Problem Solving in Mathematics Instruction and Teacher Professional Development

About the Book

Introduction

Part I. Problem solving in mathematics instruction: reflections and agendas

1. Embedding problem solving into school mathematics. Kaye Stacey (University of Melbourne, Australia)

2. School math needs to focus on mathematics as a study of structure. Peter Taylor (Queen's University, Canada)

3. Problem solving as a subject and as a pedagogical approach, and the on-going dialogue between mathematics and mathematics education. Frédéric Gourdeau (Université Laval, Canada)

4. On facilitating different types of problem-solving discourse: Focus on heuristics, connectivity and aesthetics. Boris Koichu (Weizmann Institute of Science, Israel)

Part II. Design of powerful problem-solving situations

1. Pre-parative and Post-parative Play as Key Components of Mathematical Problem Solving. John Mason (The Open University, UK)

2. Alternatives teaching methods: Means to promote pupils' mathematical understanding. Erkki Pehkonen (University of Helsinki, Finland)

3. The design of problems that promote geometric modeling as context for research on instruction. Patricio Herbst (University of Michigan, USA)

4. A Mathematical Problem-Solving Approach Based on Digital Technology Affordances to Represent, Explore and Solve Problems via Geometric Reasoning. Manuel Santos-Trigo (CINVESTAV, México)

Part III. Interplay of factors involved in student problem solving

1. Collaborative work of students when solving mathematical problems: relationships between different dimensions. Eugenio Chandía (Universidad de Chile, Chile), Rafael Arancibia (Universidad de Chile, Chile), María Luz Montes (SIP, Red de Colegios, Chile)

2. Attitude toward Mathematics; A Function that Affects Students' Learning to Solve a Non-Routine Mathematical Problem. Farzaneh Saadati (Universidad de Chile, Chile), Cristian Reyes (Universidad de Chile, Chile)

3. Problem solving, the enactivistic-metaphoric way... Jorge Soto-Andrade (Universidad de Chile, Chile)

4. Arithmetic-Algebraic Problems and Analogical Reasoning. Daniela Assmus (Martin-Luther-Universität, Germany) Torsten Fritzlar (Martin-Luther-Universität, Germany)

Part IV. Effects of engagement with problem solving

1. Changing beliefs: The case of first-person vicarious experiences. Peter Liljedahl (Simon Fraser University, Canada), Cristian Reyes (Universidad de Chile, Chile), Annette Rouleau (Simon Fraser University, Canada) and Natalia Ruiz (Universidad de Chile, Chile)

2. Examining sources of self-efficacy in whole-class problem-solving. Peter Liljedahl (Simon Fraser University, Canada), Cristian Reyes (Universidad de Chile, Chile), Annette Rouleau (Simon Fraser University, Canada) and Natalia Ruiz (Universidad de Chile, Chile)

3. Ensuring equity through using culturally embedded group worthy tasks within mathematical inquiry communities. Roberta Hunter (Massey University, New Zealand) and Jodie Hunter (Massey University, New Zealand)

Part V. On the role of teachers in problem-solving classrooms

1. Let students communicate their ideas: How instructors' interactions influence team's problem-solving capabilities. Sergio Célis (Universidad de Chile, Chile)

2. Teacher questioning to foster mathematical problem solving in two professional development programmes. Markus Hähkiöniemi (University of Jyväskylä, Finland) and John Francisco (University of Massachusetts, USA)

3. Mathematics Teachers' Specialized Knowledge for managing problem-solving tasks. José Carrillo (Universidad de Huelva, España), Nuria Climent (Universidad de Huelva, España), Luis C. Contreras (Universidad de Huelva, España) and Miguel Á. Montes (Universidad de Huelva, España),

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 also serves 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.