Investigating the statistical reasoning skills of secondary school mathematics teachers

Abstract

In this study, it is aimed to evaluate the statistical reasoning skills of secondary school mathematics teachers within the scope of their content knowledge and to examine their approaches to reveal their content knowledge about statistical reasoning. Within the scope of the study, teachers' domain knowledge of statistical reasoning and their approaches to revealing statistical reasoning domain knowledge; It was examined according to the types of reasoning about changeability, reasoning about distribution, informal inferential reasoning and reasoning about the center covered by the distribution. The case study method, which is among qualitative research, was used in the study. The participants of the study are 17 secondary school mathematics teachers (10 men, 7 women). These teachers are determined by using the typical sampling method, which is among the purposive sampling methods. As a data collection tool, it is used the statistical reasoning content information form (IAY-AB), which reveals the statistical reasoning skills in line with the field knowledge. The analysis of the data is made by using the rating scale prepared by Gökçe (2019, p. 97). The data are subjected to content analysis according to the indicators in the rating scale. In line with the findings, it was determined that secondary school mathematics teachers' field knowledge of statistical reasoning was not at the expected level and needed to be improved. As a result of the study, it was seen that a significant portion of the participants had low and medium level reasoning skills in questions that included four reasoning skills together, which they used in their approach to revealing their field knowledge of statistical reasoning. Based on the results of this study, activities for the development of statistical reasoning skills can be planned and the effects of these activities on teachers can be observed.

Keywords

• Approach to revealing content knowledge
• Statistical reasoning
• Content knowledge
• reasoning

Ortaöğretim matematik öğretmenlerinin istatistiksel akıl yürütme becerilerinin incelenmesi

Abstract

Bu çalışmada ortaöğretim (lise) matematik öğretmenlerinin istatistiksel akıl yürütme becerilerinin, alan bilgileri kapsamında değerlendirilmesi ve istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarının incelenmesi amaçlanmıştır. Çalışma kapsamında öğretmenlerin istatistiksel akıl yürütmeye dair alan bilgisi ve istatistiksel akıl yürütme alan bilgisini ortaya koyma yaklaşımları; değişebilirliğe ilişkin akıl yürütme, dağılıma ilişkin akıl yürütme, informel çıkarımsal akıl yürütme ve dağılımın kapsadığı merkez ile ilgili akıl yürütme çeşitlerine göre incelenmiştir. Çalışmada nitel araştırmalar içerisinde yer alan özel durum çalışması yöntemi kullanılmıştır. Çalışmanın katılımcılarını 17 ortaöğretim matematik öğretmeni (10 erkek, 7 kadın) oluşturmaktadır. Söz konusu öğretmenler amaçlı örnekleme yöntemleri arasında yer alan tipik durum örnekleme yöntemi kullanılarak belirlenmiştir. Veri toplama aracı olarak istatistiksel akıl yürütme becerilerini alan bilgileri doğrultusunda ortaya koyan istatistiksel akıl yürütmeye dair alan bilgisi formu (İAY-AB) kullanılmıştır. Söz konusu form Gökçe (2019) tarafından hazırlanmış olup; beş adet açık uçlu sorudan oluşmaktadır. Verilerin analizi Gökçe (2019, s. 97) tarafından hazırlanan derecelendirme ölçeği kullanılarak ve alt problemlere göre ayrı ayrı ele alınarak yapılmıştır. Derecelendirme ölçeğindeki göstergeler baz alınarak veriler içerik analizine tabii tutulmuştur. Elde edilen bulgular doğrultusunda ortaöğretim matematik öğretmenlerinin istatistiksel akıl yürütmeye dair alan bilgilerinin beklenen düzeyde olmadığı, geliştirilmesi gerektiği tespit edilmiştir. Çalışma sonucunda katılımcıların önemli bir bölümünün istatistiksel akıl yürütmeye dair alan bilgilerini ortaya koyma yaklaşımlarında kullandıkları dört akıl yürütme becerisini bir arada içeren sorularda düşük ve orta düzeyde akıl yürütme becerisine sahip oldukları görülmüştür. Bu çalışmanın sonuçlarından hareketle istatistiksel akıl yürütme becerilerinin gelişimine yönelik etkinlikler planlanarak, bu etkinliklerin öğretmenler üzerindeki etkileri gözlemlenebilir.

Keywords

• Alan bilgisi
• Alan bilgisini ortaya koyma yaklaşımı
• İstatistiksel akıl yürütme
• Akıl yürütme

References

1. Abu-Ghalyoun, O. (2021). Pre-service teachers’ difficulties in reasoning about sampling variability. Educational Studies in Mathematics, 108(3), 553-577.
2. Altun, M. (2011). Liselerde matematik öğretimi. Alfa Aktüel Basım.
3. Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. D. Ben-Zvi, & J. Garfield (Ed.), The challenge of developing statistical literacy, reasoning and thinking içinde (s. 147-168). Kluwer Academic Publıshers.
4. Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, andthinking: Goals, definitions, and challenges. D. Ben-Zvi, & J. Garfield (Ed.), The challenge of developing statistical literacy, reasoning and thinking içinde (s. 3-15). Kluwer Academic Publishers.
5. Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, J. M. (2018). Reasoning about data. D. Ben-Zvi, K. Makar, & J. Garfield (Ed.), International Handbook Of Research In Statistics Education içinde (s. 139-192). Springer.
6. Burgess, T. A. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. [Doktora Tezi, Massey University].
7. Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2018). Bilimsel araştırma yöntemleri (24. Baskı). Pegem Akademi.
8. Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American mathematical monthly, 104(9), 801-823.

9. Confrey, J., & Makar, K. (2002). Developing secondary teachers’ statistical inquiry through immersion in high-stakes accountability data. D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Ed.), 24th Annual 114 Meeting Of The North American Chapter Of The International Group For The Psychology Of Mathematics Education içinde (Vol. 3, s. 1267–1279). ERIC/CSMEE Publications.
10. Connor, D., Davies, N.,  Holmes, P. (2006). Using real data and technology to develop statistical thinking. G. Burrill (Ed.),Thinking and reasoning with data and chance: Sixty-eighth year book içinde (s. 185–194). National Council of Teachers of Mathematics.
11. Creswell, J. W. (2013). Qualitative inquiry & research design (M. Bütün, S. B. Demir, Çev. Ed.). Siyasal.
12. De Vetten, A., Schoonenboom, J., Keijzer, R., & VanOers, B. (2019). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education, 22(6), 639-661.
13. Ferrini-Mundy, J. (2000). Principles and standards for school mathematics: A guide for mathematicians. Notices of the American Mathematical Society, 47(8), 868-876.
14. Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of statistics education, 10(3).
15. Garfield, J. (2003). Assessing statistical reasoning. Statistics Education Research Journal, 2(1), 22-38.
16. Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92-99.
17. Garfield, J. B., & Ben-Zvi, D. (2008). Developing students' statistical reasoning: Connecting, research and teaching practice. Springer.
18. Garfield, J., & Chance, B. (2000). Assessment in statistics education: Issues and challenges. Mathematical Thinking and Learning, 2(1-2), 99-125.
19. Goldhaber, D. (2016). In schools, teacher quality matters most. Education Next, 56-62.
20. Gökçe, R. (2019). Ortaokul matematik öğretmenlerinin istatistiksel akıl yürütmeye ilişkin alan ve pedagojik alan bilgilerinin incelenmesi [Doktora tezi, Pamukkale Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
21. 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.
22. Gürel, R. (2016). Ortaokul matematik öğretmenlerinin merkezi eğilim ve yayılım ölçülerine ilişkin öğretim bilgilerinin incelenmesi [Doktora tezi, Hacettepe Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
23. Kader, G., Jacobbe, T., Wilson, P., & Zbiek, R.M. (2013). Developing essential understanding of statistics for teaching mathematics in grades 6-8. NCTM.
24. Karatoprak, R. (2011). Assessing preservice mathematics teachers’ statistical reasoning [Yüksek lisans tezi, Boğaziçi Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
25. Lawson, A. E. (2005). What is the role of induction and deduction in reasoning and scientific inquiry?. Journal of Research in Science Teaching, 42(6), 716-740.
26. Leavy, A. (2006). Using data comparisontosupport a focus on distribution: examining preservice teachers’ understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89-114.
27. Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics education research journal, 9(1), 46-67.
28. Leavy, A., & O’Loughlin, N. (2006). Preservice teachers understanding of the mean: Moving beyond the arithmetic average. Journal of mathematics teacher education, 9(1), 53-90.
29. Madden, S. R. (2008). High school mathematics teachers' evoling understanding of comparing distiribituons [Doktora tezi, Western Michigan University].
30. Makar, K., & Confrey, J. (2002). Comparing two distributions: Investigating secondary teachers’ statistical thinking [Sözel bildiri]. Sixth International Conference on Teaching Statistics (ICOTS-6), Cape Town, South Africa.
31. Makar, K., & Confrey, J. (2004). Secondary teachers’ statistical reasoning in comparing two groups. D. Ben-Zvi, & J. Garfield (Ed.), The challenge of developing statistical literacy, reasoning and thinking içinde (s. 353-373). Springer.
32. Makar, K., & Confrey, J. (2005). Variation talk: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54.
33. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105.
34. Maviş Sevim, F. Ö., & Akın, U. (2021). The Role of Graduate Education in Professional Development of Teachers: Is Graduation Enough?. Education and Science, 46(207), 483-511.
35. Merriam, S. B. (2018). Qualitative research a guide to design and implementation (S. Turan, Çev. Ed.). Nobel.
36. Milli Eğitim Bakanlığı [MEB], (2018a). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı. http://mufredat.meb.gov.tr/Dosyalar/201821102727101-OGM%20MATEMAT%C4%B0K%20PRG%2020.01.2018.pdf
37. Milli Eğitim Bakanlığı [MEB], (2018b). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). http://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
38. Moore, D. S. (1990). Uncertainty. L. A. Steen (Ed.), On the shoulders of giants new approaches to numeracy içinde (s. 95-138). National Academy Press.
39. National Research Council [NRC], (1996). National science education standards. National Academies Press.
40. Noll, J. (2011). Graduate teaching assistants’ statistical content knowledge of sampling. Statistics Education Research Journal, 10(2), 48–74.
41. Özen, M. (2013). Investigation of pre-service mathematics teachers' critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts [Yüksek lisans tezi, Orta Doğu Teknik Üniversitesi].Yükseköğretim Kurulu Ulusal Tez Merkezi.
42. Patton, M. Q. (2018). Qualitative research & evaluation methods (M. Bütün, S. B. Demir, Çev. Ed.). Pegem Akademi.
43. Reading, C., & Reid, J. (2010). Reasoning about variation: Rethinking theoretical  frameworks to inform practice. C. Reading (Ed.). Data and context in statistics education: Towards an evidence-based society içinde Eighth International Conference on Teaching Statistics (ICOTS). International Statistical Institute.
44. Schoenfeld, A. H., & Herrmann, D. J. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8(5), 484-494.
45. Snee, R. D. (1990). Statistical thinking and its contribution to total quality. The American Statistician, 44(2), 116-121.
46. Snee, R. D. (1993). What's missing in statistical education?. The American Statistician, 47(2), 149-154.
47. Sorto, M. A. (2004). Prospective middle school teachers’ knowledge about data analysıs and its application to teaching [Doktora tezi, Michigan State University].
48. Stronge, J. H., Ward, T. J., & Grant, L. W. (2011). What makes good teachers good? Across-case analysis of the connection between teacher effectiveness and student achievement. Journal of Teacher Education, 62(4), 339–355.
49. Toluk - Uçar, Z. & Akdoğan, E. N (2009). 6-8. Sınıf bilgilerinin anlamlarına yüklediği anlamlar. İlköğretim Online, 8 (2), 391-400.
50. Uçar, Z. T., & Akdoğan, E. N. (2009). Middle school students’ understanding of average. Elementary Education Online, 8(2), 391-400.
51. Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(3), 234-243.
52. Vermette, S., & Savard, A. (2019). Necessary knowledge for teaching statistics: example of the concept of variability. G. Burrill, & D. Ben-Zvi (Ed.) Topics and Trends in Current Statistics Education ICME-13 Monographs içinde (s. 225-244). Springer. Watson, J., & Callingham, R. (2013). Likelihood and sample size: The understandings of students and their teachers. The Journal of Mathematical Behavior, 32(3), 660-672.
53. Watson, J., Callingham, R., & Nathan, E. (2009). Probing teachers’ pedagogical content knowledge in statistics: “How will Tom get to school tomorrow?”. R. Hunter, B. Bicknell, & T. Burgess (Ed.), Crossing Divides içinde (Vol. 2, s. 563–570). MERGA.
54. Watson, J., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for research in mathematics education, 31(1), 44-70.
55. Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. Baskı). Seçkin Yayıncılık.
56. Yılmaz, N. (2020). Ortaokul matematik öğretmen adaylarının dağılım kavramına ilişkin anlamalarının incelenmesi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 50, 374-398.
57. Zieffler, A., Garfield, J., DelMas, R., & Reading, C. (2008). A frame work to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40-58.