Problem Solving in the Mathematics Classroom
Perspectives and practices from Different Countries
Diese Publikation zitieren
Kuzle Ana (Hg.), Rott Benjamin (Hg.), Hdnim Cadec Tatjana (Hg.), Problem Solving in the Mathematics Classroom (2016), WTM-Verlag, Münster, ISBN: 9783959870085
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Beschreibung / Abstract
Problem solving is a cornerstone of the school mathematics curricula in many countries, as it is an essential part of mathematical knowledge and performance. Implementation of problem solving in school mathematics is also important for meeting society†™s needs with respect to work, school, and life - as well as for stimulating the interest and enthusiasm of students.
Countries such as Finland, Germany, Hungary, and Slovenia have a long tradition of problem solving in school mathematics. Each country has faced its own specific challenges when adopting problem solving as a constituent part of school mathematics. But through this process they have gained experience and discovered chances for integrating problem solving into mathematics lessons. The heart of achieving this mission lies in choosing good mathematical problems.
Good mathematical problems are those that are not too difficult and not too easy, are interesting, challenging, and mathematically rich. They should invite students to conjecture and to explore different strategies, support extending their existing knowledge, and allow for problem extension. In this book, the reader will find such rich mathematical problems - targeting students at different school levels - that can help cultivate a problem solving culture.
The book provides the coherence and direction from different perspectives that practitioners need when integrating problem solving into their teaching practices and using problem solving to teach mathematics. We believe, that the processes which accompany problem solving, contribute to both the development of students†™ mathematical reasoning and to the development of their sense of autonomy.
Countries such as Finland, Germany, Hungary, and Slovenia have a long tradition of problem solving in school mathematics. Each country has faced its own specific challenges when adopting problem solving as a constituent part of school mathematics. But through this process they have gained experience and discovered chances for integrating problem solving into mathematics lessons. The heart of achieving this mission lies in choosing good mathematical problems.
Good mathematical problems are those that are not too difficult and not too easy, are interesting, challenging, and mathematically rich. They should invite students to conjecture and to explore different strategies, support extending their existing knowledge, and allow for problem extension. In this book, the reader will find such rich mathematical problems - targeting students at different school levels - that can help cultivate a problem solving culture.
The book provides the coherence and direction from different perspectives that practitioners need when integrating problem solving into their teaching practices and using problem solving to teach mathematics. We believe, that the processes which accompany problem solving, contribute to both the development of students†™ mathematical reasoning and to the development of their sense of autonomy.
Inhaltsverzeichnis
- BEGINN
- CONTENTS
- PREFACE
- SECTION 1 - DIFFERENT PERSPECTIVES ON MATHEMATICALPROBLEM SOLVING
- Benjamin Rott1, Ana Kuzle2 and Tatjana Hodnik ÄŒadeŠ¾3 1University of Duisburg-Essen, Germany, 2University of Potsdam, Germany,3University of Ljubljana, Slovenia
- PROBLEM SOLVING: A SHORT INTRODUCTION
- Günter Graumann1, Erkki Pehkonen2 and Bernd Zimmermann3 1University of Bielefeld, Germany, 2University of Helsinki, Finland, 3Universityof Jena, Germany
- ABOUT THE HISTORY OF THE PROMATH GROUP: THE ACTIVITIES OF 20 YEARS OF COOPERATION
- MATHEMATICS PROBLEM SOLVING IN THE CLASSROOM
- Anu Laine and Erkki Pehkonen University of Helsinki, Finland
- THE FINNISH PERSPECTIVE
- Torsten Fritzlar1 and Benjamin Rott2 1Martin-Luther-University Halle-Wittenberg, Germany, 2University ofDuisburg-Essen, Germany
- THE GERMAN PERSPECTIVE
- Éva Và¡sà¡rhelyi and Andrà¡s Ambrus Eötvös Lorà¡nd University Budapest, Hungary
- THE HUNGARIAN PERSPECTIVE
- Tatjana Hodnik ÄŒadeŠ¾1 and Mojca Š traus2 1University of Ljubljana, Slovenia, 2The Educational Research Institute,Slovenia
- THE SLOVENIAN PERSPECTIVE
- SECTION 2 - PROBLEMS FOR LEARNING AND TEACHINGMATHEMATICS PROBLEM SOLVING
- Gabriella Ambrus Eötvös Lorà¡nd University Budapest, Hungary
- THE “POCKET MONEY PROBLEM†
- Andrà¡s Ambrus and Éva Và¡sà¡rhelyi Eötvös Lorà¡nd University Budapest, Hungary
- DIVIDING A SQUARE: IS IT POSSIBLE? TRY TO DO IT!
- Lars Burman Šbo Akademi University, Finland
- USING VENN DIAGRAMS IN PROBLEM SOLVING: A SEQUENCE OF TASKS WITH FRACTIONS AND PERCENTAGES
- Torsten Fritzlar1 and Frank Heinrich2 1University of Halle-Wittenberg, Germany, 2University of Braunschweig –Institute of Technology, Germany
- ACROSS THE RIVER WITH FIBONACCI
- Tatjana Hodnik ÄŒadeŠ¾ and Vida Manfreda Kolar University of Ljubljana, Slovenia
- GEOMETRY AS A SOURCE FOR INVESTIGATING NUMBERS
- Lars Holzäpfel1, Benjamin Rott2 and Ulrike Dreher1 1University of Education Freiburg, Germany, 2University of Duisburg-Essen,Germany
- EXPLORING PERPENDICULAR BISECTORS: THE WATERWELL PROBLEM
- Ana Kuzle University of Potsdam, Germany
- ORIGAMI: UNFOLDING THE PYTHAGORAS IN THE BOX
- BoŠ¡tjan Kuzman University of Ljubljana, Slovenia
- THE SCRAMBLED DIGITS PUZZLE
- Zlatan Magajna University of Ljubljana, Slovenia
- STAIRS AS CONTEXT, STAIRS IN CONTEXT
- Bernd Zimmermann University of Jena, Germany
- COMPUTER SCIENCE UNPLUGGED: A SORTING GAME
- SECTION 3 - ACTION RESEARCH IN THE CLASSROOM: IN THEORYAND PRACTICE
- Janez Vogrinc and Janez Krek University of Ljubljana, Slovenia
- ACTION RESEARCH FOR IMPROVING SCHOOL PRACTICE
- Dirk Brockmann-Behnsen Bismarckschule, Hannover, Germany
- PROBLEMS WITH TERMS AND EQUATIONS? USE “INFORMATIVE FIGURES†!
- Ana Kuzle1 and Christian Conradi2 1University of Potsdam, Germany, 2Verbundschule Hille, Germany
- COLLABORATIVE ACTION RESEARCH ON THE LEARNING OF HEURISTICS: THE CASE OF INFORMATIVE FIGURE, TABLE, AND SOLUTION GRAPH AS HEURISTIC AUXILIARY TOOLS
- Lucija Š½eljko Sostro Primary School, Ljubljana, Slovenia
- DISCOVERING PICK†™S THEOREM
- INDEX