Posing and Solving Mathematical Problems Advances and New Perspectiv
This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal gro
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Patricio Felmer Erkki Pehkonen Jeremy Kilpatrick Editors
Posing and Solving Mathematical Problems Advances and New Perspectives
Research in Mathematics Education
Series editors Jinfa Cai James A. Middleton
More information about this series at http://www.springer.com/series/13030
Patricio Felmer • Erkki Pehkonen Jeremy Kilpatrick Editors
Posing and Solving Mathematical Problems Advances and New Perspectives
Editors Patricio Felmer University of Chile Santiago, Chile
Erkki Pehkonen University of Helskini Helsinki, Finland
Jeremy Kilpatrick University of Georgia Athens, USA
Research in Mathematics Education ISBN 978-3-319-28021-9 ISBN 978-3-319-28023-3 DOI 10.1007/978-3-319-28023-3
(eBook)
Library of Congress Control Number: 2016933779 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Introduction
Systematic research on problem solving in mathematics can be seen to have begun over 70 years ago with the work of George Pólya, whose most famous publication was likely the book How to Solve It (Pólya, 1945). Today there is a huge literature on mathematical problem solving that includes research studies, descriptions, surveys, and analyses. Among the most influential publications have been (and still are) the book by Mason, Burton, and Stacey (1985); the book by Schoenfeld (1985); and the paper by Kilpatrick (1987). The Mason et al. (1985) book emphasizes the importance of creativity and highlights the many cul-de-sacs in problem solving as well as the importance of a solver’s persistence. The book by Schoenfeld (1985) is a well-known sourcebook. Younger researchers call it the “black book” of problem solving. Kilpatrick’s (1987) paper underlines the connection between problem solving and problem posing, giving special emphasis to problem formulation. These publicati
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