| Introduction: ICTMA and the Teaching of Modeling and Applications | p. 1 |
| The Nature of Models & Modeling | |
| Introduction to Part I Modeling: What Is It? Why Do It? | p. 5 |
| What Are Models? | |
| Modeling Theory for Math and Science Education | p. 13 |
| Modeling a Crucial Aspect of Students' Mathematical Modeling | p. 43 |
| Modeling Perspectives in Math Education Research | p. 61 |
| Where Are Models & Modelers Found? | |
| Modeling to Address Techno-Mathematical Literacies in Work | p. 75 |
| Mathematical Modeling in Engineering Design Projects | p. 87 |
| The Mathematical Expertise of Mechanical Engineers-The Case of Mechanism Design | p. 99 |
| What Do Modeling Processes Look Like? | |
| Modeling and Quantitative Reasoning: The Summer Jobs Problem | p. 111 |
| Tracing Students' Modeling Processes in School | p. 119 |
| What Create ôThe Need For Modelingö | |
| Turning Ideas into Modeling Problems | p. 133 |
| Remarks on a Modeling Cycle and Interpreting Behaviours | p. 145 |
| Model Eliciting Environments as ôNurseriesö for Modeling Probabilistic Situations | p. 155 |
| Models as Tools, Especially for Making Sense of Problems | p. 167 |
| In-Depth Use of Modeling in Engineering Coursework to Enhance Problem Solving | p. 173 |
| Generative Activities: Making Sense of 1098 Functions | p. 189 |
| How Do Models Develop? | |
| Modeling the Sensorial Perception in the Classroom | p. 201 |
| Assessing a Modeling Process of a Linear Pattern Task | p. 213 |
| Single Solution, Multiple Perspectives | p. 223 |
| How is Modeling Different than Solving? | |
| Problem Solving Versus Modeling | p. 237 |
| Investigating the Relationship Between the Problem and the Solver: Who Decides What Math Gets Used? | p. 245 |
| Communication: The Essential Difference Between Mathematical Modeling and Problem Solving | p. 255 |
| Analysis of Modeling Problem Solutions with Methods of Problem Solving | p. 265 |
| Modeling in School Classrooms | |
| Modeling in K-16 Mathematics Classrooms-and Beyond | p. 275 |
| How Can Students Recognize the Need for Modeling? | |
| Modeling with Complex Data in the Primary School | p. 287 |
| Two Cases Studies of Fifth Grade Students Reasoning About Levers | p. 301 |
| Don't Disrespect Me: Affect in an Urban Math Class | p. 313 |
| How Do Classroom Modeling Communities Develop? | |
| Interdisciplinary Modeling Instruction: Helping Fifth Graders Learn About Levers | p. 327 |
| Modeling Discourse in Secondary Science and Mathematics Classrooms | p. 341 |
| A Middle Grade Teacher's Guide to Model Eliciting Activities | p. 353 |
| The Students' Discussions in the Modeling Environment | p. 365 |
| The Social Organisation of a Middle School Mathematics Group Discussion | p. 373 |
| Identifying Challenges within Transition Phases of Mathematical Modeling Activities at Year 9 | p. 385 |
| Realistic Mathematical Modeling and Problem Posing | p. 399 |
| Modeling in Class and the Development of Beliefs about the Usefulness of Mathematics | p. 409 |
| How Do Teachers Develop Models of Modeling? | |
| Insights into Teachers' Unconscious Behaviour in Modeling Contexts | p. 423 |
| Future Teachers' Professional Knowledge on Modeling | p. 433 |
| Theory Meets Practice: Working Pragmatically Within Different Cultures and Traditions | p. 445 |
| Secondary Teachers Learn and Refine Their Knowledge During Modeling Activities in a Learning Community Environment | p. 459 |
| An Investigation of Teachers' Shared Interpretations of Their Roles in Supporting and Enhancing Group Functioning | p. 471 |
| Mathematical Modeling: Implications for Teaching | p. 481 |
| A Professional Development Course with an Introduction of Models and Modeling in Science | p. 491 |
| Modeling as Isomorphism: The Case of Teacher Education | p. 501 |
| Mathematical Modeling and the Teachers' Tensions | p. 511 |
| A Case Study of Two Teachers: Teacher Questions and Student Explanations | p. 519 |
| Pre-service Teachers' Perceptions of Model Eliciting Activities | p. 531 |
| How Do New Technologies Influence Modeling in School? | |
| Modeling Practices with The Geometer's Sketchpad | p. 541 |
| A Principal Components Model of Simcalc Mathworlds | p. 555 |
| Modeling Random Binomial Rabbit Hops | p. 561 |
| Investigating Mathematical Search Behavior Using Network Analysis | p. 571 |
| Mathematical Modeling and Virtual Environments | p. 583 |
| What is The History of Modeling in Schools? | |
| On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics | p. 597 |
| The Dutch Maths Curriculum: 25 Years of Modelling | p. 611 |
| References | p. 621 |
| Index | p. 649 |
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