erdEducation Reform and Development2652-53642652-5372Bio-Byword Scientific Publishing Pty. Ltd.10.26689/erd.v8i4.14930ArticleBlended and Project-Based Learning for Numerical ODEs: A Practical Framework for Undergraduate Mathematics Programs with Limited Credit Hourshttps://artdesignp.com/journal/erd/8/4/10.26689/erd.v8i4.14930BaiNing,ZhaoDongxia2026842026-06-03Numerical solutions of ordinary differential equations (ODEs) are a basic course for undergraduates majoring in science, technology, engineering and mathematics. Due to the limitation of credit hours, there are many problems in this course, such as abstract theoretical content, insufficient practical training, and disconnection between theory and practical application. Based on the results-oriented education, the principle of construction consistency, cognitive load theory and Bloom’s classification theory of educational objectives, this paper constructs an integrated teaching framework for senior undergraduates. The framework arranges the low-level cognitive task as self-learning before online class. Classroom teaching focuses on the cultivation of high-level analytical ability, and designs a three-level progressive project experimental system to guide students to gradually complete knowledge understanding, code implementation and problem solving. The course reconstructs the teaching content around the three-dimensional training goal of knowledge, ability and literacy, and focuses on the core idea of numerical algorithm and program implementation method. After a semester of teaching practice, students’ understanding of the core concepts of the course is more solid, their ability in algorithm programming and mathematical modeling is significantly improved, and their interest in applied mathematics is also enhanced. This teaching framework has good generality and can provide a reference for the teaching reform of computational mathematics courses at home and abroad.

Hairer E, Nørsett SP, Wanner G, 1993, Solving Ordinary Differential Equations I: Nonstiff Problems. Springer-Verlag, Berlin.

Holton D, 2001, The Teaching and Learning of Numerical Methods: A Review. International Journal of Mathematical Education in Science and Technology, 32(5): 677–690.

Burden RL, Faires JD, Burden AM, 2016, Numerical Analysis 10th Edition. Cengage Learning, Boston.

Atkinson KE, Han W, 2004, Elementary Numerical Analysis. John Wiley & Sons, Hoboken, New Jersey.

Prince M, 2004, Does Active Learning Work? A Review of the Research. Journal of Engineering Education, 93(3): 223–231.

Freeman S, Eddy SL, McDonough M, Smith MK, Okoroafor N, Jordt H, Wenderoth MP, 2014, Active Learning Increases Student Performance in Science, Engineering, and Mathematics. Proceedings of the National Academy of Sciences, 111(23): 8410–8415.

Kober N, 2015, Reaching Students: What Research Says About Effective Instruction in Undergraduate Science and Engineering. National Academies Press, Washington, DC.

Biggs J, Tang C, Kennedy G, 2022, Teaching for Quality Learning at University 5th Edition. McGraw-Hill Education, United Kingdom.

Sweller J, 2011, Cognitive Load Theory. Psychology of Learning and Motivation, 55: 37–76.

Anderson LW, Krathwohl DR, 2001, A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. Longman, New York.

Crouch CH, Mazur E, 2001, Peer Instruction: Ten Years of Experience and Results. American Journal of Physics, 69(9): 970–977.