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Abstract

Mathematical proofs play a paramount role in developing 21st-century skills, and the use of technology in mathematics learning has widely paved the way in the instruction of mathematical proofs. In mathematics education, GeoGebra has a significant role as a dynamic mathematics software in supporting students' learning process. This study aims to use GeoGebra in supporting prospective elementary teachers' mathematical proofs of the volume of 3-D shapes. This research used a case study method with 23 first-year prospective elementary teachers as participants from a public university in Riau, Indonesia.  The data were gathered by means of students' work recordings in the GeoGebra classroom and video recordings from their interactions in the course of small group and classroom discussions. The videos were transcribed using verbatim, and then the mathematical proofs were analyzed using praxeological analysis. The findings show that prospective elementary teachers still had challenges to connect the construction of the volume of 3-D shapes using GeoGebra to its informal mathematical proofs. However, GeoGebra provides an opportunity to learn informal mathematical proofs for prospective elementary teachers.

Keywords

3D-Shapes GeoGebra Mathematical Proofs Prospective Elementary Teachers

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Putra, Z. H., Afrillia, Y. M., Dahnilsyah, & Tjoe, H. (2023). Prospective elementary teachers’ informal mathematical proof using GeoGebra: The case of 3D shapes. Journal on Mathematics Education, 14(3), 449–468. https://doi.org/10.22342/jme.v14i3.pp449-468
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References

  1. Azzouni, J. (2009). Why do informal proofs conform to formal norms? Foundations of Science, 14(1–2), 9–26. https://doi.org/10.1007/s10699-008-9144-9
  2. Baker, D., & Campbell, C. (2004). Fostering the development of mathematical thinking: Observations from a proofs course. PRIMUS, 14(4), 345–353. https://doi.org/10.1080/10511970408984098
  3. Balacheff, N., & Boy de la Tour, T. (2019). Proof technology and learning in mathematics: Common issues and perspectives. In G. Hanna, D. A. Reid, & M. de Villiers (Eds.), Proof Technology in Mathematics Research and Teaching (pp. 349–365). Springer.
  4. Bittinger, M. L., & Beecher, J. (2012). Developmental mathematics: College mathematics and introductory algebra (8th edition). Pearson Education Inc.
  5. Bosch, M., & Gascón, J. (2006). Twenty-Five Years of the Didactic Transposition. ICMI Bulletin, 58, 51–65.
  6. Brzezinski, T. (2022). Volume: Intutituve introduction. GeoGebra. https://www.geogebra.org/m/dp6ghmvv
  7. Bulut, M., Akçakın, H. Ü., Kaya, G., & Akçakın, V. (2015). The effects of GeoGebra on third-grade primary students' academic achievement in fractions. Mathematics Education, 11(2), 327–335. https://doi.org/10.12973/iser.2016.2109a
  8. Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. Recherches En Didactique Des Mathematiques, 131–168.
  9. Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IV Congress of the European Society for Research in Mathematics Education (pp. 21–30). La Pensée Sauvage.
  10. Christou, C., & Papageorgiou, E. (2007). A framework of mathematics inductive reasoning. Learning and Instruction, 17(1), 55–66. https://doi.org/10.1016/j.learninstruc.2006.11.009
  11. De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703–724. https://doi.org/10.1080/0020739042000232556
  12. Dhakal, B. P. (2022). The volume of pyramids (method 1). GeoGebra. https://www.geogebra.org/m/jwf5y73q
  13. Faris, M. N. (2018). Using technology in mathematics discover and prove Pythagorean theorem with GeoGebra. Proceedings of the 2nd International Conference on Learning Innovation, 21–25. https://doi.org/10.5220/0008407200210025
  14. Gerring, J. (2007). Case study research: Principles and practices. Cambridge University Press.
  15. Guerrero, F. G. (2018). An interactive approach for illustrating a proof of the sampling theorem using MATHEMATICA. Computer Applications in Engineering Education, 26(6), 2282–2293. https://doi.org/10.1002/cae.22041
  16. Hausberger, T. (2018). Structuralist praxeologies as a research program on the teaching and learning of abstract algebra. International Journal of Research in Undergraduate Mathematics Education, 4(1), 74–93. https://doi.org/10.1007/s40753-017-0063-4
  17. Heale, R., & Twycross, A. (2018). What is a case study? Evidence-Based Nursing, 21(1), 7–8. https://doi.org/10.1136/eb-2017-102845
  18. Hohenwarter, M., & Fuchs, K. (2005). Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. In Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching (Sarvari, Cs. Hrsg.) (pp. 128–133).
  19. Jankvist, U. T., & Misfeldt, M. (2019). CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks. Journal of Research in Mathematics Education, 8(3), 232. https://doi.org/10.17583/redimat.2019.3315
  20. Jovignot, J., Hausberger, T., & Durand-Guerrier, V. (2017). Praxeological analysis: the case of ideals in ring theory. Proceeding of 10th Congress on European Research in Mathematics Education, 2113–2120.
  21. Kemendikbudristek. (2022). Keputusan kepala Badan Standar Kurikulum dan Asesmen Pendidikan Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi nomor 008/H/KR/2022 tentang capaian pembelajaran PAUD SD SMP SMA SMK pada kurikulum merdeka. Kemendikbudristek. https://kurikulum.kemdikbud.go.id/wp-content/unduhan/CP_2022.pdf
  22. Kondratieva, M., & Winsløw, C. (2017). A praxeological approach to Klein's plan B: Cross-cutting from calculus to Fourier analysis. Proceeding of 10th Congress on European Research in Mathematics Education.
  23. Magana, A. J. (2014). Learning strategies and multimedia techniques for scaffolding size and scale cognition. Computers and Education, 72, 367–377. https://doi.org/10.1016/j.compedu.2013.11.012
  24. Marfori, M. A. (2010). Informal proofs and mathematical rigour. Studia Logica, 96(2), 261–272. https://doi.org/10.1007/s11225-010-9280-4
  25. Mata-Pereira, J., & da Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. https://doi.org/10.1007/s10649-017-9773-4
  26. Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266. https://doi.org/10.1007/BF01273731
  27. Nyaumwe, L., & Buzuzi, G. (2007). Teachers' attitudes towards proof of mathematical results in the secondary school curriculum: The case of Zimbabwe. Mathematics Education Research Journal, 19(3), 21–32. https://doi.org/10.1007/BF03217460
  28. Pólya, G. (1990). Mathematics and plausible reasoning: Induction and analogy in mathematics. Princeton University Press.
  29. Putra, Z. H. (2019). Praxeological change and the density of rational numbers: The case of pre-service teachers in Denmark and Indonesia. EURASIA Journal of Mathematics, Science and Technology Education, 15(5), 1–15. https://doi.org/10.29333/ejmste/105867
  30. Putra, Z. H., Hermita, N., Alim, J. A., Dahnilsyah, D., & Hidayat, R. (2021). GeoGebra integration in elementary initial teacher training: The case of 3-D shapes. International Journal of Interactive Mobile Technologies, 15(19), 21–32. https://doi.org/10.3991/ijim.v15i19.23773
  31. Radović, S., Radojičić, M., Veljković, K., & Marić, M. (2020). Examining the effects of GeoGebra applets on mathematics learning using interactive mathematics textbook. Interactive Learning Environments, 28(1), 32–49. https://doi.org/10.1080/10494820.2018.1512001
  32. Ramsay, D. (2022). The volume of a cylinder vs a cone. GeoGebra. https://www.geogebra.org/m/xfQcUDkE
  33. Rasmussen, K. (2016). Lesson study in prospective mathematics teacher education: didactic and para didactic technology in the post-lesson reflection. Journal of Mathematics Teacher Education, 19(4), 301–324. https://doi.org/10.1007/s10857-015-9299-6
  34. Reflina, R. (2020). Kesulitan mahasiswa calon guru matematika dalam menyelesaikan soal pembuktian matematis pada mata kuliah geometri. Jurnal Analisa, 6(1), 80–90. https://doi.org/https://doi.org/10.15575/ja.v6i1.6607
  35. Siswono, T. Y. E., Hartono, S., & Kohar, A. W. (2020). Deductive or inductive? prospective teachers’ preference of proof method on an intermediate proof task. Journal on Mathematics Education, 11(3), 417–438. https://doi.org/10.22342/jme.11.3.11846.417-438
  36. Sjögren, J. (2010). A note on the relation between formal and informal proof. Acta Analytica, 25(4), 447–458. https://doi.org/10.1007/s12136-009-0084-y
  37. Stefanowicz, A., Kyle, J., & Grove, M. (2014). Proofs and mathematical reasoning. In the University of Birmingham.
  38. Sumardyono, S. (2018). Teacher’s ability in compiling mathematical proof. Indonesian Digital Journal of Mathematics and Education, 5(8), 510–522.
  39. Sümmermann, M. L., Sommerhoff, D., & Rott, B. (2021). Mathematics in the digital age: The case of simulation-based proofs. International Journal of Research in Undergraduate Mathematics Education, 7(3), 438–465. https://doi.org/10.1007/s40753-020-00125-6
  40. Syamsuri, S., Marethi, I., & Mutaqin, A. (2018). Understanding of strategies for teaching mathematical proof to undergraduate students. Jurnal Cakrawala Pendidikan, 37(2). https://doi.org/10.21831/cp.v37i2.19091
  41. Tamam, B., & Dasari, D. (2021). The use of Geogebra software in teaching mathematics. Journal of Physics: Conference Series, 1882(1), 012042. https://doi.org/10.1088/1742-6596/1882/1/012042
  42. Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. https://doi.org/10.1023/A:1015535614355
  43. Zengin, Y. (2017). The effects of GeoGebra software on pre-service mathematics teachers’ attitudes and views toward proof and proving. International Journal of Mathematical Education in Science and Technology, 48(7), 1002–1022. https://doi.org/10.1080/0020739X.2017.1298855