بررسی اثربخشی آموزش بازنمایی‌‌های طرح‌واره‌ای بر توانایی حل مسائل غیرمعمولی ریاضی

محورهای موضوعی : پژوهش در برنامه ریزی درسی

مهران عزیزی محمودآباد ¹ ( دانشجوی دکتری برنامه‌ریزی درسی، دانشکده علوم تربیتی و روان‌شناسی، دانشگاه اصفهان، اصفهان، ایران. )
محمدجواد لیاقت دار ² ( استاد گروه علوم تربیتی، دانشکده علوم تربیتی و روان‌شناسی، دانشگاه اصفهان، اصفهان، ایران. )
حمید رضا عریضی ³ ( استاد گروه روانشناسی، دانشکده علوم تربیتی و روان‌شناسی، دانشگاه اصفهان، اصفهان، ایران. )

تاریخ دریافت : 1397/10/29 تاریخ پذیرش : 1398/10/14 تاریخ انتشار : 1399/02/01

کلید واژه: ریاضی, مسائل غیرمعمولی, توانایی حل مسئله, بازنمایی‌‌های طرح‌واره‌ای,

چکیده مقاله :

هدف این پژوهش، بررسی اثربخشی آموزش بازنمایی های طرح‌واره‌ای بر تواناییحل مسائل غیرمعمولی ریاضی دانش آموزان پایه ششم ابتدایی است. این پژوهش از نوع تحلیل محتوا و طرح های نیمه‌آزمایشی از نوع پیش آزمون- پس آزمون- پیگیری با گروه کنترل است. پس از مطالعه و طراحی آموزشی، 40 نفر از دانش آموزان پسر پایه ششم ابتدایی مشغول به تحصیل در یک آموزشگاه در سال تحصیلی 97-1396 در شهر یاسوج به‌صورت داوطلب در این پژوهش شرکت کردند. مشارکت کنندگان با انتساب تصادفی به دو گروه آزمایش و کنترل تقسیم شده و برای 12 جلسه (هر هفته یک جلسه) با استفاده از روش آموزش بازنمایی محور تحت آموزش قرار گرفتند. ابزار گردآوری داده ها در بخش تحلیل محتوا چک‌لیست و در بخش نیمه‌آزمایشی آزمون محقق ساخته بود. برای تجزیه‌وتحلیل داده ها در تحلیل محتوا از تکنیک آنتروپی شانون و در بخش نیمه آزمایشی از آزمون تحلیل واریانس با اندازه گیری مکرر استفاده شد. نتایج تحلیل محتوا نشان می دهد بیشترین توجه برای توزیع و حضور مسائل غیرمعمولی به ترتیب به مسائل بازنمایی سلسله مراتبی سپس بازنمایی جزء-کل و درنهایت به مسائل بازنمایی شبکه ای شده است و مسائل بازنمایی ماتریسی جایگاهی در کتاب درسی ندارند. همچنین نتایج تحلیل واریانس با اندازه گیری مکرر نشان داد که تفاوت معناداری در میانگین تمام مؤلفه‌های توانایی حل مسائل غیرمعمولی (05/0P<) بین گروه کنترل و آزمایش وجود دارد؛ لذا آموزش بازنمایی های طرح‌واره‌ای موجب افزایش توانایی حل مسائل غیرمعمولی ریاضی در دانش آموزان شده است. به علاوه این نتایج نشان می دهد که استفاده از بازنمایی های طرح‌واره‌ای در حل مسائل غیرمعمولی در طول زمان ثبات دارد. نتایج این مطالعه لزوم توجه ویژه به بازنمایی های طرح‌واره‌ای در کتاب ریاضی پایه ششم ابتدایی و استفاده معلمان و دبیران ریاضی از این بازنمایی ها در حل مسائل غیرمعمولی را مورد تأکید قرار می دهد.

چکیده انگلیسی:

The aim of the present study is to investigate the effectiveness of schematic representation-based instruction on 6th grade students' ability of solving non-routine problems in mathematics. It is a content analysis and quasi-experimental design research of the pretest-posttest type, follow up by the control group. After studying and educational designing, 40 sixth-grade male students of an elementary school in the academic year of 1396-97 in Yasouj voluntarily participated in the study. They were randomly assigned to experimental and control group and were educated for 12 sessions (one session per week) using representation-based instruction method. Data collection instruments were developed in the content analysis section of the checklist and in the semi-experimental part of the test. Shannon Entropy technique was adopted in order to analyze data in content analysis, and variance analysis test with repeated measures was used for the quasi-experimental part. The results of the content analysis show that the greatest attention for the distribution and the presence of non-routine problems has been directed to hierarchical presentation, part-whole presentation, and network presentation problems, respectively. It was indicated that matrix presentation problems have no place in textbooks. In addition, the results of the variance analysis with repeated measures reveal that there is a significant difference between the averages of all the components of the ablitiy of solving non-routine problems of control group and experimental group (p<0.05). Therefore, it can be concluded that schematic representation instruction increases students' ability of solving non-routine problems in mathematics. Besides, the results indicate that using these methods repeatedly for solving non-routine problems will be consistent over time. The results of the study emphasize the need for special attention to the schematic representations in the sixth grade elementary mathematics textbook, and the necessity of applying these representations in solving non-routine problems by mathematic teachers.

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