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Problem solving in the mathematics classroom

perspectives and practices from different countries

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.

Titel: Problem solving in the mathematics classroom
Untertitel: perspectives and practices from different countries
Herausgeber: Kuzle, Ana
Rott, Benjamin GND
Hodnik Čadež, Tatjana
Dokumenttyp: Buch
Medientyp: Text
Erscheinungsdatum: 2016
Publikation in MIAMI: 30.01.2017
Datum der letzten Änderung: 30.01.2017
Reihe Ars inveniendi et dejudicandi ; 7
Verlag/Hrsg.: WTM-Verlag für wissenschaftliche Texte und Medien
Schlagwörter: Problemlösen; Mathematikunterricht
Fachgebiete: Mathematik; Bildung und Erziehung
Rechtlicher Vermerk: © 2016 WTM – Verlag für wissenschaftliche Texte und Medien, Münster
Sprache: Englisch
Anmerkungen: Druckausgabe: Kuzle, Ana; Rott, Benjamin; Hodnik Čadež, Tatjana (Hrsg.): Problem solving in the mathematics classroom : perspectives and practices from different countries. Münster : WTM, 2016. (Ars inveniendi et dejudicandi ; 7), ISBN 978-3-95987-007-8
Format: PDF-Dokument
ISBN: 978-3-95987-008-5
URN: urn:nbn:de:hbz:6-63239467138
Permalink: https://nbn-resolving.org/urn:nbn:de:hbz:6-63239467138
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Inhalt:
PREFACE ..... 7
SECTION 1: DIFFERENT PERSPECTIVES ON MATHEMATICAL PROBLEM SOLVING ..... 9
Problem solving: A short introduction (Benjamin Rott, Ana Kuzle and Tatjana Hodnik Čadež) ..... 11
About the history of the ProMath group: the activities of 20 years of cooperation (Günter Graumann, Erkki Pehkonen and Bernd Zimmermann) ..... 19
Mathematics problem solving in the classroom ..... 25
The Finnish perspective (Anu Laine and Erkki Pehkonen) ..... 27
The German perspective (Torsten Fritzlar and Benjamin Rott) ..... 31
The Hungarian perspective (Éva Vásárhelyi and András Ambrus) ..... 37
The Slovenian perspective (Tatjana Hodnik Čadež and Mojca Štraus) ..... 41
SECTION 2: PROBLEMS FOR LEARNING AND TEACHING MATHEMATICS PROBLEM SOLVING ..... 47
The “Pocket money problem” (Gabriella Ambrus) ..... 49
Dividing a square: Is it possible? Try to do it! (András Ambrus and Éva Vásárhelyi) ..... 61
Using Venn diagrams in problem solving: A sequence of tasks with fractions and percentages (Lars Burman) ..... 73
Across the river with Fibonacci (Torsten Fritzlar and Frank Heinrich) ..... 85
Geometry as a source for investigating numbers (Tatjana Hodnik Čadež and Vida Manfreda Kolar) ..... 99
Exploring perpendicular bisectors: The water well problem (Lars Holzäpfel, Benjamin Rott and Ulrike Dreher) ..... 119
Origami: Unfolding the Pythagoras in the box (Ana Kuzle) ..... 133
The scrambled digits puzzle (Boštjan Kuzman) ..... 145
Stairs as context, stairs in context (Zlatan Magajna) ..... 155
Computer science unplugged: a sorting game (Bernd Zimmermann) ..... 165
SECTION 3: ACTION RESEARCH IN THE CLASSROOM: IN THEORY AND PRACTICE ..... 181
Action research for improving school practice (Janez Vogrinc and Janez Krek) ..... 183
Problems with terms and equations? Use “informative figures”! (Dirk Brockmann-Behnsen) ..... 197
Collaborative action research on the learning of heuristics: The case of informative figure, table, and solution graph as heuristic auxiliary tools (Ana Kuzle and Christian Conradi) ..... 211
Discovering Pick’s theorem (Lucija Željko) ..... 225
INDEX ..... 235