Kesalahan Calon Guru Matematika dalam Menggunakan Ukuran Pemusatan: Pengabaian Variansi

Kimura Patar Tamba, Meiva Marthaulina Lestari Siahaan, Oce Datu Appulembang

Abstract


The measure of the center is an essential topic in statistics. Pre-service mathematics teachers must have the ability to select and use measures of center. The inability to use and select appropriate center measures indicates a low understanding of center measures. Meanwhile, research on the ability to use and select the center's appropriate measures is very limited. This study explores the sources of error for pre-service mathematics teachers in using and selecting the appropriate measures of center. This study involved 177 pre-service mathematics teachers. This research is a qualitative study using the interpretive paradigm. Data were collected using a test containing two problems and clinical interviews. Data were analyzed qualitatively using grouping participant responses based on ways of thinking and ways of understanding to use and select center measures. The results showed that pre-service mathematics teachers could not select an appropriate measure of centers because they were too focused on measures of centers while ignoring the variance. In order to be able to select an appropriate measure of centers because variance must be considered simultaneously. The implication of this study results is the need for a learning approach that introduces concurrent measures of centers with data variance.


Keywords


mean; measures of center; median; mode; variation

Full Text:

PDF

References


Amaro, J. A. O., & Sánchez, E. A. (2019). Students reasoning about variation in risk context. In G. Burrill & D. Ben-Zvi Editors (Eds.), Topics and Trends in Current Statistics Education Research ICME-13 Monographs (pp. 51–69). Cham: Springer. https://doi.org/10.1007/978-3-030-03472-6_3.

Amiruzzaman, M. (2016). Exploring preservice teachers’ understanding of measures of central tendency. Disertasi tidak dipublikasikan, Ohio, Kent State University.

Bakker, A. (2003). The early history of average values and implications for education. Journal of Statistics Education, 11(1), 1–18. https://doi.org/10.1080/10691898.2003.11910694.

Ben-Zvi, D., & Aridor-Berger, K. (2015). Children’s wonder how to wander between data and context. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 25–36). Seoul: Springer Open. https://doi.org/10.1007/978-3-319-23470-0_3 .

Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM - International Journal on Mathematics Education, 44(7), 913–925. https://doi.org/10.1007/s11858-012-0420-3.

Blanco, T. G., & Chamberlin, S. A. (2019). Pre-service teacher statistical misconceptions during teacher preparation program. Mathematics Enthusiast, 16(1–3), 461–484.

Braham, H. M., & Ben-Zvi, D. (2017). Students’ emergent articulations of statistical models and modeling in making informal statistical inferences. Statistics Education Research Journal, 16(2), 116–143. https://doi.org/10.1007/s11858-012-0420-3.

Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education (8th ed.). New York: Routledge. https://doi.org/10.4324/9781315456539.

Dierdorp, A., Bakker, A., van Maanen, J. A., & Eijkelhof, H. M. (2014). Meaningful statistics in professional practices as a bridge between mathematics and science: an evaluation of a design research project. International Journal of STEM Education, 1(1), 1–15. https://doi.org/10.1186/s40594-014-0009-1.

English, L. D., & Watson, J. M. (2015). Exploring variation in measurement as a foundation for statistical thinking in the elementary school. International Journal of STEM Education, 2(1), 1–20. https://doi.org/10.1186/s40594-015-0016-x.

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. https://doi.org/10.1207/s15327833mtl0801_3.

Groth, R. E., Bergner, J. A., & Burgess, C. R. (2016). An exploration of prospective teachers’ learning of clinical interview techniques. Mathematics Teacher Education and Development, 18(2), 48–71.

Heng, M. A., & Sudarshan, A. (2013). “Bigger number means you plus!”-Teachers learning to use clinical interviews to understand students’ mathematical thinking. Educational Studies in Mathematics, 83(3), 471–485. https://doi.org/10.1007/s10649-013-9469-3.

Hjalmarson, M. A., Moore, T. J., & Delmas, R. (2011). Statistical analysis when the data is an image: Eliciting student thinking about sampling and variability. Statistics Education Research Journal, 10(1), 15–34.

Holt, M. M., & Scariano, S. M. (2009). Mean, median and mode from a decision perspective. Journal of Statistics Education, 17(3), 1–16. https://doi.org/10.1080/10691898.2009.11889533

Ismail, Z., & Chan, S. W. (2015). Malaysian students’ misconceptions about measures of central tendency: an error analysis. AIP Conference Proceedings, 1643(1), 93–100. https://doi.org/10.1063/1.4907430.

Kemendikbud. (2016). Peraturan menteri pendidikan dan kebudayaan nomor 21 tahun 2016 tentang standar isi pendidikan dasar dan menengah. Jakarta: Kemendikbud.

Konold, C., & Higgins, T. (2011). Reasoning about Data. In W. G. Kilpatrick, M. D. E., & R. Schifter (Eds.), A Research Companion To Principles And Standards For School Mathematics (pp. 193–215). Reston: National Council of Teachers of Mathematics.

Konold, Clifford, Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325. https://doi.org/10.1007/s10649-013-9529-8.

Konold, Clifford, & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289. https://doi.org/10.2307/749741.

Koparan, T. (2015). Difficulties in learning and teaching statistics: teacher views. International Journal of Mathematical Education in Science and Technology, 46(1), 94–104. https://doi.org/10.1080/0020739X.2014.941425.

Kuntze, S., Aizikovitsh-Udi, E., & Clarke, D. (2017). Hybrid task design: connecting learning opportunities related to critical thinking and statistical thinking. ZDM - Mathematics Education, 49(6), 923–935. https://doi.org/10.1007/s11858-017-0874-4.

Manikandan, S. (2011). Measures of central tendency: the mean. Journal of Pharmacology and Pharmacotherapeutics, 2(2), 140–142. https://doi.org/10.4103/0976-500X.81920.

Morris, B. J., & Masnick, A. M. (2015). Comparing data sets: implicit summaries of the statistical properties of number sets. Cognitive Science, 39(1), 156–170. https://doi.org/10.1111/cogs.12141

OECD. (2014). PISA 2012 results: What students know and can do - student performance in mathematics, reading and science (Vol. 1). Paris: OECD Publishing. https://doi.org/10.1787/9789264201118-en.

Zawojewski, J. S., & Shaughnessy, J. M. (2016). Mean and median: are they really so easy? Mathematics Teaching in the Middle School, 5(7), 436–440. https://doi.org/10.5951/MTMS.5.7.0436.


Article Metrics

Abstract view : 0 times
PDF - 0 times

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Authors

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


 Creative Commons License
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View My Stats