Measuring Changes of Students’ Statistical Reasoning Taught by Ethnomathematics Approach Assisted TinkerPlots: A Stacking Analysis Study
DOI:
https://doi.org/10.31764/jtam.v6i3.8375Keywords:
Stacking Analysis, Rasch Model, Statistical Reasoning, Ethnomathematics, TinkerPlots.Abstract
This study aims to use the Rasch model stacking analysis technique to assess students' statistical reasoning abilities in descriptive statistics learning utilizing a TinkerPlots-assisted ethnomathematics approach in Nias cultural environment. This research is a quasi-experimental study that uses pre-and post-test control group designs. The stacking technique is used to examine how students' statistical reasoning abilities change in the presence of the intervention. The sample for this study is students in the 12th year at Gunungsitoli High School in the Nias Islands, Sumatera Utara region. Students are administered an exam that consists of five essay questions. Their responses are evaluated using a rubric that incorporates diagnostic criteria and a response certainty index. The data is analyzed using the Rasch Partial Credit Model with WINTSTEPS 4.5.5. The results indicate that students in the experimental group improved their statistical reasoning abilities more than students in the control group when they used TinkerPlots-assisted ethnomathematics in Nias cultural environment (the group with an ordinary learning approach). Along with the intervention, it is discovered that changes in student learning capacities are achievable in some situations due to pupils receiving the correct response or cheating. In other circumstances, pupils who undergo negative changes may respond inappropriately due to carelessness, boredom, or misconceptions. Additionally, these findings demonstrate that some children provide correct responses following intervention on certain items. According to the findings of this study, stacking analysis approaches are critical for describing each change in student abilities as a result of each person and each item.
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Author Biography
Rahmi Ramadhani, Faculty of Engineering and Computer Science, Department of Informatics, Universitas Potensi Utama, Medan, Indonesia
 Universitas Potensi Utama
 Scopus ID 57202252421
 Google Scholar
 rahmiramadhani3@gmail.com
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Field of Research Interest:
Mathematics Education
Educational Research
Blended Learning
Ethnomathematics
Design Research
References
Andre, M., Lavicza, Z., & Prodromou, T. (2019). Formalizing students’ informal statistical reasoning on real data: Using Gapminder to follow the cycle of inquiry and visual analyses. Eleventh Congress of the European Society for Research in Mathematics Education (CERME11).
Aridor, K., & Ben-Zvi, D. (2018a). Statistical modeling to promote students’ aggregate reasoning with sample and sampling. ZDM , 50(7), 1165–1181. https://doi.org/10.1007/S11858-018-0994-5
Aridor, K., & Ben-Zvi, D. (2018b). Statistical modeling to promote students’ aggregate reasoning with sample and sampling. ZDM - Mathematics Education, 50(7), 1165–1181. https://doi.org/10.1007/s11858-018-0994-5
Bakker, A., Derry, J., & Konold, C. (2006). Using Technology to support diagrammatic reasoning about center and variation. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. International Statistical Institute.
Bhagat, K. K., & Chang, C.-Y. (2015). Incorporating GeoGebra into Geometry learning-A lesson from India. Eurasia Journal of Mathematics, Science & Technology Education, 11(1), 77–86.
Biehler, R., Frischemeier, D., & Podworny, S. (2018). Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context. ZDM , 50(7), 1237–1251. https://doi.org/10.1007/S11858-018-1001-X
Bina, N. S., Fitri, Y., Sihotang, S. F., & Saragih, R. M. B. (2021). Use of autograph learning media to improve mathematic communication skills. Advances in Social Science, Education and Humanities Research, 86–91. https://doi.org/10.2991/assehr.k.210413.021
Bond, T. G., & Fox, C. M. (2015). Applying in the Rasch Model, Fundamental Measurament in the Human Sciences (3rd editio). Routledge.
Boone, W. J. (2016). Rasch analysis for instrument development: Why,when,and how? CBE Life Sciences Education, 15(4). https://doi.org/10.1187/cbe.16-04-0148
Boone, W. J., Staver, J. R., & Yale, M. S. (2014). Rasch Analysis in the Human Sciences. Springer.
Chan, S. W., Ismail, Z., & Sumintono, B. (2014). A Rasch Model Analysis on Secondary Students’ Statistical Reasoning Ability in Descriptive Statistics. Procedia - Social and Behavioral Sciences, 129, 133–139. https://doi.org/10.1016/j.sbspro.2014.03.658
Chan, S. W., Ismail, Z., & Sumintono, B. (2016). A Framework for Assessing High School Students’ Statistical Reasoning. PLoS ONE, 11(11), 1–32. https://doi.org/10.1371/journal.pone.0163846
Ching, B. H. H., Kong, K. H. C., Wu, H. X., & Chen, T. T. (2020). Examining the reciprocal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children. Contemporary Educational Psychology, 63, 101919. https://doi.org/10.1016/j.cedpsych.2020.101919
Combrinck, C., Scherman, V., & Maree, D. (2017). Evaluating anchor items and reframing assessment results through a practical application of the Rasch Measurement Model. South African Journal of Psychology, 47(3), 316–329. https://doi.org/10.1177/0081246316683569
D’Ambrosio, U. (2018). The program ethnomathematics: Cognitive, anthropological, historic and socio-cultural bases. PNA, 12(4), 229–247. https://doi.org/10.30827/pna.v12i4.7851
delMas, R. C. (2002). Statistical Literacy, Reasoning, and Learning: A Commentary. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910679
English, Lyn 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). https://doi.org/10.1186/s40594-015-0016-x
Fitzallen, N. E. (2013). Characterising Students’ Interaction with TinkerPlots. Technology Innovations in Statistics Education, 7(1). http://www.escholarship.org/uc/item/1074n1dp
Fitzallen, N., & Watson, J. (2010). Developing Statistical Reasoning Facilitated By TinkerPlots. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8). www.stat.auckland.ac.nz/~iase/publications.php
Garfield, J. (2002). The Challenge of Developing Statistical Reasoning. Journal of Statistics Education, 10(3). https://doi.org/10.1080/10691898.2002.11910676
Günster, S. M., & Weigand, H.-G. (2020). Designing digital technology tasks for the development of functional thinking. ZDM , 52(7), 1259–1274. https://doi.org/10.1007/S11858-020-01179-1
Gürbüz, R., & Erdem, E. (2016). Relationship between mental computation and mathematical reasoning. Cogent Education, 3(1), 1212683. https://doi.org/10.1080/2331186X.2016.1212683
Hollebrands, K. F., & Lee, H. S. (2020). Effective design of massive open online courses for mathematics teachers to support their professional learning. ZDM , 52(5), 859–875. https://doi.org/10.1007/S11858-020-01142-0
Hughes, E. M., Riccomini, P. J., & Lee, J. Y. (2020). Investigating written expressions of mathematical reasoning for students with learning disabilities. Journal of Mathematical Behavior, 58, 100775. https://doi.org/10.1016/j.jmathb.2020.100775
Im, S. H., & Jitendra, A. K. (2020). Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. Journal of Mathematical Behavior, 57, 100753. https://doi.org/10.1016/j.jmathb.2019.100753
Jungić, V., Kaur, H., Mulholland, J., & Xin, C. (2015). On flipping the classroom in large first year calculus courses. International Journal of Mathematical Education in Science and Technology, 46(4), 508–520. https://doi.org/10.1080/0020739X.2014.990529
Justice, N., Zieffler, A., Huberty, M. D., & delMas, R. (2018). Every rose has its thorn: secondary teachers’ reasoning about statistical models. ZDM - Mathematics Education, 50(7), 1253–1265. https://doi.org/10.1007/s11858-018-0953-1
Kilpatrick, J., Martin, W. G., Schifter, D., & National Council of Teachers of Mathematics. (2009). A research companion to principles and standards for school mathematics. National Council of Teachers of Mathematics.
Konold, C., & Lehrer, R. (2008). Technology and mathematics education: An essay in honor of Jim Kaput. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd editio, pp. 49–72). Taylor & Francis.
Laliyo, L. A. R. (2021). Mendiagnosis Sifat Perubahan Konseptual Siswa: Penerapan Teknik Analisis Stacking dan Racking Rasch Model. Deepublish.
Lepak, J. R., Wernet, J. L. W., & Ayieko, R. A. (2018). Capturing and characterizing students’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations. Journal of Mathematical Behavior, 50, 57–73. https://doi.org/10.1016/j.jmathb.2018.01.003
Mackrell, K. (2011). Design decisions in interactive geometry software. ZDM , 43(3), 373–387. https://doi.org/10.1007/S11858-011-0327-4
Mahdayani, R. (2016). Analisis kesulitan siswa dalam pemecahan masalah matematika pada materi aritmetika, aljabar, statistika. dan geometri. PENDAS MAHAKAM: Jurnal Pendidikan Dan Pembelajaran Sekolah Dasar, 1(1), 86–98. https://jurnal.fkip-uwgm.ac.id/index.php/pendasmahakam/article/view/39
Moksin, A. I., Shahrill, M., Anshari, M., Huda, M., & Tengah, K. A. (2018). The Learning of integration in calculus using the autograph technology. Advanced Science Letters, 24(1), 550–552. https://doi.org/10.1166/asl.2018.12067
Mumu, J., & Tanujaya, B. (2019). Measure Reasoning Skill of Mathematics Students. International Journal of Higher Education, 8(6). https://doi.org/10.5430/ijhe.v8n6p85
Nuralam, & Gadeng, T. (2018). Kualitas Hasil Belajar Statistika Siswa MTs yang dibelajarkan dengan Pendekatan Problem Posing. Suska Journal of Mathematics Education, 4(2), 88–99.
Nurjanah, Latif, B., Yuliardi, R., & Tamur, M. (2020). Computer-assisted learning using the Cabri 3D for improving spatial ability and self- regulated learning. Heliyon, 6(11), e05536. https://doi.org/10.1016/J.HELIYON.2020.E05536
Orey, D. C., & Rosa, M. (2021). Ethnomodelling as a glocalization process of mathematical practices through cultural dynamism. Mathematics Enthusiast, 18(3), 439–468.
Pusat Penilaian Pendidikan Kementerian Pendidikan dan Kebudayaan. (2022a). Laporan Hasil Ujian Nasional-Penguasaan Materi Ujian Nasional. Https://Hasilun.Puspendik.Kemdikbud.Go.Id/#2019!Sma!Daya_serap!07&08&999!A&03&1&T&1&unbk!3!&.
Pusat Penilaian Pendidikan Kementerian Pendidikan dan Kebudayaan. (2022b). LAPORAN HASIL UJIAN NASIONAL 2015-2019. Https://Hasilun.Puspendik.Kemdikbud.Go.Id/#2015-2016-2017-2018-2019!Sma!Capaian_nasional!07&99&999!T&T&1&N&1&unbk!1!&.
Putra, M. (2018). How ethnomathematics can bridge informal and formal mathematics in mathematics learning process at school: A framework. In For the Learning of Mathematics (Vol. 38, Issue 3). https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073814935&origin=inward
Ramadhani, R. (2017). Peningkatan kemampuan pemahaman konsep dan kemampuan pemecahan masalah matematika siswa SMA melalui guided discovery learning berbantuan autograph. Jurnal Penelitian Dan Pembelajaran Matematika, 10(2), 72–81. https://doi.org/10.30870/jppm.v10i2.2032
Ramadhani, R. (2020). The effect of flipp-blended learning model using LMS-google classroom in mathematics learning. Proceedings of the 1st International Conference of Global Education and Society Science, ICOGESS 2019. https://doi.org/10.4108/EAI.14-3-2019.2292028
Ramadhani, R., & Evans, B. (2022). Measuring students’ statistical reasoning abilities using flipped classroom model with SPSS and STATCAL. Journal of Honai Math, 5(1), 1–14. https://doi.org/10.30862/jhm.v5i1.246
Ramadhani, R., & Fitri, Y. (2020). A Project-based learning into flipped classroom for ePUB3 electronic mathematics learning module (eMLM)-based on course design and implementation. Universal Journal of Educational Research, 8(7), 3119–3135. https://doi.org/10.13189/ujer.2020.080740
Ramadhani, R., & Narpila, S. D. (2018). Problem based learning method with geogebra in mathematical learning. International Journal of Engineering and Technology(UAE), 7(3.2 Special Issue 2).
Ramadhani, R., Syahputra, E., & Simamora, E. (2021). Ethno-Flipped Classroom Model: Sebuah Rekomendasi Model Pembelajaran Matematika di Masa New Normal. AXIOM: Jurnal Pendidikan Dan Matematika, 10(2), 221–240. https://doi.org/10.30821/axiom.v10i2.10331
Ridha, M., Johar, R., & Mailizar. (2018). The effectiveness of an autograph-assisted problem based learning model for improving high school students’ learning outcome on graphics functions. IOP Conf. Series: Journal of Physics: Conf. Series 1088, 012025. https://doi.org/10.1088/1742-6596/1088/1/012025
Risdiyanti, I., & Prahmana, R. C. I. (2020). Ethnomathematics (Teori dan Implementasinya: Suatu Pengantar). UAD Press.
Rocha, H. (2020). Using tasks to develop pre-service teachers’ knowledge for teaching mathematics with digital technology. ZDM , 52(7), 1381–1396. https://doi.org/10.1007/S11858-020-01195-1
Rosa, M., & Orey, D. C. (2017). STEM education in the Brazilian context: An ethnomathematical perspective. In STEM Education in the Junior Secondary: The State of Play (pp. 221–247). Springer, Singapore. https://doi.org/10.1007/978-981-10-5448-8_11
Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualisation software. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics. International Statistical Institute. http://iaseweb.org/documents/papers/icots7/2D3_RUBI.pdf
Sari, L., Syahputra, E., & Surya, E. (2020). Development of Autograph-Based Learning Tools to Improve Mathematical Communication Skills Students in vocational high school. International Journal of Multicultural and Multireligious Understanding, 7(8), 326. https://doi.org/10.18415/ijmmu.v7i8.1880
Seloraji, P., & Leong, K. E. (2016). Impact of using Tinkerplots on statistical reasoning. Proceedings the 21st Asian Conference on Technology in Mathematics (Pattaya, Thailand).
Setiawan, E. P., & Sukoco, H. (2021). Exploring first year university students’ statistical literacy: A case on describing and visualizing data. Journal on Mathematics Education, 12(3), 427–448. https://doi.org/10.22342/jme.12.3.13202.427-448
Sharma, S. (2017). Definitions and models of statistical literacy: a literature review. Open Review of Educational Research, 4(1), 118–133. https://doi.org/10.1080/23265507.2017.1354313
Soeharto, S. (2021). Development of A Diagnostic Assessment Test to Evaluate Science Misconceptions in Terms of School Grades: A Rasch Measurement Approach. Journal of Turkish Science Education, 18(3), 351–370. https://doi.org/10.36681/tused.2021.78
Soury-Lavergne, S., & Maschietto, M. (2015). Articulation of spatial and geometrical knowledge in problem solving with technology at primary school. ZDM, 47(3), 435–449. https://doi.org/10.1007/S11858-015-0694-3
Suherman, Prananda, M. R., Proboningrum, D. I., Pratama, E. R., Laksono, P., & Amiruddin. (2020). Improving Higher Order Thinking Skills (HOTS) with Project Based Learning (PjBL) Model Assisted by Geogebra. Journal of Physics: Conference Series 1467, 1467(1), 012027. https://doi.org/10.1088/1742-6596/1467/1/012027
Sumintono, B., & Widhiarso, W. (2015). Aplikasi Pemodelan Rasch pada Assessment Pendidikan. Trim Komunikata.
ten Braak, D., Lenes, R., Purpura, D. J., Schmitt, S. A., & Størksen, I. (2022). Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function. Journal of Experimental Child Psychology, 214, 105306. https://doi.org/10.1016/J.JECP.2021.105306
Utami, N. W., Sayuti, S. A., & Jailani, J. (2021). Indigenous artifacts from remote areas, used to design a lesson plan for preservice math teachers regarding sustainable education. Heliyon, 7(3). https://doi.org/10.1016/j.heliyon.2021.e06417
Uzun, Z., & Öğretmen, T. (2021). Test Equating with the Rasch Model to Compare Pre-test and Post-test Measurements. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 12(4), 336–347. https://doi.org/10.21031/epod.957614
Vahey, P., Kim, H.-J., Jackiw, N., Sela, H., & Knudsen, J. (2020). From the static to the dynamic: teachers’ varying use of digital technology to support conceptual learning in a curricular activity system. ZDM , 52(7), 1275–1290. https://doi.org/10.1007/S11858-020-01182-6
Velázquez, F. del C., & Méndez, G. M. (2021). Application in augmented reality for learning mathematical functions: A study for the development of spatial intelligence in secondary education students. Mathematics , 9(4), 369. https://doi.org/10.3390/MATH9040369
Wyse, A. E., & Mapuranga, R. (2009). Differential Item Functioning Analysis Using Rasch Item Information Functions. International Journal of Testing, 9(4), 333–357. https://doi.org/10.1080/15305050903352040
Yaqoob, I., Hashem, I. A. T., Ahmed, A., Kazmi, S. M. A., & Hong, C. S. (2019). Internet of things forensics: Recent advances, taxonomy, requirements, and open challenges. Future Generation Computer Systems, 92, 265–275. https://doi.org/10.1016/J.FUTURE.2018.09.058
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