Document Type : Original Research Paper


Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University, Mashhad, Iran


Background and Objectives: Previous studies in Iran have explored the impact of using technology on improving students’ mathematical understanding. However, no study was conducted in relation to the impact of using technology on students’ mathematical misconceptions. This study explored the impact of using software in developing students’ misconceptions. In detail, the impact of using GeoGebra software on secondary school students’ misconceptions related to concepts such as angle scale, trigonometric angles, periodicity, minimum and maximum of trigonometric functions were explored using a two-tier diagnostic test. One of the novelties of this study is the use of a two-tier diagnostic test to explore misconceptions resulting from using the software.
Methods: The statistical population of this study comprises all grade 11 students of Golbahar and Golmakan in the academic year 2015-2016. Three classes were chosen from two different schools in these cities, one was considered as the control group (40 students) and the other two classes were considered as the experimental group (26 students). The instruments were a pre-test and a post-test (two-tier diagnostic test).‎ Four categories of misconceptions were identified based on the relevant literature and students’ responses to the pre-test. Finally, these misconceptions were analyzed by the chi-square test.
Findings: The findings showed that Geogebra software helped students in the experimental group enormously in understanding concepts such as periodicity‎, ‎identifying minimum and maximum of trigonometric functions‎, ‎and prevented developing misconceptions related to them. Analyzing students’ responses in the control group that received traditional teaching showed that several students did not able to calculate the periodicity of trigonometric functions. This difficulty observed both when students calculated the periodicity from the graphs and also when calculated the periodicity from the algebraic form of trigonometric functions. The strength of using the software includes observing many trigonometric graphs in the software environment, the ability to place trigonometric functions with different input on a coordinate axis and comparing them, and the manipulations performed by the students themselves on trigonometric graphs. These strengths prevented students from developing misconceptions about the concepts of frequency and minimum and maximum values. However, in relation to trigonometric angles‎, ‎using the software caused developing more misconceptions for the test group, and had no significant impact on preventing misconceptions in relation to the scale of angle‎. It seems due to the nature of the angle scale, in which the conversion from radians to degrees (or vice versa) is done by a series of mathematical operations, using Geogebra could not impact students’ misconceptions in this matter.
Conclusion: The results of this study indicate that teachers should be very cautious in selecting and using teaching aids in the classroom to prevent developing mathematical misconceptions associated with using the teaching aids. Therefore, we recommend mathematics education researchers and mathematics curriculum planners to conduct several studies on different softwares frequently used in mathematics classes, determine the pros and cons of these tools, and share their results with mathematics teachers. Sharing these results will help mathematics teachers to adapt their teaching accordingly based on the findings of these studies.


Main Subjects

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[3] Demir O. Students’ concept development and understanding of sine and cosine functions. Ankara University Journal of Faculty of Educational Sciences. 20120; 43(1), 97-129.
[4] Brown SA. The trigonometric connection: students’ understanding of sine and cosine. Paper presented at the Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education; 2006.
[6] Alamolhodaei H. Principles of mathematics education(1st ed).Mashhad: Jahane farad; 2010. Persian.
[10] NCTM. Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics; 2000.
[11] Hesam A, Gooya Z. The role of schemas in the formation of students’ misconceptions. Roshd Mathematics Education. 2006;  1(2): 177-200. Persian.
[12] Reyhani E, Hamidi F, RashediF. A study on negative numbers conception of students and their misconceptions. Educational Technology. 2016; 10(2): 115-131. Persian.
[13] Martinez-Sierra G. On the transit from trigonometry to calculus: the case of the conceptual breaks in the construction of the trigonometric functions in school. Paper presented in the 11th International Congress on Mathematical Education; 2008.
[14] Topçu T, Kertil M, Akkoç H, Yilmaz K, & Önder O. Pre-Service and In-Service Mathematics Teachers’ Concept Images of Radian. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Educatio.; 2006. 
[16] Akkoç H, Akbaş Gül N. Analysis of a teaching approach aiming at eliminating student. Ankara University Journal of Faculty of Educational Sciences. 2010; 43(1): 97-129.
[19] Koklu O, Topcu A. Effect of Cabri-assisted instruction on secondary school students’ misconceptions about graphs of quadratic functions. International Journal of Mathematical Education in Science and Technology. 2012; 43(8): 999-1011.   
[20] Khooshecharkh M, Hemmati Nasab, M, Nejad Sadeghi N. The Effect of Using GeoGebra Software on Student’s Math Progress in the Concept of Middle-Level Geometry. Paper presented in the 45th Annual Iranian Mathematics Conference; 2014. Persian.
[21] Heidari Ghezeljeh R, Gooya Z.Integration of “Dynamic Mathematics Software” with formal calculus curriculum in the 11th grade to enhance students’ problem solving abilities.Journal of Curriculum Studies. 2012; 6(24): 83-108. Persian. 
[22] Farmehr F. The Role of Dynamic Geometry Software in Problem Solving, Emphasizing on Conjecture. [master’s dissertation]. Shahid Rajaee Teacher Training Univercity; 2008. Persian. 
[27] Tuysuz C. Development of two-tier diagnostic instrument and assess students’ understanding in chemistry. Scientific Research and Essays. 2009; 4(6): 626-631. 
[28] Tan KCD, Goh NK, Chia LS, Treagust DF. Development and application of a two‐tier multiple choice diagnostic instrument to assess high school students’ understanding of inorganic chemistry qualitative analysis. Journal of research in Science Teaching. 2002; 39(4), 283-301.
[29] Blacket N, Tall DO. Gender and the versatile learning of trigonometry using computer software. Proc. 15th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 144-151). Lisbon, Portugal: PME; 1991.