بررسی درک دانش‌آموزان دورۀ دوم ابتدایی شهر تهران از زیر ساختار جزء به‌کل مفهوم کسر بر اساس نظریۀ APOS و SOLO، با استفاده از یک تکلیف غیرمعمول

محورهای موضوعی : پژوهش در برنامه ریزی درسی

مهدی ایزدی ¹ , ابراهیم ریحانی ²

1 - دانشجوی دکتری رشته آموزش ریاضی دانشگاه تربیت دبیر شهید رجایی، تهران، ایران.
2 - دکتری رشته آموزش ریاضی، دانشیار و عضو هیئت‌علمی دانشگاه تربیت دبیر شهید رجایی، تهران، ایران.

تاریخ دریافت : 1398/05/05 تاریخ پذیرش : 1400/01/30 تاریخ انتشار : 1400/03/01

کلید واژه: زیر ساختار جزء به کل, نظریۀ APOS و SOLO, تکلیف غیر‌معمول, دانش‌آموزان دورۀ دوم ابتدایی, مفهوم کسر,

چکیده مقاله :

این پژوهش با هدف بررسی درک دانش‌آموزان دورۀ دوم ابتدایی شهر تهران از مفهوم کسر (زیر ساختار جزء به کل) بر اساس دو نظریۀ APOSوSOLO انجام شد. روش انجام این مطالعه، توصیفی - پیمایشی، جامعۀ آماری آن، دانش‌آموزان دورۀ دوم ابتدایی شهر تهران در سال تحصیلی 1398- 1397 و نمونۀ آن، 598 نفر از جامعۀ آماری بود که با روش نمونه‌گیری تصادفی چندمرحله‌ای انتخاب شدند. برای جمع‌آوری داده‌ها، از آزمونی با یک تکلیف غیرمعمول استفاده شد. روایی محتوایی آزمون از نظر متخصصان آموزش ریاضی مورد تأیید قرار گرفت و پایایی ابزار پژوهش بر اساس ضریب آلفای کرونباخ، 7/0 به دست آمد. نتایج این مطالعه نشان داد که دانش‌آموزان، درک محدودی از مفهوم کسر (زیرساختار جزء به کل) دارند و در خصوص این مفهوم، بدفهمی‌های مشترکی دارند. رایج‌ترین بدفهمی‌های به‌دست‌آمده در این مطالعه شامل 1- عدم توجه به مساوی بودن قسمت‌ها؛ 2- درک کسر به‌عنوان نسبت جزء‌به‌جزء و 3- استفاده از تقسیم‌بندی تقریبی برای تعیین مقدار کسری دقیق، بود. تحلیل پاسخ‌ها بر اساس نظریه APOS مشخص کرد که دانش‌آموزان توانایی استفاده از این مفهوم را در مواجهه با تکالیف و موقعیت‌های غیرمعمول ندارند. در تحلیل پاسخ‌ها بر اساس مدل SOLO نیز مشخص شد بیش از 60 درصد پاسخ‌ها، در سطح چند ساختاری بود. پیشنهاد این تحقیق، عدم تأکید بیش‌ازحد بر زیر ساختار جزء به کل، ارائه فرصت‌های برابر برای توسعۀ سایر زیر ساختارها و تأکید بر یادگیری مفهومی رویه‌ها و الگوریتم‌های مرتبط با مفهوم کسر در محتواها و فرصت‌های آموزشی ارائه‌شده به دانش‌آموزان است.

چکیده انگلیسی:

The aim of this research was investigating understanding of Tehran’s second ‎elementary school students of the fraction concept (part-whole subconstruct) based on APOS and ‎SOLO theories. This study’s method was descriptive-survey ‎method, its statistical population was Tehran’s second elementary school students in the academic ‎year 1397-1398 and its sample was 598 people of the statistical population that selected by multistage sampling method. A test with an unusual task used for collecting data. The content validity of the research tools were confirmed by experts and scholars of mathematics education, and the reliability of the research tools was obtained based on Cronbach's alpha of 0.7. Results of this ‎study showed that students have a limited understanding of fraction’s concept and they have common misconceptions. The most common misconceptions ‎found include: (1) Disregarding the requirement of ‎equal parts in part- whole ‎subconstruct; 2- Understanding fraction in part- whole subconstruct as ‎the part-to-part ratio & 3- ‎Using approximate partitioning ‎to determine the exact fraction of the specified part.‎ Analyzing the responses based on the APOS theory also revealed students did not have ability to use this concept in dealing with unusual situations. In analyzing ‎the responses based on the Solo model, more than 60% of the responses were ‎in the multistructural level. The suggestions of this research ‎are not to over-emphasize the part -whole subconstruct, creating ‎equal opportunities for developing other subconstruct‎s of fraction and emphasizing on ‎conceptual learning of procedures and algorithms relative to fraction ‎concept in content and ‎opportunities presented to students.‎

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