students in Ho Chi Minh City participated in a three-phase outdoor learning intervention: (1) identifying standard staircase criteria and defining the mathematical problem (slope angle between 20°-45°); (2) measuring actual school staircases and applying trigonometric ratios (tangent, sine, cosine) to calculate slope angles; and (3) presenting findings, evaluating solutions, and comparing methodological approaches. Data were collected through observation notes, group worksheets, photographs, and video recordings, then analyzed qualitatively using the four core indicators of problem-solving competency specified in the 2018 General Education Program in Mathematics. Findings demonstrate that students successfully identified relevant mathematical problems, selected and justified appropriate measurement strategies, accurately applied trigonometric knowledge, and critically evaluated their solutions against safety standards. All seven student groups correctly calculated slope angles falling within the safe range, employing diverse trigonometric approaches that reflected flexible mathematical reasoning. The study provides empirical evidence that structured experiential activities are practical pedagogical tools for developing mathematical problem-solving competency.
Từ khóa
Học tập trải nghiệm, năng lực giải quyết vấn đề, tỉ số lượng giác, độ dốc
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Tài liệu tham khảo
Abakah, F.,& Antwi, A. (2024). Using experiential learning in solving 3-dimensional problems in trigonometry. Gulf Journal of Mathematics, 16(2), 364-379. https://doi.org/10.56947/gjom.v16i2.1817.
Abrahamson, D., & Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. Cognitive Research: Principles and Implications, 1(33), 1-13. https://doi.org/10.1186/s41235-016-0034-3
Anjewierden, A., Kamp, E. T., & de Jong, T. (2013). Ziggy: Very Interactive Trigonometry. In C. Lange, D. Aspinall, & J. Carette (Eds.), CICM-WS-WiP 2013: Workshops and Work in Progress at CICM 2013 CEUR. http://ceur-ws.org/Vol-1010/paper-11.pdf
Beard,C., & Wilson, J.P. (2013). Experiential Learning: A handbook for Education, Training and Coaching. London: Kogan Page.
Blum, W., & Leiss, D. (2007). How Do Students and Teachers Deal with Mathematical Modelling Problems? The Example Sugaloaf and the DISUM Project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling (ICTMA12)-Education, Engineering and Economics (pp.222-231). Chichester: Horwood.
Dewey, J. (1963). Experience and Education. Collier Books.
Dhungana, S., Pant, B. P., & Dahal, N. (2023). Students' experience in learning trigonometry in high school mathematics: A phenomenological study. Mathematics teaching research journal, 15(4), 184-201. Retrieved January 4th, 2026, from https://files.eric.ed.gov/fulltext/EJ1409234.pdf
English, L. D, & Watson, J. (2016). Modelling with authentic data in sixth grade. ZDM Mathematics Education, 49(1), 103-115. https://doi.org/10.1007/s11858-017-0896-y
Hokor, E. K. (2021). Analysis of High School Students’ Errors in Solving Trigonometry Problems. Journal of Mathematics and Science Teacher, 1(1), em003. https://doi.org/10.29333/mathsciteacher/11076
Itin, C. M. (1999). Reasserting the Philosophy of Experiential Education as a Vehicle for Change in the 21st Century. Journal of Experiential Education, 22(2), 91-98. Retrieved January 4th, 2026, from https://eric.ed.gov/?id=EJ602249.
Kissane, B. & Kemp, M. (2009, December 17-21). Teaching and learning trigonometry with technology. The 14th Asian Technology Conference in Mathematics, Beijing Normal University, Beijing, China. Mathematics and Technology, LLC. https://atcm.mathandtech.org/ep2009/papers_full/2812009_17288.pdf
Kolb, D. A. (2015). The Process of Experiential Learning. In D. A. Kolb, Experiential learning: Experience as the source of learning and development (pp. 31-61). Pearson Education.
Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.
Lerman, S. (2014). Epistemological obstacles in teaching mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp.214-217). Springer. https://doi.org/10.1007/978-94-007-4978-8_57
Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age Publishing.
Mainemelis, C., Boyatzis, R. E., & Kolb, D. A. (2002). Learning Styles and Adaptive Flexibility: Testing Experiential Learning Theory. Management Learning, 33(1), 5-33. https://doi.org/10.1177/1350507602331001
Maknun, C. L., Rosjanuardi, R., & Jupri, A. (2019). From ratios of right triangle to unit circle: an introduction to trigonometric functions. Journal of Physics Conference Series, 1157(2), 022124. https://doi.org/10.1088/1742-6596/1157/2/022124
Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction. Mathematics Education Research Journal, 12(3), 209-238. https://doi.org/10.1023/A:1003927811079
Moon, J. A. (2004). A Handbook of Reflective and Experiential Learning. London: Routledge.
Ngcobo, A. Z., Madonsela, S. P., & Brijlall, D. (2019). The teaching and learning of trigonometry. South African Journal of Education, 14(2), 72-91. Retrieved January 4th, 2026, from https://www.scielo.org.za/pdf/ijtl/v14n2/07.pdf
Nguyen, D. A., Do, D. A., Pham, T. C. G., Phung, P. D., & Dang, B. K. L. (2024). Teaching Trigonometry Based on Realistic Mathematics Education and Game-Based Learning Approach. Journal of Instructional Mathematics, 5(2), 168-179. https://doi.org/10.37640/jim.v5i2.2173
Piaget, J. (1971). Psychology and Epistemology. The Viking Press.
Santiago, E. (2024). The manipulable trigonometric cycle: A tool for teaching trigonometric functions. In E. Seven (Ed.), The Evolution of Research in Health Science, (pp. 77-91). https://doi.org/10.56238/sevened2024.006-007
Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). Macmillan.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36. https://doi.org/10.1007/BF00302715
Tang, M. D., & Vo, N. H. (2024). Enhancing students’ mathematical competence in learning spatial geometry in grade 11 through practical and experiential activities. Dong Thap University Journal of Science, 13(7), 99-108. https://doi.org/10.52714/dthu.13.7.2024.1342
Vygotsky, L. (1978). Mind in society: the Development of Higher Psychological Processes. Harvard University Press.
Waite, S. (2017). Children Learning Outside the Classroom: From Birth to Eleven. London: SAGE.
Abrahamson, D., & Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. Cognitive Research: Principles and Implications, 1(33), 1-13. https://doi.org/10.1186/s41235-016-0034-3
Anjewierden, A., Kamp, E. T., & de Jong, T. (2013). Ziggy: Very Interactive Trigonometry. In C. Lange, D. Aspinall, & J. Carette (Eds.), CICM-WS-WiP 2013: Workshops and Work in Progress at CICM 2013 CEUR. http://ceur-ws.org/Vol-1010/paper-11.pdf
Beard,C., & Wilson, J.P. (2013). Experiential Learning: A handbook for Education, Training and Coaching. London: Kogan Page.
Blum, W., & Leiss, D. (2007). How Do Students and Teachers Deal with Mathematical Modelling Problems? The Example Sugaloaf and the DISUM Project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling (ICTMA12)-Education, Engineering and Economics (pp.222-231). Chichester: Horwood.
Dewey, J. (1963). Experience and Education. Collier Books.
Dhungana, S., Pant, B. P., & Dahal, N. (2023). Students' experience in learning trigonometry in high school mathematics: A phenomenological study. Mathematics teaching research journal, 15(4), 184-201. Retrieved January 4th, 2026, from https://files.eric.ed.gov/fulltext/EJ1409234.pdf
English, L. D, & Watson, J. (2016). Modelling with authentic data in sixth grade. ZDM Mathematics Education, 49(1), 103-115. https://doi.org/10.1007/s11858-017-0896-y
Hokor, E. K. (2021). Analysis of High School Students’ Errors in Solving Trigonometry Problems. Journal of Mathematics and Science Teacher, 1(1), em003. https://doi.org/10.29333/mathsciteacher/11076
Itin, C. M. (1999). Reasserting the Philosophy of Experiential Education as a Vehicle for Change in the 21st Century. Journal of Experiential Education, 22(2), 91-98. Retrieved January 4th, 2026, from https://eric.ed.gov/?id=EJ602249.
Kissane, B. & Kemp, M. (2009, December 17-21). Teaching and learning trigonometry with technology. The 14th Asian Technology Conference in Mathematics, Beijing Normal University, Beijing, China. Mathematics and Technology, LLC. https://atcm.mathandtech.org/ep2009/papers_full/2812009_17288.pdf
Kolb, D. A. (2015). The Process of Experiential Learning. In D. A. Kolb, Experiential learning: Experience as the source of learning and development (pp. 31-61). Pearson Education.
Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.
Lerman, S. (2014). Epistemological obstacles in teaching mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp.214-217). Springer. https://doi.org/10.1007/978-94-007-4978-8_57
Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age Publishing.
Mainemelis, C., Boyatzis, R. E., & Kolb, D. A. (2002). Learning Styles and Adaptive Flexibility: Testing Experiential Learning Theory. Management Learning, 33(1), 5-33. https://doi.org/10.1177/1350507602331001
Maknun, C. L., Rosjanuardi, R., & Jupri, A. (2019). From ratios of right triangle to unit circle: an introduction to trigonometric functions. Journal of Physics Conference Series, 1157(2), 022124. https://doi.org/10.1088/1742-6596/1157/2/022124
Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction. Mathematics Education Research Journal, 12(3), 209-238. https://doi.org/10.1023/A:1003927811079
Moon, J. A. (2004). A Handbook of Reflective and Experiential Learning. London: Routledge.
Ngcobo, A. Z., Madonsela, S. P., & Brijlall, D. (2019). The teaching and learning of trigonometry. South African Journal of Education, 14(2), 72-91. Retrieved January 4th, 2026, from https://www.scielo.org.za/pdf/ijtl/v14n2/07.pdf
Nguyen, D. A., Do, D. A., Pham, T. C. G., Phung, P. D., & Dang, B. K. L. (2024). Teaching Trigonometry Based on Realistic Mathematics Education and Game-Based Learning Approach. Journal of Instructional Mathematics, 5(2), 168-179. https://doi.org/10.37640/jim.v5i2.2173
Piaget, J. (1971). Psychology and Epistemology. The Viking Press.
Santiago, E. (2024). The manipulable trigonometric cycle: A tool for teaching trigonometric functions. In E. Seven (Ed.), The Evolution of Research in Health Science, (pp. 77-91). https://doi.org/10.56238/sevened2024.006-007
Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). Macmillan.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36. https://doi.org/10.1007/BF00302715
Tang, M. D., & Vo, N. H. (2024). Enhancing students’ mathematical competence in learning spatial geometry in grade 11 through practical and experiential activities. Dong Thap University Journal of Science, 13(7), 99-108. https://doi.org/10.52714/dthu.13.7.2024.1342
Vygotsky, L. (1978). Mind in society: the Development of Higher Psychological Processes. Harvard University Press.
Waite, S. (2017). Children Learning Outside the Classroom: From Birth to Eleven. London: SAGE.