Investigation of Eighth Grade Students’ Performance on Tasks Involving Statistical Thinking About Measures of Central Tendency

Year 2025, Volume: 12 Issue: 1, 18 - 42

Şeyda Aydın Karaca , Zeynep Sonay Ay

https://doi.org/10.17275/per.25.2.12.1

Abstract

Given that students are and will continue to be in constant interaction with statistical data throughout their lives, they must be equipped to read, understand, and interpret such data. As a result, engaging in statistical thinking becomes essential. Statistical thinking can be defined as viewing the statistical process holistically in order to comprehend its underlying purpose. The aim of this study is to investigate eighth-grade students’ performance on tasks related to measures of central tendency, and to analyse their statistical thinking processes in detail. This research was designed as a case study, with tasks developed by the researchers focusing on measures of central tendency used during the data collection phase. These tasks were analysed within the framework of the M3ST (Middle School Students' Statistical Thinking), and the students' statistical thinking levels were identified. Concurrently, the solution strategies employed by the students were examined, as well as their performance in solving problems related to measures of central tendency. The analysis revealed that the students' statistical thinking was predominantly at level 3 or level 4 for the components of organizing and reducing data, respectively, while it was at level 2 for the components of representing data and analysing and interpreting data. It was found that the participants possessed procedural knowledge regarding measures of central tendency but struggled to provide explanations or draw inferences about the concepts. Moreover, most of the participants appeared to lack a deep understanding of the fundamental concepts of measures of central tendency. These findings are discussed in the context of the existing literature.

Keywords

statistical thinking, measures of central tendency, statistics education

References

• Akkas, E. N. (2009). Investigation of the middle school students' statistical thinking [Master’s thesis, Abant Izzet Baysal University]. Council of Higher Education Thesis Center.
• Altaylar, B., & Kazak, S. (2021). The effect of Realistic Mathematics Education on sixth grade students’ statistical thinking. Acta Didactica Napocensia, 14(1), 76-90. https://doi.org/10.24193/adn.14.1.6
• Altintas, S., & Keskin, C. (2019). Mathematics Textbook for Middle School 7th Grade. Ekoyay Publishing.
• Ben-Zvi, D., & Friedlander, A. (1997). Statistical thinking in a technological environment. In J. Garfield and G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics (pp. 45-55). International Statistical Institute.
• Biggs, J. B. & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). Academic.
• Bluman, A. G. (2012). Elementary statistics: A step by step approach, 8th ed. Mc Graw Education.
• Bond, M. E., Perkins, S. N., & Ramirez, C. (2012). Students’ perceptions of statistics: An exploration of attitudes, conceptualizations, and content knowledge of statistics. Statistics Education Research Journal, 11(2), 6-25. https://www.stat.auckland.ac.nz/serj
• Bruner, J. S. (1960). The Process of Education. Harvard University Press.
• Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment, Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910677
• Chick, H. L., & Watson, J. M. (2002). Collaborative influences on emergent statistical thinking — A case study. The Journal of Mathematical Behavior, 21(3), 371-400.
• Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five approaches. SAGE Publications.
• Doluzengin, B. (2019). The effect of realistic mathematics education on sixth grade students' statistical thinking, achievement motivation and persistence of knowledge [Master’s thesis, Pamukkale University]. Council of Higher Education Thesis Center.
• Erenkus, M. A., & Eren-Savaskan, D. (2018). Mathematics Textbook for Middle School 7th Grade. Koza Publishing.
• Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., and Scheaffer, R. (2007), Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, American Statistical Association.
• Gal, I. (2000). Adult numeracy development: Theory, research, practice. Hampton Press.
• Groth, R. E. (2003). Development of a high school statistical thinking framework. [Doctoral dissertation, Department of Mathematics Illinois State University]. ProQuest.
• Groth, R. E. (2006). An exploration of students’ statistical thinking. Teaching Statistics, 28(1), 17-21. https://doi.org/10.1111/j.1467-9639.2006.00003.x
• 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. https://doi.org/10.1207/s15327833mtl0801_3
• Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A framework for characterizing children's statistical thinking. Mathematical Thinking and Learning, 2(4), 269-307. https://doi.org/10.1207/S15327833MTL0204_3
• Keskin-Ogan, A., & Ozturk, S. (2019). Mathematics Textbook for Middle School 7th Grade. MoNE Publishing.
• Konold, C., & Pollatsek, A. (2002). Data analysis as a research for signals in noisy processes. Journal for Research in Mathematics Education, 33, 259-289.
• Koparan, T., & Guven, B. (2013). A study on the differentiation levels of middle school students’ statistical thinking. Elementary Education Online, 12(1), 158-178.
• Koparan, T. & Guven, B. (2014). According to the m3st model analyze of the statistical thinking levels of middle school students. Education and Science, 39(171).
• Ministry of National Education [MoNE] (2018). Mathematics Curriculum (Elementary and Middle School 1, 2, 3, 4, 5, 6, 7 and 8th Grades).
• Mooney, E. S. (2002). A framework for characterizing middle school students' statistical thinking. Mathematical Thinking and Learning, 4(1), 23-63, https://doi.org/10.1207/S15327833MTL0401_2
• Mooney, E. S., Hofbauer, P. S., Langrall, C. W., Johnson, Y. A. (2001). Refining a framework on middle school students' statistical thinking. Proceedings of 141 the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (23rd, Snowbird, Utah, October 18-21, 2001). p437-47.
• NCTM. (2000). Principles and standards for school mathematics. NCTM.
• Ozdemir, S. (2014). The effect of cooperative learning in statistics course on the academic success and attitude of the students and analyzing their level of statistical thinking [Master’s thesis, Cukurova University]. Council of Higher Education Thesis Center.
• Pollatsek, A., Lima, S., & Well, A. D. (1981). Concept or computation: Students' understanding of the mean. Educational Studies in Mathematics, 12(2), 191-204.
• Randall, G. (2006). An exploration of students’ statistical thinking. Teaching Statistics, 28(1), 17-21.
• Smith, T. M. F. (1999), “Discussion” in response to Wild and Pfannkuch, International Statistical Review, 67, 248-250.
• Watson J. M. (2006). Statistical Literacy at School, Growth and Goal. Lawrence Erlbaum Associates, Publishers.
• Watson, J. M., & Moritz, J. B. (2000). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2(1), 11-50, https://doi.org/10.1207/S15327833MTL0202_2
• Van de Walle, J. A., Karp, K. S., & Bay-Williams J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th Ed.). Pearson Education, Inc.
• Toluk-Ucar, Z. & Akdogan, E. N. (2009). Middle school students’ understanding of average. Elementary Education Online, 8(2), 391-400.
• Yilmaz, N. (2019). An investigation of pre-service teachers' statistical knowledge for teaching in a practicum-based lesson study [Doctoral dissertation, Hacettepe University]. Council of Higher Education Thesis Center.
• Yilmaz, N. (2023). An investigation of 4th grade students’ statistical thinking. Education and Science, 48(216), 39-66.
• Zainal, Z. (2007). Case study as a research method. Jurnal Kemanusiaan, 9, 1-6.
• Zawojewski, J. S. & Shaughnessy, J. M. (2000). Mean and median: Are they really so easy?. Mathematics Teaching in the Middle School, 5(7), 436-440.