A Study on The Differentiation Levels of Middle School Students\' Statistical Thinking

Year 2013, Volume: 12 Issue: 1, 158 - 178, 26.06.2013

Timur Koparan , Bülent Güven

Abstract

In this study, the statistical thinking levels of 6th , 7 th and 8 th grade primary school students were analyzed by using a statistical thinking model. A total of 90 students from 6th , 7 th and 8th grades participated in this study. In accordance with the statistical acqusitions of primary school education, open-ended and multiple choice questions were prepared by analyzing the questions in the literature and taking opinions of professionals. Analyzing the responses of students from different grades, the levels of students were searched within the framework of the statistical thinking model. According to the results, the thinking differences between levels were stated by qualitative data. Although the 6th , 7 th and 8th

Keywords

Statistical Thinking, Mathematics Education, Middle School Students

İlköğretim İkinci Kademe Öğrencilerinin İstatistiksel Düşünme Seviyelerindeki Farklılaşma Üzerine Bir Araştırma

Abstract

Bu çalışmada ilköğretim 6,7 ve 8. sınıf öğrencilerinin istatistiksel düşünme seviyeleri bir istatistiksel düşünme modeli kullanılarak incelenmiştir. Çalışmaya 6, 7 ve 8. sınıf öğrencilerinden toplam 90 öğrenci katılmıştır. İlköğretim 6, 7 ve 8.sınıf matematik dersindeki istatistik konusu kazanımları doğrultusunda ve literatürdeki sorular incelenerek açık uçlu ve çoktan seçmeli sorular, uzman görüşleri alınarak hazırlanmıştır. Sorular geliştirildikten sonra matematik eğitimi alanında doktora yapan 5 araştırmacıya ölçütlerle birlikte verilip incelenmesi istenmiştir. İncelemeler sonucunda 32 sorudan 26’sının kullanılmasına karar verilmiştir. Çoktan seçmeli 5 ve açık uçlu 21 sorunun bulunduğu ölçme aracında 5 soru verinin tanımlanması, 5 soru verinin organize edilmesi ve indirgenmesi, 8 soru veri gösterimi ve 8 soru verinin analiz edilmesi ve yorumlanmasını ölçmeye yöneliktir. Farklı sınıflardaki öğrencilerin sorulara verdikleri cevaplar analiz edilerek, istatistiksel düşünme modeli çerçevesinde öğrencilerin hangi seviyede olduğu araştırılmıştır. Elde edilen bulgulara göre seviyeler arasındaki düşünme farklılıkları nitel verilerle ortaya konulmuştur. İlköğretim 6, 7 ve 8. sınıf öğrencilerinin verinin tanımlanmasında dördüncü seviyede yoğunlaşmasına rağmen, verinin organize edilmesi ve indirgenmesi, veri gösterimi ve verinin analiz edilmesi ve yorumlanmasında birinci seviyede olduğu görülmüştür

Keywords

İstatistiksel Düşünme, Matematik Eğitimi, İlköğretim İkinci Kademe Öğrencileri

References

• Beaton, A. E., Mullis, I.V.S., Martin, M.O., Gonzales, E. J., Kelly, D.L., & Smith, T. A. (1996). Mathematics achievement in the middle school years: IEA’s third international mathematics and science study (TIMMS). Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College.
• 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. & 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. (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.
• Bright, G. W. & Friel, S. N. (1998). Interpretation of data in a bar graph by students in grade 6 and 8. Paper presented at the Annual Meeting of America Educational Research Association, San Diego, CA, the United States of America.
• Berg, C.A. & Phillips, D.G. (1994). An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs. Journal of Research in Science Teaching, 31, 323-344.
• Biggs, J. & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the observed learning outcome). New York, NY: Academic.
• Biggs, J. & Collis, K., (1991), Multimodal Learning and The Quality of Intelligent Behaviour. In H. Rowe (Ed.), Intelligence, Reconceptualization and Measurement. New Jersey: Laurence Erlbaum Ass.
• Cai, J. & Moyer, J. C. (1995). Middle school students’ understanding of average: a problem- solving approach. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH. (ED 389 574).
• Cerrito, P. B. (1999). Teaching statistical literacy. College Teaching, 47(1), 1-7.
• Çepni, S. (2008). Araştırma ve proje çalışmalarına giriş (3.Baskı). Trabzon: Celepler Matbaacılık. Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3).
• 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. delMas, R. C. (2002) "Statistical Literacy, Reasoning, and Learning: A Commentary" Journal of Statistics Education [Online], 10(3). www.amstat.org/publications/jse/v10n3/delmas_discussion.html
• 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.
• Friel, S.N., Curcio, F.R. & Bright, G.W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32, 124-158.
• GAISE (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A curriculum framework for PreK-12 statistics education. The American Statistical Association (ASA). http://www.amstat.org/education/gaise/
• Gal, I. (2002). Adult statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25.
• Garfield, J. & Ben-Zvi, D. (2008). Developing Students’ Statistical Reasoning Research and Teaching Practice. Springer Publishers.
• Garfield, J.B. & Gal, I. (1999). Assessment and statistics education: Current challenges and directions. International Statistical Review, 67(1), 1-12.
• Garfield, J.B. (2002). The challenge of developing statistical reasoning journal of statistics education. http://www.amstat.org/publications/jse/v10n3/garfield.html
• 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. Hoerl, R.W. & Snee, R.D. (2001). Statistical thinking: Improving business performance. Pacific Grove, CA: Duxbury.
• 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), 269-30
• Lehohla, P. (2002). Promoting statistical literacy: A South African perspective. In B. Phillips, (Ed.), Proceedings of the Sixth International Conferences on Teaching Statistics. Voorburg, the Netherlands: International Statistical Institute.
• Leinhardt, G. Zaslavsky, O., & Stein, M.K. (1990). Functions, graphs, and graphing: Tasks, learning and teaching. Review of Educational Research, 60(1), 1-64.
• Mevarech, Z.A. & Kramarsky, B. (1997). From verbal descriptions to graphic representations: stability and change in students’ alternative conceptions. Educational Studies in Mathematics, 32, 2292
• Mokros, J. & Russell, Susan J. (1995). Children's concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20-39.
• Mooney, E.S. (2002). Development of a middle school statistical thinking framework. Submitted for publication. Mathematical Thinking and Learning, 4(1), 23-63.
• Murray, S. & Gal, I. (2002). Preparing for diversity in statistics literacy: Institutional and educational implications. In B. Phillips, (Ed)., Proceedings of the Sixth International Conference on Teaching Statistics, Voorburg, the Netherlands: International Statistical Institute.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
• Pereira-Mendoza, L. & Mellor, J. (1991). Students’ concepts of bar graphs: Some preliminary findings. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics: Vol. 1 (pp. 150-157). The Netherlands: International Statistical Institute. Reading, C. & Pegg, J. (1996). Exploring understanding of data reduction. İn L. Puig and A.Gutiérrez (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education: Vol. 4 (pp. 187-194). Spain: Universitat de Valencia.
• Rumsey, D.J. (2002) Statistical literacy as a goal for introductory statistics courses Journal of Statistics Education, 10(3). www.amstat.org/publications/jse/v10n2/rumsey.html
• Shaughnessy, J. M. & Zawojewski, J.S. (1999). Scondary students’ performance on data and chance in the 1996 NAEP. The Mathematics Teacher, 92, 713-718.
• Strauss, S. & Bicher, E. (1998). The development of children’s concepts of the aritmetic average. Journal for Research in Mathematics Education, 19, 64-80.
• Uçar, Z.T. & Akdoğan E.N. (2009). 6.-8. sınıf öğrencilerinin ortalama kavramına yüklediği anlamlar. İlköğretim Online, 8(2), 391-400.
• 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.
• Watson, J. & Callingham, R. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2, 3-46
• Wild, C. J. & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223-265.
• Zawojewski, J.S. & Heckman, D.S. (1997). What do students know about data analysis, statistics, and probability? In P.A. Kenney & E.A. Silver (Eds.), Results from the sixth mathematics assesment of the national assesment of educational progress (pp. 195-223). Reston, VA: NCTM.