Problem Solving in Mathematics Instruction and Teacher Professional Development

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

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

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),

Part VI. Teacher professional development and problem solving

1. Chaos, control, and need: Success and sustainability of professional development in problem solving. Lisa Darragh (Universidad de Chile, Chile) and Darinka Radovic (Universidad de Chile, Chile) 

2. Teachers' mathematical tensions surfacing during the first session of a professional development workshop based on problem solving. Josefa Perdomo-Díaz (Universidad de La Laguna, España), Patricio Felmer (Universidad de Chile, Chile), Cristóbal Rojas, and (Universidad de Chile, Chile)