Document Type : Original Research Paper
Authors
- F. Radmehr ^{} ^{}
- H. Rahimian
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University, Mashhad, Iran
Abstract
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.
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