Designing a High‑School Math Modeling Curriculum Using Textbook Problems
The author proposes a systematic approach to select high‑school textbook examples, analyze their features, build a difficulty model, and create a comprehensive math‑modeling exercise book that can serve as a school‑based curriculum resource.
The author plans to use Lu Xiaoli's paper on “cognitive level – extensibility application” to establish a strict mathematical‑modeling definition for analyzing textbook example problems, focusing especially on application problems.
In Lu's work, problems that involve fully mathematizing a real‑world issue, solving it, and verifying the solution are classified under “cognitive level – extensible application”. The author will treat this class as the scope of their research, selecting textbook problems that meet this definition and then searching related literature for problems appropriate for high‑school students or slightly above.
By identifying modeling examples in textbooks, the author can examine their characteristics, pinpoint strengths and weaknesses, and construct a difficulty model for mathematical modeling. After clarifying all required knowledge points and skills, they can create a bank of modeling exercises, potentially compiling them into a problem book with classifications, detailed solutions, introductions, commentary, and knowledge explanations, forming a “quasi‑textbook” for a school‑based curriculum.
There are existing precedents for integrating mathematical modeling into school curricula, such as the Shanghai Middle‑School Mathematics Modeling Competition collection and the high‑school textbook “Mathematical Modeling Special Topic”. The author has already purchased several related books, including collections of modeling problems and applied mathematics texts.
The author outlines possible innovative angles for their thesis: (1) the relationship between the People’s Education Press textbook and information‑based teaching or flipped classrooms; (2) the relationship between the textbook and mathematics‑modeling competitions, exploring how to adapt textbook examples to meet competition requirements.
Model Perspective
Insights, knowledge, and enjoyment from a mathematical modeling researcher and educator. Hosted by Haihua Wang, a modeling instructor and author of "Clever Use of Chat for Mathematical Modeling", "Modeling: The Mathematics of Thinking", "Mathematical Modeling Practice: A Hands‑On Guide to Competitions", and co‑author of "Mathematical Modeling: Teaching Design and Cases".
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