Mathematical Modelling for Teachers

Resources, Pedagogy and Practice

Keng Cheng Ang

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351247955
• Edition: 1
• Topic: Pedagogía
• Subtopic: Enseñanza de matemáticas

Mathematical Modelling for Teachers: Resources, Pedagogy and Practice provides everything that teachers and mathematics educators need to design and implement mathematical modelling activities in their classroom. Authored by an expert in Singapore, the global leader in mathematics education, it is written with an international readership in mind.

This book focuses on practical classroom ideas in mathematical modelling suitable to be used by mathematics teachers at the secondary level. As they are interacting with students all the time, teachers generally have good ideas for possible mathematical modelling tasks. However, many have difficulty translating those ideas into concrete modelling activities suitable for a mathematics classroom. In this book, a framework is introduced to assist teachers in designing, planning and implementing mathematical modelling activities, and its use is illustrated through the many examples included. Readers will have access to modelling activities suitable for students from lower secondary levels (Years 7 and 8) onwards, along with the underlying framework, guiding notes for teachers and suggested approaches to solve the problems. The activities are grouped according to the types of models constructed: empirical, deterministic and simulation models. Finally, the book gives the reader suggestions of different ways to assess mathematical modelling competencies in students.

1Introducing mathematical modelling

Introduction

As an activity in the mathematics classroom, mathematical modelling has grown in popularity in the past decades. There have been numerous reports by mathematics educators from all over the world on what has been done and what is possible or can be done to promote mathematical modelling among students, with varying degrees of success. Competitions and contests related to mathematical modelling, such as those organized by the Consortium for Mathematics and Its Applications (COMAP)¹ and the International Mathematical Modelling Challenge (IMMC)², have sprouted across different countries at different levels. The importance of mathematical modelling in the cultivation and development of twenty-first century skills among students has also been discussed by mathematics teachers and educators.

In this introductory chapter, the idea of mathematical modelling and the process of mathematical modelling is introduced and described in some detail. The main approaches of mathematical modelling will also be discussed, together with simple but useful examples to illustrate these approaches. The chapter concludes with a discussion on the skills and competencies required of a student who wishes to learn or embark on a mathematical modelling activity.

What is mathematical modelling?

Mathematical modelling is a process of representing or describing real-world problems in mathematical terms in an attempt to find solutions to the problems or to gain a better understanding of the problems. The result of this process is a mathematical model, which can sometimes be considered as a simplification or abstraction of a real-world problem or a system into a mathematical form.

In other words, mathematical modelling begins with a real-world problem whose real-world solution is what we wish to find. However, a direct route from the real-world problem to the real-world solution can sometimes be difficult, if not impossible. This could be because of the complexity of the problem or the need for some analysis of the situation. A first step in mathematical modelling is thus to formulate the problem into a mathematical problem. This is often the most difficult step, yet the most crucial, and involves having to identify the factors or variables in the problem and then formulating a mathematical problem by studying the relationships among these factors.

In the process of formulating the problem, one would normally see if certain assumptions need to be made or stated. Usually, assumptions are made in order to define the boundaries of the problem as well as to simplify the problem. For instance, while identifying the factors that may influence a particular phys...