How to Analyze Math Modeling Examples in High School Textbooks: A Research Roadmap

From January 6 to March 3 the author reviewed nearly two months of activities related to the thesis titled “Analysis of Example Problems on Mathematical Modeling in the People’s Education Press High School Mathematics Textbook”.

The thesis aims to study the six high‑school mathematics competencies—mathematical abstraction, modeling, computation, logical reasoning, visual imagination, and data handling—focusing on the modeling competency, which the author is passionate about.

Initially, the author prepared for the 2016 U.S. Mathematical Modeling Competition (January 29 – February 2), revisiting modeling textbooks such as “Mathematical Modeling Methods and Analysis”, “Mathematical Models”, and older works like “Applications of Advanced Mathematics”. This period (January 10 – February 2) is labeled the “mathematical modeling stage”.

Through the competition preparation, the author deepened understanding of the modeling process, common models (optimization, dynamic, probabilistic), and reflected on fundamental questions like “What is a mathematical model?” and “What is mathematical modeling?”. The experience reinforced the belief that modeling can be valuable in secondary education and may become a popular high‑school competition.

During the “adjustment stage” (February 3 – February 23, the Chinese New Year break), the author attempted to apply modeling to everyday problems (talent model, course‑selection model, time‑allocation model) but faced challenges due to lack of theory and data.

Returning to school, the author prepared the thesis proposal, realizing that the work must go beyond modeling to include textbook analysis. Relevant books such as “Textbook Analysis Introduction”, “Mathematics Textbook Analysis”, and “Comparative Difficulty of Chinese and English Middle‑School Mathematics” were consulted.

The author then outlined a concrete research plan:

Define what constitutes a modeling‑related example problem, locate and code all such examples in the textbooks (March 5 – March 10).

Conduct literature review on the definition of mathematical modeling and evaluation models for modeling problems (March 10 – March 20).

Develop an evaluation model to assess the quality of each example problem (March 20 – March 31).

Provide an overall assessment of how the People’s Education Press textbook cultivates modeling competence and suggest extensions for teaching and curriculum design (April 1 – April 10).

Finalize and polish the thesis (April 10 – April 20).

The article concludes with a reflection on the completed review and the next steps for the research.