• 沒有找到結果。

Opportunity to Learn Data Distribution through Reading Statistics Texts Written in English as a Second Language for Indonesian Pre-Service English as a Foreign Language Teachers

N/A
N/A
Protected

Academic year: 2021

Share "Opportunity to Learn Data Distribution through Reading Statistics Texts Written in English as a Second Language for Indonesian Pre-Service English as a Foreign Language Teachers"

Copied!
298
0
0

加載中.... (立即查看全文)

全文

(1)國立臺灣師範大學數學系博士班博士論文 指導教授:楊凱琳 博士. Opportunity to Learn Data Distribution through Reading Statistics Texts Written in English as a Second Language for Indonesian Pre-Service English as a Foreign Language Teachers. 研究生: Khairiani Idris (伊凱蒂). 中 華 民 國 2017 年 10 月.

(2) ACKNOWLEDGEMENTS “Don’t be so 𝑥̅ ” [Rangecroft, 2002]. First of all, I thank Allah for the numerous blessings He has granted that have made this work possible. I have been always blessed with family, friends, colleagues, and incredible teachers without whom I would not likely have reached this life stage. It was a highly challenging decision for me as an ‘average’ student to step away from my comfort zone and try to improve my thinking way. There are many people who have given so generously their time and intellectual as well as spiritual supports, to whom I am eternally grateful.. I wish to thank the faculty associated with the Ph.D. program in Mathematics Education, Department of Mathematics at National Taiwan Normal University. It has been a great pleasure to study under such a talented and diverse group of faculty members during the past few years. I am particularly indebted to my advisor, Dr. KaiLin Yang for her patience, encouragement, and knowledge. Her extraordinary patience in guiding me to continually refine my learning style and thinking and pushing me beyond what I believed I could achieve. I will be eternally grateful to her for her commitment of countless hours of time and energy to consult and meet with me, to read, comments on and criticize the drafts of my writings and provide constructive feedback. Through her brilliant insights and commitment to and passion for. i.

(3) mathematics education, she provides an example of a true teacher and scholar to which I aspire. I also wish to thank other faculty who served on my dissertation committee: Professor Der-Ching Yang, Professor Mei-Shiu Chiu, Professor Tai-Yih Tso, and Professor Fou-Lai Lin. The effort each one of you has put into reading and commenting upon my work has helped extraordinarily. I am fortunate and grateful to have had the opportunity to work with each one of you. Especially to Professor FouLai Lin who had encouraged and provided supportive critiques on my work, introduced me to research and continually pushed me to think deeply about the meaning of educational theories related to mathematics since my first year in the department. There are a number of people who have become friends and colleagues over my stay and adventure in Taiwan. To all the incredible women in SALIMAH Taiwan, from whom I have learned a lot about sisterhood, hard work, and sincerity fi sabilillah. To each of the incredible housemates and sisters who have shared their cares, patience, and supports, I cannot thank you all enough. I always believe that the togetherness we have had was a great blessing in my life. To all of my great and supportive colleagues in the State Institute for Islamic Studies of Lhokseumawe, special for those in the Department of Mathematics Education, who have always showed their care and supports for my study and been happily waiting for my return to share knowledge. I truly appreciate all of your help and kindness. Last but not least, to my dearest family, I could not have done this without your love and support. To my beloved husband, my greatest gratitude for your loves, support and prayers. Thanks for putting up with my grumpiness and being always patience. To my beloved Abi, it must have been extremely tough to raise three ii.

(4) daughters during your life, to silently sacrifice for our ambition and to always mention our names in your prayers. I would never be able to repay for all those you have provided me. To my two extraordinary women, my beloved sisters, who always provide endless loves, support and care, and being proud of my work. From you I learned a lot about hard work, ambition, sacrifice and loves for family. I love you all dearly and cannot possibly thank you enough. To all of you and others, you have profoundly and positively influenced my life. This is the initial stage of my lifelong learning process from an x̅ person to become a more beneficial to others.. Khairiani Idris. iii.

(5) ABSTRACT The ability to understand statistical information written in English is prominent given the global status of English and the importance of statistics to understand data, variation and chance which are omnipresent in modern life. Furthermore, college students might need to read and understand statistical results of research in their field of study, while English continues to be the preferred language of scientific communication in most published articles. The main purpose of this research was to investigate the issue concerning the opportunities of learning through reading statistics texts written in English as a second language for Indonesian pre-service English as a Foreign Language (EFL) teachers by taking two components of reading, i.e., reader and text, and the interaction between the two. Accordingly, three studies were compiled to reach the purpose. Initially, Indonesian pre-service EFL teachers’ views on statistics were explored in study one, which involved their values on the learning and conceptions of statistics. Study two concerned on statistics text, in which a framework for analyzing the accessibility of statistics text was developed and subsequently utilized to analyze two versions of college statistics textbooks. By taking the components under one of the accessibility attributes proposed in study two, i.e., the integration of verbal and visual information, six versions of statistics reading materials were designed. Subsequently, study three explored the relationships between different versions of statistics reading materials and students’ reading comprehension. Findings from study one revealed that almost all Indonesian preservice EFL teachers in this study acknowledged the utility of statistics, yet only 60% of them had a positive intrinsic value in learning the course. Conflicting beliefs expressed by both positive and negative intrinsic value were also found on some iv.

(6) students. Meanwhile, three types of conceptions of meanings of data were found underlying the six categories and the three factors of conceptions of statistics: data as numerical numbers, data as numbers in problem contexts; data as information for investigation. Additionally, an instrument for measuring conceptions of statistics was developed and validated in this study. Findings from study two proposed five accessibility attributes of statistics texts, which might reveal not only the strengths and weakness of statistics texts for particular readers, but also to what extent the content knowledge of statistics is presented in the textbooks. The textbooks analysis conducted using the framework revealed several different characteristics between English and Indonesian version textbooks. Indonesian textbook more likely emphasizes on a knowledge-based view of statistics, in which statistical basic knowledge and data as numerical numbers with or without contexts are presented dominantly. English version presents both knowledge based and problem solving views of statistics and more dominantly addresses data as numbers in problem contexts or data as information for investigation. Findings from study three revealed that the verbal information in form of data scales provided on boxplot hinder students reading comprehension. Moreover, providing not scaled-labeled boxplots by sequencing the boxplot before the corresponding verbal information was more favorable for reading comprehension. The implications of the findings and further research were discussed.. Keywords: College statistics; Conceptions of statistics; Reading to learn; Reading materials; Text accessibility; Textbook analysis; Values on the learning of statistics. v.

(7) TABLE OF CONTENTS page ACKNOWLEDGEMENT ....................................................................................... i. ABSTRACT ......................................................................................................... iv TABLE OF CONTENTS ...................................................................................... vi LIST OF TABLES ................................................................................................ xi LIST OF FIGURES .............................................................................................. xiii LIST OF APPENDICES ....................................................................................... xiv CHAPTER ONE INTRODUCTION TO STUDY ..................................................... 1 1.1 Background of study ...................................................................................... 1 1.1.1 Role of statistics for pre-service teachers............................................... 1 1.1.2 Views on statistics and the learning of statistics ................................... 3 1.1.3 Learning statistics through reading ........................................................ 4 1.1.4 Reading statistics text written in English as a second language ........... 6 1.2 Statement of problem ..................................................................................... 8 1.3 Purpose of study ............................................................................................ 9 1.4 Research questions ....................................................................................... 10 1.4.1 Research questions for study one ......................................................... 10 1.4.2 Research questions for study two ......................................................... 10 1.4.3 Research questions for study one ......................................................... 11 1.5 Contributions of study .................................................................................... 11 1.5.1 Contribution from reader component ..................................................... 12 1.5.2 Contributions from the text component .................................................. 13 1.5.3 Contributions from the relationship of reader and text ........................... 14 1.6 Chapter preview ............................................................................................. 15 CHAPTER TWO LITERATURE REVIEW ............................................................ 17 2.1 Statistical literacy for college students ........................................................... 17 2.1.1 Definition of statistical literacy .............................................................. 17 2.1.2 Statistical literacy as a goal in college statistics .................................... 20 2.1.3 Research on statistical literacy of college students .............................. 22 2.2 Learning in college statistics .......................................................................... 24 2.2.1 Factors influencing learning statistics ................................................... 24 2.2.1.1 Linguistic factors ...................................................................... 24 2.2.1.2 Basic mathematics skills .......................................................... 25 2.2.1.3 Values on learning statistics ..................................................... 26 vi.

(8) 2.2.1.4 Conceptions of statistics ........................................................... 30 2.2.2 Topic of data distribution ...................................................................... 32 2.2.2.1 Student understanding of data distribution ............................... 34 2.2.2.2 Factors influencing understanding of data distribution .............. 36 2.2.2.3 Boxplots and students’ misinterpretations ................................ 37 2.3 Teaching in college statistics .......................................................................... 39 2.3.1 Current research on instructional methods in college statistics ............. 39 2.3.2 Teaching materials for college statistics ............................................... 43 2.3.2.1 Aspects of statistics contents ................................................... 44 2.3.2.2 Text analysis in college statistics education ............................. 47 2.4 Models of reading comprehension ................................................................. 48 2.4.1 Construction Integration theory ............................................................ 48 2.4.1.1 The process of comprehension: construction and integration ... 49 2.4.1.2 Levels of representation ........................................................... 50 2.4.1.3 Microstructure and macrostructure ........................................... 51 2.4.1.4 Cohesion, coherence, and the situation model ......................... 51 2.4.2 Dual coding theory ............................................................................... 51 2.5 Content area reading ..................................................................................... 53 2.5.1 Five attributes of text accessibility for science text ............................... 54 2.5.2 Critical components related to the readability of mathematics texts ...... 56 2.5.3 Combination of verbal and visual information for text comprehension .. 58 2.6 Content and language integrated learning (CLIL) ........................................... 59 2.6.1 Issues from CLIL in Mathematics and Science ..................................... 60 2.6.1.1 Learning outcome in CLIL classroom ....................................... 60 2.6.1.2 Teaching in CLIL classroom ..................................................... 61 2.7 Issues for exploration in the present study ..................................................... 62 CHAPTER THREE METHODOLOGY ................................................................. 65 3.1 Study one: Views on statistics ........................................................................ 67 3.1.1 Values on learning and conceptions of statistics .................................. 67 3.1.1.1 Participants .............................................................................. 67 3.1.1.2 Data collection .......................................................................... 69 3.1.1.3 Data analysis ........................................................................... 71 3.1.2 Developing and validating instrument .................................................... 73 3.1.2.1 Participants .............................................................................. 73 3.1.2.2 Data collection and analysis ..................................................... 74 vii.

(9) 3.2 Study two: Textbook analysis ......................................................................... 74 3.2.1 Development of analytical framework .................................................. 75 3.2.1.1 Determining components for accessibility attributes ................. 76 3.2.2 Textbook analysis ............................................................................... 77 3.2.2.1 Selecting textbooks to be analyzed .......................................... 77 3.2.2.2 Determining units of analysis ................................................... 78 3.2.2.3 Topics focused in the analysis ................................................. 80 3.2.2.4 Development of a coding scheme ............................................ 81 3.2.2.5 Exemplary coding procedure .................................................... 91 3.2.2.6 Reliability of coding .................................................................. 98 3.3. Study three: reading comprehension of statistics texts ................................... 99 3.3.1 Participants ......................................................................................... 100 3.3.2 Design ................................................................................................ 100 3.3.3 Materials ............................................................................................. 100 3.3.3.1 Statistics reading materials ..................................................... 101 3.3.3.2 Reading comprehension test ................................................... 103 3.3.3.3 Prior knowledge in statistics .................................................... 104 3.3.3.4 Competency in English ........................................................... 106 CHAPTER FOUR FINDINGS OF STUDY ONE: VIEWS ON STATISTICS .......... 109 4.1 Values on the learning and conceptions of statistics ..................................... 109 4.1.1 Overview ............................................................................................ 109 4.1.2 Indonesian pre-service EFL teachers’ values on learning and conceptions of statistics ........................................................................................ 110 4.1.2.1 Three components of values on learning statistics .................. 110 4.1.2.2 Relationships among components of values on learning statistics ..................................................................................... 113 4.1.3 Indonesian pre-service EFL teachers’ conceptions of statistics .......... 115 4.1.3.1 Six categories of conceptions of statistics .............................. 117 4.1.4 Relationships between conceptions of statistics and values on the learning of statistics ........................................................................... 121 4.1.5 Discussions ........................................................................................ 124 4.1.5.1 Values on the learning of statistics .......................................... 124 4.1.5.2 Features of pre-service EFL teachers’ conceptions of statistics 129 4.1.5.3 The relationships of positive values and conceptions of statistics................................................................................... 131 viii.

(10) 4.2 Development and validation of conceptions of statistics instrument ............. 131 4.2.1 Overview .......................................................................................... 131 4.2.2 Piloting stage .................................................................................... 132 4.2.3 Modelling stage ................................................................................ 133 4.2.4 Discussions ...................................................................................... 137 4.2.4.1 The meaning of three factors of conceptions of statistics ....... 137 4.2.4.2 Conceptions of data ............................................................... 137 4.2.4.3 Limitations of study ................................................................ 139 4.2.5 Conclusion ....................................................................................... 140 4.4 Summary of study one ................................................................................. 140 CHAPTER FIVE FINDINGS OF STUDY TWO: TEXT ANALYSIS ..................... 143 5.1 Framework development .............................................................................. 143 5.1.1 Overview ........................................................................................... 143 5.1.2 Accessibility attributes of statistics texts ............................................ 144 5.1.2.1 Concreteness of text ................................................................ 144 5.1.2.2 Voice of author ........................................................................ 145 5.1.2.3 Text coherence ........................................................................ 146 5.1.2.4 Selective use of visual information ........................................... 147 5.1.2.5 Integration of visual and verbal information .............................. 147 5.1.3 Discussions ....................................................................................... 150 5.2 Textbook analysis ........................................................................................ 151 5.2.1 Overview .......................................................................................... 151 5.2.2 The sequence of concepts under data distribution ............................ 151 5.2.3 Presentation of text goals ................................................................. 151 5.2.4 Presentation of accessibility attributes of statistics texts ................... 154 5.2.4.1 Text concreteness ................................................................... 154 5.2.4.2 Voice of author ........................................................................ 159 5.2.4.3 Text coherence ........................................................................ 163 5.2.4.4 Selective use of visual information ........................................... 169 5.2.4.5 Integration of visual and verbal information .............................. 173 5.2.5 Discussions and conclusions ............................................................ 180 5.2.5.1 Text concreteness ..................................................................... 180 5.2.5.2 Voice of author ........................................................................ 181 5.2.5.3 Text coherence ........................................................................ 184 5.2.5.4 Selective use of visual information ........................................... 185 ix.

(11) 5.2.5.5 Integration of visual and verbal information ............................... 186 5.3 Summary of study two .................................................................................. 187 CHAPTER SIX FINDINGS OF STUDY THREE: READING COMPREHENSION OF STATISTICS TEXTS .......................................................................................... 189 6.1 Overview ....................................................................................................... 189 6.2 Effects of sequence and information on reading comprehension .................. 190 6.3 Effects of sequence and information on reading comprehension controlled by prior knowledge in statistics and English competency ................................... 192 6.3.1 Effects of types of sequence ............................................................. 193 6.3.2 Effects of types of information ........................................................... 194 6.4 Discussions .................................................................................................. 195 6.5 Summary of study three ................................................................................ 199 CHAPTER SEVEN CONCLUDING REMARKS ................................................. 201 7.1 Summary of findings ....................................................................................... 201 7.1.1 Characteristics of Indonesian pre-service EFL teachers’ views on statistics ............................................................................................ 201 7.1.2 Characteristics of Indonesian statistics textbooks and its crucial differences with English textbooks ..................................................... 202 7.1.3 Effects of different versions of reading materials on reading comprehension .................................................................................. 203 7.2 Implications and further research .................................................................. 204 7.2.1 Views on statistics and text analysis ................................................... 204 7.2.2 Text analysis and relationship between text and reading comprehension ................................................................................... 206 7.2.3 Views on statistics and relationship between text and reading comprehension ................................................................................... 207 7.2.4 Views on statistics, text analysis, and relationship between text and reading comprehension ....................................................................... 208 REFERENCES ................................................................................................... 210 APPENDICES .................................................................................................... 231. x.

(12) LIST OF TABLES Table 2.1 Components of statistical literacy ....................................................... 19 Table 2.2 Categories of conceptions of statistics from previous studies and their common concerns .............................................................................. 32 Table 3.1.1 Demographics of 38 students in questionnaire survey ..................... 69 Table 3.2.1 Operational definitions of four types of text goals ............................ 80 Table 3.2.2 The topics and sub-topics for the concept of data distribution ......... 81 Table 3.2.3 The components of attributes of statistics text accessibility and their operational classifications ............................................................... 88 Table 3.3.1. The six versions of statistics texts .................................................. 103 Table 3.3.2. Structure of test items for measuring reading comprehension of statistics texts .................................................................................. 104 Table 3.3.3 Structure of test items for the instrument of prior knowledge in statistics ............................................................................................ 106 Table 3.3.4 Structure of test items for English competency instrument .............. 107 Table 4.1.1 Components of values on learning of statistics ................................ 111 Table 4.1.2 Relationship between intrinsic and attainment components ............. 114 Table 4.1.3 Relationship between utility and attainment components ................ 114 Table 4.1.4 Relationship between intrinsic and utility components ..................... 115 Table 4.1.5 Students’ distributions for the initial category based on written responses ......................................................................................... 116 Table 4.1.6 Categories of Conception of Statistics from the Phenomenographic Study ............................................................................................... 121 Table 4.1.7 Relations between students’ conceptions of statistics and their positive, negative and other values for each component of values on learning statistics ......................................................................................... 122 Table 4.1.8 Relationships between positive values on the learning of statistics and conceptions of statistics ................................................................. 123 Table 4.2.1 Confirmatory Factor Analysis Loadings .......................................... 135 Table 5.1.1 Components underlying the accessibility attributes of statistics texts and their significance ............................................................................ 148 Table 5.2.1 Types of text and their distributions in the two versions of textbooks 149 Table 5.2.2 The distribution of the multiple meanings of statistical term for the two textbook versions ........................................................................... 153. xi.

(13) Table 5.2.3 Categories of focused statistical terms in the topics under data distribution in English language ...................................................... 155 Table 5.2.4 Categories of the focused statistical terms in the topics under data distribution in Bahasa Indonesia .................................................... 157 Table 5.2.5 The distributions of meanings of data addressed with regard to statistical cognitions (English version, Indonesian version) ............................ 162 Table 5.2.6 Percentages of coherence categories of approach to statistical cognitions (English version, Indonesian version) ............................ 165 Table 5.2.7 Percentages of coherence of approach to statistical cognitions (English version, Indonesian version) .......................................................... 166 Table 5.2.8 Percentages of coherence categories of approach to meanings of data (English version, Indonesian version) ............................................. 167 Table 5.2.9 Percentages of coherence of approach to meaning of data (English version, Indonesian version) .......................................................... 168 Table 5.2.10 Percentages of analysis units referring to visual information ........ 170 Table 5.2.11 The percentages of purposes of visual information for each type of visual information in the two versions of textbooks (English, Indonesian) ...................................................................................... 172 Table 5.2.12 The percentages of types of captions for each type of sequence of verbal and visual information (English version, Indonesian version) 176 Table 5.2.13 The percentages of label for each type of sequence of verbal and visual information (English version, Indonesian version) ................ 178 Table 5.2.14 Percentages of scale of visual information for each types of sequences of verbal and visual information (English version, Indonesian version)............................................................................................ 180 Table 6.2.1. Mean and standard deviation of reading comprehension scores ... 190 Table 6.2.2 Source Table for 3 x 2 ANOVA for reading comprehension scores. 191. Table 6.3.1 Source Table for factorial ANCOVA for reading comprehension scores .............................................................................................. 193 Table 6.3.2 Adjusted marginal means and standard deviations on the reading comprehension scores ................................................................... 194 Table 6.3.3 Adjusted marginal means and standard deviations for reading comprehension scores ................................................................... 195. xii.

(14) LIST OF FIGURES Figure 1.1 Domain of study .................................................................................. 7 Figure 2.1 Concept map of data distribution in college statistics .......................... 34 Figure 2.2 Example of a boxplot ......................................................................... 37 Figure 2.3 Model of dual coding theory (Sadoski & Paivio, 2004, p. 15) ............... 53 Figure 2.4 The components of reading focused in the present study ................... 63 Figure 3.1 Stages of research procedures ........................................................... 66 Figure 3.2.1 Analysis units in the sub-section of The five-number Summary and Boxplots in English version textbook (Moore, McCabe, & Craig, 2009, pp. 36–38) ....................................................................................... 92 Figure 3.2.2 The attribute of voice of author presented in analysis units for the sample texts in Figure 3.2.1 ............................................................. 95 Figure 3.2.3 The attribute of text coherence presented in analysis units for the sample texts in Figure 3.2.1 ............................................................. 97 Figure 4.2.1 Three-factor structure of Conceptions of Statistics of Indonesian Preservice Teachers (N = 232) ............................................................. 136 Figure 5.2.1 The distribution of types of text goals for the three topics in data distribution for English and Indonesian versions of textbooks .......... 154 Figure 5.2.2 The distribution of statistical cognitions weighted to the total of analysis in the three topics ............................................................................ 160 Figure 5.2.3 The distribution of meanings of data weighted to the total of analysis units in the three topics ................................................................... 161 Figure 5.2.4 The distribution of types of visual information referred in the two versions of textbooks ...................................................................... 170 Figure 5.2.5 The distribution of purposes of visual information referred in the two versions of textbooks ...................................................................... 167 Figure 5.2.6 The distribution of types of sequence of visual and verbal information in the two versions of textbooks .......................................................... 171 Figure 5.2.7 The distribution of types of information provided in captions of visual information in the two versions of textbooks .................................... 174 Figure 5.2.8 The distribution of label of visual information in the two versions of textbooks ........................................................................................ 177 Figure 5.2.9 The distribution of scale of visual information ................................. 179. xiii.

(15) LIST OF APPENDICES A. Appendices for study one A.1 Open-ended questionnaire for assessing values on learning statistics and conceptions of statistics ............................................................................ 231 A.2 Questions for semi-structured interviews ................................................... 235 A.3 Conceptions of Statistics Instrument (CSI) – Indonesian version .............. 236 A.4 Conceptions of Statistics Instrument (CSI) – English version ................... 239 B. Appendices for study two B.1 Topics under data distributions ............................................................... 242 B.2 Guidelines for coding analysis of textbooks ............................................ 246 B.3 Diagrams for analysis of attributes of voice of author and text coherence . 253 C. Appendices for study three C.1 Text version 1........................................................................................... 261 C.2 Text version 2 ......................................................................................... 263 C.3 Text version 3 ......................................................................................... 266 C.4 Text version 4 ......................................................................................... 268 C.5 Text version 5 ......................................................................................... 271 C.6 Text version 6 ......................................................................................... 273 C.7 Test for reading comprehension of statistics texts .................................. 276 C.8 Instrument for prior knowledge in statistics ............................................. 278 C.9 Instrument for English competency ......................................................... 282. xiv.

(16) CHAPTER ONE INTRODUCTION. “Nothing exists except through language” [Hans-Georg Gadamer]. The structure of this chapter was arranged by firstly introducing study backgrounds, in which roles of statistics for pre-service teachers, learning statistics through reading and reading statistics texts written in English as a second language were discussed. Afterwards, in the second section, the problems focused in this study were identified and the purposes of study were subsequently elaborated in the third section. Based on these purposes, several research questions were formulated, which were explicated in the fourth section. In the fifth section, the contributions of study were argued. Finally, the chapter preview was provided in the sixth section. 1.1 Background of study 1.1.1 Roles of statistics for pre-service teachers Statistics education is drawing more attention at college level as more and more departments realize the importance of statistics not only as the fundamental skills required by citizens in general but also as the essential skills for professionals in their own disciplines (Scheaffer & Stasny, 2004). The skills consist of basic statistical literacy for citizens (Rumsey, 2002; Utts, 2003), way of thinking in society (Giesbrecht, 1996) and knowledge required in the whole process of research (Wild & Pfannkuch, 1999). Therefore, to produce statistically educated students which means that they should develop statistical literacy is the goal of all college statistics courses (Aliaga et al., 2005; Rumsey, 2002). For most service students of introductory statistics courses, statistics is an essential tool for their future profession (Scheaffer and Stasny 2004). Accordingly, as 1.

(17) college students, pre-service teachers also require the skills to understand statistical results of research in their field of study and doing their undergraduate research as part of study requirements in some countries like Indonesia (Sailah, 2014). Meanwhile, as teachers in the future, pre-service teachers might need statistical investigation skills for doing educational research including analyzing their own teaching which necessitate learning investigation process (Heaton and Mickelson 2002). Learning the investigation process also entails a deep understanding of statistical knowledge, not only about how to carry out data analysis, but also about how to find problems and formulate investigation questions (Franklin & Garfield, 2006; Wild & Pfannkuch, 1999). Pre-service English as a Foreign Language (EFL) teachers, in particular, have at least two other professional roles in the future in which they might need to utilize statistics. First, as English Language Learners, pre-service EFL teachers may also require statistics to improve their knowledge and expertise. For example, since most of the useful studies published in linguistics journals are quantitative in nature (Lazaraton 2005), they would need statistical skills to understand findings from these studies. Third, statistics might be used as one of the contents they would introduce in their reading classes, because the ‘content’ in teaching language may go beyond literature. Moreover, due to the emergence of English immersion programs in some countries to promote students’ English language competencies while learning content subjects, including mathematics (e.g., Cheng, Li, Kirby, Qiang, & Wade-Woolley, 2010; Padilla & Gonzalez, 2001; Yushau, 2009), English language teachers may play a crucial role in such program. Referring to the suggestion from Crandall (1987), EFL teachers may use the relevant mathematics texts that students will read in their mathematics classes, which is significant to let students acquire reading skills they can apply in learning mathematics. Thus, learning statistics, which is one of the 2.

(18) contents included in school mathematics, is one way to promote EFL teachers’ knowledge and expertise which has been identified as increasingly marginalized within content areas (Cross, 2011). Due to the evolving nature of statistics as a discipline, the knowledge should be subject to lifelong learning for pre-service EFL teachers. Among the concepts learned in college statistics is data distribution, which has critical role in the web of statistical ideas to connect variation and sampling (Bakker & Gravemeijer, 2004; Garfield & Ben-Zvi, 2008). Subsequently, among the data displays used for presenting data distribution is boxplot, which is considered special by its typical characteristic compared to other data displays. Unlike histograms or line graphs, boxplot illustrates the signal (the center) and noise (the spread of data from the center) in representing distribution (Pfannkuch, 2006) by using five-number summary values. Hence, the concepts of data distribution and boxplots are essential which can bridge student thinking from descriptive to inferential statistics. In this way, the concept of data distribution is insisted as a prominent topic for college students and, therefore, for pre-service teachers. 1.1.2 Views on statistics Several studies have shown that students’ further involvement in the activities related to the subject learned is associated with the way they value the learning of the subject (Eccles & Wigfield, 2002; Liem, Lau, & Nie, 2008; Yang, 1999). Likewise, students’ appreciation of the course was found to correlate with conceptions of statistics (Petocz & Reid, 2005), dominate their willingness to learn statistics and lead to a mature approach in learning the course (Gordon 1995b; Petocz & Reid 2005). This may imply the need for pre-service EFL teachers to hold a disposition towards the values on the learning of statistics in addition to the values on the knowledge obtained through investigation (Heaton & Mickelson, 2002) because they might need to learn and utilize 3.

(19) statistical investigation in the future. Moreover, when reading is viewed as an approach to learning content, like that in the English immersion program, not only content area teachers’ conceptions and values on the content area reading (Hall, 2005), but also language teachers’ values and conceptions about the content are required for investigation in research concerned. Furthermore, the ways students approach their learning and the quality of their learning outcome have been shown to be related to the variation of conceptions on the subject matter (Kathryn Crawford, Gordon, Nicholas, & Prosser, 1998; Liang, Su, & Tsai, 2014; Trigwell & Prosser, 1991). Thus, students’ conceptions are acknowledged as a crucial basis for more effective teaching design in higher education (Wells & Ball, 2008). The importance of measuring students’ conceptions of statistics has also been suggested, including that for testing the efficacy of a teaching design and that with regard to its relation to other constructs such as attitudes toward statistics (e.g., Gal, Ginsburg, & Schau, 1997). Nonetheless, instruments for measuring conceptions of statistics have not been found until recently. Some studies have used a phenomenographic approach to derive conception categories (e.g., Gordon, 2004; Petocz & Reid, 2005; Yang, 2014), but the lengthy process of analysis involved in this approach makes its use impractical where large numbers of participants are involved. Yet, the categories found from these studies are beneficial for developing an instrument. 1.1.3. Learning statistics through reading. The concept of lifelong learning in wider context requires college students to interact with academic texts. Particularly, as has been stated previously in subsection 1.1.1 that statistics is an evolving science, it implies the ability to learn through reading becomes prominent for college students. For example, when pre-service teachers intend to conduct educational research in the future, they would need to read the 4.

(20) information on current investigative method in the educational research field. In this respect, the ability to learn statistics using any available learning resources is also essential skill for this student. Moreover, some studies focusing on college statistics courses suggested that reading comprehension is significantly related to achievement (Collins & Onwuegbuzie, 2002), as well as motivation and perception of the course (Harwell, Herrick, Curtis, Mundfrom, & Gold, 1996). Reading statistics texts, identical to reading in other content area (e.g., Draper & Siebert, 2004; Moje, Dillon, & O’Brien, 2000; Weinberg & Wiesner, 2011), involves the interaction or transaction between a reader and a text situated in a particular context. All the three components may have influences on the reading activity. Particularly, the density of statistical text (Cobb, 1987), lexical ambiguity terms and multi-words phrases (Kaplan, Fisher, & Rogness, 2009, 2010; Lesser, Wagler, Esquinca, & Valenzuela, 2013; Lesser & Winsor, 2009) may be problematic for student reading. Graphical displays, as one type of statistical texts (Gal, 2002) also have specific characteristics which might be difficult to comprehend (Friel, Curcio, & Bright, 2001; Shah & Hoeffner, 2002). Additionally, like reading mathematics, reading statistics usually requires a process of reading text, inspecting associated graphs, reading more texts, considering some symbolic expressions, more text, more graphs and etc. (Freitag, 1997; Noonan, 1990). Thus, reading statistics is not a linear process because in addition to reading left to right and top to bottom, reader must jump around the page to associate text with tables, graphs, symbols and vice versa. On the other hand, reader’s prior experiences with statistics and mathematics, and beliefs about the nature of knowledge have been found to be related to statistics text comprehension (Schommer, Crouse, & Rhodes, 1992). In general, reader’s factor for reading includes social, emotional and cognitive aspects of his/her experiences (Moje et al., 2000). The third component, context, can be defined as a frame that 5.

(21) encompasses the reading activity and provides resources for its interpretation (Duranti & Goodwin, 1992). Further, it can be classified as classroom context (e.g., mode of instruction, lecturers, peers, physical layout of classroom) and social context outside classroom (e.g., college environment, family, society). 1.1.4. Reading statistics texts written in English as a second language. The ability to understand statistical information written in English is prominent given the global status of English and the importance of statistics to understand data, variation and chance which are omnipresent in modern life. Furthermore, college students might need to read and understand statistical results of research in their field of study, while English continues to be the preferred language of scientific communication in most published articles, as noted by van Weijen (2012). More specifically for pre-service EFL teachers, statistics knowledge is required in understanding research findings which are often useful to improve their knowledge and expertise in their future teaching while most studies in linguistics journals were quantitative in nature (Lazaraton, 2005). In addition, understanding statistics in English is also important for these students in doing their undergraduate research as part of their study requirements in some countries like Indonesia (Sailah, 2014). Specific for Indonesian situation, there is a current policy of the Indonesian Ministry of Research and Technology about bilingual education and using learning sources written in English in higher education to meet the issue of ASEAN Economic Community (AEC; Tempo News, November 2015; December 2015). Furthermore, the ability to access the current international learning sources and ICT (Coyle, Hood, & Marsh, 2010), as well as qualified assessment (e.g., ARTIST, CAOS), is also the benefit of learning statistics course in English. Meanwhile, in the perspective of second language theory, a second language is best acquired without explicit attention to language form but to language usage (Krashen, 1984), while 6.

(22) academic language skills cannot be acquired in a context devoid of academic content (Crandall, 1987). Taking the above arguments into consideration, there is an emerging issue for exploration within the area of statistics education, i.e., learning statistics through reading text written in English as a second language. Thus, within the broad area of statistics education, this study concentrates on the issues of learning statistics texts written in English as a second language for pre-service teachers (Figure 1.1).. Figure 1.1 Domain of study. However, many challenges are also emerged from this field, including all the three components (i.e., text, reader, and context) influencing reading activity of other texts (Draper & Siebert, 2004; Moje, Dillon, & O’Brien, 2000; Weinberg & Wiesner, 2011)). Related to text component, the density of statistical texts, including technical level (Cobb, 1987), lexical ambiguity terms and multi-word phrases (e.g., Lesser et al., 2013; Lesser & Winsor, 2009) may be problematic for English language learner. Moreover, different culture and unfamiliar context used in English textbooks are also among the obstacles in comprehending statistics texts (Abdelbasit, 2011; Lesser et al., 2013). From the reader component, prior experience with statistics and mathematics is related to the ways students approach their learning (Crawford et al.,. 7.

(23) 1998; Liang, Su, & Tsai, 2014) as well as their comprehension when reading mathematics and statistics texts (Schommer et al., 1992). In this study, however, not all the three components were addressed. Instead, the main focus was on the text component, since the textual feature is among the variables related to comprehension and memory (Armbruster, 1983) and one prominent factor associated to achievement and perception of statistics (Cobb, 1987). The relationships between texts and students’ comprehension were explored to propose the effective text versions for learning through reading. Students’ background knowledge related to both statistics and English language were taken into consideration when proposing the effective texts. In addition, as a preliminary study, students’ views on statistics and the learning of statistics, which might be resulted from their previous experiences with statistics and mathematics, were also investigated. 1.2 Statement of Problem Despite the significance of students’ values and conceptions, studies on this area are sparse in statistics education literature. As a preliminary stage of this study, I aimed to explore the qualitatively different ways in which pre-service EFL teachers value the learning of statistics and conceptions of statistics. Since value on learning as part of approaches to learning (Biggs, 1985) has been found to correlate with conceptions in some areas (e.g., Crawford et al. 1998; Liang et al., 2014), I also intended to clarify the potential connection between the two constructs in statistics. Afterwards, an instrument for measuring students’ conceptions of statistics were developed and validated on the basis of findings from a phenomenograpic study. The importance of statistics texts as the source for learning through reading for college students and the lack of systematic framework for analyzing texts with regard to the opportunity to learn statistics through reading indicate a need for 8.

(24) developing analytical framework based on the perspective of learning statistics through reading. This study addressed this issue and proposed that such framework can be utilized to analyze a statistics textbook as well as to compare different versions of statistics textbooks with regard to the opportunity to learn through reading. Besides, such an analytical framework is expected to contribute on statistics teaching with regard to the features should be possessed by learning materials or textbooks for student learning statistics through reading. Alongside the text component, reader component is another essential issue for the reading to learn to be efficacious (Schommer et al., 1992). Among the issues related to reader component are the influence of reader’s background knowledge in statistics and English competency on learning through reading statistics texts written in English, given that statistics texts consist of various structures, specific forms of text with specific meaning and other specific features such as graph and symbols. Therefore, this research examines how different statistics texts containing graphs relate to student reading comprehension by taking into account their background knowledge in statistics and English competency. 1.3 Purpose of the Study This study was carried out to investigate the issue concerning the opportunities of learning through reading statistics texts written in English as a second language for pre-service EFL teachers by taking the text and reader components. More specifically, the purpose of the study was three-fold: (1) to investigate pre-service EFL teachers’ views on statistics which involved values on learning and conceptions of statistics, as well as the relationships between the two factors; (2) to develop an analytical framework for analyzing the accessibility of statistics texts and to apply the framework for analyzing college statistics textbooks written in English and Indonesian, (3) to explore how different types of texts containing boxplots within the topic of data 9.

(25) distribution which are written in English relate to students’ reading comprehensions of statistics texts, controlled by their prior knowledge in statistics and competency in English. 1.4 Research Questions For the three purposes stated above, the research questions of this study were formulated as follows. 1.4.1 Research questions for study one The purpose for study one was: To investigate pre-service EFL teachers’ views on statistics which involved values on learning and conceptions of statistics, as well as the relationships between the two factors. This purpose was divided into three research questions as follows: 1. What are categories of Indonesian pre-service EFL teachers’ value on the learning of statistics? 2. What are categories of Indonesian pre-service EFL teachers’ conceptions of statistics? 3. Is there any relationship between their values on the learning statistics and conceptions of statistics? 4. What are Indonesian pre-service teachers’ conceptions of statistics as indicated by an instrument? 1.4.2 Research questions for study two The purpose for study two was: To develop an analytical framework for analyzing the accessibility of statistics texts and to apply the framework for analyzing college statistics textbooks written in English and Indonesian languages.. 10.

(26) This purpose was divided into two research questions as below. 1. What are the accessibility attributes of statistics texts which may relate to student learning through reading? 2. How do the English and Indonesian versions of statistics textbooks present the topics under data distribution with regard to accessibility attributes of statistics texts? 1.4.3. Research questions for study three. In the context of this study, the research purpose was to explore the different versions of reading materials containing boxplots which are written in English relate to students’ reading comprehensions of statistics texts. The purpose was separated into two research question as follows: 1. How do the different versions of modified statistics reading materials affect Indonesian pre-service EFL teachers’ reading comprehension? 2. How do the different versions of modified statistics reading materials affect Indonesian pre-service EFL teachers’ reading comprehension, controlled by their prior knowledge in statistics and competency in English? 1.5 Contributions of study The issue of learning opportunity in college statistics from the perspective of reading to learn was the main concern in this study. This study contributes to the literature in some essential parts. In general, although there have been some studies focusing on statistics texts used in college statistics (e.g., Cobb, 1987; Harwell et al., 1996; Huberty & Barton, 1990), none has taken the perspective of reading to learn by including the accessibility of statistics text. In addition, since research using. 11.

(27) Indonesian context is scarce in statistics education, the use of Indonesian pre-service EFL teachers as participants of this study may enrich the study field. More particularly, the components of reading focused in the three studies may give insights on the ways in which learning materials in statistics could be analyzed and improved for student reading to learn statistics. In the following, the detailed contributions of this study were deciphered with regard to the components of reading focused in the study: readers, texts, and the relationship between reader and texts. 1.5.1 Contribution from reader component Reader component was the focus of study one, in which three essential contributions could be proposed to the field of statistics education research. Firstly, by exploring the different ways in which Indonesian pre-service EFL teachers’ value on the learning of statistics on the basis of motivation theory of task value (Eccles et al., 1983; Eccles & Wigfield, 2002), this study sheds light on the elaboration of this theory, more particularly for statistics learning. Secondly, Indonesian EFL preservice teachers’ conceptions of statistics which were characterized and compared to previous related studies in different cultures has extended the studies in this field. In addition, relationships between these students’ conceptions of statistics and their values on learning statistics were explored. Acknowledging students’ conceptions of statistics, values on learning statistics, and the relationships between the two can shed some lights on the ways in which learning materials for these students should be designed, since students’ characteristics need to be taken into account when designing teaching materials for students learning statistics. For instances, if there were students having limited conceptions of statistics and tended to have less or no positive values on learning it, learning materials emphasizing on conceptual understanding rather than relying heavily on formulas would be more effective for student learning; it was also shown by (Harwell et al., 12.

(28) 1996) that statistics texts having low mathematical level are more readable, easy for students to understand and follow. Thirdly, an instrument for measuring conceptions of statistics has been developed and validated. Although the importance of measuring students’ conceptions of statistics has been suggested, including that for testing the efficacy of a teaching design and that with regard to its relation to other constructs such as attitudes toward statistics (Gal et al., 1997; Schau, Stevens, Dauphinee, & Vecchio, 1995), instruments for measuring conceptions of statistics have not been found in literature until recently. Some studies have used a phenomenographic approach to derive conception categories (e.g., Gordon, 2004; Petocz & Reid, 2005; Reid & Petocz, 2002; Yang, 2014), but the lengthy process of analysis involved in this approach makes its use impractical where large number of participants are involved. The conceptions of statistics instrument (CSI) resulted in this study provides a useful tool for statistics teachers and researchers who aim at efficiently obtaining information about students’ conceptions of statistics. 1.5.2 Contributions from the text component Text component was the focus on study two, which consisted of the development of an analytical framework and textbook analysis. Three main contributions could be offered to literature from the framework development. First, by developing an analytical framework for analyzing the accessibility of statistics texts, the study not only enriched the lack of analytical framework in current statistics education literature, but also extended the literature on accessibility text. Text accessibility is a broader concept of text readability since it also considers the content and the intended reader instead of merely relying on the surface features of the text and the quality of writing style as in the readability analysis (Gunning, 2003). The five attributes of text accessibility proposed by McTigue and Slough (2010) in science texts were adopted 13.

(29) in this study, which may contribute to the extension of the accessibility attributes of science texts into statistics texts. Second, the analytical framework proposed in this study can be operationalized by teachers or researchers in statistics education to compare different versions of statistics textbooks with regard to the accessibility attributes. Besides, it can contribute on statistics teaching since it can identify the features should be possessed by learning materials or textbooks for learning statistics through reading to particular students. Third, although the framework in this study is specifically assigned for statistics texts, it is not restricted for further expansion in other mathematics topics. For instance, when geometry is taken as the content to be analyzed, the components for each accessibility attribute can be modified and elaborated by referring to the levels of geometric thinking (Van Hiele, 1986) and cognitive processes and reasoning in learning geometry (Duval, 1995, 1998). On the other hand, the textbook analysis conducted in this study may contribute to the lack of text analysis in current literature in statistics education, more specifically for college level. In addition, analyzing statistics textbooks by using the accessibility framework can reveal not only the strengths and weakness of the textbooks for particular readers to comprehend, but also to what extent the content knowledge of statistics is presented in the textbooks. 1.5.3 Contributions from the relationship of reader and text Relationship between reader and text was the focus of study three, in which the effects of different presentations related to the accessibility attribute of integration of verbal and visual information on reading comprehension were explored. There were two main contributions provided by this study. First, since such study has not been explored in current research, it can enrich the literature on the comprehension of 14.

(30) statistics texts and graphs. There have been studies on reasoning distribution with boxplots (Pfannkuch, 2006; Reading & Reid, 2006), but none concerning on the relation of different boxplot presentations on student reading comprehension. There have been also studies exploring graph comprehension (e.g., delMas, Garfield, & Ooms, 2005; Shah & Hoeffner, 2002), but none specifically focusing on boxplots in college statistics. Second, the two variables modified in designing the different versions of reading materials were related to the one of accessibility attribute of statistics texts proposed in the analytical framework in this study. There are some studies focusing on the effects of modifying worked examples (Paas, 1992) or the structure of graph presentations, including boxplots (Bakker & Gravemeijer, 2004; Lem et al., 2015), on students’ comprehension, but none focusing on modifying types of verbal information provided in the visual and the sequence of verbal and visual information as in the present study. 1.6 Chapter Preview The dissertation is organized into seven chapters. Chapter One provides the backgrounds of study including the significances of learning statistics through reading for the pre-service EFL teachers, problem statements, purposes and contributions of study. Chapter Two gives a review of the research literature related to study and that has provided the framework for the study. Since this study concerns on learning through reading statistics text written in English as a second language for pre-service EFL teachers, two directions were used to organized the literature review: college statistics and reading. The literature related to college statistics includes literature about statistical literacy as well as learning and teaching in college statistics. The literature related to reading includes models of reading comprehension, content area reading, and content and language integrated learning (CLIL). Chapter Three describes the research methodology – detailed research questions, design, and 15.

(31) assumptions of the three studies. Specifically, it describes the procedures and research instruments involved in Study One, the assumptions, procedures and exemplary textbook coding for Study Two, and the design, assumptions, and reliability of materials used for Study Three. Chapters Four, Five, and Six concern the investigations conducted to answer the research questions for each of the three study. The findings in Study One were depicted in Chapter Four, including the findings from the phenomenographic study about values on the learning and conceptions of statistics and the relationships between the two. In addition, it describes the finding from the quantitative study about development and validation of an instrument for measuring conceptions of statistics. The findings of Study Two were presented in Chapter Five. The study was about the text analysis, in which an analytical framework to analyze the accessibility attributes of statistics text was developed and then, by using the framework, two versions of statistics textbooks were analyzed. The findings from the experimental study conducted in Study Three were presented in Chapter Five. This study explored the relationships of different versions of statistics reading materials with pre-service EFL teachers’ reading comprehensions. The reading materials were modified by using one of the attributes of statistics text accessibility proposed in Study Two. Finally, based on the findings from the three studies, concluding remarks were presented in Chapter Seven. Initially, the major findings of the three studies were discussed. After that, the implications and possible directions for future research were addressed based on the combinations of the three studies.. 16.

(32) CHAPTER TWO LITERATURE REVIEW. In this chapter, some existing literatures related to the three studies were reviewed. The reviews were arranged into two directions: statistics and reading. Literatures related to statistics include three subsections: (1) statistical literacy for college students, (2) learning of data distribution, in which the topic of data distribution in college statistics, student understanding of data distribution as well as factors influencing their understanding were discussed, and (3) teaching in college statistics, in which the current research on instructional methods and learning materials used in college statistics, included some research on textbook analysis were discussed. Meanwhile, literatures related to reading also have three subsections: (1) models of reading comprehension, (2) content area reading which is related to the reading to learn in this study, and (3) content and language integrated learning which concerns on using second language to learn content area. Some specific aims of the study that emerged out of the review of the literature were also outlined. 2.1 Statistical Literacy for college students 2.1.1 Definition of statistical literacy The term statistical literacy has been variously defined and, until recently, no formal consensus has been made regarding the definition of the term among scholars in the area of statistics education. In general, those various definitions can be classified into knowledge skills, reasoning or critical thinking skills, and disposition. I presented some definitions of statistical literacy proposed in the area of statistics education and how they can fit into the three classifications. 17.

(33) Some scholars in statistics education (delMas, 2002; Garfield & Ben-Zvi, 2004; Garfield, delMas, & Zieffler, 2010) gave definition to statistical literacy as understanding basic language and some fundamental ideas of statistics. Basic language includes statistical terms and symbols, and statistical graphs. This definition was also referred by (Garfield & Franklin, 2011) as one component in statistical cognition for learning goal, while Rumsey (2002) use different phrase: “statistical competence”. This definition can be classified into knowledge skill due to the emphasis on some basic contents need to be understood. On the other hand, (Wallman, 1993) emphasized on reasoning and critical thinking skills and disposition in defining statistical literacy as follow: “… the ability to understand and critically evaluate statistical results that permeate our daily lives—coupled with the ability to appreciate the contributions that statistical thinking can make in public and private, professional and personal decisions.” (p.1). This definition is akin to that proposed by Gal (2002), who referred the concept of statistical literacy to two interrelated components, that is, the ability to interpret and critically evaluate statistical information in diverse media channels, and the ability to discuss and communicate their reactions to such statistical information, such as their understanding of the meaning of information, their opinions about the implications of this information, or their concerns regarding acceptability of given conclusions. This definition is in line with the intention of scientific and mathematical literacy: “to promote informed and fuller participation in the public debate about science, technology, mathematics, and environmental issues within the society” (Yore, Pimm, & Tuan, 2007, p. 560). More specifically, English (2002) suggested that mathematical literacy provides continued access to powerful mathematical ideas, which need to involve informal learning contexts and life-long learning, while to be a life-long learner requires. 18.

(34) the ability to learn through reading (Guthrie, 1982a; Maclellan, 1997). Thus, for students to be able to access the evolving knowledge of statistics for their life-long learning, the skill to learn through reading is essential. For this reason, another definition of statistical literacy is proposed for this study by taking more comprehensive perspective from content area literacy (Fang & Schleppegrell, 2010). Statistical literacy is the integrated components composed of statistical cognitions (Garfield & Franklin, 2011) and statistical dispositions (Garfield & Gal, 1999), as well as learning proficiency (Knox, 1980). Table 2.1 Components of statistical literacy Components Statistical cognitions. Statistical disposition. Learning proficiency. Definition The way students represent knowledge and develop competence in statistics, which includes three categories: - Statistical basic knowledge: understanding and using the basic language and tools of statistics - Statistical reasoning: reasoning with statistical ideas and making sense of statistical information - Statistical thinking: recognizing the importance of examining and trying to explain variability and knowing where the data came from, as well as connecting data analysis to the larger context of a statistical investigation Productive disposition on: - the role of statistical concepts in the world - the power and usefulness of statistical investigation method for making personal and professional decisions in the face of uncertainty - the role of statistical thinking to evaluate and criticize the results or conclusions from statistical investigation. The ability to use the statistical cognitions and disposition to interact with various sources of statistics knowledge or information such as texts and technologies.. Reference. Garfield and Franklin (2011); Lei and Yang (2012). (Garfield & Gal, 1999). (Knox, 1980); Lesley (2014). The first component, statistical cognition (Garfield & Franklin, 2011), is defined as the way students represent knowledge and develop competence in statistics, which composed of three categories: statistical basic knowledge, reasoning and. 19.

(35) thinking. The second component, statistical disposition (Garfield & Gal, 1999) is the ability to appreciate the role of statistical concepts in the world, the power and usefulness of statistical investigation method for making decision in the face of uncertainty, and statistical thinking to evaluate and criticize the results or conclusions from statistical investigation. The third component, learning proficiency (Knox, 1980) was the ability to use both statistical cognitions and disposition to interact with various sources of statistics knowledge or information such as texts and technologies (see Table 2.1). This kind of literacy is essential considering the lifelong learning issue, especially for college students. As such, included in this study was the focus on the way student using statistics text as source of learning the knowledge presented. 2.1.2 Statistical literacy as a goal in college statistics There was an increasingly strong call for statistics education to focus more on statistical literacy, reasoning and thinking in the late of 1990s, which arose by the concern that most statistics courses failed to produce statistically educated students (Garfield & Ben-Zvi, 2008). Since then, the reform movement has been noted in statistics education, which was described by Moore (1997) through changes in content (more data and analysis, less probability), pedagogy (fewer lectures, more active learning), and technology (for data analysis and simulation). The expected results of the course are more on conceptual understanding and attainment of statistical literacy and thinking while less on learning procedural knowledge and tools. More specifically, (Garfield, 1995) classified four goals for introductory statistics course: concepts, skills, types of thinking and attitudes. Started in 1990s, statisticians have discussed about the concepts should be taught in introductory statistics course. A list of topics was proposed by (Hogg, 1990) based on a discussion with statisticians, resulted in four levels of prioritized topics for the course. The highest priority emphasized on understanding basic knowledge, following by 20.

(36) methods for investigation in second priority, probability and inference in the third priority, and more advanced methods for investigating data involved in the fourth level. Burrill and Biehler (2011) identified seven statistical ideas that seem to be fundamental for understanding and being able to use statistics in the work place, in personal lives, and as citizens. The seven ideas are as follows: a. Data – including types of data, ways of collecting data, measurement, respecting that data are numbers with a context. b. Variation – identifying and measuring variability to predict, explain, or control. The term “variability” is used for the general phenomenon of change and “variation” for describing the total effect of the change. c. Distribution – including notions of tendencies and spread that are foundational for reasoning about statistical variables from empirical distributions, random variables from theoretical distributions, and summaries in sampling distributions. d. Representation – graphical or other representations that reveal stories in the data including the notion of transnumeration. e. Association and modelling relations between two variables – nature of the relationships among statistical variables for categorical and numerical data including regression for modelling statistical associations. f.. Probability models for data-generating processes – modelling hypothetical structural relationships generated from theory, simulations, or large data set approximations, quantifying the variability in data including long-term stability.. g. Sampling and inference – the relation between samples and the population and the essence of deciding what to believe from how data are collected to drawing conclusions with some degree of certainty. (pp. 62-63). 21.

(37) This study focused on the topic of data distribution which is the third idea topic in the list, more specifically on empirical distribution. Yet, there are other related ideas required for learning distribution, such as data, variation and representation. The topic of empirical distribution was explicated in section 2.2.1. 2.1.3 Research on statistical literacy of college student In this section, I reviewed current research concerning on the state of statistical literacy among college students. I based the reviewed on my definition of statistical literacy explicated in section 2.1.1. Thus, I took the three main components, statistical cognitions, dispositions and learning strategy, as the criteria to select the articles to be reviewed in this section. There are several researchers investigating students’ understanding of basic concepts, reasoning and thinking skills in statistics which can be classified into statistical cognitions. Some misconceptions and inappropriate reasoning about statistical concepts which are essential for citizens’ statistical skills were identified to be held by students, such as the ideas regarding histograms (Kaplan et al., 2014) and measures of spread (Turegun & Reeder, 2011). Kaplan et al. (2014) found that the misconceptions were found to persist not only before the course but also at the end of the course. Unlike the two studies which relied on written assessments, (Noll & Hancock, 2014) made use of students’ metonymy to reveal their misunderstanding on distribution and sampling through interview. They found that students tended to use normal distribution properties for all distributions due to the emphasis placed on this distribution in the course. On the other hand, lack of reasoning competency were also revealed among students who have taken statistics course (McAlevey & Sullivan, 2010). McAlevey and Sullivan (2010) identified lack of reasoning competency on confidence interval and effect of sample size in the statistical information from media while all of the 22.

參考文獻

相關文件

Building on the strengths of students and considering their future learning needs, plan for a Junior Secondary English Language curriculum to gear students towards the learning

For example, the teacher librarians teach students reading strategies while English and Chinese language subject teachers provide reading materials for students to

Objectives  To introduce the Learning Progression Framework LPF for English Language as a reference tool to identify students’ strengths and weaknesses, and give constructive

• To enhance teachers’ knowledge and understanding about the learning and teaching of grammar in context through the use of various e-learning resources in the primary

• enhance teachers’ capacity to integrate language arts rich in cultural elements into the school- based English language curriculum to broaden students’ understanding of the

Building on the strengths of students and considering their future learning needs, plan for a Junior Secondary English Language curriculum to gear students towards the

ii. Drama as a Second Language: a Practical Handbook for Language Teachers. Cambridge: National Extension College Trust. Drama Techniques in Language Learning: a Resource Book

In 2006, most School Heads perceived that the NET’s role as primarily to collaborate with the local English teachers, act as an English language resource for students,