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بررسی درک دانشجویان از فرایند اثبات ریاضی بر اساس مدل مژیا راموس و همکاران | ||
| فناوری آموزش | ||
| مقاله 5، دوره 10، شماره 2 - شماره پیاپی 38، فروردین 1395، صفحه 121-132 اصل مقاله (1.99 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22061/tej.2016.493 | ||
| نویسندگان | ||
| ابراهیم ریحانی* 1؛ فاروق فتحالهی2؛ فهیمه کلاهدوز3 | ||
| 1گروه ریاضی دانشگاه تربیت دبیر شهید رجایی تهران، تهران، ایران | ||
| 2آموزش ریاضی و دبیر ریاضی شهرستان اشنویه، ایران | ||
| 3آموزش ریاضی دانشگاه فردوسی مشهد، مشهد، ایران | ||
| تاریخ دریافت: 28 تیر 1395، تاریخ پذیرش: 28 تیر 1395 | ||
| چکیده | ||
| استدلال و اثبات در آموزش ریاضیات در همة مقاطع تحصیلی از مدرسه تا دانشگاه از اهمیت خاصی برخوردار است و درک و فهم ریاضی بدون تأکید بر استدلال و اثبات تقریباً غیر ممکن است. در این مطالعه که به روش توصیفی از نوع زمینهیابی انجام گرفته است، هدف مقاله، بررسی درک و فهم دانشجویان از فرایند اثبات ریاضی میباشد. نمونة مورد مطالعه، 170 نفر از دانشجویان مقطع کارشناسی ریاضی از چهار دانشگاه شهید رجایی، شهید بهشتی، امیر کبیر و علم و صنعت است که نمونة در دسترس محسوب میشود. ابزار اندازهگیری در پژوهش حاضر، پرسشنامهای است که طراحی آن بر اساس تعمیمی از پرسشنامه روی[i] و همکاران[ii] انجام گرفته است. در این پرسشنامه قضیهای همراه با اثباتش ارائه گردید و سپس از دانشجویان خواسته شد تا به سؤالاتی در مورد فرایند ساخت اثبات ریاضی، پاسخ دهند. مدلی که به منظور ارزیابی پاسخ دانشجویان به سؤالات پرسشنامه استفاده شده است بر اساس مدل مژیا راموس[iii] و همکاران[iv] میباشد که از دو جنبة موضعی و کلی اثبات تشکیل شده است. این مدل، هفت سطح مختلف از درک و فهم دانشجویان از فرایند اثبات ریاضی را بررسی مینماید. نتایج به دست آمده از این تحقیق نشان داد که اکثر دانشجویان مورد مطالعه به جنبههای موضعی اثبات دست یافتهاند. در واقع آنها توانستهاند رابطهی بین مفاهیم و گزارههای موجود در یک اثبات را درک کنند و ارتباط بین چند گزارة خاص را نشان دهند، ولی درصد کمی از آنها ساختار کلی اثبات را درک نمودهاند که به نظر میرسد عوامل متعددی از جمله عدم توجه دانشجویان به فرض قضیه، ناتوانی آنها در ارائه استدلال منطقی و سازماندهی منطقی گزارههای اثبات و از همه مهمتر، دانش ناکافی دانشجویان در برخی موارد میتواند از دلایل این ضعف باشد. [i] Roy [ii] Alcock& Inglis [iii] Mejia-Ramos [iv] Weber & Fuller & Rhoads & Samkoff | ||
| کلیدواژهها | ||
| استدلال؛ اثبات ریاضی؛ دانشجویان؛ درک اثبات | ||
| موضوعات | ||
| فناوری آموزش- آموزش عمومی | ||
| عنوان مقاله [English] | ||
| Study on Students' Understanding of the Process Mathematical Proof Based on Mejia Ramos et al | ||
| نویسندگان [English] | ||
| E. Reyhani1؛ F. Fathollahi2؛ F. Kolahdouz3 | ||
| 1Departments of Mathematics, University Shahid Rajaee, Tehran. Iran | ||
| 2Department of mathematics education and mathematics teacher Oshnavieh,Azarbaijan. Iran | ||
| 3mathematics education University of Ferdowsi Mashhad. Mashhad. Iran | ||
| چکیده [English] | ||
| Reasoning and proof in mathematics education are important at all educational levels, from school to university. Understanding mathematics without emphasis on reasoning and proving is almost impossible. The purpose of this study was to investigate the university students’ conception of mathematical proof. For this, a survey method was used. The participants of this study were 170 students collected from four universities; Shahid Rajaee Teacher Training, Shahid Beheshti, Science and Technology and Amirkabir University of Technology as available samples. The data collecting Instrument was a questionnaire based on the modified version of Roy and et.al (2010). In this questionnaire a theorem with its proving was presented and then the students were asked to answer the questions about the process of making the mathematical proof. A model was used to evaluate the students’ answers to questions based on Ramos and et.al (2011). It is consists of both global and local aspects. This model investigates seven different levels of understanding of the process of making mathematical proof. The findings of the study showed that most of the students had a local comprehension of the proof. In fact, they understood the relations between the concepts and statements in the proof. But a small percentage of them had a more holistic comprehension of the proof. It seems several factors, including the lack of attention to the assumptions of the theorem, their inability to provide logical reasoning and rational organization of statements of the proof, and most importantly, the lack of students’ knowledge may be insufficient in this inability. | ||
| کلیدواژهها [English] | ||
| Reasoning, Mathematical Proof, students, Comprehension of Proof | ||
| مراجع | ||
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