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研究生: Nurul Taflihati Masykar
Nurul Taflihati Masykar
論文名稱: Exploring 8th Grade Students' Statistical Competency through the Investigation Enquiry Cycle
Exploring 8th Grade Students' Statistical Competency through the Investigation Enquiry Cycle
指導教授: 楊凱琳
Yang, Kai-Lin
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2019
畢業學年度: 107
語文別: 英文
論文頁數: 99
中文關鍵詞: statistical investigationinvestigation enquiry cyclestatistical competenceattitudes towards statistics
英文關鍵詞: statistical investigation, investigation enquiry cycle, statistical competence, attitudes towards statistics
DOI URL: http://doi.org/10.6345/NTNU201900469
論文種類: 學術論文
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  • This study investigates the effect of the statistical investigation activity in positively enhancing students’ statistical competence and students’ attitudes towards statistics for 8th-grade students. The statistical investigation included five phases in the teaching and learning activities such as problem phase, plan phase, data collection phase, analysis phase, and conclusion phase. This study adopted the qualitative and quantitative methods (mixed method). The qualitative method is used to analyze the development of students’ statistical competency during the teaching and learning process using statistical investigation inquiry cycle while the quantitative analysis is used to describe the student's pre-test and post-test of statistical competence and students’ attitudes towards statistics. The qualitative data used in this study was videotaped of classroom learning. At the problem phase of the statistical investigation activities, most of the students are at the uni-structural level of posing questions in the statistical inquiry. As the students critique each other questions and discuss the context, there is a possibility that students can develop to relational level. At the planning phase, the students understanding of sample can be enhanced from the informal towards critical. At the data collection phase, the students showed that they could collect data from the specific population without regard to the sample size. In the analysis phase, students ability in describing data mostly quantitative part, focusing mainly on a single data point and at the consistent non-critical as the students straightforward used the measures of center. The discussion ensued by teachers also did not provide ample opportunities for students as it still primarily based on teacher-centered. As in the conclusion phase, students showed that they could make claims only appropriate for the group of data they collected. As for the evaluation of students’ statistical competence and attitudes towards statistics was conducted through the administration of two instruments: the pre-test and post-test in the investigation inquiry cycle classroom and the survey of students’ attitudes towards statistics. The result of paired t-test of the pre-test and post-test indicated that there is a significant difference of students’ statistical competency before and after the implementation of the investigative activity. It suggested that students’ statistical competency after the implementation of the investigative activity is higher than before. For students’ attitudes towards statistics, based on the results of Wilcoxon Sign-Rank, it is shown that students’ attitudes towards statistics after the implementation of the investigative activities are higher than before the implementation of the investigative activities. In conclusion, the statistical investigation inquiry cycle is an effective strategy to promote students’ statistical competence and students’ attitudes towards statistics.

    This study investigates the effect of the statistical investigation activity in positively enhancing students’ statistical competence and students’ attitudes towards statistics for 8th-grade students. The statistical investigation included five phases in the teaching and learning activities such as problem phase, plan phase, data collection phase, analysis phase, and conclusion phase. This study adopted the qualitative and quantitative methods (mixed method). The qualitative method is used to analyze the development of students’ statistical competency during the teaching and learning process using statistical investigation inquiry cycle while the quantitative analysis is used to describe the student's pre-test and post-test of statistical competence and students’ attitudes towards statistics. The qualitative data used in this study was videotaped of classroom learning. At the problem phase of the statistical investigation activities, most of the students are at the uni-structural level of posing questions in the statistical inquiry. As the students critique each other questions and discuss the context, there is a possibility that students can develop to relational level. At the planning phase, the students understanding of sample can be enhanced from the informal towards critical. At the data collection phase, the students showed that they could collect data from the specific population without regard to the sample size. In the analysis phase, students ability in describing data mostly quantitative part, focusing mainly on a single data point and at the consistent non-critical as the students straightforward used the measures of center. The discussion ensued by teachers also did not provide ample opportunities for students as it still primarily based on teacher-centered. As in the conclusion phase, students showed that they could make claims only appropriate for the group of data they collected. As for the evaluation of students’ statistical competence and attitudes towards statistics was conducted through the administration of two instruments: the pre-test and post-test in the investigation inquiry cycle classroom and the survey of students’ attitudes towards statistics. The result of paired t-test of the pre-test and post-test indicated that there is a significant difference of students’ statistical competency before and after the implementation of the investigative activity. It suggested that students’ statistical competency after the implementation of the investigative activity is higher than before. For students’ attitudes towards statistics, based on the results of Wilcoxon Sign-Rank, it is shown that students’ attitudes towards statistics after the implementation of the investigative activities are higher than before the implementation of the investigative activities. In conclusion, the statistical investigation inquiry cycle is an effective strategy to promote students’ statistical competence and students’ attitudes towards statistics.

    TABLE OF CONTENTS page ABSTRACT i TABLE OF CONTENTS iii LIST OF TABLES v LIST OF FIGURES vi CHAPTER ONE INTRODUCTION 1 1.1 Background of study 1 1.2 Purpose of study 5 1.3 Research questions 5 1.4 Significance of study 5 CHAPTER TWO LITERATURE REVIEW 7 2.1 The Purpose of Learning Statistics 7 2.1.1 Statistical literacy 7 2.1.2 Attitudes towards learning statistics 12 2.2 Students’ learning of statistics 14 2.2.1 Difficulties in statistics learning 14 2.3 Effective teaching strategies 15 2.3.1 Statistical Investigation enquiry Cycle 15 2.3.2 The use of real data 16 2.3.3 Exploratory data analysis 17 2.3.4 The Focus on distribution, sample and population 18 2.3.5 The Classroom discourse 19 2.3.6 The use of assessment 20 CHAPTER THREE METHODOLOGY 21 3.1 Research design 21 3.2 Participant 23 3.3 Pilot study 24 3.4 Research instrument and data collection 25 3.4.1 Pre-test and post-test 26 3.4.1.1 Development and Validity Pre-test and Post-test 26 3.4.1.2 Pilot study of the pre-test and post-test 27 3.4.1.3 Reliability of the pre-test and post-test 28 3.4.2 Questionnaire of attitudes towards statistics 29 3.4.2.1 The Development and Validity SATSQ 29 3.4.2.2 Reliability of SATSQ 30 3.4.3 Video-recordings 30 3.5. Data analysis 30 3.5.1 The Pre-test and post-test 30 3.5.2 Questionnaire of attitudes towards statistics 31 3.5.3 The Videotape 32 CHAPTER FOUR RESULTS AND DISCUSSION 36 4.1 Pre-test and Post-test 36 4.1.1 The Result of Each Specification of the Questions 37 4.1.2 Normality test 40 4.1.3 Paired t-test 40 4.2 Students' Attitudes towards statistics 41 4.2.1 Effort component 41 4.2.2 Interest Component 41 4.2.3 Cognitive confidence component 42 4.2.4 Affective component 43 4.3 Teaching and learning process 43 4.3.1 The Nature and the Beginning of the Class 43 4.3.2 Findings concerning the problem phase 46 4.3.3 Findings concerning the plan phase 53 4.3.4 Findings concerning the data collection phase 57 4.3.5 Findings concerning the analysis phase 60 4.3.6 Findings concerning the conclusion phase 64 4.3 Discussion 65 CHAPTER FIVE CONCLUSION 68 5.1 Conclusion 68 REFERENCES 69 APPENDICES 74

    REFERENCES
    Ajzen, I. (2005). Attitudes, personality, and behavior: McGraw-Hill Education (UK).

    Arnold, P. (2013). Statistical investigative questions. An enquiry into posing and answering investigative questions from existing data. ResearchSpace@ Auckland,

    Arsaythamby, V., & Zubainur, C. M. (2014). How A Realistic Mathematics Educational Approach Affect Students’ Activities In Primary Schools? Procedia-Social Behavioral Sciences, 159, 309-313.

    Ashley, M. J., Room, R., Single, E., Bondy, S., Ferrence, R., & Giesbrecht, N. (1996). On the emerging paradigm of drinking patterns and their social and health consequences. 91(11), 1615-1621.

    Bakker, A., Biehler, R., & Konold, C. (2004). Should young students learn about box plots. Curricular Development in Statistics Education: International Association for Statistical Education, 163-173.

    Ben-Zvi, D. (2011). Statistical reasoning learning environment. 2(2).

    Ben-Zvi, D., & Garfield, J. B. (2004). The challenge of developing statistical literacy, reasoning and thinking: Springer.

    Ben-Zvi, D., Gil, E., & Apel, N. (2007). What is hidden beyond the data? Helping young students to reason and argue about some wider universe. Paper presented at the Reasoning about informal inferential statistical reasoning: A collection of current research studies. Proceedings of the Fifth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5), University of Warwick, UK.

    Biehler, R. (2014). On the delicate relation between informal statistical inference and formal statistical inference. Paper presented at the Proceedings of the Ninth International Conference on Teaching Statistics. The Hague: ISI.

    Brannen, J. (2005). Mixing methods: The entry of qualitative and quantitative approaches into the research process. International Journal of Social Research Methodology, 8(3), 173-184.
    Callingham, R. A. (1997). Teachers’ multimodal functioning in relation to the concept of average. Mathematics Education Research Journal, 9(2), 205-224.

    Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007). The Role of Technology in Improving Student Learning of Statistics.

    Chick, H. L., & Pierce, R. (2008). Teaching statistics at the primary school level: Beliefs, affordances and pedagogical content knowledge. Paper presented at the ICMI study 18 and 2008 IASE round table conference.

    Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In The challenge of developing statistical literacy, reasoning and thinking (pp. 375-395): Springer.

    Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches: Sage publications.

    DelMas, R. C. (2002). Statistical literacy, reasoning, and learning: A commentary. Journal of Statistics Education, 10(3).

    Diamond, N. T., & Sztendur, E. M. (2002). Simplifying consulting problems for use in introductory statistics lectures. Paper presented at the Proceedings of the Sixth International Conference on Teaching of Statistics, Cape Town. Voorburg, The Netherlands: International Statistical Institute.

    Fitzallen, N., Watson, J., & English, L. (2015). Assessing statistical inquiry. Paper presented at the The 39th Conference of the International Group for the Psychology of Mathematics Education.

    Fraenkel, J. R., & Wallen, N. (2006). How to design and evaluate research in education. In: New York: McGraw-Hill.

    Gal, I. (2002). Adults' statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25.

    Gal, I. (2004). Statistical literacy. In The challenge of developing statistical literacy, reasoning and thinking (pp. 47-78): Springer.

    Gal, I., & Garfield, J. (1997). Curricular goals and assessment challenges in statistics education. The assessment challenge in statistics education, 1-13.

    Gal, I., Ginsburg, L., & Schau, C. (1997). Monitoring attitudes and beliefs in statistics education. The assessment challenge in statistics education, 12, 37-51.

    Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice: Springer Science & Business Media.

    Garfield, J., & Ben-Zvi, D. (2009). Helping Students Develop Statistical Reasoning: Implementing a Statistical Reasoning Learning Environment. 31(3), 72-77. doi:10.1111/j.1467-9639.2009.00363.x

    Garfield, J., & Ben‐Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372-396.

    Garfield, J., & Ben‐Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72-77.

    Garfield, J., & DelMas, R. (2010). A web site that provides resources for assessing students' statistical literacy, reasoning and thinking. Teaching Statistics, 32(1), 2-7.

    Garfield, J., & Franklin, C. (2011). Assessment of learning, for learning, and as learning in statistics education. In Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 133-145): Springer.

    Groth, R. (2003). High school students’ levels of thinking in regard to statistical study design. Mathematics Education Research Journal, 15(3), 252-268.

    Groth, R. E. (2005). An investigation of statistical thinking in two different contexts: Detecting a signal in a noisy process and determining a typical value. The journal of mathematical behaviour, 24(2), 109-124.

    Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37-63.

    Guven, B., Ozturk, T., & Ozmen, Z. M. (2015). Examining the Statistical Process Experiences of 8th Grade Students. Egitim Ve Bilim-Education and Science, 40(177), 343-363.

    Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337-364.

    Hawkins, A., Jolliffe, F., & Glickman, L. (2014). Teaching statistical concepts: Routledge.

    Huynh, M., Baglin, J., & Bedford, A. (2014). Improving the attitudes of high school students towards statistics: An island-based approach. Paper presented at the Sustainability in Statistics Education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, Arizona, USA. Voorburg: International Association of Statistics Education.

    Ke, F., & Kwak, D. (2013). Constructs of student-centered online learning on learning satisfaction of a diverse online student body: A structural equation modeling approach. Journal of Educationa Computing Research, 48(1), 97-122.

    Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 259-289.

    Koparan, T., & Güven, B. (2014). The Effect of Project Based Learning on the Statistical Literacy Levels of Student 8th Grade. European Journal of Educational Research, 3(3), 145-157.
    Langrall, C. W., & Mooney, E. S. (2002). The development of a framework characterizing middle school students’ statistical thinking. Paper presented at the Sixth International Conference on Teaching Statistics (ICOTS6), Cape Town.

    Leavy, A., & Hourigan, M. (2016). Crime scenes and mystery players! Using driving questions to support the development of statistical literacy. Teaching Statistics, 38(1), 29-35.

    Leavy, A., Hourigan, M., & McMahon, A. (2010). Facilitating inquiry based learning in mathematics teacher education.

    Mahmud, Z., & Osman, N. (2010). Statistical competency and attitude towards learning elementary statistics: A case of SMK Bandar Baru Sg Buloh. Paper presented at the Proceedings of the Regional Conference on Statistical Sciences.

    Mathews, D., & Clark, J. (2003). Successful students’ conceptions of mean, standard deviation, and the Central Limit Theorem. Unpublished Paper.

    Mokros, J., & Russell, S. J. (1995). Children's concepts of average and representativeness. Journal for Research in Mathematics Education, 20-39.

    Mooney, E. S. (2002). A Framework for Characterizing Middle School Students' Statistical Thinking. Mathematical Thinking and Learning, 4(1), 23-63. doi:10.1207/S15327833MTL0401_2

    Moore, D. S., & McCabe, G. P. (2005). Introduction to the Practice of Statistics. New York: W. H. Freeman & Company.

    NCTM. (2000). Principles and standards for school mathematics (Vol. 1): National Council of Teachers of Mathematics.

    Neumann, D. L., Hood, M., & Neumann, M. M. (2013). Using real-life data when teaching statistics: student perceptions of this strategy in an introductory statistics course. Statistics Education Research Journal, 12(2).

    Padmi, I. G. A. R. S. (2015). Developing 7th Grade Students' Informal Inferential Reasoning. Thesis. Mathematics Education Study Program.,

    Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young students’ informal inference skills in data analysis. Statistics Education Research Journal, 7(2), 83-106.
    Pfannkuch, M. (2006). Informal Inferential Reasoning. Paper presented at the ICOTS-7.

    Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The journal of mathematical behaviour, 22(4), 405-435.

    Qasem, M. A. N., Govil, P., & Gupta, S. (2015). A Comparative Study of the Levels of Statistical Competency among Post-Graduate Students of the Universities of Yemen and India. Open Journal fo Social Science, 3(02), 130.

    Rumsey, D. J. (2002). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10(3).

    Schau, C. (2003). Students’ attitudes: The “other” important outcome in statistics education. Paper presented at the Proceedings of the joint statistical meetings.

    Scheaffer, R. L. (2003). Statistics and quantitative literacy. Quantitative literacy: Why numeracy matters for schools and colleges, 145-152.

    Scheaffer, R. L., & Stasny, E. A. (2004). The state of undergraduate education in statistics: A report from the CBMS 2000. 58(4), 265-271.

    Shulte, A. P., & Smart, J. R. (1981). Teaching Statistics and Probability: 1981 Yearbook: ERIC.
    Tukey, J. W. (1977). Exploratory Data Analysis: Limited Preliminary Ed. Reading, MA, United States: Pearson Education (US).

    Wallman, K. K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88(421), 1-8.

    Watson, J. (2006). Issues for statistical literacy in the middle school. Paper presented at the ICOTS-7 Conference Proceedings. IASE, Salvador (CD-Rom).

    Watson, J. (2009). The development of statistical understanding at the elementary school level. 8(1), 89-109.

    Watson, J. (2013). Statistical literacy at school: Growth and goals: Routledge.

    Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. 67(3), 223-248.
    Wilkinson, L. (1999). Dot plots. The American Statistician, 53(3), 276-281.

    Yolcu, A. (2012). An investigation of eighth grade students’ statistical literacy, attitudes towards statistics and their relationship. (Unpublished doctoral dissertation). Middle East Technical University, Ankara, Turkey,

    Zawojewski, J. S., & Shaughnessy, J. M. (2000). Mean and median: Are they really so easy? Mathematics Teaching in the Middle School, 5(7), 436.

    Zieffler, A., Garfield, J., Delmas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2).

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