A Case Study of Promoting Informal Inferential Reasoning in Learning Sampling Distribution for High School Students

Authors

DOI:

https://doi.org/10.35706/sjme.v4i1.3132

Abstract

Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is known about how to teach the topic for high school students, especially in Indonesian context. Therefore, the present study provides a teaching experiment to support the students’ informal inferential reasoning in understanding the sampling distribution, as well as the students’ perceptions toward the teaching experiment. The subjects in the present study were three 11th-grader of one private school in Yogyakarta majoring in mathematics and natural science. The method of data collection was direct observation of sampling distribution learning process, interviews, and documentation. The present study found that that informal inferential reasoning with problem-based learning using contextual problems and real data could support the students to understand the sampling distribution, and they also gave positive responses about their learning experience.

Downloads

Download data is not yet available.

Author Biography

Yosep Dwi Kristanto, Universitas Sanata Dharma

Yosep Dwi Kristanto is a lecturer and researcher at the Department of Mathematics Education, Universitas Sanata Dharma, Yogyakarta. His research topics of interest are mathematics and statistics education, learning and instructional technology, instructional design, and higher education.

References

Abdullah, I. (2016). Penerapan Model Pembelajaran Berbasis Masalah dengan Pendekatan Problem Solving untuk Meningkatkan Kualitas Pembelajaran Matematika (Studi Materi Fungsi Komposisi dan Fungsi Invers di Kelas XI Al Farisi SMA Negeri 2 Labakkang Boarding School) (Thesis). Universitas Negeri Makasar.

Aliaga, M., Cobb, G., Cuff, C., Garfield, J., Gould, R., Lock, R., Moore, T., Rossman, A., Stephenson, B., Utts, J., Velleman, P., & Witmer, J. (2010). Guidelines for Assessment and Instruction in Statistics Education: College Report. Technical report, American Statistical Association.

Farida, T. Z., & Kusmanto, B. (2014). Upaya Meningkatkan Minat Dan Prestasi Belajar Matematika Melalui Metode Pembelajaran Berbasis Masalah Siswa Kelas VIID SMP Negeri 1 Alian. Jurnal Ilmiah Pendidikan Matematika, 2(2), 111-118.

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational psychology review, 16(3), 235-266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3

Garfield, J., Ben-Zvi, D., Chance, Medina, Roseth, & Zieffler (2008). Developing students’ statistical reasoning: Connecting research and teaching. New York: Springer. https://doi.org/10.1007/978-1-4020-8383-9

Lane, D. M. (2015). Simulations of the Sampling Distribution of the Mean Do Not Necessarily Mislead and Can Facilitate Learning. Journal of Statistics Education, 23(2). https://doi.org/10.1080/10691898.2015.11889738

Makar, K. (2014). Young children's explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86(1), 61-78. https://doi.org/10.1007/s10649-013-9526-y

Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105.

McClave, J. T., Benson, P. G., & Sincich, T. (2011). Statistik untuk Bisnis dan Ekonomi (Jilid 1) (11th ed.). Jakarta: Erlangga.

Merriam, S. B. (2009). Qualitative Research: A Guide to Design and Implementation. Revised and Expanded from Qualitative Research and Case Study Applications in Education. San Francisco, CA: Jossey-Bass.

Ministry of Education and Culture of the Republic of Indonesia. (2018). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 37 Tahun 2018 Tentang Perubahan Atas Peraturan Menteri Pendidikan dan Kebudayaan Nomor 24 Tahun 2016 Tentang Kompetensi Inti dan Kompetensi Dasar Pelajaran Pada Kurikulum 2013 Pada Pendidikan Dasar dan Pendidikan Menengah. Jakarta: The Ministry of Education and Culture.

Ozmen, Z. M., & Guven, B. (2019). Evaluating students’ conceptual and procedural understanding of sampling distributions. International Journal of Mathematical Education in Science and Technology, 50(1), 25-45. https://doi.org/10.1080/0020739X.2018.1467507

Partono. (2009). Pengaruh Model Pembelajaran Kontekstual terhadap Prestasi Belajar Barisan dan Deret Ditinjau dari Kemampuan Awal Siswa (Thesis). Universitas Sebelas Maret, Surakarta.

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. Voorburg, The Netherlands: International Statistical Institute.

Pfannkuch, M. (2011). The Role of Context in Developing Informal Statistical Inferential Reasoning: A Classroom Study. Mathematical Thinking and Learning, 13 (1 & 2), 27-46. https://doi.org/10.1080/10986065.2011.538302

Pratt, D & Ainley, J. (2008). Introducing the Special Issue on Informal Inferential Reasoning. Statistics Education Research Journal, 7(2), 3–4.

Prodromou, T. (2013). Informal Inferential Reasoning Using a Modelling Approach within a Computer-Based Simulation. In A. M. Lindmeier dan H. Aiso (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (vol 4, pp.57-64). Kiel, Germany: PME.

Rahmadonna, S., dan Fitriyani. (2011). Penerapan Pembelajaran Kontekstual Pada Mata Pelajaran Matematika Untuk Meningkatkan Motivasi Belajar Siswa SMA. Majalah Ilmiah Pembelajaran, 7(1), 76-95.

Sahrudin, A., & Trisnawati, T. (2018). Pengembangan metode problem based learning melalui permainan engklek untuk meningkatkan thinking math peserta didik MA Global School. SJME (Supremum Journal of Mathematics Education), 2(1), 32-43.

Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Hillsdale, NJ: Lawrence Erlbaum Associates.

Stockburger, D. W. (2011). Sampling Distribution. In: Lovric M. (eds) International Encyclopedia of Statistical Science. Berlin: Springer. https://doi.org/10.1007/978-3-642-04898-2_502

Sudjana. (2005). Metoda Statistika. Bandung: Tarsito.

Triola, M. F. (2018). Elementary Statistics (13th ed.). Boston, MA: Pearson.

Turner, S., & Dabney, A. R. (2015). A Story?based Simulation for Teaching Sampling Distributions. Teaching Statistics, 37(1), 23-25. https://doi.org/10.1111/test.12067

Watkins, A. E., Bargagliotti, A., & Franklin, C. (2014). Simulation of the sampling distribution of the mean can mislead. Journal of Statistics Education, 22(3). https://doi.org/10.1080/10691898.2014.11889716

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.

Downloads

Published

2020-01-24

How to Cite

Setyani, G. D., & Kristanto, Y. D. (2020). A Case Study of Promoting Informal Inferential Reasoning in Learning Sampling Distribution for High School Students. SJME (Supremum Journal of Mathematics Education), 4(1), 64–77. https://doi.org/10.35706/sjme.v4i1.3132