Mathematical Modelling for Teachers

1. Front Matter

   Pages i-xvi

   PDF

2. Introduction to Modelling

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 1-21

3. Motivation—Why Teach Applicable Mathematics?

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 23-29

4. Adapting Textbook Problems to Create a More Reality-Based Mathematics Education

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 31-42

5. Tasks Derived from Everyday Occurrences

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 43-79

6. An Example of a More Extensive Project

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 81-113

7. How Do Experts Model? Using This Knowledge and Understanding in the Mathematics Classroom

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 115-126

8. Further Tips for Teachers Who Want to Implement Applicable Mathematics Education

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 127-138

9. Empirical Findings on Modelling in Mathematics Education

   • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

   Pages 139-147

10. Teaching Real World Mathematics: Some Background Theory

    • Jürgen Maaß, Niamh O’Meara, Patrick Johnson, John O’Donoghue

    Pages 149-159

While there are many areas of focus in mathematics education, there are many good reasons for offering applicable mathematics education in schools. Let us just mention two of the most important reasons. On the one hand, a focus on the practical side of mathematics presents a convincing and motivating answer to the typical student question: ‘Why study mathematics?’ On the other hand, education policy seems inclined to move in this direction by implementing international testing, curricula and catalogues of skills.

The most important feature of this book is that the authors speak directly to you, the mathematics teachers. The authors attempt to draw you into a continuous dialogue about activities you are asked to engage in as learners. You are asked to do something, and through doing and reflecting you will gain first-hand experience of new approaches and materials. In this way, you can learn to teach applicable mathematics to your students using your own experience as learners of applicable mathematics, motivated and supported by the book.

Here applicable mathematics education is the phrase we use to describe reality-based mathematics education. Reality-based mathematics relies heavily on problem solving and a positive disposition to engage with mathematics. Modelling reality and simulating selected aspects of reality are other pillars of reality-based mathematics education.

• reality-based mathematics education
• problem solving
• mathematical modelling
• mathematical simulation
• school mathematics
• math problems
• maths class
• Teaching mathematics
• Teaching real world problems
• Teaching mathematical modelling
• Useful guideline for teachers
• Practical help for mathematics teachers
• learning and instruction

“A practical guide for those who intend to augment their current classroom instruction with opportunities for students to engage in modeling. … The primary audience for this volume is secondary school teachers. It could be read independently, incorporated into pre-service preparation courses, or used as the focus of a departmental study circle. … the methodology promoted by the authors extends well into the college-level courses particularly elementary calculus.” (Katherine Safford-Ramus, MAA Reviews, February, 2019)

• Institut für Didaktik der Mathematik, Universität Linz, Linz, Austria

  Jürgen Maaß

• EPISTEM, National Centre for STEM Education, School of Education, University of Limerick, Limerick, Ireland

  Niamh O’Meara, John O’Donoghue

• School of Education, University of Limerick, Limerick, Ireland

  Patrick Johnson

Jürgen Maaß (Juergen Maasz in English) is a Professor for Mathematics Education at the Kepler University in Linz (Austria). He started thinking about improving teaching mathematics by using real world problems about 40 years ago when he joined the group “MUED” a year before it was founded officially by Heinz Böer. He is a prominent member, author, and editor of several books of the “ISTRON” group.Other areas of his research and published books and papers are mathematics and society (mathematics as technology, mathematics as a social system, industrial mathematics, adults and mathematics), mathematics and philosophy (ethics, theory of recognition). He was previously the chair of ALM (Adults Learning Mathematics) and of the Austrian Mathematics Educators.

Niamh O’Meara is a Lecturer in Mathematics Education in EPISTEM, the national centre for STEM Education, at the University of Limerick. She has worked as a lecturer since 2014 and prior to that was the Senior Project Officer (Mathematics) in the National Centre for Excellence in Mathematics and Science Teaching and Learning (NCE-MSTL). Niamh was awarded her PhD in 2011 from the University of Limerick. This work investigated the knowledge required to teach mathematics effectively and she developed a model of teacher knowledge for the 21^st Century. Her current research interests include teacher knowledge; mathematics teacher education; numeracy; mathematics in the workplace and issues surrounding the mathematics curriculum.

Patrick Johnson is a Lecturer in Mathematics Education in the School of Education at the University of Limerick where he has been a faculty member since 2012. Prior to this he was a Research Fellow in the National Centre for Excellence in Mathematics and Science Teaching and Learning. Patrick received a Doctor of Philosophy (PhD) from the University of Limerick in the field of Applied Mathematics before switching into the area of Mathematics Education. His current research interests focus on the topics of mathematical modelling, problem solving, and attitudes towards mathematics.

John O’Donoghue is Associate Professor (Emeritus) of Mathematics Education at the University of Limerick. He has served as co-founder and Director of the National Centre for Excellence in Mathematics and Science Teaching and Learning (NCE-MSTL), now EPI*STEM: National Centre for STEM Education, at University of Limerick (UL). He is founder and past director of the Mathematics Learning Centre, UL. He is also a past chair and honorary trustee of Adult learning Mathematics – A Research Forum.  He has a long history of involvement with mathematics teacher education in Ireland. His research interests include mathematics teacher education (Secondary), adult mathematics education/numeracy, service mathematics teaching, and mathematics learner support (HE). He has supervised many PhD and Masters’ research candidates to completion.

 

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