University of Warwick Institutional Repository
Total Page:16
File Type:pdf, Size:1020Kb
University of Warwick institutional repository: http://go.warwick.ac.uk/wrap A Thesis Submitted for the Degree of PhD at the University of Warwick http://go.warwick.ac.uk/wrap/73122 This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page. Investigating critical sense in the interpretation of media graphs by Carlos Eduardo Ferreira Monteiro A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics Education University of Warwick, Institute of Education April 2005 INDEX Contents ......................................................................................... List of Figures...... .. .... ... ... ......... ... ..... .......... ..... .......... ...... ... ..... ..... ..... v List of Tables............................ ........ ...... ............ ...... ............... ... ...... VI Acknowledgments .............................................................................. viii Declaration ....................................... " . .. .. .. .. ix Abstract........................................................................................... x Contents CHAPTER 1 - Introduction...... ....... ........... ............... ... ..... .... .......... ... 1 1.1 Setting the scene .............. ,.. ........ ......... ......... ....... ...... ...... ........ ...... 1 1.2 The purpose of this study.. .... .............. ...... ...... ... ... .... ........ ...... ..... ... 6 1.3 The structure of this thesis........................................................... ... 6 CHAPTER 2 - Literature review - interpretation of graphs........... .... .••.. .•.... 8 2.1 Ovef'\l'iew.................................................................................... 8 2.2 The development of graphs............................................................. 9 2.3 Components of graphs................................................................... 11 2.4 Types of gra.phs... ... ......... ...... ..... ................ ............ ...... ......... .... ... 14 2.5 Graphs presenting data... ...... ...... ... ... ...... ...... ... ..... ....... ..... ... ....... ... 16 2.6 Statistical literacy •.....•...............••.••.•...••.•....••.•••.••.•...•......•.•••..••• ..• 18 2.7 The research in interpretation of graphs ............................................. 21 2.7.1 Misconceptions and errors in interpretations of graphs ............. , ................ 22 2.7.2 Assessment in interpretation of graphs ................................................. 23 2.7.3 Influence of other aspects in interpretation of graphs................................ 25 2.7.4 Interpretation of media graphs .............................. " . .. .. .. .. 28 2.8 Contexts of interpretation of graphs.................................................. 29 2.9 Teacher education and teaching graphing .......................................... 31 2.10 Summa~ of chapter 2.................................................................. 34 CHAPTER 3 - Approaching the complexity of interpretation of media graphs.• 36 3.1 Ovenriew ..................................................................................... 36 3.2 Socio-cultural aspects of the interpretations of graphs ..•.....•...............••... 36 3.3 Interpretation of graphs as an interactive process .............•.............•••.... 38 3.4 Interpretation of media graphs in out-of-school and school contexts ............ 40 3.5 Critical thinking and critical education ................................................ 44 3.6 Affective aspects involved in interpretations of graphs ............................. 49 3.7 Summal)" of chapter 3 ..................................................................... 51 CHAPTER 4 - Findings of the pilot study ................................................. 52 4.1 Ove"iew ..................................................................................... 52 4.2 Method ....................................................................................... 53 4.2.1 Ethical considerations ...................................................................... 54 4.2.2 Participants ................................................................................. 56 4.2.3 Questionnaires ............................................................................... 56 4.2.4 Interviews ................................................................................... 57 4.2.5 Interview media graphs tasks ............................................................ 60 4.2.5.1 Contraception-fertility graph .................................................................... 61 4.2.5.2 Road accidents graphs ........................................................................... 63 4.2.5.3 Contraception-fertility graph items ............................................................. 64 4.2.5.4 Road accidents graphs items ..................................................................... 65 4.3 Analyses of the responses of media graph tasks ...................................... 66 4.3.1 Contraception-fertility graph items ...................................................... 67 4.3.2 Road accident graphs items ............................................................... 69 4.3.3 Discussion of the interview tasks ....................................................... 73 4.4 Directions for the main study .............................................................75 4.5 SummaI)' of chapter 4 ......................................................................76 CHAPTER 5 - Main study method ......................................................... 78 5.1 Ove"iew ..................................................................................... 78 5.2 Defining the methodology-................................................................ 78 5.3 Data coUection .............................................................................. 80 5.3.1 Participants ................................................................................. 80 11 5.3.1.1 British participants ............. ,. '" ...................... , ...................................... 82 5.3.1.2 Brazilian participants ............................................................................ 84 5.3.2 Questionnaire .............................................................................. 86 5.3.2.1 Contraception-fertility graph and related questionnaire items ............................. 89 5.3.2.2 Road accidents' graph and related questionnaires items .................................... 90 5.3.3 Interviews .................................................................................. 92 5.4 Data Analy'sis............................................................................... 96 5.4.1 Coding the questionnaires............................................................... 96 5.4.2 Analyses of the interviews ................................................................ 98 5.5 Summaf)' of chapter S ..................................................................... 99 CHAPTER 6 - Findings from the questionnaires ..................................... 100 6.1 Ovel'\'iew .................................................................................... 100 6.2 Analy"sis of questionnaire data ......................................................... 101 6.3 Responses to reading background items •••.••....•.••....•.•.••...•..•..••••...••..• 103 6.4 Responses to contraception-fertility graph items ....•.......••..................•.. 110 6.4.1 Contraception-fertility graph statements ............................................. 112 6.4.2 Contraception-fertility graph questions ............................................... 119 6.S Responses to road accident graph items .•.•••.•.•.•.•.•••.•..••...•••.•..••.••.•••.. 126 6.5.1 Road accidents graphs questions .................................... '" ............... 127 6.5.2 Drawing a graph which combined the data from road accident graphs .......... 129 6.5.3 Analysing road accidents graphs targets ............................................. 133 6.6 Discussion of the participants' questionnaire responses ...•••...•..•••...••.•••. 136 6.7 SummaI)' of ehapter 6 .................................................................. 140 CHAPTER 7 - Findings from the interviews •••............••.••.•...•...•••..•..•...•. 141 7.1 Ovenriew ................................................................................... 141 7.2 The intefV"iews ............................................................................ 142 7.3 Briefing: Starting the interviews ...................................................... 143 7.4 Questions about the contraception-fertility graph .•.•••.•••..•••.......••..•...... 145 7.4.1 Reading the data questions (contraception-fertility) ................................ 146 7.4.2 Reading between the data questions (contraception-fertility) ..................... 147 7.4.3 Reading beyond the data questions (contraception-fertility) ....................... 150 III 7.5 RecaU of the questionnaire responses to the contraception-fertility graph task•.• 159 7.6 Questions about the road accidents graphs ...••••..••..•••••••••••..•.•••.•......•.....••• 162 7.6.1 Reading the data questions (road accidents) ...............................................