International Electronic Journal of Mathematics Education_Vol 2_N2

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International Electronic Journal of Mathematics Education_Vol 2_N2
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  Mahmoud AL-HAMZA,  RUSSIAN FEDERATION  Mara ALAGIC, USA Ahmet ARIKAN, TURKEY Nicolas BALACHEFF,  FRANCE  Carmen BATANERO , SPAIN  Catherine A. BROWN, USA Leone BURTON,  UNITED KINGDOM  Olive CHAPMAN, CANADA Kwok-cheung CHEUNG, CHINA Megan CLARK,  NEW ZEALAND Willibald DÖRFLER,  AUSTRIA Paul DRIJVERS,  NETHERLANDS  Lyn ENGLISH,  AUSTRALIA Peter GATES, UNITED KINGDOM  Juan D. GODINO, SPAIN  Marjorie HENNINGSEN,  LEBANON Noraini IDRIS,  MALAYSIA Cyril JULIE, SOUTH AFRICA Jeremy KILPATRICK, USA Siew-Eng LEE,  MALAYSIA Frederick K.S. LEUNG, CHINA Shiqi LI, CHINA Romulo LINS,  BRAZIL Denise S. MEWBORN, USA John MONAGHAN, UNITED KINGDOM  Judy MOUSLEY,  AUSTRALIA Richard NOSS, UNITED KINGDOM  Ildar S. SAFUANOV,  RUSSIAN FEDERATION  Mamokgethi SETATI, SOUTH AFRICA Anna SFARD,  ISRAEL Kaye STACEY,  AUSTRALIA Khoon Yoong WONG, SINGAPORE  Oleksiy YEVDOKIMOV, UKRAINE  Sharifah Norul Akmar bt Syed ZAMRI,  MALAYSIA Nurit ZEHAVI,  ISRAEL Ismail Ozgur ZEMBAT, TURKEY  i Volume 2, Number 2, July 2007 EditorZiya ARGUN , TURKEY  Editorial Board International Electronic Journal of  Mathematics Education  Welcome to the  International Electronic Journal of Mathematics Education (IEJME) .We are happy to launch the new issue with thecontribution of individuals from all around theworld both as authors and reviewers. Bothresearch and position papers, not excludingother forms of scholarly communication, areaccepted for review. The long term mission of the IEJME is to continue to offer qualityknowledge and research base to the educationcommunity and increased global availability of the articles published each issue. The editorsand review board hope that you find the published articles academically and professionally valuable. Online - It is our intention to make the journalavailable over the internet. All submissions,reviewing, editing, and publishing are done viae-mail and the Web, allowing for quality of theend product and increased speed andavailability to all readers. Publication Frequency - IEJME is publishedthree times a year in February, July andOctober for every year.Published by: GOKKUSAGI LTD. STI.TURKEY © Gokkusagi all rights reversed. Apart fromindividual use, no part of this publication may be reproduced or stored in any form or by anymeans without prior written permission from publisher. ISSN 1306-3030 www.iejme.com CONTENTS 1.Linking School Mathematics to Out-of-School Mathematical Activities: StudentInterpretation of Task, Understandings andGoals Monaghan, J.50  2.Didactic Effectiveness of MathematicalDefinitions: The Case of the Absolute Value  Wilhelmi, M. R., Godino, J. D. and Lacasta, E. 72 3.Empiricism, Contigency andEvolutionary Metaphors: Getting Beyondthe Math Wars Stemhagen, K.91 Manuscript Submission Guidelines 106   ii Volume 2, Number 2, July 2007 International Electronic Journal of  Mathematics Education  Volume 2, Number 2, July 2007 www.iejme.com   LINKING SCHOOL MATHEMATICS TO OUT-OF-SCHOOL MATHEMATICALACTIVITIES: STUDENT INTERPRETATION OF TASK,UNDERSTANDINGS AND GOALSJohn Monaghan . INTRODUCTION This article reports on the work of one class of high school students in a project1 whichinvestigated ways of linking school mathematics to out-of-school mathematical activities. Theclass worked on one task, identifying when a vehicle is in a specific area, given to them by adirector of a transport/haulage company. This article presents detail of what the students did andargues that they did not address the company director’s task because they transformed the task and that this transformation is interrelated with their understandings and their goals. The next section briefly considers the literature on the use of mathematics in and out of school and the words ‘understanding’, ‘goals’ and ‘activity’. This is followed by a description of the wider project and this classroom project. Results for students working in groups are thendetailed. The Discussion section attends to student transformation of the task and theinterrelations of this with their understandings and goals. The final section considers educationalimplications. Copyright © 2007 byGOKKUSAGIISSN:1306-3030 International Electronic Journal of  Mathematics Education ABSTRACT. This article considers one class of high school students as they worked on a task given to them by a company director of a haulage firm. The article provides details of students’ transformation of the giventask into a subtly different task. It is argued that this transformation is interrelated with students’understandings of mathematics, of technology and of the real world and students’ emerging goals. It isargued that the students did not address the company director’s task. Educational implications with regardto student engagement with realistic tasks are considered.. KEYWORDS. Goals, Mathematics, Out-Of-School, School, Tasks, Understandings. 1 See http://www.education.leeds.ac.uk/research/cssme/outofschool.phpfor the project description.
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