Document Type : Original Research Paper-English Issue
Authors
1 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
2 Department of Artificial Intelligence, Faculty of Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
3 Center for Cognitive Science, Institute for Convergence Science and Technology, Sharif University of Technology, Tehran, Iran
Abstract
Background and Objectives: Geometric transformations have played a crucial role throughout history in various aspects of human life. Symmetry is one of the important concepts in school mathematics. Students' academic performance is intricately connected to the knowledge and skills of their educators. Recognizing the importance of prospective teachers )PTs( as future educators, in the initial stage, the aim of this research is to assess and analyze the levels of geometric thinking among prospective elementary teachers )PETs( utilizing Van Hiele's theory. Subsequently, the research seeks to delve into the thinking process and gaze patterns of prospective mathematics education teachers (PMETs) using the cognitive science method of eye tracking.
Materials and Methods: This study focuses on investigating and evaluating the thinking of geometric transformations and problem-solving skills among prospective teachers (PTs(. The research method employed a combined survey method, encompassing two distinct tests conducted on two groups of PTs. The accessible statistical sample includes 50 participating PETs and 21 participating PEMTs from Iran. The PETs of Farhangian University of Isfahan were divided into two groups: 42 students who had not learned the concept of geometric transformations in their undergraduate program (NPGT), and 8 students who had learned this concept in their undergraduate program )PGT). To assess the level of geometric thinking among participants, a self-made geometric test based on Van Hiele’s theory was utilized. The test reliability was assessed using Cronbach's alpha coefficient, which yielded a value of 0.68. Additionally, the validity of the test has been confirmed by some professors. In evaluating geometric thinking, a cognitive science method was performed. This method involved designing a psychophysical experiment and recording eye movements of the PMETs. The psychophysical experiment part was conducted in the computer laboratory of Shahid Rajaee Teacher Training University, Tehran, and was performed by Eyelink device and MATLAB software on student teachers of mathematics education of this university.
Findings: The results of the research show that students recognize the shape with symmetry as a symmetrical shape, but they perform poorly in determining the type of symmetry of symmetrical shapes, especially when a shape has rotational symmetry or oblique axial symmetry or a combination of several types of symmetry. In the first stage, the evaluation of PETs responses showed that 34% of them were in the first level and 18% in the second level of Van Hiele. The cognitive findings revealed that PMETs demonstrated superior performance in recognizing symmetries characterized by a single type of symmetry, in contrast to shapes involving combinations of various symmetries. Examining the recorded eye-tracking images of the students revealed a difference in gaze patterns between the groups that gave correct and incorrect answers. In addition, this difference is also evident among images with different symmetries (reflection, central, rotational).
Conclusions: The current research confirms the weakness of students in identifying the type of symmetry in symmetrical shapes. It also emphasizes the need to pay more attention to the training of PTs during their academic years. To address this, it is suggested to revise the curriculum concerning geometric transformations in the university courses for PTs training, additionally, the utilization of software such as Augmented Reality (AR) and GeoGebra can .contribute to enhancing cognitive and visual abilities of PTs in comprehending the concept of symmetry
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© 2024 The Author(s). This is an open-access article distributed under the terms and conditions of the Creative Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)
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