Examination of Statistical Thinking Models

Year 2013, Volume: 12 Issue: 3, 730 - 739, 26.06.2013

Timur Koparan

Abstract

Statistical thinking has gained importance recently. The purpose of the research study is to analyze terms associated with statistical thinking, statistical thinking models, and to examine differences among statistical thinking models. These models have been developed by researchers in order to identify species of statistical thinking and how the students solved problems. In addition, these models provide the material for educational research. In this study, five statistical thinking models are discussed compared by considering different aspects of these models. These statistical models are Ben-Zvi and Friedlander (1997), Wild and Pfannkuch (1999), Jones et al (2000), Hoerl and Snee (2001) and Mooney (2002). This study provides researchbased knowledge that can be used by teachers and researchers to inform statistical thinking. If these models are known by teachers and researchers, they can be useful for overcoming the difficulties encountered in the teaching of statistics.

Keywords

Statistical Thinking, Statistical Thinking Models, Mathematics Education.

İstatistiksel Düşünme Modellerinin İncelenmesi

Abstract

Bu çalışmada son yıllarda önem kazanan istatistiksel düşünme, istatistiksel düşünme terimleri ve modelleri ele alınmıştır. Bu modeller, problem çözme ve istatistik için düşünme türlerinin belirlemesi amacıyla araştırmacılar tarafından geliştirilmiştir ve geliştirilmeye devam etmektedir. İstatistiksel düşünme modelleri öğrencilerin istatistik problemlerini nasıl çözdüğünü, hangi zihinsel süreçleri yaşadıklarını anlamayı sağlar ve eğitim araştırmacıları için materyal geliştirmeyi amaçlar. Bu çalışmada literatürden beş istatistiksel düşünme modeli incelenmiş ve bu modeller farklı yönler ele alınarak karşılaştırılmıştır. İncelenen istatistiksel düşünme modelleri sıra ile Ben-Zvi ve Friedlander (1997), Wild ve Pfannkuch (1999), Jones vd. (2000), Hoerl ve Snee (2001) ve Mooney (2002) modelleridir.İstatistiksel düşünme, istatistik eğitimi araştırmalarında yeni ve gelişmekte olan bir kavram olduğundan, bu alanda öğrenme, değerlendirme ve öğretimi geliştirmek için yapılacak girişimlere önem verilmesi gerekmektedir. Bu modellerin amaç ve içeriklerine farkındalık oluşması, istatistik öğretiminin daha iyi planlanması, istatistik öğretiminde karşılaşılan zorlukların aşılması bakımından çalışmanın araştırmacı ve öğretmenlere ışık tutacağı düşünülmektedir.

Keywords

İstatistiksel Düşünme, İstatistiksel Düşünme Modelleri, Matematik Eğitimi

References

• Chance, B. L., (2002). Components of statistical thinking and implications for instruction and assesment. Journal of Statistics Education. www.amstat.org/publications/jse/v10n3/chance.html
• Cobb, P., Wood, T., Yeckel, E., Nicholls, J., Wheattey, G., Tigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22 (1), 3-29.
• Curcio, F.R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18, 382-393.
• 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). Voorburg, The Netherlands: International Statistical Institute.
• Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35-65.
• Ben-Zvi, D. (2002). Seventh grade students sense making of data and data representations. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching of Statistics, Cape Town, South Africa. Voorburg, The Netherlands: International Statistical Institute.
• Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the observed learning outcome). New York: Academic.
• Biggs, J. ve Collis, K., (1991), Multimodal Learning and The Quality of Intelligent Behaviour, Ed: H. Rowe, Intelligence, Reconceptualization and Measurement, Laurence Erlbaum Assoc., New Jersey.
• Brown, M. (1998). The paradigm of modeling by iterative conceptualization in mathematics education research. In A. Sierpinska and J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity, Vol. 2 (263-276). Dordrecht, The Netherlands Kluwer Academic Publishers. Deming, W.E. (1986). Out of the crises. Boston: M.I.T. Center for Advanced Engineering Study.
• Fennema, E., & Franke, M.L. (1992). Teacher’s knowledge and its impact. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York, NY:Macmillan.
• Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.
• Gal, I. (2002). Adult statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25.
• Garfield, J., & Gal, I. (1999). Assessment and statistics education: Current challenges and directions. International Statistical Review, 67(1), 1-12.
• Hoerl, R.W., & Snee, R.D. (2001). Statistical thinking: Improving business performance. Pacific Grove, CA: Duxbury
• 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. Mooney, E.S. (2002). Development of a middle school statistical thinking framework. Submitted for publication, Mathematical Thinking and Learning, 4, 1, 23-63.
• Pfannkuch, M. & Wild, C. (2002). Statistical Thinking Models. The University of Auckland. NewZealand. ICOTS6.
• Rumsey, D. J. (2002). Discussion: Statistical literacy: Implications for teaching, research and practice. International Statistical Review, 70, 32–36.
• Senge, P. (1990). The fifth discipline: The art and practice of the learning organization. New York: Doubleday/Currency.
• Wainer, H. (1992). Understanding graphs and tables. Educational Researcher, 21 (1), 14-23.
• Wallman, K. K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88, 1-8.
• Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265.
• Yoon, C. (2001). An analysis of students’ statistical thinking. Unpublished masters dissertation, The University of Auckland, New Zealand.