Modelling and Applications in Mathematics Education: The 14th ICMI Study (New ICMI Study Series)

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Introduction....Pages 3-32
Front Matter....Pages 33-33
Less Chalk, Less Words, Less Symbols ... More Objects, More Context, More Actions....Pages 35-44
What’s all the Fuss about Competencies?....Pages 45-56
A Theory of Mathematical Modelling in Technological Settings....Pages 57-68
What Knowledge Do Teachers Need for Teaching Mathematics Through Applications and Modelling?....Pages 69-78
Beyond the Low Hanging Fruit....Pages 79-88
Modelling for Life: Mathematics and Children’s Experience....Pages 89-98
Modelling in Lower Secondary Mathematics Classroom — Problems and Opportunities....Pages 99-108
Mathematical Modelling — a Conversation with Henry Pollak....Pages 109-120
Front Matter....Pages 121-121
Epistemology and Modelling — Overview....Pages 125-128
Modelling Body Motion: an Approach to Functions Using Measuring Instruments....Pages 129-136
Emergent Modelling as a Precursor to Mathematical Modelling....Pages 137-144
Proving and Modelling....Pages 145-152
A Developmental Approach for Supporting the Epistemology of Modeling....Pages 153-160
What is Distinctive in (Our Views about) Models & Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?....Pages 161-170
Everyday Instruments: On the Use of Mathematics....Pages 171-178
Authenticity and Goals — Overview....Pages 181-184
How to Replace Word Problems with Activities of Realistic Mathematical Modelling....Pages 185-192
The Relevance of Modelling and Applications: Relevant to Whom and for What Purpose?....Pages 193-200
Features and Impact of the Authenticity of Applied Mathematical School Tasks....Pages 201-208
Front Matter....Pages 121-121
Applications and Modelling for Mathematics — Overview....Pages 267-274
The Roles of Modelling in Learning Mathematics....Pages 275-284
Developing Mathematical Literacy....Pages 285-294
Classroom Activities and the Teacher....Pages 295-308
Uses of Technologies in Learning Mathematics through Modelling....Pages 309-318
Modelling Pedagogy — Overview....Pages 321-324
Mathematical Modelling in High School Mathematics: Teachers’ Thinking and Practice....Pages 325-332
Mathematical Modelling in Teacher Education — Necessity or Unnecessarily....Pages 333-340
Building Concepts and Conceptions in Technology-Based Open Learning Environments....Pages 341-348
Towards a Wider Implementation of Mathematical Modelling at Upper Secondary and Tertiary Levels....Pages 349-356
How Might we Share Models Through Cooperative Mathematical Modelling? Focus on Situations Based on Individual Experiences....Pages 357-364
Implementation and Practice — Overview....Pages 367-370
Some Conditions for Modelling to Exist in Mathematics Classrooms....Pages 371-378
Elementary Modelling in Mathematics Lessons: The Interplay Between “Real-World” Knowledge and “Mathematical Structures”....Pages 209-216
Modelling Competencies — Overview....Pages 219-224
Levels of Modelling Competencies....Pages 225-232
Modelling Both Complexity and Abstraction: A Paradox?....Pages 233-240
Studying and Remedying Students’ Modelling Competencies: Routine Behaviour or Adaptive Expertise....Pages 241-248
Assessing the “Phases” of Mathematical Modelling....Pages 249-256
The Arithmetic Operations as Mathematical Models....Pages 257-264
Front Matter....Pages 121-121
Picture (Im)Perfect Mathematics!....Pages 379-386
Learning Mathematical Modelling — From the Perspective of Probability and Statistics Education....Pages 387-394
Considering Workplace Activity from a Mathematical Modelling Perspective....Pages 395-402
Assessment and Evaluation - Overview....Pages 405-408
Modelling Based Project Examination....Pages 409-416
Mathematical Modelling and Applications: Ability and Competence Frameworks....Pages 417-424
“To Model, or to Let Them Model?” That is the Question!....Pages 425-432
Modelling and Applications in Pisa....Pages 433-440
Assessment of Applied Mathematics and Modelling: Using a Laboratory-Like Environment....Pages 441-448
Front Matter....Pages 449-449
Modelling and Applications in Primary Education....Pages 451-456
Possibilities for, and Obstacles to Teaching Applications and Modelling in the Lower Secondary Levels....Pages 457-462
Upper Secondary Perspectives on Applications and Modelling....Pages 463-468
Teaching Applications and Modelling at Tertiary Level....Pages 469-474
Modelling in Teacher Education....Pages 475-482
Front Matter....Pages 483-483
Moving the Context of Modelling to the Forefront: Preservice Teachers’ Investigations of Equity in Testing....Pages 485-490
Modelling in Ontario: Success in Moving Along the Continuum....Pages 491-496
Implementation Case Study: Sustaining Curriculum Change....Pages 497-502
Mathematical Modelling of Social Issues in School Mathematics in South Africa....Pages 503-510
Front Matter....Pages 511-511
Bibliography....Pages 513-517
Back Matter....Pages 519-523