Problem Solving in Mathematics Instruction and Teacher Professional Development

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto-secondly-the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students' engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences,combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.

List of contents

Introduction.- Part I. Problem Solving in Mathematics Instruction: Reflections and Agendas.- Chapter 1: Embedding Problem Solving into School Mathematics.- Chapter 2: School Math Needs to Focus on Mathematics as a Study of Structure.- Chapter 3: Problem Solving as a Subject and as a Pedagogical Approach, and the On-Going Dialogue between Mathematics and Mathematics Education.- Chapter 4: On Facilitating Different Types of Problem-Solving Discourse: Focus on Heuristics, Connectivity and Aesthetics.- Part II. Design of Powerful Problem-Solving Situations.- Chapter 5: Pre-Parative and Post-Parative Play as Key Components of Mathematical Problem Solving.- Chapter 6: Alternatives Teaching Methods: Means to Promote Pupils' Mathematical Understanding.- Chapter 7:  The Design Of Problems That Promote Geometric Modeling As Context For Research On Instruction.- Chapter 8: A Mathematical Problem-Solving Approach Based on Digital Technology Affordances to Represent, Explore and Solve Problems via Geometric Reasoning.- Part III. Interplay of Factors Involved in Student Problem Solving.- Chapter 9: Collaborative Work of Students when Solving Mathematical Problems: Relationships between Different Dimensions.- Chapter 10: Attitude toward Mathematics; A Function that Affects Students' Learning to Solve a Non-Routine Mathematical Problem.- Chapter 11: Problem Solving, the Enactivistic-Metaphoric Way.- Chapter 12: Arithmetic-Algebraic Problems and Analogical Reasoning.- Part IV. Effects of Engagement with Problem Solving Chapter 13: Changing Beliefs: The Case of First-Person Vicarious Experiences.- Chapter 14: Examining Sources of Self-Efficacy in Whole-Class Problem-Solving.- Chapter 15: Ensuring Equity through Using Culturally Embedded Group Worthy Tasks within Mathematical Inquiry Communities.-  Part V. On the Role of Teachers in Problem-Solving Classrooms.- Chapter 16: Let Students Communicate their Ideas: How Instructors' Interactions Influence Team's Problem-Solving Capabilities.- Chapter 17: Teacher Questioning to Foster Mathematical Problem Solving in Two Professional Development Programmes.- Chapter 18: Mathematics Teachers' Specialized Knowledge for Managing Problem-Solving Tasks.- Part VI. Teacher Professional Development and Problem Solving.- Chapter 19: Chaos, Control, and Need: Success and Sustainability of Professional Development in Problem Solving.- Chapter 20: Teachers' Mathematical Tensions Surfacing during the First Session of a Professional Development Workshop Based on Problem Solving.- Chapter 21: Teachers' Learning to Enhance Urban Students' Participation through Problem Solving in Mathematics Classroom: The Case of Juan.
 
 

About the author

¿Patricio Felmer is a mathematician working at the University of Chile, specialized in the area of Partial Differential Equations. During the last ten years, he has steadily moved towards Mathematics Education, working in projects for the Chilean government on the definition of Standards for the Formation of Mathematics Teachers and on the development of material for them. In the last years, he has been working in R&D projects with the aim of implementing professional development strategies for in-service teachers based on problem solving. In this direction, he is leading ARPA Initiative, an independent program for introducing problem solving in Chilean Classrooms through professional development of teachers teaching mathematics in all levels, preschool, primary, secondary and tertiary education.

Peter Liljedahl is a Professor of Mathematics Education in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University in Vancouver, Canada. He is the coordinator of the MSc and PhD Program in Mathematics Education and is a co-director of the David Wheeler Institute for Research in Mathematics Education at Simon Fraser University. More globally, Dr. Liljedahl is the current president of the International Group for the Psychology of Mathematics Education. Dr. Liljedahl serves on the editorial boards of ESM, JMTE, MTL, FMEJ, MERJ, and CJSMTE and is a senior editor of IJSME. He has authored or co-authored 7 books, 17 book chapters, 26 journal articles, and over 50 conference papers.  Dr. Liljedahl is also a member of the executive of the British Columbia Mathematics Teachers Association (BCAMT) and former co-editor of their flagship journal, Vector. Dr. Liljedahl is a former high school mathematics teacher who has kept his research interest and activities close to the classroom. His research interests are creativity, insight, and discovery in mathematics teaching and learning; the role of the affective domain on the teaching and learning of mathematics; the professional growth of mathematics teachers; mathematical problem solving; numeracy; and engaging student thinking. He consults regularly with schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy.
Boris Koichu is an Associate Professor at the Department of Science Teaching of the Weizmann Institute of Science. His research focus is on learning for and through mathematical problem solving and problem posing, with special focus on the interplay of cognitive, affective and situational factors involved. Prof. Koichu is an author of about a hundred of papers published in peer-reviewed journals, edited books and peer-reviewed conference proceedings, and a co-editor of a book on mathematical creativity and giftedness. He is an editorial board member of Journal of Mathematical Behavior and International Journal of Science and Mathematics Education. He alsoserves as a member of the Education Committee of the European Mathematical Society. Koichu received his M.Sc. in mathematics from Lviv State University, Ukraine, in 1991, and his Ph.D. in mathematics education from the Technion - Israel Institute of Technology, in 2004. Following two-year post-doctoral fellowship at the Faculty of Mathematics of the University of California, San Diego, he joined the faculty of the Technion in 2006. Boris Koichu has been an academic advisor of 13 Ph.D. students and a PI of several research projects funded by the Israel Science Foundation and the Ministry of Education of Israel. He moved to the Weizmann Institute of Science in March 2017 and is currently working on a new project entitled TRAIL - Teacher-Researcher Alliance for Investigating Learning.      

Report

"This book is a great repository of knowledge for graduate students, mathematics researchers and teacher educators who wants to effectively implement problem-solving in classrooms." (Sandra Richy John, MAA Reviews, January 23, 2021)

Product details

• Assisted by: Patricio Felmer (Editor), Boris Koichu (Editor), Pete Liljedahl (Editor), Peter Liljedahl (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 17.12.2020
• EAN: 9783030292171
• ISBN: 978-3-0-3029217-1
• No. of pages: 410
• Dimensions: 156 mm x 31 mm x 234 mm
• Illustrations: XVII, 410 p. 81 illus., 47 illus. in color.
• Series: Research in Mathematics Education
• Subject: Humanities, art, music > Education > School education, didactics, methodology