Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences

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