Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (International Perspectives on the Teaching and Learning of Mathematical Modelling)

In this volume cultural, social and cognitive influences on the research and teaching of mathematical modelling are explored from a variety of theoretical and practical perspectives. The authors of the current volume are all members of the International Community of Teachers of Mathematical Modelling and Applications, the peak research body in this field. A distinctive feature of this volume is the high number of authors from South American countries. These authors bring quite a different perspective to modelling than has been showcased in previous books in this series, in particular from a cultural point of view. As well as recent international research, there is a strong emphasis on pedagogical issues including those associated with technology and assessment, in the teaching and learning of modelling. Applications at various levels of education are exemplified. The contributions reflect common issues shared globally and represent emergent or on-going challenges. Front Matter....Pages i-xi Cultural, Social, Cognitive and Research Influences on Mathematical Modelling Education....Pages 1-32 Front Matter....Pages 33-33 Mathematical Modelling as a Strategy for Building-Up Systems of Knowledge in Different Cultural Environments....Pages 35-44 The Meaning of the Problem in a Mathematical Modelling Activity....Pages 45-54 Extending the Reach of the Models and Modelling Perspective: A Course-Sized Research Site....Pages 55-66 Prescriptive Modelling – Challenges and Opportunities....Pages 67-79 An Approach to Theory Based Modelling Tasks....Pages 81-91 Facilitating Mathematisation in Modelling by Beginning Modellers in Secondary School....Pages 93-104 Authenticity in Extra-curricular Mathematics Activities: Researching Authenticity as a Social Construct....Pages 105-113 The Teaching Goal and Oriented Learning of Mathematical Modelling Courses....Pages 115-125 Front Matter....Pages 127-127 Modelling Competencies: Past Development and Further Perspectives....Pages 129-149 How to Support Teachers to Give Feedback to Modelling Tasks Effectively? Results from a Teacher-Training-Study in the Co2CA Project....Pages 151-160 A Reflection on Mathematical Modelling and Applications as a Field of Research: Theoretical Orientation and Diversity....Pages 161-171 Problem Solving Methods for Mathematical Modelling....Pages 173-183 Improving Mathematical Modelling by Fostering Measurement Sense: An Intervention Study with Pre-service Mathematics Teachers....Pages 185-194 How Do Students Share and Refine Models Through Dual Modelling Teaching: The Case of Students Who Do Not Solve Independently....Pages 195-206 Exploring Interconnections Between Real-World and Application Tasks: Case Study from Singapore....Pages 207-217 Mathematical Modelling Tasks and the Mathematical Thinking of Students....Pages 219-228 Measurement of Area and Volume in an Authentic Context: An Alternative Learning Experience Through Mathematical Modelling....Pages 229-240 Mathematical Modelling and Culture: An Empirical Study....Pages 241-250 Mathematical Modelling of a Social Problem in Japan: The Income and Expenditure of an Electric Power Company....Pages 251-261 Front Matter....Pages 263-263 The Place of Mathematical Modelling in the System of Mathematics Education: Perspective and Prospect....Pages 265-276 Moving Within a Mathematical Modelling Map....Pages 277-282 Negotiating the Use of Mathematics in a Mathematical Modelling Project....Pages 283-292 Moving Beyond a Single Modelling Activity....Pages 293-303 The Possibility of Interdisciplinary Integration Through Mathematical Modelling of Optical Phenomena....Pages 305-316 Activation of Student Prior Knowledge to Build Linear Models in the Context of Modelling Pre-paid Electricity Consumption....Pages 317-326 Mathematical Modellers’ Opinions on Mathematical Modelling in Upper Secondary Education....Pages 327-337 Modelling, Education, and the Epistemic Fallacy....Pages 339-349 Reconsidering the Roles and Characteristics of Models in Mathematics Education....Pages 351-361 Developing Statistical Numeracy: The Model Must Make Sense....Pages 363-373 Mathematical Modelling and Cognitive Load Theory: Approved or Disapproved?....Pages 375-384 Social-critical Dimension of Mathematical Modelling....Pages 385-395 Pedagogical Actions of Reflective Mathematical Modelling....Pages 397-406 Context Categories in Mathematical Modelling in Fundamentals of Calculus Teaching....Pages 407-416 Applied Mathematical Problem Solving: Principles for Designing Small Realistic Problems....Pages 417-427 Front Matter....Pages 429-429 Visualisation Tactics for Solving Real World Tasks....Pages 431-442 Developing Modelling Competencies Through the Use of Technology....Pages 443-452 Model Analysis with Digital Technology: A “Hybrid Approach”....Pages 453-463 Collective Production with Mathematical Modelling in Digital Culture....Pages 465-474 Front Matter....Pages 475-475 Learners’ Dealing with a Financial Applications-Like Problem in a High-Stakes School-Leaving Mathematics Examination....Pages 477-486 Front Matter....Pages 475-475 Evidence of Reformulation of Situation Models: Modelling Tests Before and After a Modelling Class for Lower Secondary School Students....Pages 487-498 Front Matter....Pages 499-499 Mathematical Modelling in the Teaching of Statistics in Undergraduate Courses....Pages 501-512 Models and Modelling in an Integrated Physics and Mathematics Course....Pages 513-522 Research-Based Modelling Teaching Activities: A Case of Mathematical Positioning with GNSS....Pages 523-533 Mathematical Texts in a Mathematical Modelling Learning Environment in Primary School....Pages 535-543 A Differential Equations Course for Engineers Through Modelling and Technology....Pages 545-555 Contributions of Mathematical Modelling in Education of Youth and Adults....Pages 557-566 Pre-service Mathematics Teachers’ Experiences in Modelling Projects from a Socio-critical Modelling Perspective....Pages 567-578 A Mathematical Modelling Challenge Program for J.H.S. Students in Japan....Pages 579-589 Front Matter....Pages 591-591 Modelling the Wall: The Mathematics of the Curves on the Wall of Colégio Arquidiocesano in Ouro Preto....Pages 593-603 Back Matter....Pages 605-613