Modeling Students' Mathematical Modeling Competencies: ICTMA 13

Front Matter....Pages i-xiv
Front Matter....Pages 3-3
Introduction: ICTMA and the Teaching of Modeling and Applications....Pages 1-2
Introduction to Part I Modeling: What Is It? Why Do It?....Pages 5-10
Front Matter....Pages 11-11
Modeling Theory for Math and Science Education....Pages 13-41
Modeling a Crucial Aspect of Students’ Mathematical Modeling....Pages 43-59
Modeling Perspectives in Math Education Research....Pages 61-71
Front Matter....Pages 73-73
Modeling to Address Techno-Mathematical Literacies in Work....Pages 75-86
Mathematical Modeling in Engineering Design Projects....Pages 87-98
The Mathematical Expertise of Mechanical Engineers – The Case of Mechanism Design....Pages 99-108
Front Matter....Pages 109-109
Modeling and Quantitative Reasoning: The Summer Jobs Problem....Pages 111-118
Tracing Students’ Modeling Processes in School....Pages 119-129
Front Matter....Pages 131-131
Turning Ideas into Modeling Problems....Pages 133-144
Remarks on a Modeling Cycle and Interpreting Behaviours....Pages 145-154
Model Eliciting Environments as “Nurseries” for Modeling Probabilistic Situations....Pages 155-166
Models as Tools, Especially for Making Sense of Problems....Pages 167-172
In-Depth Use of Modeling in Engineering Coursework to Enhance Problem Solving....Pages 173-188
Generative Activities: Making Sense of 1098 Functions....Pages 189-198
Front Matter....Pages 199-199
Modeling the Sensorial Perception in the Classroom....Pages 201-212
Assessing a Modeling Process of a Linear Pattern Task....Pages 213-221
Single Solution, Multiple Perspectives....Pages 223-233
Front Matter....Pages 235-235
Problem Solving Versus Modeling....Pages 237-243
Front Matter....Pages 235-235
Investigating the Relationship Between the Problem and the Solver: Who Decides What Math Gets Used?....Pages 245-254
Communication: The Essential Difference Between Mathematical Modeling and Problem Solving....Pages 255-264
Analysis of Modeling Problem Solutions with Methods of Problem Solving....Pages 265-271
Front Matter....Pages 273-273
Modeling in K-16 Mathematics Classrooms – and Beyond....Pages 275-283
Front Matter....Pages 285-285
Modeling with Complex Data in the Primary School....Pages 287-299
Two Cases Studies of Fifth Grade Students Reasoning About Levers....Pages 301-312
Don’t Disrespect Me: Affect in an Urban Math Class....Pages 313-324
Front Matter....Pages 325-325
Interdisciplinary Modeling Instruction: Helping Fifth Graders Learn About Levers....Pages 327-339
Modeling Discourse in Secondary Science and Mathematics Classrooms....Pages 341-352
A Middle Grade Teacher’s Guide to Model Eliciting Activities....Pages 353-364
The Students’ Discussions in the Modeling Environment....Pages 365-372
The Social Organization of a Middle School Mathematics Group Discussion....Pages 373-383
Identifying Challenges within Transition Phases of Mathematical Modeling Activities at Year 9....Pages 385-398
Realistic Mathematical Modeling and Problem Posing....Pages 399-408
Modeling in Class and the Development of Beliefs about the Usefulness of Mathematics....Pages 409-420
Front Matter....Pages 421-421
Insights into Teachers’ Unconscious Behaviour in Modeling Contexts....Pages 423-432
Future Teachers’ Professional Knowledge on Modeling....Pages 433-444
Theory Meets Practice: Working Pragmatically Within Different Cultures and Traditions....Pages 445-457
Secondary Teachers Learn and Refine Their Knowledge During Modeling Activities in a Learning Community Environment....Pages 459-469
An Investigation of Teachers’ Shared Interpretations of Their Roles in Supporting and Enhancing Group Functioning....Pages 471-480
Front Matter....Pages 421-421
Mathematical Modeling: Implications for Teaching....Pages 481-490
A Professional Development Course with an Introduction of Models and Modeling in Science....Pages 491-500
Modeling as Isomorphism: The Case of Teacher Education....Pages 501-510
Mathematical Modeling and the Teachers’ Tensions....Pages 511-517
A Case Study of Two Teachers: Teacher Questions and Student Explanations....Pages 519-529
Pre-service Teachers’ Perceptions of Model Eliciting Activities....Pages 531-538
Front Matter....Pages 539-539
Modeling Practices with The Geometer’s Sketchpad....Pages 541-554
A Principal Components Model of Simcalc Mathworlds....Pages 555-560
Modeling Random Binomial Rabbit Hops....Pages 561-570
Investigating Mathematical Search Behavior Using Network Analysis....Pages 571-581
Mathematical Modeling and Virtual Environments....Pages 583-593
Front Matter....Pages 595-595
On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics....Pages 597-609
The Dutch Maths Curriculum: 25 Years of Modelling....Pages 611-620
Back Matter....Pages 621-651