Table of Contents
Foreword
Chapter 1 Introduction: Modeling with Mathematics
- What is Mathematical Modeling?
- The Process of Modeling?
- Why Modeling?
- Mathematical Autonomy
Chapter 2 Rich Mathematical Modeling Tasks
- Characteristics of Rich Modeling Tasks
- Word Problems versus Modeling Tasks
- Finding Rich Mathematical Modeling Tasks
Chapter 3 Investigation and Problem Identification
- Getting Started: Student Autonomy
- The Teacher's Role
- More Problem Identification: Old MacDonald's Farm
- 1000 Paper Cranes: Getting Started
Chapter 4 Mathematical Formulation of the Model, Data Collection, and Finding a Solution
- Formulating a Model
- Multiple Representations
- The 1000 Cranes Problem: Formulating the Model and Collecting Data
- Conclusion
Chapter 5 Interpreting the Solution and Comparing with Reality
- The Importance of Interpretation
- Interpreting the Solution
- Examples of Students Interpreting Solutions
- Conclusion
Chapter 6 Communicating and Implementing the Solution
- Communicating the Solution
- Multiple Representations
- Implementing the Solution
- 1000 Cranes Work
Chapter 7 Assessment of Mathematical Modeling
- Goals of Assessment
- Informal Assessment
- Formal Assessments
Chapter 8 Conclusion