Unlock Problem‑Solving Power with the DEED Framework for Mathematical Modeling

Hello readers, I am Wang Haihua. I would like to introduce my new book Model, the Mathematics of Thinking , which shares my approach and methods for mathematical modeling and serves as a useful reference for enthusiasts, including middle‑school teachers and students, who wish to systematically understand and improve their modeling abilities.

Why Write This Book?

Mathematical modeling is vital in research and everyday decision‑making, and it is a core component of mathematical literacy. However, many teachers and students lack deep understanding and effective teaching resources, so this book aims to fill that gap.

Drawing on years of experience in modeling competitions, research, classroom teaching, and competition guidance, I have accumulated abundant modeling materials and practical insights, previously publishing Mathematical Modeling Practice: A Hands‑On Guide to Competitions and co‑authoring other works.

The book’s distinctive feature is the problem‑oriented DEED framework , representing four problem types: Description, Explanation, Estimation, and Decision. Based on these, the book proposes 20 thinking patterns (e.g., comparative, inductive, goal‑oriented) and explains how to “mathematize” these thoughts into concrete models, accompanied by rich cases and exercises.

The approach deconstructs the traditionally implicit modeling steps into explicit stages: problem type, thinking, and mathematization, encouraging learners to move beyond “template” models and develop flexible, creative solutions.

All case studies are drawn from my teaching practice, many of them novel, and the exercises compile classic modeling problems from research papers, providing valuable learning and teaching resources.

Book Overview

The following outlines the book’s structure and chapter contents:

Chapter 1: Problem Solving – Introduces basic concepts of models and modeling, details the four problem types, and presents the full problem‑solving process with end‑of‑chapter questions.

Chapter 2: Mathematical Abstraction – Uses a compelling case (tree morphology) to illustrate the importance of abstraction and the key thinking skills involved.

Chapter 3: Description and Understanding – Covers decomposition, aggregation, analogy, and systems thinking strategies with concrete examples.

Chapter 4: Explanation and Causality – Explores literature, experimental, hypothesis‑testing, correlation, and Bayesian thinking for causal analysis.

Chapter 5: Estimation and Prediction – Teaches deductive, probabilistic/simulation, trend, and inductive thinking for handling uncertainty and forecasting.

Chapter 6: Evaluation and Decision – Introduces screening, goal/constraint, trade‑off, reference, and game‑theoretic thinking for complex decisions.

Chapter 7: Integrated Thinking – Shows how to combine previous thinking patterns to tackle more complex, variable problems.

Chapter 8: Innovative Thinking – Provides brainstorming, morphological analysis, SCAMPER, and ideal‑solution methods to foster creative solutions.

While the book strives for completeness, I acknowledge possible oversights and welcome expert feedback for future revisions.

Reference: Wang Haihua. (2024). Model, the Mathematics of Thinking. Harbin Publishing House.