Students’ and Lecturers’ Perceptions of Students’ Difficulties in Geometry Courses
Abstract
Geometry is one of the compulsory courses that should be taken by students majoring in Mathematics. In the Foundations of Geometry (MAT123) course, proving is one of the most important mathematical problem-solving techniques. Students must comprehend several theorems, definitions and basic concepts of Geometry, as well as how to use the two-column proof method. It's crucial to understand the concept of proof in problem-solving because it'll be used throughout the MAT123 syllabus. However, it has been discovered that students have difficulty answering questions related to proving. In addition, the Covid-19 pandemic makes it more difficult for lecturers to teach how to solve each proving question to students via online distance learning. Hence, to speed up the process of understanding the proving technique, both lecturers' and students' perceptions are needed to discover the best teaching technique for the MAT123 courses.
References
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Amaludin Septiriadi Argawi, Heni Pujiastuti, Analisis Kemampuan Pemahaman Konsep Matematis Siswa Sekolah Dasar Pada Masa Pandemi Covid-19, Al Khawarizmi: Jurnal Pendidikan danPembelajaran Matematika. ISSN 2549-3906E-ISSN 2549-3914
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Blanton, M. L., Stylianou, D. A., David, M. M. (2003). The nature of scaffolding in undergraduate students’ transition to mathematical proof. N. Pateman, B. Dougherty, J. Zilliox (Eds.), Proceedings of the 27th Annual Meeting for the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 113-120). Honolulu: University of Hawaii.
Dhawan, S. (2020). Online Learning: A Panacea in the Time of Covid-19 Crisis. Journal of Educational Technologies Systems Vol 49(1), 5-22.
Donnelly, S. & Parmar, R. (2022). A Comparison of IXL Math Online Software and Textbook Problems for Homework In An Urban Middle School. Journal of Computers in Mathematics and Science Teaching, 41(1), 45-67. Waynesville, NC USA: Association for the Advancement of Computing in Education (AACE). Retrieved June 24, 2022 from https://www.learntechlib.org/p/219062.
Ferrie Jane Bactung-Arostique, The Influence of Learning Style andTest Anxiety on Students' Performance in Mathematics, International Journal of Advanced Research in Engineering and Technology, 13(4), 2022, pp. 12-21. https://doi.org/10.34218/IJARET.13.4.2022.002
Hanna, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics. 15(3), 42-49.
Hanna, G., de Villiers, M. (2008). ICMI Study 19: Proof and proving in mathematics education. ZDM Mathematics Education. 40(2), 329-336.
Hazzan, O., Zazkis, R. (2003). Mimicry of proofs with computers: The case of linear algebra. International Journal of Mathematics Education in Science and Technology. 34, 385-402.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education. 31(4), 396-428.
Herbst, P.G. (2002). Engaging students in proving: a double bind on the teacher. Journal for Research in Mathematics Education. 33(3), 176-203.
Hussin, C. H. C., Juhan, N., Lasaraiya,S., & Nasrullah, A. A. (2021). Students' Perspectives In Studying Mathematics Subject Through ELearning Tools At Foundation Education Level. Journal of Information System and Technology Management, 6 (23), 108-117. DOI: 10.35631/JISTM.623004
Jones, K. (1997). Student teachers’ conceptions of mathematical proof. Mathematics Education Review. 9, 21-32.
Justice Banson, Arthur-Nyarko Emmanuel, Interactive courseware and academic performance in geometry injunior high schools. British Journal of EducationVol. 9, Issue 9, pp.31-54, 2021. https://doi.org/10.37745/bje.2013
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Kuchemann, D., & Hoyles, C. (1999). The Longitudinal Proof Project. A Longitudinal Study of Mathematical Reasoning: Student Development and School Influences.
Lamport, L. (2012). How to write a 21st century proof. Journal of Fixed Point Theory and Applications. 11, 43-63.
Libasin, Z., Azudin, A. R., Idris, N. A., Rahman, M. S. A., & Umar, N. (2021). Comparison of Students’ Academic Performance in Mathematics Course with Synchronous and Asynchronous Online Learning Environments during COVID-19 Crisis. International Journal of Academic Research in Progressive Education and Development, 10(2), 492–501. http://dx.doi.org/10.6007/IJARPED/v10-i2/10131 DOI:10.6007/IJARPED/v10-i2/10131
Marty, R. H. (1986). Teaching proof techniques. Mathematics in college (Spring/Summer), 46-53.
Martin, W.G. & Harel, G. (1989) Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education. 20(1), 41-51.
Moore, R.C. (1994). Making the transition to formal proof. Educational Studies in Mathematics. 27(3), 249-266.
Patkin, D. (2011). High school students’ perceptions of geometrical proofs proving and refuting geometrical claims of the ‘for ever …’ and ‘there exists’ type. International Journal of Mathematics Education in Science and Technology. 43(8), 985-998.
Pfeiffer, K. (2010). The role of proof validation in students’ mathematical learning. MSOR Connections. 10(2), 17-21.
Pokorný, M., 2021. E-Learning in Manipulative Geometry Teaching. In: The 17th International Scientific Conference eLearning and Software for Education Bucharest. Carol I National Defence University Publishing House, pp.247-252.
Selden, A., Selden, J. (2003). Validations of proofs considered as texts: can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education. 34(1), 4-36.
Stavrou, S. G. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.
Stylianides, A. J. (2009). Breaking the Equation. Mathematics Teaching. 213, 9-14.
Stylianides, A. J., & Al-Murani, T. (2010). Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation. Research in Mathematics Education. 12(1), 21-36.
Tucker, T.W. (1999). On the role of proof in calculus courses. Contemporary Issues in Mathematics Education MSRI Publications. 36, 31-36.
Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal. 20(2), 5-24.
Varghese, T. (2009). Secondary-level student teachers’ conceptions of mathematical proof. Issues in the Undergraduate Mathematics Preparation of School Teachers. 1, 1-14.
Volminik, J. D. (1990). The nature and role of proof in mathematics education. Pythagoras. 23, 7-10.
Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education. 39(4), 431-459.
Weber, K., Alcock, L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics. 25(1), 34-38.
Wing-Kwong Wong, Sheng-Kai Yin, Hsi-Hsun Yang, & Ying-Hao Cheng. (2011). Using Computer-Assisted Multiple Representations in Learning Geometry Proofs. Journal of Educational Technology & Society, 14(3), 43–54. http://www.jstor.org/stable/jeductechsoci.14.3.43
Amaludin Septiriadi Argawi, Heni Pujiastuti, Analisis Kemampuan Pemahaman Konsep Matematis Siswa Sekolah Dasar Pada Masa Pandemi Covid-19, Al Khawarizmi: Jurnal Pendidikan danPembelajaran Matematika. ISSN 2549-3906E-ISSN 2549-3914
Balacheff, N. (1988). A study of students’ proving processes at the junior high school level. I. Wirszup and R. Streit (Eds.), Proceedings of the Second UCSMP International Conference on Mathematics Education (pp. 284-297). Reston, VA: National Council of Teachers of Mathematics.
Blanton, M. L., Stylianou, D. A., David, M. M. (2003). The nature of scaffolding in undergraduate students’ transition to mathematical proof. N. Pateman, B. Dougherty, J. Zilliox (Eds.), Proceedings of the 27th Annual Meeting for the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 113-120). Honolulu: University of Hawaii.
Dhawan, S. (2020). Online Learning: A Panacea in the Time of Covid-19 Crisis. Journal of Educational Technologies Systems Vol 49(1), 5-22.
Donnelly, S. & Parmar, R. (2022). A Comparison of IXL Math Online Software and Textbook Problems for Homework In An Urban Middle School. Journal of Computers in Mathematics and Science Teaching, 41(1), 45-67. Waynesville, NC USA: Association for the Advancement of Computing in Education (AACE). Retrieved June 24, 2022 from https://www.learntechlib.org/p/219062.
Ferrie Jane Bactung-Arostique, The Influence of Learning Style andTest Anxiety on Students' Performance in Mathematics, International Journal of Advanced Research in Engineering and Technology, 13(4), 2022, pp. 12-21. https://doi.org/10.34218/IJARET.13.4.2022.002
Hanna, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics. 15(3), 42-49.
Hanna, G., de Villiers, M. (2008). ICMI Study 19: Proof and proving in mathematics education. ZDM Mathematics Education. 40(2), 329-336.
Hazzan, O., Zazkis, R. (2003). Mimicry of proofs with computers: The case of linear algebra. International Journal of Mathematics Education in Science and Technology. 34, 385-402.
Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education. 31(4), 396-428.
Herbst, P.G. (2002). Engaging students in proving: a double bind on the teacher. Journal for Research in Mathematics Education. 33(3), 176-203.
Hussin, C. H. C., Juhan, N., Lasaraiya,S., & Nasrullah, A. A. (2021). Students' Perspectives In Studying Mathematics Subject Through ELearning Tools At Foundation Education Level. Journal of Information System and Technology Management, 6 (23), 108-117. DOI: 10.35631/JISTM.623004
Jones, K. (1997). Student teachers’ conceptions of mathematical proof. Mathematics Education Review. 9, 21-32.
Justice Banson, Arthur-Nyarko Emmanuel, Interactive courseware and academic performance in geometry injunior high schools. British Journal of EducationVol. 9, Issue 9, pp.31-54, 2021. https://doi.org/10.37745/bje.2013
Knuth, E.J. (2002). School mathematics teachers’ conception of proof. Journal for Research in Mathematics Education. 33(5), 379-405.
Kuchemann, D., & Hoyles, C. (1999). The Longitudinal Proof Project. A Longitudinal Study of Mathematical Reasoning: Student Development and School Influences.
Lamport, L. (2012). How to write a 21st century proof. Journal of Fixed Point Theory and Applications. 11, 43-63.
Libasin, Z., Azudin, A. R., Idris, N. A., Rahman, M. S. A., & Umar, N. (2021). Comparison of Students’ Academic Performance in Mathematics Course with Synchronous and Asynchronous Online Learning Environments during COVID-19 Crisis. International Journal of Academic Research in Progressive Education and Development, 10(2), 492–501. http://dx.doi.org/10.6007/IJARPED/v10-i2/10131 DOI:10.6007/IJARPED/v10-i2/10131
Marty, R. H. (1986). Teaching proof techniques. Mathematics in college (Spring/Summer), 46-53.
Martin, W.G. & Harel, G. (1989) Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education. 20(1), 41-51.
Moore, R.C. (1994). Making the transition to formal proof. Educational Studies in Mathematics. 27(3), 249-266.
Patkin, D. (2011). High school students’ perceptions of geometrical proofs proving and refuting geometrical claims of the ‘for ever …’ and ‘there exists’ type. International Journal of Mathematics Education in Science and Technology. 43(8), 985-998.
Pfeiffer, K. (2010). The role of proof validation in students’ mathematical learning. MSOR Connections. 10(2), 17-21.
Pokorný, M., 2021. E-Learning in Manipulative Geometry Teaching. In: The 17th International Scientific Conference eLearning and Software for Education Bucharest. Carol I National Defence University Publishing House, pp.247-252.
Selden, A., Selden, J. (2003). Validations of proofs considered as texts: can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education. 34(1), 4-36.
Stavrou, S. G. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1.
Stylianides, A. J. (2009). Breaking the Equation. Mathematics Teaching. 213, 9-14.
Stylianides, A. J., & Al-Murani, T. (2010). Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation. Research in Mathematics Education. 12(1), 21-36.
Tucker, T.W. (1999). On the role of proof in calculus courses. Contemporary Issues in Mathematics Education MSRI Publications. 36, 31-36.
Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal. 20(2), 5-24.
Varghese, T. (2009). Secondary-level student teachers’ conceptions of mathematical proof. Issues in the Undergraduate Mathematics Preparation of School Teachers. 1, 1-14.
Volminik, J. D. (1990). The nature and role of proof in mathematics education. Pythagoras. 23, 7-10.
Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education. 39(4), 431-459.
Weber, K., Alcock, L. (2005). Using warranted implications to understand and validate proofs. For the Learning of Mathematics. 25(1), 34-38.
Wing-Kwong Wong, Sheng-Kai Yin, Hsi-Hsun Yang, & Ying-Hao Cheng. (2011). Using Computer-Assisted Multiple Representations in Learning Geometry Proofs. Journal of Educational Technology & Society, 14(3), 43–54. http://www.jstor.org/stable/jeductechsoci.14.3.43
Published
2022-06-30
How to Cite
JUMADI, Azlina et al.
Students’ and Lecturers’ Perceptions of Students’ Difficulties in Geometry Courses.
International Journal of Advanced Research in Education and Society, [S.l.], v. 4, n. 2, p. 50-64, june 2022.
ISSN 2682-8138.
Available at: <https://myjms.mohe.gov.my/index.php/ijares/article/view/18612>. Date accessed: 02 dec. 2023.
Section
Articles
