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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 | ||
|
[1]
|
polya, G., How to solve the problem (translated by Ahmad Aram) (Eighth Edition. (Tehran: kayhan) publication of 1954), 1386.[In Persian].
|
|
|
[2]
|
National Council of Teachers of Mathematics, ed. Principles and standards for school mathematics. Vol. 1. National Council of Teachers of, )2000(.
|
|
|
[3]
|
Kolahdooz, F.,Evaluation of students understand second year high school from the reasoning and mathematical proofs. MA thesis Mathematics Education, Shahid Rajaee Teacher Training, Basic Sciences, Tehran, Iran, . )1390( .[In Persian].
|
|
|
[4]
|
zamani Abyaneh, A. ,the role of reasoning and proof in teaching school mathematics. MA thesis in mathematics education, Shahid Beheshti University, Faculty of Mathematics and Computer Sciences, Tehran, Iran, (1386) [In Persian].
|
|
|
[5]
|
Moore, Robert C. "Making the transition to formal proof." Educational Studies in mathematics, Vol. 27, No. 3 ,(1994), pp. 249-266.
|
|
|
[6]
|
Harel, Guershon, and Larry Sowder. "Students’ proof schemes: Results from exploratory studies." Research in collegiate mathematics education III 7 ,(1998), pp. 234-282.
|
|
|
[7]
|
Selden, John, and Annie Selden. "Unpacking the logic of mathematical statements." Educational Studies in Mathematics, Vol. 29, No. 2 ,(1995), pp. 123-151.
|
|
|
[8]
|
Mejía-Ramos, Juan Pablo, and Matthew Inglis. "Argumentative and proving activities in mathematics education research." Proceedings of the ICMI study 19 conference: Proof and proving in mathematics education. Vol. 2. (2009).
|
|
|
[9]
|
Anapa, Pınar, and Hatice Şamkar. "Investigation of undergraduate students’ perceptions of mathematical proof." Procedia-Social and Behavioral Sciences Vol. 2, No. 2, (2010), pp. 2700-2706.
|
|
|
[10]
|
Mejia-Ramos, Juan Pablo, et al. "An assessment model for proof comprehension in undergraduate mathematics." Educational Studies in Mathematics, Vol. 79, No.1 (2012), pp. 3-18.
|
|
|
[11]
|
Hanna, Gila, and Ed Barbeau. "Proofs as bearers of mathematical knowledge," ZDM , Vol. 40, No. 3, (2008), pp. 345-353.
|
|
|
[12]
|
Weber, K., Students’ difficulties with proof. MAA Online: Research Sampler, Cited from http://www.maa.org, (2003).
|
|
|
[13]
|
Roy, S., Alcock, L., and Inglis, M., Undergraduates’ proof comprehension: A comparative study of three forms of proof presentation. Paper presented at the Thirteenth Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, (2010).
|
|
|
[14]
|
Varghese, T., Student teachers conception of mathematical proof. Unpuplished doctoral dissertation, University of Alberta, Canada, (2007).
|
|
|
[15]
|
Mingus, T. T. Y., and Grassl, R. M., Preservice teacher beliefs about proofs, School Science and Mathematics, Vol. 99, No. 8, (1999), pp. 438-444.
|
|
|
[16]
|
Hemmi, K.,Three styles characterising mathematicians’ pedagogical perspectives on proof. Educational studies in mathematics, Vol. 75, No. 3, (2010), pp. 271-291.
|
|
|
[17]
|
Gholamazad, .S, goya, Z., roles Proof in school mathematics the curriculum, Journal of Mathematics Education, Vol. 83, (1385), pp. 10-4. [In Persian].
|
|
|
[18]
|
Fathollahi, F., A Study on Mathematics Proofprocesses Conception of undergraduates and Their attitudes about Mathematics Proof. MA thesis Mathematics Education, Shahid Rajaee Teacher Training, Basic Sciences, Tehran, Iran, (1392). [In Persian].
|
|
|
[19]
|
Dee Vanspronsen, H. , Proof processes of novice mathematics proof writers, Unpuplished doctoral dissertation, university of Montana,USA. Retrieved from ProQuest Digital Dissertations, (2008).
|
|
|
[20]
|
McNamara, D. S. , Reading both high-coherence and low-coherence texts: Effects of text sequence and prior knowledge, Canadian Journal of Experimental Psychology, Vol. 55, No. 1, (2001), pp. 51-62.
|
|
|
[21]
|
Hawro, J. ,University students' difficulties with formal proving and attempts to overcome them. In CERME 5, (2007), pp. 2290-2299.
|
|
|
|
|
|
|
|
|
|
|
[22]
|
Yang, K.-L., and Lin, F.-L., A model of reading comprehension of geometry proof. Educational Studies in Mathematics, Vol. 67, No. 1, (2008), pp. 59-76.
|
|
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