Research Article
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Examination of Eighth Grade Students’ Statistical Reasoning Skills Regarding Pie Chart

Year 2023, Volume: 10 Issue: 1, 63 - 90, 15.08.2023
https://doi.org/10.59409/ojer.1257451

Abstract

The aim of the study is to examine in depth the eighth grade students’ levels of statistical reasoning on the data displayed by pie chart by using “The Middle School Student Statistical Thinking Model”. The study used the case study design, which is a qualitative research method. The study group consists of three eight-grade students attending a public school in İstanbul, Turkey. The activities developed by the researchers, the clinical interviews based on activities and the researcher notes were used as the data collection tools. According to the findings obtained; in the process of describing data, the statistical reasoning levels of the students differed significantly according to their academic achievement levels. In addition, the sub-process with the lowest reasoning levels of the students is to determine the effectiveness of data display types that representing data. It was determined that the most significant differentiation between the reasoning levels of the students is in the process of analyzing and interpreting data. Students mostly had difficulties in the sub-process of making inferences about a data display. In line with the finding of the study, recommendations for future studies were presented.

References

  • Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. The challenge of developing statistical literacy, reasoning, and thinking, 66, 3-15.
  • Bursal, M., & Yetiş, S. (2020). Middle school students' graph skills and affective states about graphs. International Journal of Research in Education and Science (IJRES), 6(4), 692-704.
  • Cai, J., Moyer, J. C., & Grochowski, J. N. (1999). Making the mean meaningful: An instructional study. Research in Middle Level Education, 22(4), 1-24. doi:10.1080/10848959.1999.11670153
  • Çakmak, Z. T., & Durmuş, S. (2015). Determining the concepts and subjects in the area of learning statistics and probability that 6-8th grade math students have difficulties. Abant Izzet Baysal University Journal of Faculty of Education, 15(2), 27-58.
  • Creswell, J. W. (2013). Qualitative research methods. (M. Bütün & S.B. Demir, Trans.). İstanbul: Siyasal Kitapevi.
  • Chan, S. W., Ismail, Z., & Sumintono, B. (2016). A framework for assessing high school students' statistical reasoning. Plos one, 11(11), 1-32. doi: 0.1371/journal.pone.0163846
  • Common Core State Standards Initiative (2010), “Common core state standards for mathematics (CCSSI report)” Available at https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf.
  • delMas, R. C. (2002). Statistical literacy, reasoning, and learning: A commentary. Journal of Statistics Education, 10(3), 1-11. Doi: 0.1080/10691898.2002.11910674
  • Diezmann, C. M., Lowrie, T. (2009). The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart. ZDM Mathematics Education, 41, 651-662. doi: 0.1007/s11858-009-0212-6
  • GAISE. College Report ASA Revision Committee. (2016). “Guidelines for assessment and instruction in statistics education college report 2016” Available at http://www.amstat.org/education/gaise.
  • Gal, I. (2002). Adults' statistical literacy: meanings, components, responsibilities. International Statistical Review, 70(1), 1–52. Doi: 10.1111/j.1751-5823.2002.tb00336.x
  • Gal, I., Rothschild, K., & Wagner, D. A. (1989). Which group is better? the development of statistical reasoning in elementary school children. Paper presented at meeting of the Society for Research in Child Development, Kansas City.
  • Garfield, J.B., & Ben-Zvi, D. (2008). Creating statistical reasoning learning environment. In J.B. Garfield, and D. Ben-Zvi (Ed.), Developing students’ statistical reasoning: Connecting research and teaching practice (pp.45-63). Springer.
  • Greer, B. (2000). Statistical thinking and learning. Mathematical thinking and Learning, 2(1-2), 1-9.
  • Groth, R.E. (2003). Development of a high school statistical thinking framework (3087867). [Doctoral dissertation, Illinois State University]. ProQuest Dissertations and Theses Global.
  • Gültekin, C. (2009). Examining 9th grade students' abilities on drawing, reading and interpreting of graphs about solutions and their properties (Master’s Thesis). Balıkesir University, Balıkesir.
  • Gürbüz, R., & Şahin, S. (2015). 8th grade students’ skills in translating among multiple representations. Kastamonu Education Journal, 23(4), 1869-1888.
  • Hacısalihoğlu Karadeniz M. (2016). Determining the data processing learning domain attainments of 5th grade students. Mediterrean Journal of Humanities, 6(1), 221-236.
  • Jones, D.L., Brown, M., Dunkle, A., Hixon, L., Yoder, N., & Silbernick, Z. (2015). The statistical content of elementary school mathematics textbooks. Journal of Statistics Education, 23(3), 1-22.
  • Jones, G., Thornton, C., Langrall, C., Mooney, E., Perry, B., & Putt, I. (2000). A framework for characterizing children’s statistical thinking. Mathematical Thinking and Learning, 2(4), 269-307.
  • Kaynar, Y. (2012). The investigation of the “statistics” dimension of the new middle school mathematics curriculum (Master’s Thesis). Afyon Kocatepe University, Afyon.
  • Kazak, S. (2015). Matematik eğitiminde teoriler. In E. Bingölbali, S. Arslan ve İ.Ö. Zembat (Ed) İstatistiksel akıl yürütme üzerine teorik çerçeveler (pp. 202-213). Ankara: Pegem Akademi Yayınevi.
  • Koparan, T. (2013). Examination of statistical thinking models. Elementary Education Online, 12(3), 730-739.
  • Koparan, T., & Güven, B. (2013). A study on the differentiation levels of middle school students’ statistical thinking. Elementary Education Online, 12(1), 158-178.
  • Lovett, M. (2001). A collaborative convergence on studying reasoning processes: A case study in statistics. In S.
  • M. Carver & D. Klahr (Ed), Cognition and instruction: Twenty-five years of progress (pp. 347-384). Hillsdale, NJ: Erlbaum.
  • McGatha, M., Cobb, P., & McClain, K. (2002). An analysis of student's initial statistical understandings: Developing a conjectured learning trajectory. The Journal of Mathematical Behavior, 21(3), 339-355.
  • MEB (2018). Mathematic curriculum and guide K-8. Ankara: Devlet Kitapları Müdürlüğü
  • Merriam, S. B. (2013). Qualitative Research: A guide to design and implementation (3rd ed.). A Wiley Imprint.
  • Miles, M. B., & Huberman, A. M. (2015). Early steps in analysis (A. Ersoy, Trans.). In S. Akbaba Altun, and A. Ersoy (Trans Ed.), Qualitative Data Analysis. Ankara: Pegem Akademi
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: An Expanded Sourcebook. Sage.
  • Mooney, E. S. (2002). A framework for characterizing middle school students’ statistical thinking. Mathematical Thinking and Learning, 4(1), 23–63.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author
  • Next Generation Science Standards [NGSS]. (2013). Next generation science standards: For states, by states. Washington, DC: The National Academies Press.
  • Oruç, Ş., & Akgün, İ. H. (2010). The acquisition level of graphic reading skills of elementary social studies 7th grade students. International Journal of Eurasia Social Sciences, 1(1), 51-58.
  • Özsevgeç, T., & Yayla, G. (2014). The examination of elementary school students’ graphic skills: construction and interpretation of line graphs. Kastamonu Educational Journal, 23(3), 1381-1400.
  • Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17-46). Netherlands: Kluwer Academic Publishers.
  • Polat, F. (2016). The skills of reading graphics used in science lessons and the visions of secondary school students towards graphics (Master’s Thesis). Cumhuriyet University, Sivas.
  • Savard, A., & Manuel, D. (2016). Teaching statistics: Creating an intersection for intra and interdisciplinarity. Statistics Education Research Journal, 15(2), 239-256.
  • Şahin, S. (2020). Graphic literacy skills and challenges to secondary scholl students: pie graph example (Doctoral Dissertation). Anadolu University, Eskişehir.
  • Schield, M. (2001). Statistical literacy: Reading tables of rates and percentages. In Proceedings of the Annual Meeting of the American Statistical Association.
  • Schield, M. (2006). Statistical literacy survey analysis: reading graphs and tables of rates and percentages. Paper presented at meeting of the International Conference on Teaching Statistics (ICOTS-7) Conference, Salvador, Brazil.
  • Selamet, C. S. (2014). The examination of reading and interpretation achievement levels of 5th grade students about frequency table and graphs (Master’s Thesis). Afyon Kocatepe University, Afyon.
  • Tairab, H. H., & Al-Naqbi, A. K. (2004). How do secondary school science students interpret and construct scientific graphs? Journal of Biological Education, 38(3), 127-132.
  • Toluk Uçar. Z., & Akdoğan, N. E. (2009). Middle school students’ understanding of average. İlköğretim Online, 8(2), 391-400.
  • Tosun, T. (2021). Examining of graph sense and graph construction competences of secondary school students (Master's Thesis). Adnan Menderes University, Aydın.
  • Utts, J. (2003). What educated citizens should know about statistics and probability. The American Statistician, 57(2), 74-79.
  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265.
  • Yanık, H. B., Özdemir, G., & Eryılmaz Çevirgen, A. (2017). Investigating data processing related tasks in middle school mathematics textbooks. Inonu University Journal of the Faculty of Education, 18(2), 45-61. doi: 10.17679/inuefd.323407
  • Yıldız, S. G. (2022). “Matematik eğitiminde istatistiksel düşünmenin yeri ve önemi”, In Eğitim Bilimleri Alanında Uluslararası Araştırmalar XIV, (103-114), Eğitim Yayınevi.
Year 2023, Volume: 10 Issue: 1, 63 - 90, 15.08.2023
https://doi.org/10.59409/ojer.1257451

Abstract

References

  • Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. The challenge of developing statistical literacy, reasoning, and thinking, 66, 3-15.
  • Bursal, M., & Yetiş, S. (2020). Middle school students' graph skills and affective states about graphs. International Journal of Research in Education and Science (IJRES), 6(4), 692-704.
  • Cai, J., Moyer, J. C., & Grochowski, J. N. (1999). Making the mean meaningful: An instructional study. Research in Middle Level Education, 22(4), 1-24. doi:10.1080/10848959.1999.11670153
  • Çakmak, Z. T., & Durmuş, S. (2015). Determining the concepts and subjects in the area of learning statistics and probability that 6-8th grade math students have difficulties. Abant Izzet Baysal University Journal of Faculty of Education, 15(2), 27-58.
  • Creswell, J. W. (2013). Qualitative research methods. (M. Bütün & S.B. Demir, Trans.). İstanbul: Siyasal Kitapevi.
  • Chan, S. W., Ismail, Z., & Sumintono, B. (2016). A framework for assessing high school students' statistical reasoning. Plos one, 11(11), 1-32. doi: 0.1371/journal.pone.0163846
  • Common Core State Standards Initiative (2010), “Common core state standards for mathematics (CCSSI report)” Available at https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf.
  • delMas, R. C. (2002). Statistical literacy, reasoning, and learning: A commentary. Journal of Statistics Education, 10(3), 1-11. Doi: 0.1080/10691898.2002.11910674
  • Diezmann, C. M., Lowrie, T. (2009). The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart. ZDM Mathematics Education, 41, 651-662. doi: 0.1007/s11858-009-0212-6
  • GAISE. College Report ASA Revision Committee. (2016). “Guidelines for assessment and instruction in statistics education college report 2016” Available at http://www.amstat.org/education/gaise.
  • Gal, I. (2002). Adults' statistical literacy: meanings, components, responsibilities. International Statistical Review, 70(1), 1–52. Doi: 10.1111/j.1751-5823.2002.tb00336.x
  • Gal, I., Rothschild, K., & Wagner, D. A. (1989). Which group is better? the development of statistical reasoning in elementary school children. Paper presented at meeting of the Society for Research in Child Development, Kansas City.
  • Garfield, J.B., & Ben-Zvi, D. (2008). Creating statistical reasoning learning environment. In J.B. Garfield, and D. Ben-Zvi (Ed.), Developing students’ statistical reasoning: Connecting research and teaching practice (pp.45-63). Springer.
  • Greer, B. (2000). Statistical thinking and learning. Mathematical thinking and Learning, 2(1-2), 1-9.
  • Groth, R.E. (2003). Development of a high school statistical thinking framework (3087867). [Doctoral dissertation, Illinois State University]. ProQuest Dissertations and Theses Global.
  • Gültekin, C. (2009). Examining 9th grade students' abilities on drawing, reading and interpreting of graphs about solutions and their properties (Master’s Thesis). Balıkesir University, Balıkesir.
  • Gürbüz, R., & Şahin, S. (2015). 8th grade students’ skills in translating among multiple representations. Kastamonu Education Journal, 23(4), 1869-1888.
  • Hacısalihoğlu Karadeniz M. (2016). Determining the data processing learning domain attainments of 5th grade students. Mediterrean Journal of Humanities, 6(1), 221-236.
  • Jones, D.L., Brown, M., Dunkle, A., Hixon, L., Yoder, N., & Silbernick, Z. (2015). The statistical content of elementary school mathematics textbooks. Journal of Statistics Education, 23(3), 1-22.
  • Jones, G., Thornton, C., Langrall, C., Mooney, E., Perry, B., & Putt, I. (2000). A framework for characterizing children’s statistical thinking. Mathematical Thinking and Learning, 2(4), 269-307.
  • Kaynar, Y. (2012). The investigation of the “statistics” dimension of the new middle school mathematics curriculum (Master’s Thesis). Afyon Kocatepe University, Afyon.
  • Kazak, S. (2015). Matematik eğitiminde teoriler. In E. Bingölbali, S. Arslan ve İ.Ö. Zembat (Ed) İstatistiksel akıl yürütme üzerine teorik çerçeveler (pp. 202-213). Ankara: Pegem Akademi Yayınevi.
  • Koparan, T. (2013). Examination of statistical thinking models. Elementary Education Online, 12(3), 730-739.
  • Koparan, T., & Güven, B. (2013). A study on the differentiation levels of middle school students’ statistical thinking. Elementary Education Online, 12(1), 158-178.
  • Lovett, M. (2001). A collaborative convergence on studying reasoning processes: A case study in statistics. In S.
  • M. Carver & D. Klahr (Ed), Cognition and instruction: Twenty-five years of progress (pp. 347-384). Hillsdale, NJ: Erlbaum.
  • McGatha, M., Cobb, P., & McClain, K. (2002). An analysis of student's initial statistical understandings: Developing a conjectured learning trajectory. The Journal of Mathematical Behavior, 21(3), 339-355.
  • MEB (2018). Mathematic curriculum and guide K-8. Ankara: Devlet Kitapları Müdürlüğü
  • Merriam, S. B. (2013). Qualitative Research: A guide to design and implementation (3rd ed.). A Wiley Imprint.
  • Miles, M. B., & Huberman, A. M. (2015). Early steps in analysis (A. Ersoy, Trans.). In S. Akbaba Altun, and A. Ersoy (Trans Ed.), Qualitative Data Analysis. Ankara: Pegem Akademi
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: An Expanded Sourcebook. Sage.
  • Mooney, E. S. (2002). A framework for characterizing middle school students’ statistical thinking. Mathematical Thinking and Learning, 4(1), 23–63.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author
  • Next Generation Science Standards [NGSS]. (2013). Next generation science standards: For states, by states. Washington, DC: The National Academies Press.
  • Oruç, Ş., & Akgün, İ. H. (2010). The acquisition level of graphic reading skills of elementary social studies 7th grade students. International Journal of Eurasia Social Sciences, 1(1), 51-58.
  • Özsevgeç, T., & Yayla, G. (2014). The examination of elementary school students’ graphic skills: construction and interpretation of line graphs. Kastamonu Educational Journal, 23(3), 1381-1400.
  • Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17-46). Netherlands: Kluwer Academic Publishers.
  • Polat, F. (2016). The skills of reading graphics used in science lessons and the visions of secondary school students towards graphics (Master’s Thesis). Cumhuriyet University, Sivas.
  • Savard, A., & Manuel, D. (2016). Teaching statistics: Creating an intersection for intra and interdisciplinarity. Statistics Education Research Journal, 15(2), 239-256.
  • Şahin, S. (2020). Graphic literacy skills and challenges to secondary scholl students: pie graph example (Doctoral Dissertation). Anadolu University, Eskişehir.
  • Schield, M. (2001). Statistical literacy: Reading tables of rates and percentages. In Proceedings of the Annual Meeting of the American Statistical Association.
  • Schield, M. (2006). Statistical literacy survey analysis: reading graphs and tables of rates and percentages. Paper presented at meeting of the International Conference on Teaching Statistics (ICOTS-7) Conference, Salvador, Brazil.
  • Selamet, C. S. (2014). The examination of reading and interpretation achievement levels of 5th grade students about frequency table and graphs (Master’s Thesis). Afyon Kocatepe University, Afyon.
  • Tairab, H. H., & Al-Naqbi, A. K. (2004). How do secondary school science students interpret and construct scientific graphs? Journal of Biological Education, 38(3), 127-132.
  • Toluk Uçar. Z., & Akdoğan, N. E. (2009). Middle school students’ understanding of average. İlköğretim Online, 8(2), 391-400.
  • Tosun, T. (2021). Examining of graph sense and graph construction competences of secondary school students (Master's Thesis). Adnan Menderes University, Aydın.
  • Utts, J. (2003). What educated citizens should know about statistics and probability. The American Statistician, 57(2), 74-79.
  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265.
  • Yanık, H. B., Özdemir, G., & Eryılmaz Çevirgen, A. (2017). Investigating data processing related tasks in middle school mathematics textbooks. Inonu University Journal of the Faculty of Education, 18(2), 45-61. doi: 10.17679/inuefd.323407
  • Yıldız, S. G. (2022). “Matematik eğitiminde istatistiksel düşünmenin yeri ve önemi”, In Eğitim Bilimleri Alanında Uluslararası Araştırmalar XIV, (103-114), Eğitim Yayınevi.
There are 50 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Articles
Authors

Leyla Öztürk

Pınar Anapa Saban

Publication Date August 15, 2023
Published in Issue Year 2023 Volume: 10 Issue: 1

Cite

APA Öztürk, L., & Anapa Saban, P. (2023). Examination of Eighth Grade Students’ Statistical Reasoning Skills Regarding Pie Chart. Osmangazi Journal of Educational Research, 10(1), 63-90. https://doi.org/10.59409/ojer.1257451