Unlocking Real-World Problem Solving: A Practical Guide to Mathematical Modeling

Preface

The author recounts his first university‑level mathematical modeling competition, describing how the experience revealed both the broad applicability of mathematics and personal shortcomings in writing, collaboration, and programming. Motivated by a desire to become a true problem‑solver rather than a mere "problem‑solver for exams," he spent over a decade studying models, coding, and teaching.

With the reform of basic education, many schools now offer modeling courses and competitions, helping students see mathematics as a tool for real‑world problem solving. The author, having taught at a key high school, observes that modeling transforms students’ attitudes: they move from viewing math as exam‑oriented to using it to address everyday challenges.

Because modeling spans a vast knowledge domain, mastering or teaching it is difficult. The author has compiled ten years of reading, practice, and teaching experience into a book that focuses on the competition perspective, using it as a concrete entry point to discuss broader modeling learning and teaching insights.

The book condenses the author’s competition and training experience for students and teachers. Readers will quickly learn what mathematical modeling is, the skills required for competitions, how to participate, and how to develop a clear problem‑solving mindset and personal learning path.

Comprehensive coverage of knowledge and abilities needed for competitions: mathematics, programming, writing, and teamwork.

Rich, original case studies that are life‑oriented and contemporary, stimulating curiosity about underlying models and methods.

Step‑by‑step walkthrough of complete modeling projects, helping readers grasp required abilities and the logical flow of a modeling paper.

Unique "situation‑thinking‑method" (境‑道‑术) framework that moves from problem context, to thinking strategies, to specific modeling techniques, classified into four problem types (description & understanding, causal & explanation, estimation & prediction, evaluation & decision).

Detailed code explanations; all important results are presented with annotated Python code that readers can reproduce.

The author emphasizes that while modeling provides a logical, quantitative framework, it cannot replace practical experiments or real‑world validation. Modeling is a powerful approach but has limits; it solves problems rather than generates them.

Problem classification is illustrated with examples such as describing a distant building (description), comparing marketing strategies (causal), forecasting stock prices (prediction), and optimizing production plans (decision). The four categories cover most everyday questions, though overlaps can occur.

To apply these categories, the author proposes a thinking framework: first define the problem situation, then select appropriate thinking patterns (e.g., subdivision, hypothesis, clustering), and finally choose concrete mathematical models that implement those thoughts.

The book’s structure is as follows:

Chapter 1: Introduction – concepts, major competitions, required abilities, and four original problems.

Chapter 2: Tools – collaboration, writing, and programming tools (Python basics and key libraries).

Chapter 3: Modeling Process – positioning, problem‑type taxonomy, and case structure.

Chapters 4‑7: Detailed treatment of the four problem types with thinking strategies and implementation cases.

Chapter 8: Paper Writing – structure and writing tips for modeling reports.

Chapter 9: Teamwork – cooperation tips for competition members.

Data and code resources are available via the public account “模型视角” or the Zhihu account of the same name; readers can request the “数学建模实战资料包”.

Teacher Modeling Teaching and Training Community

Despite strong policy support, modeling education in Chinese primary and secondary schools faces several obstacles: uneven research focus, scarce empirical studies, lack of long‑term dedicated research teams, and insufficient high‑quality case libraries.

The author proposes establishing a voluntary, collaborative community for teachers to share teaching experiences, develop excellent modeling cases, and conduct research. The community’s initial goals are:

Exchange teaching experiences.

Research and design high‑quality modeling cases.

Discuss modeling‑related research topics.

Interested teachers may join by contacting the author (providing name, school, and research direction). The community is purely nonprofit, with a screening process to ensure healthy development.

References:

Wang Haihua. Mathematical Modeling in Practice . Harbin: Harbin Institute of Technology Press, 2023.

Niu Weiqiang, Zhang Ti, Xiong Bin. “A Review of Primary and Secondary School Mathematical Modeling Research in China—Based on Core Journal Literature from 1989‑2015.” In: Proceedings of the 2016 International Academic Conference of the National Mathematics Education Research Association, 2016:31‑39.