ارزیابی تفکر تبدیلات هندسی دانشجو معلمان: تحلیل مبتنی بر نظریه ون هیلی با استفاده از روش علوم شناختیِ ردیاب چشم

قربانی, مجتبی; ایزدی, فاطمه سادات; روشن, ستاره سادات; ابراهیم پور, رضا

doi:10.22061/tej.2023.10350.2997

نوع مقاله : مقاله پژوهشی-شماره انگلیسی

نویسندگان

¹ گروه ریاضی، دانشکده علوم پایه، دانشگاه تربیت دبیر شهید رجائی، تهران، ایران

² گروه هوش مصنوعی، دانشکده مهندسی کامپیوتر، دانشگاه تربیت دبیر شهید رجائی، تهران، ایران

³ مرکز علوم شناختی، پژوهشکده جامع علوم و فناوری‌های همگرا، دانشگاه صنعتی شریف، تهران، ایران

https://doi.org/10.22061/tej.2023.10350.2997

چکیده

پیشینه و اهداف: تبدیلات هندسی در طول تاریخ نقش مهمی در جنبه‌های مختلف زندگی بشر داشته‌اند. تقارن یکی از مفاهیم مهم در ریاضیات مدرسه است. واضح است که عملکرد تحصیلی دانش‌آموزان به طور پیچیده‌ای با دانش و مهارت‌های مربیان آن‌ها مرتبط است. با توجه به اهمیت نقش دانشجو معلمان به عنوان مربیان آینده، در مرحله اول، هدف این تحقیق بررسی و ارزیابی سطوح تفکر تبدیلات هندسی در بین دانشجو معلمان ابتدایی بر اساس نظریه یادگیری ون هیلی است. پس از آن، این تحقیق به دنبال بررسی فرآیند تفکر و ارزیابی الگوهای نگاه دانشجو معلمان آموزش ریاضی به عنوان گروه متخصص، با استفاده از روش علوم شناختیِ ردیاب چشم است.
روش‌ها‌: این مطالعه به بررسی و ارزیابی تفکر تبدیلات هندسی و مهارت‌های حل مسئله در میان دانشجو معلمان متمرکز است. روش تحقیق مورد استفاده پیمایشی آمیخته است. نمونه آماری در دسترس شامل 50 دانشجو معلم ابتدایی و 21 دانشجو معلم آموزش ریاضی ایرانی است. دانشجو معلمان ابتدایی از دانشگاه فرهنگیان اصفهان انتخاب شده‌ و به دو گروه شامل 42 نفر از دانشجویانی که مفهوم تبدیلات هندسی را در مقطع کارشناسی نیاموخته بودند و 8 نفر از دانشجویانی که این مفهوم را در مقطع کارشناسی آموخته بودند، تقسیم شدند. برای بررسی سطح تفکر هندسی شرکت‌کنندگان، از آزمونی محقق ساخته بر اساس نظریه ون هیلی استفاده شد. پایایی آزمون با استفاده از ضریب آلفای کرونباخ ارزیابی شد که مقدار 0.68 بدست آمد. روایی آزمون نیز توسط اساتید مورد تایید قرار گرفت. در ارزیابی تفکر هندسی، یکی از روش‌های علوم شناختی به کار گرفته شد. این روش شامل طراحی آزمون روان-فیزیک همراه ثبت حرکات چشم در گروه دانشجو معلمان آموزش ریاضی بود. آزمون روان-فیزیک در آزمایشگاه کامپیوتر دانشگاه تربیت معلم شهید رجایی تهران با دستگاه Eyelink و نرم افزار MATLAB بر روی دانشجو معلمان آموزش ریاضی این دانشگاه، انجام شد.
یافته‌ها: یافته‌های تحقیق نشان داد که دانشجویان، شکل با تقارن را به عنوان شکل متقارن تشخیص می‌دهند، اما در تعیین نوع تقارن اشکال متقارن عملکرد ضعیفی دارند، به ویژه زمانی که یک شکل دارای تقارن چرخشی یا تقارن محوری مایل یا ترکیبی از چندین نوع تقارن باشد. 34% از دانشجو معلمان آموزش ابتدایی در سطح اول و 18% در سطح دوم نظریه ون هیلی قرار گرفتند. یافته‌های شناختی نشان داد که دانشجو معلمان آموزش ریاضی در تشخیص اشکال متقارنی که با یک نوع تقارن مشخص شده‌اند نسبت به شکل‌هایی که شامل ترکیبی از تقارن‌های مختلف هستند، عملکرد نسبتا موفق‌تری داشته‌اند. بررسی تصاویر ثبت‌شده ردیابی چشم دانشجویان، تمایزی را در الگوهای نگاه، بین گروه‌هایی که پاسخ‌های درست و نادرست در ارائه می‌دادند، نشان داد. علاوه بر این، این تفاوت در بین تصاویر با تقارن‌های مختلف(خطی، مرکزی، چرخشی) نیز مشهود است.
نتیجه‌گیری: پژوهش حاضر ضعف دانشجو معلمان در شناسایی نوع تقارن در اشکال را تائید می‌کند. همچنین بر نیاز به توجه بیشتر به امور برای رسیدگی به این موضوع، پیشنهاد می‌شود که برنامه درسی مربوط به تبدیلات هندسی در دوره‌ آموزشی دانشگاه دانشجو معلمان مورد بازنگری قرار گیرد. علاوه بر این، استفاده از نرم‌افزارهایی مانند واقعیت افزوده و جئوجبرا می‌تواند به افزایش توانایی‌های شناختی و بصری دانشجو معلمان در درک و تشخیص مفهوم تقارن کمک کند.

کلیدواژه‌ها

موضوعات

علوم شناختی

عنوان مقاله [English]

Assessing Prospective Teachers' Geometric Transformations Thinking: A Van Hiele Theory-Based Analysis with Eye Tracking Cognitive Science Method

نویسندگان [English]

M. Ghorbani ¹
F.S Izadi ¹
S.S Roshan ²
R Ebrahimpour ³

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

چکیده [English]

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

کلیدواژه‌ها [English]

Transformations
Rotational Symmetry
Central Symmetry
Prospective Teacher
Cognitive Science

COPYRIGHTS
© 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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