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Abstract

Nowadays, digital technologies are crucial in supporting students in geometry in secondary mathematics classrooms. However, in some cases, the role of visual function in technology was only utilized for seeing and conjecturing, not for experimenting, while to develop a relational understanding of geometry concepts, students should actively participate in the learning process. To address the issue, this study investigated how students learn geometry with digital technology assistance based on students' diversity in their mathematics abilities. A task with a dynamic geometry software called Techno-based Mathematical Tasks (TbMT) was designed to assist students in exploring geometrical activities and solving a problem through investigations on tessellation. This research employs educational design research and focuses on the preliminary design by conducting a pilot study on three students based on the diversity in their ability in mathematics classrooms, i.e., low, middle, and high. As part of data collection, we captured students' works to examine critical information in their responses based on their differences in abilities. We collected the data through online meetings and recorded the data. We analyzed students' work from the recording by capturing critical information. The results revealed that the TbMT might provide students with opportunities to learn by exploring tessellation activities that might contribute to students' understanding of geometry concepts. Due to the limited number of participants in this study, further research can be an opportunity to expand the number of participants to enhance the contribution to the literature with more comprehensive empirical evidence.

Keywords

Design Research Dynamics Geometry Software Geometry Students’ Diversity Tessellation

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How to Cite
Laksmiwati, P. A., Hidayah, M., Schmidthaler, E., Prahmana, R. C. I., Sabitzer, B., & Lavicza, Z. (2023). Linking diversity in learning Geometry: Exploring tessellation in techno-based mathematical tasks. Journal on Mathematics Education, 14(3), 585–602. https://doi.org/10.22342/jme.v14i3.pp585-602
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References

  1. Abeysekera, L., & Dawson, P. (2015). Motivation and cognitive load in the flipped classroom: Definition, rationale and a call for research. Higher Education Research & Development, 34(1), 1–14. https://doi.org/10.1080/07294360.2014.934336
  2. Avcu, R. (2022). Middle-school mathematics teachers’ provision of non-examples and explanations in rational number instruction. International Journal of Mathematical Education in Science and Technology, 1–29. https://doi.org/10.1080/0020739X.2022.2105759
  3. Bakker, A. (2018). Design research in education: A practical guide for early career researchers. Routledge.
  4. Bays, C. (2005). A note on the game of life in hexagonal and pentagonal tessellations. Complex Systems.
  5. Cerrone, K. L. (2006). Tessellations: Lesson for every age [Master’s Thesis, The University of Akron]. http://rave.ohiolink.edu/etdc/view?acc_num=akron1151427935
  6. Clements, D. H., & Battista, M. T. (1992). "Geometry and Spatial Reasoning." In Handbook of Research on Mathematics Teaching and Learning (pp. 420-464).
  7. Cesaria, A., & Herman, T. (2019). Learning obstacles in geometry. Journal of Engineering Science and Technology, 14(3), 1271–1280. https://jestec.taylors.edu.my/Vol%2014%20issue%203%20June%202019/14_3_12.pdf
  8. Chakraborty, D., & Caglayan, G. (2017). Semiregular tessellations with pattern blocks. The Mathematics Teacher, 111(2), 90–94. https://doi.org/10.5951/mathteacher.111.2.0090
  9. de Villiers, M. (1996). The future of secondary school geometry. the SOSI Geometry Imperfect Conference.
  10. Falcón, R. M. (2011). Integration of CAS/DGS as a CAD system in the mathematics curriculum for architecture students. International Journal of Mathematical Education in Science and Technology, 42(6), 737–750. https://doi.org/10.1080/0020739X.2011.573871
  11. Felder, R. M., & Brent, R. (2005). Understanding student differences. Journal of Engineering Education, 94(1), 57–72. https://doi.org/10.1002/j.2168-9830.2005.tb00829.x
  12. Fonna, M., & Mursalin, M. (2019). Using of wingeom software in geometry learning to improving the of mathematical representation ability. Malikussaleh Journal of Mathematics Learning (MJML), 1(2). https://doi.org/10.29103/mjml.v1i2.1174
  13. Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, 19(1), 3-19. https://doi.org/10.2307/749957
  14. Ghavifekr, S., & Rosdy, W. A. W. (2015). Teaching and learning with technology: Effectiveness of ICT integration in schools. International Journal of Research in Education and Science, 1(2), 175–191. https://www.ijres.net/index.php/ijres/article/view/79/43
  15. Goedhart, N. S., Blignaut-van Westrhenen, N., Moser, C., & Zweekhorst, M. B. M. (2019). The flipped classroom: Supporting a diverse group of students in their learning. Learning Environments Research, 22(2), 297–310. https://doi.org/10.1007/s10984-019-09281-2
  16. Gökdağ, K., Özgeldi, M., & Yakın, İ. (2022). Unveiling students’ explorations of tessellations with Scratch through mathematical aesthetics. International Journal of Mathematical Education in Science and Technology, 1–19. https://doi.org/10.1080/0020739X.2021.2021306
  17. Goldman, S. R. (2009). Explorations of relationships among learners, tasks, and learning. Learning and Instruction, 19(5), 451–454. https://doi.org/10.1016/j.learninstruc.2009.02.006
  18. Groher, I., Vierhauser, M., Sabitzer, B., Kuka, L., Hofer, A., & Muster, D. (2022). Exploring diversity in introductory programming classes: An experience report. 2022 IEEE/ACM 44th International Conference on Software Engineering: Software Engineering Education and Training (ICSE-SEET), 102–112. https://doi.org/10.1109/ICSE-SEET55299.2022.9794193
  19. Hariati, A., & Septiadi, D. D. (2019). Analysis of students’ mistakes in solving system of linear equation in three variables: A case on HOTS problems. International Journal on Teaching and Learning Mathematics, 2(1), 29. https://doi.org/10.18860/ijtlm.v2i1.7616
  20. Hendroanto, A., van Galen, F., Van Eerde, D., Prahmana, R. C. I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029. https://doi.org/10.1088/1742-6596/943/1/012029
  21. Hulse, T., Daigle, M., Manzo, D., Braith, L., Harrison, A., & Ottmar, E. (2019). From here to there! Elementary: A game-based approach to developing number sense and early algebraic understanding. Educational Technology Research and Development, 67(2), 423–441. https://doi.org/10.1007/s11423-019-09653-8
  22. Klasa, J. (2010). A few pedagogical designs in linear algebra with Cabri and Maple. Linear Algebra and Its Applications, 432(8), 2100–2111. https://doi.org/10.1016/j.laa.2009.08.039
  23. Kurtulus, A., & Uygan, C. (2010). The effects of Google Sketchup based geometry activities and projects on spatial visualization ability of student mathematics teachers. Procedia - Social and Behavioral Sciences, 9, 384–389. https://doi.org/10.1016/j.sbspro.2010.12.169
  24. Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6, 283–317. https://doi.org/10.1023/A:1013309728825
  25. Laksmiwati, P. A. (2015, May 17). Developing Interactive Cabri 3D Assitance Media in Three-Dimensional Space For Grade X Students Of Senior High School Using Guided Inquiry Learning. Recent Innovative Issues and Findings on the Development and the Education of Mathematics and Science. 2nd ICRIEMS The 2nd International Conference on Research, Implementation and Education of Mathematics and Science, Yogyakarta, Indonesia.
  26. Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM, 43(3), 325–336. https://doi.org/10.1007/s11858-011-0329-2
  27. McKenney, S., & Reeves, T. C. (2020). Educational design research: Portraying, conducting, and enhancing productive scholarship. Medical Education, 55(1), 82–92. https://doi.org/10.1111/medu.14280
  28. Moreau, S., & Coquin-Viennot, D. (2003). Comprehension of arithmetic word problems by fifth‐grade pupils: Representations and selection of information. British Journal of Educational Psychology, 73, 109–121. https://doi.org/10.1348/000709903762869941
  29. Ng, O.-L., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: Dynamic geometry and 3D printing. International Journal of STEM Education, 7(1), 50. https://doi.org/10.1186/s40594-020-00244-1
  30. Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. Problems of Education in the 21st Century, 77(1), 82–96. https://doi.org/10.33225/pec/19.77.82
  31. Ozdemir, G. (2010). Exploring visuospatial thinking in learning about mineralogy: spatial orientation ability and spatial visualization ability. International Journal of Science and Mathematics Education, 8(4), 737–759. https://doi.org/10.1007/s10763-009-9183-x
  32. Patchan, M. M., Hawk, B., Stevens, C. A., & Schunn, C. D. (2013). The effects of skill diversity on commenting and revisions. Instructional Science, 41(2), 381–405. https://doi.org/10.1007/s11251-012-9236-3
  33. Patton, M. Q. (1987). How to use qualitative methods in evaluation. Sage.
  34. Prahmana, R. C. I., & D'Ambrosio, U. (2020). Learning geometry and values from patterns: Ethnomathematics on the batik patterns of Yogyakarta, Indonesia. Journal on Mathematics Education, 11(3), 439-456. https://doi.org/10.22342/jme.11.3.12949.439-456
  35. Prediger, S., & Buró, R. (2021). Fifty ways to work with students’ diverse abilities? A video study on inclusive teaching practices in secondary mathematics classrooms. International Journal of Inclusive Education, 1–20. https://doi.org/10.1080/13603116.2021.1925361
  36. Ra, S., Shrestha, U., Khatiwada, S., Yoon, S. W., & Kwon, K. (2019). The rise of technology and impact on skills. International Journal of Training Research, 17(sup1), 26–40. https://doi.org/10.1080/14480220.2019.1629727
  37. Şahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers’ pedagogical content knowledge on fractions in terms of students’ mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178
  38. Silmi Juman, Z. A. M., Mathavan, M., Ambegedara, A. S., & Udagedara, I. G. K. (2022). Difficulties in learning geometry component in mathematics and active-based learning methods to overcome the difficulties. Shanlax International Journal of Education, 10(2), 41–58. https://doi.org/10.34293/education.v10i2.4299
  39. Straesser, R. (2001). Cabri-géomètre: Does dynamic geometry software (dgs) change geometry and its teaching and learning? International Journal of Computers for Mathematical Learning, 6, 319–333. https://doi.org/10.1023/A:1013361712895
  40. Sukirwan, Darhim, Herman, T., & Prahmana, R. C. I. (2018). The students’ mathematical argumentation in geometry. Journal of Physics: Conference Series, 943(1), 012026. https://doi.org/10.1088/1742-6596/943/1/012026
  41. Tatar, E., Akkaya, A., & Kağizmanli, T. B. (2014). Using dynamic software in mathematics: The case of reflection symmetry. International Journal of Mathematical Education in Science and Technology, 45(7), 980–995. https://doi.org/10.1080/0020739X.2014.902129
  42. Tatsuoka, K. K., Corter, J. E., & Tatsuoka, C. (2004). Patterns of diagnosed mathematical content and process skills in TIMSS-R across a sample of 20 countries. American Educational Research Journal, 41(4), 901–926. https://doi.org/10.3102/00028312041004901
  43. Temsah, L. O., & Moukarzel, D. M. (2018). Effect of technology on elementary students’ reasoning & communication skills in science at Lebanese private schools: An exploratory study. European Scientific Journal, ESJ, 14(25), 107. https://doi.org/10.19044/esj.2018.v14n25p107
  44. Tikoo, M. (1998). Integrating geometry in a meaningful way (a point of view). International Journal of Mathematical Education in Science and Technology, 29(5), 663–675. https://doi.org/10.1080/0020739980290503
  45. Tutak, T., Türkdoğan, A., & Birgin, O. (2009). The effect of geometry teaching with cabri to learning levels of fourth grade students. Physical Sciences, 4(2), 26–35. https://dergipark.org.tr/en/download/article-file/365356
  46. Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. Journal for Research in Mathematics Education, 13(1), 65-80. https://ucsmp.uchicago.edu/resources/van_hiele_levels.pdf
  47. van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145–160. https://doi.org/10.1177/0731948712438558
  48. Voyer, D. (2011). Performance in mathematical problem solving as a function of comprehension and arithmetic skills. International Journal of Science and Mathematics Education, 9(5), 1073–1092. https://doi.org/10.1007/s10763-010-9239-y
  49. Watson, R. (1973). Semi-Regular Tessellations. The Mathematical Gazette, 57(401), 186–188. https://doi.org/10.2307/3615563
  50. White, D. Y. (2003). Promoting productive mathematical classroom discourse with diverse students. The Journal of Mathematical Behavior, 22(1), 37–53. https://doi.org/10.1016/S0732-3123(03)00003-8

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