Mathematical Problem Solving

This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment.

Mathematical problem solving has long been recognized as an important aspect of mathematics, teaching mathematics, and learning mathematics. It has influenced mathematics curricula around the world, with calls for the teaching of problem solving as well as the teaching of mathematics through problem solving. And as such, it has been of interest to mathematics education researchers for as long as the field has existed. Research in this area has generally aimed at understanding and relating the processes involved in solving problems to students' development of mathematical knowledge and problem solving skills. The accumulated knowledge and field developments have included conceptual frameworks for characterizing learners' success in problem solving activities, cognitive, metacognitive, social and affective analysis, curriculum proposals, and ways to promote problem solving approaches.

Inhalt

Introduction

Section 1: problem solving heuristics

1.Looking Back to Solve Differently: Familiarity, Fluency, and Flexibility - Hartono Tjoe

2.Future-oriented Thinking and Activity in Mathematical Problem Solving - Wes Maciejewski

Section 2: problem solving and technology

3.A model of mathematical problem solving with technology: the case of Marco solving-and-expressing two geometry problems - Susana Carreira and Hélia Jacinto

4.Mathematical problem solving and the use of digital technologies - Manuel Santos-Trigo

5.The spreadsheet affordances in solving complex word problems - Nélia Amado, Susana Carreira and Sandra Nobre

Section 3: inquiry and problem posing in mathematics education

6.Is Inquiry-Based Approach possible at the elementary school? - Magali Hersant and Christine Choquet

7.How to stimulate in-service teachers' competence in didactic analysis by means of problem posing Uldarico Malspina, Carlos Torres, and Norma Rubio

Section 4: assessment of and through problem solving

8.Exploring Methods in Evaluating Metacognitive Strategies in Mathematical Problem Solving LOH Mei Yoke and Lee Ngan Hoe

9.Assessing Inquiry-Based-Mathematics-Education with both a summative and formative purpose - Maud Chanudet

10.Beyond the standardized assessment of mathematical problem solving competencies: from products to processes - Pietro Di Martino and Giulia Signorini

11.Toward Designing and Developing Likert Items to Assess Mathematical Problem Solving - James A. Mendoza Alvarez, Kathryn Rhoads, and Cavender Campbell Section 5: the problem solving environment

12.Creating and sustaining online problem-solving forums: Two perspectives - Boris Koichu and Nelly Keller

13.Conditions for Supporting Problem Solving: Vertical Non-Permanent Surfaces - Peter Liljedahl

14.The ARPA Experience in Chile: Problem Solving for Teachers' Professional Development - Patricio Felmer, Josefa Perdomo-Díaz, and Cristián Reyes 15.Understanding the Sustainability of a Teaching Innovation for Problem Solving: A Systems Approach Ho Weng Kin, Romina Ann S. Yap, Tay Eng Guan, Leong Yew Hoong, Toh Tin Lam, Quek Khiok Seng, Toh Pee Choon, and Jaguthsing Dindyal

Conclusion