Posing and Solving Mathematical Problems: Advances and New Perspectives

✍ Scribed by Patricio Felmer, Erkki Pehkonen, Jeremy Kilpatrick (eds.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 400
• Series: Research in Mathematics Education
• Edition: 1
• Category: Library

✦ Synopsis

This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers.

The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.

✦ Table of Contents

Front Matter....Pages i-xi
Front Matter....Pages 1-1
How Do Textbooks Incorporate Mathematical Problem Posing? An International Comparative Study....Pages 3-22
Problem-Posing and Questioning: Two Tools to Help Solve Problems....Pages 23-36
Affective Factors and Beliefs About Mathematics of Young Chilean Children: Understanding Cultural Characteristics....Pages 37-51
On the Role of Corporeality, Affect, and Metaphoring in Problem-Solving....Pages 53-67
Reformulating: Approaching Mathematical Problem Solving as Inquiry....Pages 69-81
Improving of Mathematical Problem-Solving: Some New Ideas from Old Resources....Pages 83-108
Part 1 Reaction: Problem Posing and Solving Today....Pages 109-113
Front Matter....Pages 115-115
Can Mathematical Problem Solving Be Taught? Preliminary Answers from 30 Years of Research....Pages 117-135
Teaching Mathematical Problem Solving in Hungary for Students Who Have Average Ability in Mathematics....Pages 137-156
“Memorable Diagonals”: Exploratory Problems as Propositions for Doing Mathematics....Pages 157-165
Pupils’ Drawings as a Research Tool in Mathematical Problem-Solving Lessons....Pages 167-188
The Use of Digital Technology to Frame and Foster Learners’ Problem-Solving Experiences....Pages 189-207
Proportional Word Problem Solving Through a Modeling Lens: A Half-Empty or Half-Full Glass?....Pages 209-229
Conceptual Model-Based Problem Solving....Pages 231-254
Reaction: Students, Problem Posing, and Problem Solving....Pages 255-260
Front Matter....Pages 261-261
When Is a Problem…? “When” Is Actually the Problem!....Pages 263-285
Novice Chilean Secondary Mathematics Teachers as Problem Solvers....Pages 287-308
Infusing Mathematical Problem Solving in the Mathematics Curriculum: Replacement Units....Pages 309-325
Mathematical Problem Posing: A Case of Elementary School Teachers Developing Tasks and Designing Instructions in Taiwan....Pages 327-344
Mathematical Problem Solving and Teacher Professional Learning: The Case of a Modified PISA Mathematics Task....Pages 345-360
Front Matter....Pages 261-261
Building Thinking Classrooms: Conditions for Problem-Solving....Pages 361-386
Reaction: Teachers, Problem Posing and Problem-Solving....Pages 387-391
Back Matter....Pages 393-402

✦ Subjects

Mathematics Education;Learning & Instruction