ASSESSING STATISTICAL REASONING IN DESCRIPTIVE STATISTICS: A QUALITATIVE META-ANALYSIS

Authors

  • Shiau Wei Chan Department of Production and Operation Management, Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia, Batu Pahat – 86400, Malaysia
  • Zaleha Ismail Department of Educational Mathematics, Science and Multimedia Creative, Faculty of Education, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Bambang Sumintono Institute of Educational Leadership, Deputy Vice Chancellor (Academic & International), University of Malaya, Kuala Lumpur -50603, Malaysia

DOI:

https://doi.org/10.11113/jt.v78.8995

Keywords:

Statistical reasoning, descriptive statistics, qualitative meta-analysis

Abstract

To date, there are abundant studies on statistical reasoning in descriptive statistics and inferential statistics. Nevertheless, the types of statistical reasoning assessments used in those studies are different from each other. Hence, this qualitative meta-analysis is aimed to explore the methods utilized in assessing statistical reasoning among students from all levels in descriptive statistics. A total of 36 studies on reasoning about measures of central tendency, variability and distribution were found and reviewed in this paper. It was noticed that six major types of methods were employed to assess students’ statistical reasoning in descriptive statistics, namely interview, survey or questionnaire, tasks, tests, minute paper, and teaching. This study contributes considerably to the statistical reasoning area as it provides new information on statistical reasoning in descriptive statistics. For future studies, some recommendations are proposed to improve statistical reasoning assessments.

References

Vasasova, Z. 2010. The Influence Of Criterion-Referenced Assessment On Students’ Attitudes Towards Education. The New Educational Review. 20(1): 261-274.

Pellegrino, J. W., Chudowsky, N. & Glaser, R. 2001. Knowing what Students Know: The Science and Design of Educational Assessment. Washington, DC: National Academy Press.

Williams, D. 2008. Changing Classroom Practice. Educational Leadership. 65(4): 36-41.

Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. 2010. Elementary & Middle School Mathematics: Teaching Developmentally. 7th Ed. Boston, MA: Pearson.

Zieffler, A., Garfield, J., Alt, S., Dupuis, D., Holleque, K. & Chang, B. 2008. What does Research Suggest about the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature. Journal of Statistics Education. 16(2).

Lovett, M. 2001. A Collaborative Convergence on Studying Reasoning Processes: A Case Study in Statistics. In Klahr, D. & Carver, S. (Eds.). Cognitive and Instruction: Twenty-five Years of Progress. Mahwah, NJ: Lawrence Erlbaum. 347-384.

Garfield, J. & Chance, B. 2000. Assessment in Statistics Education: Issues and Challenges. Mathematical Thinking and Learning. 2(1 and 2): 99-125.

Martin, G. 2009. Focus in School Mathematics: Reasoning and Sense Making. National Council of Teachers of Mathematics.

Garfield, J. B. & Ben-Zvi, D. 2008. Developing Students’ Statistical Reasoning: Connecting Research and Teaching Practice. Springer.

Carter, T. A. 2005. Knowledge and Understanding of Probability and Statistics Topics by Preservice PK-8 Teachers. Doctor Philosophy. Texas A and M University.

Konold, C. & Pollastek, A. 2002. Data Analysis as the Search for Signals in Noisy Processes. Journal for Research in Mathematics Education. 33(4): 259-289.

Konold, C. & Pollastek, A. 2004. Conceptualizing an average as a stable feature of a noisy process. In Ben-Zvi, D. & Garfield, J. (Eds.). The Challenge Of Developing Statistical Literacy, Reasoning, And Thinking. The Netherlands: Kluwer Academic Publishers. 169-199.

Strauss, S. & Bichler, E. 1988. The Development of Children’s Concept of the Arithmetic Average. Journal for Research in Mathematics Education. 19(1): 64-80.

Konold, C. & Garfield, J. 1992. Statistical Reasoning Assessment: Part 1. Intuitive Thinking. Scientific Reasoning Research Institute. University of Massachusetts, Amherst, MA.

Mokros, J. & Russell, S. J. 1995. Children’s Concepts of Average and Representativeness. Journal for Research in Mathematics Education. 26: 20-39.

Sirvik, M. & Kmetic, S. 2010. Understanding of Arithmetic Mean. Proceedings of the 8th International Conference on Teaching Statistics (ICOTS-8). July 11-16. Ljubljana, Slovenia.

Reading, C. & Shaughnessy, M. 2004. Reason about Variation. In Ben-Zvi, D. & Garfield, J. (Eds.). The Challenge of Developing Statistical Literacy, Reasoning, and Thinking. The Netherlands: Kluwer Academic Publishers. 201-226.

Pfannkuch, M. & Reading, C. 2006. Reasoning about Distribution: A Complex Process. Statistics Education Research Journal. 5(2): 4-9.

Wild, C. 2006. The Concept of Distribution. Statistics Education Research Journal. 5(2): 10-26.

Garfield, J. B. & Gal, I. 1999. Assessment and Statistics Education: Current Challenges and Directions. International Statistical Review. 67(1): 1-12.

Bakker, A. & Gravemeijer, K. P. E. 2004. Learning to Reason about Distribution. In Ben-Zvi, D. & Garfield, J (Eds.). The Challenge of Developing Statistical Literacy, Reasoning, and Thinking. Dordrecht, The Netherlands: Kluwer Academic Publishers. 147-168.

Pfannkuch, M. & Reading, C. 2006. Reasoning about Distribution: A Complex Process. Statistics Education Research Journal. 5(2): 4-9.

Sovak, M. M. 2010. The Effect of Student-driven Projects of the Development of Statistical Reasoning. Doctor Philosophy, Unversity of Pittsburgh.

Blumberg, B., Cooper, D. R., & Schindler, P. S. 2011. Business Research Methods. 3rd Edition. Berkshire: McGraw-Hill Education.

Leon, M. R. & Zawojewski, J. S. 1990. Use of Arithmetic Mean: An Investigation of Four Properties Issues and Preliminary Results. Proceedings of the Third International Conference on Teaching Statistics. Dunedin, New Zealand.

Cai, J. 1998. Exploring Students’ Conceptual Understanding of the Averaging Algorithm. School Science and Mathematics. 98(2): 93-98.

Watson, J. M. & Moritz, J. B. 2000. The Longitudinal Development of Understanding of Average. Mathematical Thinking and Learning. 2(1 and 2): 11-50.

Batanero, C., Cobo, B. & Diaz, C. 2003. Assessing Secondary School Students’ Understanding of Averages. Proceedings of CERME 3. Bellaria, Italia.

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. Journal of Mathematical Behavior. 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: 37-63.

Cruz, J. A. G. & Garrett, A. J. 2006. Students’ Actions in Open and Multiple-choice Questions regarding Understanding of Averages. In Novotná, J., Moraová, H., Krátká, M. and Stehlíková, N. (Eds.). Proceedings 30th Conference of the International Group for the psychology of Mathematics Education. Prague: PME. 3: 161-168.

Leavy, A. & O’Loughlin, N. 2006. Preservice Teachers Understanding of the Mean: Moving beyond the Arithmetic Average. Journal of Mathematics Teacher Education. 9: 53-90.

Cruz, J. A. G. & Garrett, A. J. 2008. Understanding the Arithmetic Mean: A Study with Secondary and University students. Research in Mathematical Education. 12(1): 49-66.

Sharma, S. 2008. Exploring Fijian High School Students’ Conceptions of Averages. Pacific-Asian Education Journal. 20(2): 29-45.

Chatzivasileiou, E., Michalis, I. &Tsaliki, C. 2010. Elementary School Students’ Understanding of Concept of Arithmetic Mean. Proceedings of the 8th International Conference on Teaching Statistics (ICOTS-8). July 11-16. Ljubljana, Slovenia.

Jacobbe, T. 2012. Elementary School Teachers’ Understanding of the Mean and Median. International Journal of Science and Mathematics Education. 10: 1143-1161.

Torok, R. & Watson, J. 2000. Development of the Concept of Statistical Variation: An Exploratory Study. Mathematics Education Research Journal. 12(2): 147-169.

Watson, J. M., Kelly, B. A., Callingham, R. A. & Shaughnessy, J. M. 2003. The Measurement of Statistics Students’ Understanding of Variation. Canadian Journal of Science, Mathematics, and Technology Education. 34: 1-29.

Reading, C. 2004. Student Description of Variation while Working with Weather Data. Statistics Education Research Journal. 3(2): 84-105.

delMas, R. C. & Liu, Y. 2005. Exploring Students’ Conceptions of the Standard Deviation. Statistics Education Research Journal. 4(1): 55-82.

delMas, R. C. & Liu, Y. 2007. Students’ Conceptual Understanding of the Standard Deviation. In Lovett, M. C. & Shah, P. (Eds.). Thinking with Data. New York: Lawrence Erlbaum. 87-116.

Sharma, S. 2007. Exploring Pre-service Teachers’ Reasoning about Variability: Implications for Research. Australian Senior Mathematics Journal. 21: 31-43.

Watson, J. M., Callingham, R. A. & Kelly, B .A. 2007. Students’ Appreciation of Expectation and Variation as a Foundation for Statistical Understanding. Mathematical Thinking and Learning. 9(2): 83-130.

Watson, J. M. 2009. The Influence of Variation and Expectation on the Developing Awareness of Distribution. Statistics Education Research Journal. 8(1): 32-61.

Peters, S. A. 2011. Robust Understanding of Statistical Variation. Statistics Education Research Journal. 10(1): 52-88.

Turegun, M. & Reeder, S. 2011. Community College Students’ Conceptual Understanding of Statistical Measures of Spread. Community College Journal of Research and Practice. 35: 410-426.

Watson, J. M. & Moritz, J. B. 1999. The Beginning of Statistical Inference: Comparing Two Data Sets. Educational Studies in Mathematics. 37: 145-168.

Makar, K. & Confrey, J. 2004. Secondary Teachers’ Statistical Reasoning in Comparing Two Groups. In Ben-Zvi, D. & Garfield, J. (Eds.). The Challenge of Developing Statistical Literacy, Reasoning, and Thinking. The Netherlands: Kluwer Academic Publishers. 353-373.

Reading, C. & Reid, J. 2005. Consideration of Variation: A Model for Curriculum Development. In Burrill, G. & Camden, M. (Eds.). Curriular Development in Statistics Education: International Association for Statistical Education 2004 Roundtable. Voorburg, The Netherlands: International Statistical Institute. 36-53.

Reading, C. & Reid, J. 2006. A Emerging Hierarchy of Reasoning about Distributions: From a Variation Perspective. Statistics Education Research Journal. 5(2): 46-68.

Pfannkuch, M. 2006. Comparing Box Plot Distributions: A Teacher’s Reasoning. Statistics Education Research Journal. 5(2): 27-45.

Ciancetta, M. A. 2007. Statistics Students Reasoning when Comparing Distributions of Data. Doctor Philosophy, Portland State University.

Reid, J. & Reading, C. 2008. Measuring the Development of Students’ Consideration of Variation. Statistics Education Research Journal. 7(1): 40-59.

Canada, D. L. 2008. Conceptions of Distribution held by Middle School Students and Preservice Teachers. In Batanero, C., Burrill, G., Reading, C. & Rossman, A. (Eds.). Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference.

Makar, K. & Confrey, J. 2003. Chunks, Clumps and Spread Out: Secondary Pre-service Teachers’ Notions of Variation and Distribution. In Lee, C. (Ed.). Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-3). Mount Pleasant, Michigan: Central Michigan University.

Reid, J. & Reading, C. 2006. A Hierarchy of Tertiary Students’ Consideration of Variation. In Rossman, A. and Chance, B. (Eds.) Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics. 2-7 July. Salvador, Brazil.

Reading, C. & Reid, J. 2007. Reasoning about Variation: Student Voice. International Electronic Journal of Mathematics Education. 2(3): 110-127.

Gay, L.R., Mills, G.E. & Airasian, P. 2009. Educational Research: Competencies For Analysis And Applications. New Jersey: Pearson Education International.

Ben-Zvi, D. 1999. Alternative Assessment in Statistics Education. Proceedings of the 52nd Session of the International Statistical Institute.. Helsinki, Finland: Edita Ltd. 3: 175-176

Amiruddin M. H. & Masek, A. 2014. Inovasi dalam Teknologi Pendidikan: Isu dan Cabaran. Malaysia: Penerbit UTHM.

Pratt, D., Davies, N., & Connor, D. 2011. The Role of Technology in Teaching and Learning Statistics. In Batanero, C., Burrill, G., & Reading, C. (Eds.). Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education: A Joint ICMI/IASE Study. Springer. 97-107.

Garfield, J., & Ben-Zvi, D. 2009. Helping Students Develop Statistical Reasoning: Implementing a Statistical Reasoning Learning Environment. Teaching Statistics. 31(3): 72-77.

Downloads

Published

2016-06-13

Issue

Section

Science and Engineering

How to Cite

ASSESSING STATISTICAL REASONING IN DESCRIPTIVE STATISTICS: A QUALITATIVE META-ANALYSIS. (2016). Jurnal Teknologi, 78(6-5). https://doi.org/10.11113/jt.v78.8995