Ebook: Modeling Students' Mathematical Modeling Competencies: ICTMA 13

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

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As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners’ futures. Modeling Students’ Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach—and how both can become better learners. Dispatches as varied as classroom case studies, analyses of math in engineering work, and an in-depth review of modeling-based curricula in the Netherlands illustrate modeling activities on the job, methods of overcoming math resistance, and the movement toward replicable models and lifelong engagement.

A sampling of topics covered:

• How students recognize the usefulness of mathematics
• Creating the modeling-oriented classroom
• Assessing and evaluating students’ modeling capabilities
• The relationship between modeling and problem-solving
• Instructor methods for developing their own models of modeling
• New technologies for modeling in the classroom

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

---

As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners’ futures. Modeling Students’ Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach—and how both can become better learners. Dispatches as varied as classroom case studies, analyses of math in engineering work, and an in-depth review of modeling-based curricula in the Netherlands illustrate modeling activities on the job, methods of overcoming math resistance, and the movement toward replicable models and lifelong engagement.

A sampling of topics covered:

• How students recognize the usefulness of mathematics
• Creating the modeling-oriented classroom
• Assessing and evaluating students’ modeling capabilities
• The relationship between modeling and problem-solving
• Instructor methods for developing their own models of modeling
• New technologies for modeling in the classroom

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

Content:
Front Matter....Pages i-xiv
Front Matter....Pages 3-3
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
Introduction: ICTMA and the Teaching of Modeling and Applications....Pages 1-2
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
A Principal Components Model of Simcalc Mathworlds....Pages 541-554
Modeling Random Binomial Rabbit Hops....Pages 555-560
Investigating Mathematical Search Behavior Using Network Analysis....Pages 561-570
Mathematical Modeling and Virtual Environments....Pages 571-581
Front Matter....Pages 583-593
On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics....Pages 595-595
The Dutch Maths Curriculum: 25 Years of Modelling....Pages 597-609
Back Matter....Pages 611-620
....Pages 621-651