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Fulltext I DIVA STUDENTS’ NARRATIVES FROM GRAPHICAL ARTEFACTS Exploring the use of mathematical tools and forms of expression in students’ graphicacy Oduor Olande Department of Science Education and Mathematics Faculty of Science, Technology, and Media Mid Sweden University ISSN 1652-893X Doctoral Dissertation No. 162 ISBN 978-91-87557-05-7 Akademisk avhandling som med tillstånd av Mittuniversitetet framlägges till offentlig granskning för avläggande av filosofie doktorsexamen den 27 september, 2013, klockan 13:15 i Alfhild Agrell-salen, Sambiblioteket, Mittuniversitetet Härnösand. Seminariet kommer att hållas på engelska. STUDENTS’ NARRATIVES FROM GRAPHICAL ARTEFACTS Exploring the use of mathematical tools and forms of expression in students’ graphicacy Oduor Olande © Oduor Olande, 2013 Cover picture: A bubble graph of items success rate from PISA 2003 for the Nordic countries including the OECD average Department of Science Education and Mathematics, Faculty of Science, Technology, and Media Mid Sweden University, SE-851 70 Sundsvall Sweden Telephone: +46 (0)771-975 000 Printed by Mid Sweden University, Sundsvall, Sweden, 2013 ii Supervisors: Prof. Karl-Göran Karlsson Department of Science Education and Mathematics, Mid Sweden University Prof. Astrid Pettersson Department of Mathematics and Science Education, Stockholm University The studies leading to this dissertation was funded by the Swedish government through a PhD fellowship offered by Mittuniversitet [Mid Sweden University]. iii NEVER GIVE IN (Feat. Mr. Lynx) Written by Mark Mohr and Andrew Cartwright Arranged by Solomon Jabby, Mark Mohr, Bobby Cressey, Rob Alo and Reggie Grisham Inspired by Gal 6:9, Col 2:6, Matt 24:12-13, Isaiah 26:3 Jam 1:12, II Chron 15:7, Gal 2:5, Gal 6:9-10, I John 2:28, Jam 1:2-4, Heb 12:1, Jam 5:10-11 & Prov 1:10 I can't let them stop you from what you gotta be doing you know? Especially for the Most High/Emotion/Chorus: Oh, never give up/Don't give in and don't you ever give up(Repeat)/I won't go down quietly into the night/I won't go down quietly without a fight/I won't give up/No won't give in/I won't go down quietly into the night/This love is far too precious to requite/It's far too precious got to fight/I won't give up/No won't give in/I won't go down quietly into the night/You are reluctant to continue/And your resistance won't let you go through/In this instant you gotta change what you do and have faith/For you can take it just so far in length/You won't make it, not on your own strength/Don't bother fake it in your moment of angst just have faith/(CHORUS)/I say we never give up/Never gonna give it up (Repeat)/Sing out/Oh never give up/Youth never give up/With Jesus in your life--He's more than enough/Youth never give up/Please never give up/You got to keep it up/Oh never give up/Youth never give up/Sweet Jesus in your life and He's more than enough/Oh never give up/Please never give up/So no matter what they say or do/Don't you let them ever discourage you/From the things that you've got to do/I know Jah will be there for you/I know He cares for you/So you just keep pressing through/The mark of the prize that is in Him and not you/(CHORUS)/I said we're never giving up though they fight this/I got to stand up and then be a witness/I'm gonna preach the Word of God like John the Baptist/Even if they wanna kill me and leave me headless/I still preach it everywhere that I go/So all the people in the World they can know that Jesus alone yes Him love them so/We a real warrior/We nah stopping now! (CHORUS). iv STUDENTS’ NARRATIVES FROM GRAPHICAL ARTEFACTS Exploring the use of mathematical tools and forms of expression in students’ graphicacy Oduor Olande, 2013 Department of Science Education and Mathematics Mid Sweden University, SE-851 70 Sundsvall, Sweden ISSN 1652-893X, Mid Sweden University Doctoral Dissertation 162; ISBN 978-91-87557-05-7 ABSTRACT The research concerns presented in this dissertation addresses aspects of students’ interaction with commonly occurring graphical artefacts in teaching and learning environments. In particular, focus is on how the students make sense of these artefacts in relation to subject specific tools and forms of expression. The dissertation comprises of four studies guided by a semiotics cultural- historical perspective to cognition. The first study which is largely quantitative, analyses the percentage scores from students’ responses to selected items from OECD PISA surveys for items containing graphical elements. The second and the third studies in keeping with a more sociocultural perspective to learning as point of departure, examine the students’ collaborative interaction around tasks containing graphical elements. The fourth study explores the nature of students’ solutions from the Swedish national test in mathematics based on a tools and forms of expression sensitive empirically derived construct of Identification contra Critical-analytical approach to graphicacy. The main outcomes of these studies can be summarised as follows: first there is justification for re-examining the predominant characterisation of students’ interaction with graphical artefacts. Secondly, while it is not uncommon for students to take a more visual-perceptive and intuitive approach to graphicacy, results from task items interactions indicate that a Critical-analytical approach seems to be more reliable and capable of yielding desirable outcomes. The outcomes of these studies call for vigilance on the type of tasks used in relation v to graphicacy and how these can be used to foster students’ Critical-analytical disposition. Keywords: Critical-analytical approach, Graph comprehension, Graphicacy, Graphical artefacts, Statistical literacy, Mathematics literacy, Semiotics vi SAMMANFATTNING De forskningsresultat som presenteras i denna avhandling behandlar aspekter av elevers interaktion med vanligt förekommande grafiska artefakter i lärande miljöer. En särkilt fokus riktas på hur eleverna tar del av kärnan [innehållet] i dessa artefakter i relation till ämnesspecifika redskap och uttrycksformer. Avhandlingen består av fyra studier som utgår ifrån de semiotisk kulturhistoriska perspektiven på kognition: I den första studien, som till stor del är kvantitativ, analyseras lösningsfrekvenser från elevernas svar på utvalda uppgifter från OECD PISA undersökningen som innehåller diagram. Den andra och den tredje studien har i linje med ett mer sociokulturellt perspektiv på lärande fokus på elevernas kollaborativa interaktion vid lösning av uppgifter som innehåller diagram. Den fjärde studien undersöker hur elever löser uppgifter i det svenska nationella provet i matematik. Detta görs genom att använda sig av ett analytiskt verktyg [konstruktion] vars fokus är på identifikation kontra kritiska-analytiska förhållningssätt till interaktion med diagram. Konstruktionen uppmärksammar de uttrycksformer som används i interaktioner med grafiska artefakter. De viktigaste resultaten från dessa studier kan sammanfattas på följande sätt: För det första finns det belägg för att ifrågasätta den vanligen förekommande forskningsbaserade karakteriseringen av elevernas interaktion med grafiska artefakter. Det andra är att det inte är ovanligt att eleverna har ett mer visuellt och intuitivt tillvägagångssätt när de handskas med grafiska artefakter. Samtidigt visar resultatet att interaktioner som präglas av ett kritisk-analytiskt tillvägagångssätt verkar vara mer tillförlitligt och ha tendenser att ge korrekta resultat. En slutsats som kan dras av resultaten av dessa studier är att det är viktigt att vara medveten om vilka typer av uppgifter som används i undervisningen i samband med grafiska artefakter och hur dessa uppgifter kan användas för att främja elevers kritiska-analytiska förhållningsätt. vii FOREWORD As I write the foreword to this dissertation I am reminded of myself as a lad listening to luo benga hits. I noticed that often when the music was reaching its climax, [thum oguro], the lead musician apportioned accolades and acknowledgements to the accompanying musicians and it dawned on me that this almost always signalled the end of the music. While there might be a few parallels between writing a PhD dissertation and benga music, I find it necessary to acknowledge the fact that the process attaining its climax in the submission and defence of this dissertation would not have been possible without the direct and indirect intervention of several persons, my accompanying musicians. To all of you, named and unnamed, you’ve meant a lot to me and I hope that we will all find satisfaction in the ‘rhythm’ of the dissertation. I would like to express my gratitude to my main supervisor Prof. KG Karlsson and assistant supervisor Prof. Astrid Pettersson, I deeply appreciate your being there for me. You have been a source of encouragement, inspiration and support throughout a process that, at times, felt quite hopeless. KG, your ‘hawk-eyed’ approach to my texts was especially appreciated. That it was fine with you to have some supervision meetings in Stockholm highlights your quality as an ‘understanding man’. Thanks also for getting me started with PISA database. Astrid, your insightful comments on my texts and involvement in connecting me with specialised persons illustrates in many ways, your concern for the quality of this dissertation. Thanks for connecting me with PRIM-gruppen and seminariegruppen i matematikdidaktik. I also wish to express my gratitude to all the students whose participation in the studies provided material for this dissertation. In this regard I wish to acknowledge the help provided by Eva-Karin Rosén former Principal at Härnösands gymnasium, her staff and students as well as my pre-service teacher students. I would also like to thank Ulla Damber for showing me how to communicate with reviewers, to Katarina Kjellström for ironing out my queries on Nationella provet, as well as to Nina Eliasson and Maria Edlund for helping out with diverse information on PISA.
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