RESEARCH PAPER
The Effect of Proof Format on Reading Comprehension of Geometry Proof: The Case of Indonesian Prospective Mathematics Teachers
 
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1
Institute for Science Education and Communication, University of Groningen, Nijenborgh 7, 9747 AG Groningen, NETHERLANDS
 
2
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Jl. Semarang No.5, Malang, East Java 65145, INDONESIA
 
 
Publication date: 2021-03-18
 
 
EURASIA J. Math., Sci Tech. Ed 2021;17(4):em1952
 
KEYWORDS
ABSTRACT
This study aims to investigate the effects of the use of multiple geometry proof formats on Indonesian students’ reading comprehension of geometry proof (RCGP). Four classes of prospective secondary mathematics teachers (N=125), aged 18 to 19 years, participated in this quasi-experimental study. While the experimental group was instructed in three proof formats (paragraph, two-column and flow-chart proof), the control group was instructed in only the two-column proof format. Similar pre- and post-tests, based on Yang and Lin’s (2008) RCGP test, were administered to both groups. N-Gain scores were used to determine the improvement of both groups. The N-Gain scores showed significantly more improvement of students’ RCGP in the experimental group. More detailed analysis indicated that the use of multiple proof formats supports the students’ understanding of the facets of logical status of statements and the critical ideas in the proof. This study shows the benefits of offering multiple proof formats to support prospective mathematics teachers’ RCGP.
 
REFERENCES (30)
1.
Ahmadpour, F., Reid, D., & Reza Fadaee, M. (2019). Students’ ways of understanding a proof. Mathematical Thinking and Learning, 21(2), 85-104. https://doi.org/10.1080/109860....
 
2.
Brandell, J. (1994). Helping students write paragraph proofs in geometry. Mathematics Teacher, 87(7), 498-502. https://doi.org/10.5951/MT.87.....
 
3.
Cirillo, M., & Herbst, P. G. (2011). Moving toward more authentic proof practices in geometry. Mathematics Educator, 21(2), 11-33.
 
4.
Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64-74. https://doi.org/10.1119/1.1880....
 
5.
Hake, R. R. (2002). Relationship of individual student normalized learning gains in mechanics with gender, high-school physics, and pretest scores on mathematics and spatial visualization. Physics Education Research Conference, 8(1), 1-14.
 
6.
Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3), 283-312. https://doi.org/10.1023/A:1020....
 
7.
Inglis, M., & Aberdein, A. (2015). Beauty is not simplicity: An analysis of mathematicians’ proof appraisals. Philosophia Mathematica, 23(1), 87-109. https://doi.org/10.1093/philma....
 
8.
Knuth, E. J. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61-88. https://doi.org/10.1023/A:1013....
 
9.
Lin, F. L., & Yang, K. L. (2007). The reading comprehension of geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education, 5(4), 729-754. https://doi.org/10.1007/s10763....
 
10.
Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3-18. https://doi.org/10.1007/s10649....
 
11.
Ministry of Education and Culture. (2013). Act Ministry of Education and Culture No. 68 of 2013 about Content Standard for Junior Secondary School. Retrieved from https://lldikti12.ristekdikti.....
 
12.
Ministry of Education and Culture. (2016). Act Ministry of Education and Culture no. 21 of 2016 about Content Standard for Secondary School. Retrieved from https://bsnp-indonesia.org/wp-....
 
13.
Miyazaki, M., Fujita, T., & Jones, K. (2014). Functions of open flow-chart proving in introductory lessons of formal proving. In P. Liljedahl, S. Oesterle, C. Nicol & D. Allan (Eds.), Proceedings of the Joint Meeting of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Group for the Psychology of Mathematics Education (Vol. 4, pp. 225-232). Vancouver, Canada: PME.
 
14.
Miyazaki, M., Fujita, T., & Jones, K. (2015). Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs. ZDM - Mathematics Education, 47(7), 1211-1224. https://doi.org/10.1007/s11858....
 
15.
Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223-239. https://doi.org/10.1007/s10649....
 
16.
National Education Standard Board. (2020). Fokus Pembelajaran SD/MI, SMP/MTs, SMA/MA [Focuses of Learning in Elementary and Secondary School]. In W. Kamdi & B. Suryadi (Eds.), Badan Standar Nasional Pendidikan. Retrieved from https://bsnp-indonesia.org/wpc....
 
17.
Panse, A., Alcock, L., & Inglis, M. (2018). Reading proofs for validation and comprehension: An expert-novice eye-movement study. International Journal of Research in Undergraduate Mathematics Education, 4(3), 357-375. https://doi.org/10.1007/s40753....
 
18.
Pape, S. J. (2004). Middle school children’s problem-solving behavior: A cognitive analysis from a reading. Journal for Research in Mathematics Education, 35(3), 187-219. https://doi.org/10.2307/300349....
 
19.
Pereira-Laird, J. A., & Deane, F. P. (1997). Development and validation of a self-report measure of reading strategy use. Reading Psychology, 18(3), 185-235. https://doi.org/10.1080/027027....
 
20.
Rota, G. (1997). The phenomenology of mathematical beauty. Synthese, 111(2), 171-182. https://doi.org/10.1023/A:1004....
 
21.
Roy, S., Alcock, L., & Inglis, M. (2010). Undergraduates proof comprehension: A comparative study of three forms of proof presentation [Paper presentation]. Proceedings of the 13th Conference on Research in Undergraduate Mathematics Education. Retrieved from http://mathed.asu.edu/crume200....
 
22.
Selden, A. (2012). Transitions and proof and proving at tertiary level. In G. Hanna & M. De Villiers (Eds.), Proof and Proving in Mathematics Education: The 19th ICMI Study (Vol. 15, pp. 391-420). Heidelberg: Springer. https://doi.org/10.1007/978-94....
 
23.
Selden, A., & Selden, J. (2017). A comparison of proof comprehension, proof construction, proof validation and proof evaluation. In R. Göller, R. Biehler, R. Hochmuth, & H. G. Rück (Eds.) Proceedings of kompetenzzentrum hochschuldidaktik mathematik Conference (pp. 339-345). Hanover, Germany: khdm.
 
24.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26. https://doi.org/10.5951/MTMS.1....
 
25.
Weber, K. (2009). Mathematics majors’ evaluation of mathematical arguments and their conception of proof. In Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education. Retrieved from http://sigmaa.maa.org/rume/‌‌c....
 
26.
Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329-344. https://doi.org/10.1007/s10649....
 
27.
Wong, W. K., Yin, S. K., Yang, H. H., & Cheng, Y.-H. (2011). Using computer-assisted multiple representations in learning geometry proofs. Educational Technology and Society, 14(3), 43-54.
 
28.
Yang, K. L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80(3), 307-326. https://doi.org/10.1007/s10649....
 
29.
Yang, K. L., & Lin, F. L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59-76. https://doi.org/10.1007/s10649....
 
30.
Yang, K. L., & Lin, F. L. (2012). Effects of reading-oriented tasks on students’ reading comprehension of geometry proof. Mathematics Education Research Journal, 24(2), 215-238. https://doi.org/10.1007/s13394....
 
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