Research Article
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Examination of 9th-Grade Students’ Informal Statistical Inferences with Regard to Measures of Central Tendency and Variability

Year 2017, Volume: 45 Issue: 45, 1 - 21, 01.01.2017
https://doi.org/10.15285/maruaebd.308618

Abstract

Statistical
inference is a process of interpretation of data. Considering the importance of
making a statistical inference without receiving any formal instruction on
statistics, revealing the ways in which these processes occur is vital.
Therefore, the aim of this study is to investigate how 9th- grade students make
informal statistical inference in the context of central tendency and measures
of variability. Informal Statistical Inference Test (İİÇTT) which includes
open-ended questions was administered to 34 students who have just begun 9th
grade. Data obtained from students’ written responses were analyzed using Makar
and Rubin’s (2009) theoretical framework of informal statistical inference.
Findings indicated that the majority of students can make informal statistical
inference about measures of central tendency and variability. It was also found
that students can use formal concepts with informal references.

 
























 

References

  • Aliaga, M., Cobb, G., Cuff, C., Garfield, J., Gould, R., Lock, R., Moore, T., Rossman, A., Stephenson, B., Utts, J., Velleman, P., Witmer, J. (2012). Guidelines for Assessment and Instruction in Statistics Education: College Report. Alexandria, VA: American Statistical Association.
  • Akkoç, H., Yeşildere-İmre, S. (2015). Teknolojik Alan Bilgisi Temelli Olasılık ve İstatistik Öğretimi. Ankara: Pegem Akademi.
  • Balcı, A. (2011). Sosyal Bilimlerde Araştırma Yöntem, Teknik ve İlkeler. Ankara: Pegem Akademi.
  • Ben-Zvi, D., Gil, E., Apel, N. (2007). What is hidden beyond the data? Helping young students to reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Reasoning about Informal Inferential Statistical Reasoning: A collection of current research studies. Proceedings of the Fifth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5), University of Warwick, UK, August 11-17, 2007.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş. ve Demirel, F. (2013). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi.
  • Cohen, L., Manion, L., Morrison, K. (2007). Research Methods in Education (6th ed.). New York: Routledge. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., Scheaffer, R. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework. Alexandria, VA: American Statistical Association.
  • Garfield, J., Le, L., Zieffler, A., Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88, 327–342.
  • Gil, E., Ben-Zvi, Dani. ve Apel, N. (2008). Creativity in Learning to Reason Informally about Statistical Inference in Primary School. In Leikin, R., Proceedings of the 5th International Conference on Creativity in Mathematics and the Education of Gifted Students, (pp. 125-135). Haifa: Israel.
  • Koparan, T., Güven, B. (2013). A Study on The Differentiation Levels of Middle School Students’ Statistical Thinking. Elementary Education Online, 12(1), 158-178.
  • Makar, K., Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105.
  • Makar, K., Bakker, A., Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152-173.
  • Makar, K. (2013). Teaching Statistics using informal statistical inference. The Australian Mathematics Teacher, 69(4), 34-40.
  • MEB (2004). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlköğretim Matematik Dersi 1–5. Sınıflar Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2005). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlköğretim Matematik Dersi 6–8. Sınıflar Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2013). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2015). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlkokul Matematik Dersi (1, 2, 3 ve 4. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
  • Paparistodemou, E. ve Mavrotheris, M. (2010). Engaging Young Children in Informal Statistical Inference. C. Reading (Ed.) içinde, Proceedings of the 8th International Conference on Teaching Statistics (ICOTS 8) [CD-ROM]. Ljubljana, Slovenia, 11-16 July 2010.
  • Park, J. (2012). Developing and Validating an Instrument to Measure College Students’ Inferential Reasoning in Statistics: An Argument-Based Approach to Validation. (Unpublished doctoral dissertation). http://search.proquest.com/docview/1564044334 adresinden 5 Ekim 2014 tarihinde edinilmiştir.
  • Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.
  • Pfannkuch, M. (2007). Year 11 students’ informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematics Education, 2(3), 149-167.
  • PISA (2014). PISA 2012 Technical Report, OECD. Rossman, A. (2007, August). A statistician’s view on the concept of inferential reasoning. Proceedings of the 5th International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-5), University of Warwick, UK.
  • Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. A. Rossman, & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
  • Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view (Accessed 10 March 2013). Statistics Education Research Journal, 7(2), 5-19. http://www.stat.auckland. ac.nz/˜iase/serj/SERJ7(2) Rossman.pdf adresinden 5 Ekim 2014 tarihinde edinilmiştir.
  • Weinberg, A., Wiesner, E., Pfaff, T. J. (2010). Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity. Journal of Statistics Education Volume 18, Number 2.
  • Zieffler, A., Garfield, J., Delmas, R., Reading, C. (2008). A Framework to Support Research on Informal Inferential Reasoning. Statistics Education Research Journal: 7(2), 40-58. http://www.stat.auckland. ac.nz/serj adresinden 5 Ekim 2014 tarihinde edinilmiştir.

Dokuzuncu sınıf öğrencilerinin merkezi eğilim ve yayılım ölçüleri konusundaki informel istatistiksel çıkarsamaları üzerine bir inceleme

Year 2017, Volume: 45 Issue: 45, 1 - 21, 01.01.2017
https://doi.org/10.15285/maruaebd.308618

Abstract

İstatistiksel
çıkarsama verilerin yorumlanmasını gerektiren bir süreçtir. Formel olarak
istatistik öğretimi almadan istatistiksel çıkarsama yapılabilmenin önemli olduğu
göz önüne alındığında, bu durumun nasıl olduğunun ortaya konması önem arz etmektedir.
Buradan hareketle araştırmanın amacı, ortaöğretime yeni başlamış dokuzuncu
sınıf öğrencilerinin merkezi eğilim ve yayılım ölçüleri konusundaki informel
istatistiksel çıkarsamalarının nasıl olduğunu ortaya koymaktır. Bu amaç doğrultusunda
araştırmada nicel araştırma yöntemlerinden tarama yöntemi kullanılmıştır.
Dokuzuncu sınıfa yeni başlamış 34 öğrenciye açık uçlu sorulardan oluşan İnformel
İstatistiksel Çıkarsama Tespit Testi (İİÇTT)
uygulanmıştır. Öğrencilerin
informel istatistiksel çıkarsamalarının nasıl olduğu belirlenirken Makar ve
Rubin’in (2009) ortaya koyduğu informel istatistiksel çıkarsama teorik
çerçevesi kullanılmıştır. Araştırma bulguları öğrencilerin çoğunluğunun
merkezi eğilim ve yayılım ölçüleri konusunda informel istatistiksel çıkarsama
yapabildiklerini göstermektedir. Ayrıca araştırmada öğrencilerin formel
kavramları informel referanslarla kullanabildiği görülmüştür.
 

References

  • Aliaga, M., Cobb, G., Cuff, C., Garfield, J., Gould, R., Lock, R., Moore, T., Rossman, A., Stephenson, B., Utts, J., Velleman, P., Witmer, J. (2012). Guidelines for Assessment and Instruction in Statistics Education: College Report. Alexandria, VA: American Statistical Association.
  • Akkoç, H., Yeşildere-İmre, S. (2015). Teknolojik Alan Bilgisi Temelli Olasılık ve İstatistik Öğretimi. Ankara: Pegem Akademi.
  • Balcı, A. (2011). Sosyal Bilimlerde Araştırma Yöntem, Teknik ve İlkeler. Ankara: Pegem Akademi.
  • Ben-Zvi, D., Gil, E., Apel, N. (2007). What is hidden beyond the data? Helping young students to reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Reasoning about Informal Inferential Statistical Reasoning: A collection of current research studies. Proceedings of the Fifth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5), University of Warwick, UK, August 11-17, 2007.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş. ve Demirel, F. (2013). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi.
  • Cohen, L., Manion, L., Morrison, K. (2007). Research Methods in Education (6th ed.). New York: Routledge. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., Scheaffer, R. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework. Alexandria, VA: American Statistical Association.
  • Garfield, J., Le, L., Zieffler, A., Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88, 327–342.
  • Gil, E., Ben-Zvi, Dani. ve Apel, N. (2008). Creativity in Learning to Reason Informally about Statistical Inference in Primary School. In Leikin, R., Proceedings of the 5th International Conference on Creativity in Mathematics and the Education of Gifted Students, (pp. 125-135). Haifa: Israel.
  • Koparan, T., Güven, B. (2013). A Study on The Differentiation Levels of Middle School Students’ Statistical Thinking. Elementary Education Online, 12(1), 158-178.
  • Makar, K., Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105.
  • Makar, K., Bakker, A., Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152-173.
  • Makar, K. (2013). Teaching Statistics using informal statistical inference. The Australian Mathematics Teacher, 69(4), 34-40.
  • MEB (2004). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlköğretim Matematik Dersi 1–5. Sınıflar Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2005). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlköğretim Matematik Dersi 6–8. Sınıflar Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2013). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
  • MEB (2015). Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı, İlkokul Matematik Dersi (1, 2, 3 ve 4. Sınıflar) Öğretim Programı. Ankara: MEB Yayınları.
  • Paparistodemou, E. ve Mavrotheris, M. (2010). Engaging Young Children in Informal Statistical Inference. C. Reading (Ed.) içinde, Proceedings of the 8th International Conference on Teaching Statistics (ICOTS 8) [CD-ROM]. Ljubljana, Slovenia, 11-16 July 2010.
  • Park, J. (2012). Developing and Validating an Instrument to Measure College Students’ Inferential Reasoning in Statistics: An Argument-Based Approach to Validation. (Unpublished doctoral dissertation). http://search.proquest.com/docview/1564044334 adresinden 5 Ekim 2014 tarihinde edinilmiştir.
  • Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.
  • Pfannkuch, M. (2007). Year 11 students’ informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematics Education, 2(3), 149-167.
  • PISA (2014). PISA 2012 Technical Report, OECD. Rossman, A. (2007, August). A statistician’s view on the concept of inferential reasoning. Proceedings of the 5th International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-5), University of Warwick, UK.
  • Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. A. Rossman, & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
  • Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view (Accessed 10 March 2013). Statistics Education Research Journal, 7(2), 5-19. http://www.stat.auckland. ac.nz/˜iase/serj/SERJ7(2) Rossman.pdf adresinden 5 Ekim 2014 tarihinde edinilmiştir.
  • Weinberg, A., Wiesner, E., Pfaff, T. J. (2010). Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity. Journal of Statistics Education Volume 18, Number 2.
  • Zieffler, A., Garfield, J., Delmas, R., Reading, C. (2008). A Framework to Support Research on Informal Inferential Reasoning. Statistics Education Research Journal: 7(2), 40-58. http://www.stat.auckland. ac.nz/serj adresinden 5 Ekim 2014 tarihinde edinilmiştir.
There are 25 citations in total.

Details

Subjects Studies on Education
Journal Section Articles
Authors

Hatice Akkoç

Abdullah Selman Selçuk

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 45 Issue: 45

Cite

APA Akkoç, H., & Selçuk, A. S. (2017). Dokuzuncu sınıf öğrencilerinin merkezi eğilim ve yayılım ölçüleri konusundaki informel istatistiksel çıkarsamaları üzerine bir inceleme. Marmara Üniversitesi Atatürk Eğitim Fakültesi Eğitim Bilimleri Dergisi, 45(45), 1-21. https://doi.org/10.15285/maruaebd.308618