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بررسی تأثیر آموزش تلفیقی مدلسازی ریاضی و نرمافزار GeoGebra بر عملکرد دانشآموزان در یادگیری توابع مثلثاتی: یک مطالعه آمیخته | ||
| فناوری و دانش پژوهی در تعلیم و تربیت | ||
| مقاله 6، دوره 6، شماره 3 - شماره پیاپی 22، مهر 1405، صفحه 73-88 اصل مقاله (936.78 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.30473/t-edu.2026.76688.1379 | ||
| نویسندگان | ||
| سمیرا مهرآئین1؛ علی ایرانمنش* 2؛ محسن رستمی مال خلیفه3؛ محمد حسن بهزادی4 | ||
| 1دانشجوی دکترای، آموزش ریاضی، دانشکده علوم و فناوری های همگرا، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران | ||
| 2استاد، ریاضی محض، دانشکده علوم ریاضی، دانشگاه تربیت مدرس، تهران، ایران | ||
| 3دانشیار، ریاضی کاربردی، دانشکده علوم و فناوری های همگرا، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران | ||
| 4دانشیار، آمار، دانشکده علوم و فناوری های همگرا، واحد علوم وتحقیقات، دانشگاه آزاد اسلامی ، تهران، ایران | ||
| چکیده | ||
| پژوهش حاضر با هدف بررسی تأثیر آموزش مبتنی بر فناوری دیجیتال (GeoGebra) و فعالیتهای مدلسازی ریاضی بر عملکرد دانشآموزان در یادگیری توابع مثلثاتی انجام شد. این مطالعه کاربردی و کمی- کیفی با غلبه رویکرد کمی و طرح نیمهآزمایشی پیشآزمون-پسآزمون با دو گروه اصلی آزمایش و کنترل بود. جامعه آماری شامل دانشآموزان پایه یازدهم بود و نمونه نهایی ۲۷۰ نفر (۱۳۲ دانشآموز در 4 زیر گروه آزمایش و ۱۳۸ دانشآموز در 4 زیر گروه کنترل) بود. ابزار گردآوری دادهها شامل آزمونهای مسئلهمحور مبتنی بر مدلسازی ریاضی و تحلیل عملکرد دانشآموزان بر اساس سطوح مهارت فنی در GeoGebra و سطوح مفهومی مدلسازی بود. گروه آزمایش از طریق فعالیتهای مدلسازی ریاضی مبتنی بر GeoGebra آموزش دید، در حالی که گروه کنترل به روش سنتی و بدون فناوری آموزش داده شد. دادههای کمی با پیشآزمون و پسآزمون جمعآوری و با تحلیل کوواریانس تکمتغیره بررسی شدند. یافته ها نشان دادند آموزش مبتنی بر فناوری و مدلسازی ریاضی عملکرد دانشآموزان را بهطور معنادار بهبود داد (001/0p<) با اندازه اثر بزرگ برای فناوری دیجیتال (715/0 η² =) و مدلسازی ریاضی (712/0η² =). مقایسه عملکرد دو مداخله تفاوت معناداری نشان نداد (339/5 = p)، که حاکی از تأثیر مثبت هر دو رویکرد است. یافتههای کیفی نیز نشان داد دانشآموزان در فرآیند یادگیری فعال و تعامل گروهی، درک مفهومی عمیقتر و مشارکت بیشتری داشتند. در مجموع، نتایج پژوهش نشان میدهد ادغام فناوری دیجیتال و مدلسازی ریاضی میتواند الگویی مؤثر برای آموزش تعاملی و ارتقای عملکرد دانشآموزان در مباحث پیچیده ریاضی ارائه دهد. | ||
| کلیدواژهها | ||
| آموزش تلفیقی؛ مدلسازی مثلثاتی؛ GeoGebra؛ عملکرد دانشآموزان؛ درک مفهومی | ||
| عنوان مقاله [English] | ||
| The Effect of Integrated Mathematical Modeling and GeoGebra on Students’ Learning of Trigonometric Functions: A Mixed-Methods Study | ||
| نویسندگان [English] | ||
| Samira Mehraein1؛ Ali Iranmanesh2؛ Mohsen Rostamy-Malkhalifeh3؛ Mohammad Hassan Behzadi4 | ||
| 1PhD student, Department of Mathematics, Institute of Convergin Sciences and Technologies, SR.C., Islamic Azad University ,Tehran, Iran | ||
| 2Professor, Department of Mathematics, Tarbiat Modares University, Tehran, Iran | ||
| 3Associate Professor, Department of Mathematics, Institute of Convergin Sciences and Technologies, SR. C., Islamic Azad University ,Tehran, Iran | ||
| 4Associate Professor, Department of Statistics, Institute of Convergin Sciences and Technologies, SR. C., Islamic Azad University ,Tehran, Iran | ||
| چکیده [English] | ||
| The present study investigated the effect of an integrative instructional intervention combining mathematical modeling activities with GeoGebra on students’ performance in learning trigonometric functions. A quasi-experimental pretest–posttest design with two main groups (experimental and control) was employed. The final sample included 270 eleventh-grade students (132 in four experimental subgroups and 138 in four control subgroup). Data were collected using problem-based tests grounded in mathematical modeling and analyzed based on students’ technical skills in GeoGebra and conceptual modeling levels. The experimental group received GeoGebra-based mathematical modeling instruction, whereas the control group was taught using traditional methods without technology. Quantitative analyses using one-way ANCOVA indicated significant improvements in students’ performance (p < 0.001) with large effect sizes for digital technology (η² = 0.715) and mathematical modeling (η² = 0.712). Comparison of the two interventions showed no significant difference (p = 0.339), indicating the positive impact of both approaches. Qualitative findings revealed that students’ active learning, group interaction, and deeper conceptual understanding were enhanced. Overall, integrating digital technology and mathematical modeling provides an effective model for interactive instruction and improving students’ performance in complex mathematical topics. | ||
| کلیدواژهها [English] | ||
| Integrative Instruction, Trigonometric Modeling, GeoGebra, Student Performance, Conceptual Understanding | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 116 تعداد دریافت فایل اصل مقاله: 74 |
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