An Instructional Design for Math Problem Lessons Based on the Alignment of the Problems with Curriculum Standards—"The Cosine Formula for the Sum and Difference of Two Angles" as an Example
DOI: 10.23977/trance.2024.060416 | Downloads: 13 | Views: 265
Author(s)
Na Zhao 1, Jinping Jia 1
Affiliation(s)
1 Faculty of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu, China
Corresponding Author
Na ZhaoABSTRACT
Exercises are an important part of teaching materials, which is the consolidation and deepening of classroom teaching content and provides a platform for students' core literacy in mathematics [1]. The cosine formula of sum and difference of two angles is one of the important contents of trigonometric function in high school mathematics teaching. According to the requirements of the course, students need and can flexibly use these formulas for evaluation and deformation application. The cosine formula of sum and difference of two angles is the basis of trigonometric identical deformation. Other trigonometric function formulas are derived from these basic formulas. Therefore, the exercise should cover all aspects from formula derivation to concrete application, including but not limited to: deriving cosine formula of sum and difference of two angles (such as cos (α + β) = cos α cos β-sin α sin β). Students are able to solve practical problems by applying these formulas, such as using vector or geometric methods for proof. This paper aims to provide a systematic teaching plan for high school mathematics teachers through an in-depth analysis of the teaching content, learning situation, and selection and organization of the "cosine formula of the sum and difference of two angles" [3-7].
KEYWORDS
Consistency, Instructional Design, Teaching Exercises, High School MathCITE THIS PAPER
Na Zhao, Jinping Jia, An Instructional Design for Math Problem Lessons Based on the Alignment of the Problems with Curriculum Standards—"The Cosine Formula for the Sum and Difference of Two Angles" as an Example. Transactions on Comparative Education (2024) Vol. 6: 128-135. DOI: http://dx.doi.org/10.23977/trance.2024.060416.
REFERENCES
[1] Ministry of Education of the People's Republic of China. General High School Mathematics Curriculum Standards (2017 Edition Revised in 2020) [M]. Beijing: People's Education Press, 2020.
[2] People's Education Press•Curriculum and Textbook Research Institute•Middle School Mathematics Curriculum and Textbook Research and Development Center. Ordinary high school textbook•Mathematics compulsory course volume 2 (A edition) [M]. Beijing: People's Education Press, 2019:9
[3] Gong Huibin. Give full play to the power of free thinking to improve the core literacy of mathematics - a new design for teaching the concept of line, plane and angle [J]. Bulletin of Mathematics, 2024, 63(04): 15-18+39.
[4] Wu Lipao, Song Wenqian, Wang Zixu, Wang Dejiang. Inverse mathematics unit assignment design to promote deep learning - taking "Pythagorean Theorem" as an example [J]. Journal of Mathematics Education, 2024, 33(02): 14-19.
[5] Chang Ning, Hu Dianshun. Analysis of mathematics unit teaching design under the unified control of big concepts - taking functions in junior high schools as an example [J]. Journal of Mathematics Education, 2024, 33(02): 20-26.
[6] Zhu Yongqiang. Research on the design of junior high school mathematics problem teaching based on the concept of educational mathematics [J]. Test Questions and Research, 2022, (07): 50-51.
[7] Yu Xiaojie. Use questions to lead inquiry and promote students' independent construction - taking "the cosine formula of two angle differences" as an example [J]. Middle School Mathematics Teaching Reference, 2023, (34): 26-28.
[8] Bhola, D., Impara, J., &Buckendahl, C. Aligning tests with states' content standards: Methods and issues[J]. Educational M easurement: Issues and Practice, 2003, 22(3).
[9] Colman, D. K. A revolution in one classroom: The case of Mrs[J]. Oublier. Educational Evaluation and Policy Analysis, 1982, 12(3).
[10] Koretz, D. M., & Hamilton, L. S. Educational Measurement [M]. Westport, CT: American Council on Education/Praeger, 2006.
[11] Martone A, Reci S. Evaluating Alignment between Curriculum, Assessment and Instruction [J].Review of Educational Research, 2009,79(4):1332-1361.
[12] Common Core State Standards Initiative. Common Core State Standards for Mathematics.(2010)[2011-04-01].
[13] The Republic of China. Mathematics Curriculum in Ordinary Senior High School (Experiment) [M]. Beijing: Education Press, 2003.
[14] Yu Ping. A framework for evaluating mathematics core literacy [J]. Journal of Mathematics Education, 2017, 26 (02): 19-23 +59.
[15] Cao Yiming, Wang Lidong, Paul Cobb. A review of high school mathematics in the core curriculum of the United States [J]. Journal of Mathematics Education, 2010, 19 (5).
Downloads: | 7327 |
---|---|
Visits: | 221618 |