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

پژوهش در برنامه ریزی درسی

دوره 18، شماره 68، خرداد 1400، صفحه 124-141   

نوع مقاله: مقاله پژوهشی

شناسه دیجیتال (DOI): 10.30486/jsre.2021.1875155.1435

نویسندگان

مهدی ایزدی¹؛ ابراهیم ریحانی^{* 2}

¹دانشجوی دکتری رشته آموزش ریاضی دانشگاه تربیت دبیر شهید رجایی، تهران، ایران.

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

چکیده

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.

کلیدواژه‌ها

تکلیف غیر‌معمول؛ دانش‌آموزان دورۀ دوم ابتدایی؛ زیر ساختار جزء به کل؛ مفهوم کسر؛ نظریۀ APOS و SOLO

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