Mathematical Proving Ability of Pre-service Teachers in Online and Blended Learning
Abstract
Mathematical proving is an important ability to learn. However, mathematics pre-service teachers often find this skill difficult. This research aimed to describe the mathematical proving ability of mathematics pre-service teachers in an online classroom and in the blended classroom. A descriptive mixed methods approach was used. A mathematical proving test was used to collect the data. The results showed that the average score of mathematical proving ability from the blended classroom was 82.6 (categorized as high). Meanwhile, the average score of mathematics pre-service teachers in the online classroom was 65.4 (categorized as intermediate). Given these findings, there is a significant need to improve the mathematical proving ability of the mathematical preservice teachers in the online classroom by enhancing the conceptual understanding of group properties and ensuring the teachers are accustomed to practicing proving tasks.
Keywords: mathematical proving, online learning, blended learning, mathematics pre-service teachers, group theory
References
[1] A.S. Pramasdyahsari, R.D. Setyawati, and I.U. Albab, “How group theory and school mathematics are connected: an identification of mathematics in-service teachers.,” Journal of Physics: Conference Series. vol. 1663, no. 1, pp. 1–10, 2020.
[2] I Isnarto. Kemampuan konstruksi bukti dan berpikir kritis matematis mahasiswa pada perkuliahan struktur aljabar melalui guided discovery learning pendekatan motivation to reasoning and proving tasks
[Dissertation]. Bandung: Universitas Pendidikan Indonesia; 2014.
[3] Findel BR. Learning and understanding in abstract algebra [Dissertation]. University of New Hampshire, New Hampshire; 2001.
[4] Arnawa IM, Yerizon Y, Enita S. Improvement students’ level of proof ability in abstract algebra through APOS theory approach. International Journal of Scientific & Technology Research. 2019;8(7):128-131.
[5] Hanna G, Jahnke HN, Pulte H. Explanation and proof in mathematics. New York: Springer; 2010.
[6] Maya R, Sumarmo U. Mathematical understanding and proving abilities: Experiment with undergraduate student by using modified Moore learning approach. Journal on Mathematics Education. 2011;2(2):231-250.
[7] Selden A, Selden J. Validations of proof considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education. 2003;34(1):4-36.
[8] Stylianides GJ, Stylianides AJ, Philippou GN. Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education. 2007;10(3):145-166.
[9] Ozdemir E, Ovez FTD. A research on proof perceptions and attitudes towards proof and proving: Some implications for elementary mathematics prospective teachers. Procedia-Social and Behavioral Sciences. 2012;46:2121–2125.
[10] S. Cyr, “DEVELOPMENT OF BEGINNING SKILLS IN PROVING AND PROOF-WRITING BY ELEMENTARY SCHOOL STUDENTS.,” In: M. Pytlak, T. Rowland, and E. Swoboda, Eds. Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education. pp. 263–272. University of Rzeszów, Poland (2011).
[11] G. Güler, “The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views.,” Higher Education Studies. vol. 6, no. 1, pp. 145–158, 2016.
[12] Hart EW. Research issues in undergraduate mathematics learning. Kaput JJ, Dubinsky D, editors. Washington: American Mathematical Society; 1994.
[13] Moore RC. Making the transition to formal proof. Educational Studies in Mathematics. 1994;27(3):249-266.
[14] Race P. 500 tips for open and online learning. 500 tips. Taylor & Francis, London; 2008.
[15] Campbell M, Gibson W, Hall A, Richards D, Callery P. Online vs face-to-face discussion in a webbased research methods course for postgraduate nursing students: A quasiexperimental study. International Journal of Nursing Studies. 2008;45(5):750-759.
[16] A. Kitchenham, Blended Learning across Disciplines: Models for Implementation. IGI Global, Pennsylvania , 2011..
[17] Cohen L, Manion L, Morrison K. Research methods in education. London: Routledge; 2007.
[18] Ranjan P. Is blended learning better than online learning for B.Ed students? Journal of Learning for Development. 2020;7(3):349-366.
[19] Smith JG, Suzuki S. Embedded blended learning within an algebra classroom: A multimedia capture experiment. Journal of Computer Assisted Learning. 2015;31(2):133-147.
[20] Beile PM, Boote DN. Library instruction and graduate professional development: Exploring the effect of learning environments on self-efficacy and learning outcomes. Alberta Journal of Educational Research. 2002;48(4):364–367.
[21] W.L.P. Ruchti and M. Odell, Comparison and evaluation of online and classroom instruction in elementary science teaching methods courses. University of Idaho, Idaho , 2001..
[22] Gaddis B, Napierkowski H, Guzman N, Muth R. A comparison of collaborative learning and audience awareness in two computer-mediated writing environments. Paper presented at: 1st Annual Conference ESRC Teaching and Learning Research Programme (TLRP), National Convention of the Association for Educational Communications and Technology; 1-3 Feb 2000; Denver, United States.
[23] Caldwell ER. A comparative study of three instructional modalities in a computer programming course: Traditional instruction, web-based instruction, and online instruction
[Ph.D thesis] University of North Carolina at Greensboro; 2006.
[24] Scoville SA, Buskirk TD. Traditional and virtual microscopy compared experimentally in a classroom setting. Clinical Anatomy. 2007;20(5):565-570.
[25] McNamara JM, Swalm RL, Stearne DJ, Covassin TM. Online weight training. Journal of Strength and Conditioning Research. 2008;22(4):1164-1168.
[26] Weber K. Student difficulty in constructing proofs: The need for strategic knowledge. Education Studies in Mathematics. 2001;48:101-119.
[27] Weber K. Students’ difficulties with proof. Mathematical Association of America, Washington, 2003. Available at: https://www.maa.org/programs/faculty-anddepartments/ curriculum-department-guidelines-recommendations/teaching-andlearning/ research-sampler-8-students-difficulties-with-proof
[28] Harel G, Sowder L. Second handbook of research on mathematical teaching and learning. Lester F, editor. Washington, DC: National Council of Teachers of Mathematics 2007.
[29] Agustyaningrum N, Asmaul H, Yudhi H, Agus MA, Ali M. Analysis of mathematical proof ability in abstract algebra course. Universal Journal of Educational Research. 2020;8(3):823-834.
[30] A.S. Pramasdyahsari and M.R. Rubowo, “PEMAHAMAN KONSEP GRUP MAHASISWA CALON GURU MATEMATIKA DENGAN KEMAMPUAN MATEMATIKA TINGGI.,” Prismatika: Jurnal Pendidikan dan Riset Matematika. vol. 2, no. 2, pp. 71–84, 2020.
[31] Pramasdyahsari AS, Setyawati RD, Albab IU. Connecting university mathematics and school mathematics to address Klein’s double discontinuity: A case of ring theory. Beta: Jurnal Tadris Matematika. 2019;12(2):122–132. https://doi.org/10.20414/betajtm.v12i2.336
[32] Zazkis R, Sinclair N and Liljedahl, P. Lesson play in mathematics education: A tool for research and professional development. Dordrecht: Springer; 2013.
[33] A.S. Pramasdyahsari, “Developing the scripting task for mathematical connection between the university and school mathematics content.,” Journal of Physics: Conference Series. vol. 1957, no. 1, pp. 1–8, 2021..
[34] Suominen AL. Abstract algebra and secondary school mathematics: Identifying and classifying mathematical connections [Dissertation]. University of Georgia, Athens - USA; 2015.
[35] Saefudin AA. Pengembangan kemampuan berpikir kreatif siswa dalam pembelajaran matematika dengan pendekatan pendidikan matematika realistik Indonesia (PMRI). Jurnal Al-Bidayah. 2012;4(1):37-48.
[36] S. Fadillah and J. Jamilah, “PENGEMBANGAN BAHAN AJAR STRUKTUR ALJABAR UNTUK MENINGKATKAN KEMAMPUAN PEMBUKTIAN MATEMATIS MAHASISWA.,” Jurnal Cakrawala Pendidikan. vol. 1, no. 1, pp. 106–113, 2016
[37] S. Chamundeswari, “Conceptual Errors Encountered in Mathematical Operations in Algebra among Students at the Secondary Level.,” IJISET-International Journal of Innovative Science, Engineering & Technology. vol. 1, no. 8, pp. 24–38, 2014