This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.
Author(s): Raphael Wess; Heiner Klock; Hans-Stefan Siller; Gilbert Greefrath
Series: International Perspectives on the Teaching and Learning of Mathematical Modelling
Publisher: Springer
Year: 2021
Language: English
Pages: 120
City: Cham
Series Preface
Introduction
Contents
Part I Theoretical Background
1 Mathematical Modelling
1.1 Terms and Definitions Used in Mathematical Modelling
1.1.1 Mathematical Modelling and Mathematical Model
1.1.2 Modelling Processes and Modelling Cycles
1.1.3 Modelling Competencies
1.2 Aims and Perspectives of Mathematical Modelling
1.3 Modelling Tasks
1.3.1 General Categories of Tasks
1.3.2 Task Categories for Realistic Tasks
1.3.3 Selected Criteria for Modelling Tasks
1.4 Difficulties in the Modelling Process
1.5 Interventions in the Modelling Process
2 Professional Competence for Teaching Mathematical Modelling
2.1 The Concept of Competence
2.2 Professional Competence of Teachers
2.2.1 Professional Competence
2.2.2 Conceptualisations of Professional Competence of Mathematics Teachers
2.3 Competence Dimensions for Teaching Mathematical Modelling
2.4 A Competence Model for Teaching Mathematical Modelling
2.4.1 Modelling-Specific Pedagogical Content Knowledge
2.4.2 Beliefs Regarding Mathematical Modelling
2.4.3 Self-Efficacy Expectations for Mathematical Modelling
2.4.4 Empirical Validation of the Structural Model
Part II Assessment of Professional Competence for Teaching Mathematical Modelling
3 Test Instrument
3.1 Test Development
3.2 Operationalisation of Test Items: First Test Part
3.2.1 Self-reported Previous Experiences in Mathematical Modelling
3.2.2 Beliefs in Mathematical Modelling
3.2.3 Self-efficacy Expectations for Mathematical Modelling
3.3 Operationalisation of Test Items: Second Test Part
3.3.1 Knowledge about Modelling Tasks
3.3.2 Knowledge about Concepts, Aims and Perspectives
3.3.3 Knowledge about Modelling Processes and Knowledge about Interventions
3.4 Information for Conducting the Test
3.5 Test Book
4 Test Quality
4.1 Objectivity
4.2 Reliability
4.3 Validity
4.4 Secondary Quality Criteria
Part III Discussion and Outlook
5 Discussion
6 Outlook
Test Book—Correct Answers
References
