نقش استدلال‌های ترکیبیاتی در آموزش ریاضی دانشگاهی

نوع مقاله: مقاله پژوهشی

نویسنده

دانشگاه شهید بهشتی

چکیده

چکیده: در حل مسایل ترکیبیات در ریاضی، تنوع روش‌های ترکیبیاتی برای اثبات قضیه‌ها و استفاده از ابزارهای مختلف برای ارائه راه حل‌های گوناگون، موجب می‌شود که مسیر استدلال‌های ترکیبیاتی به راه‌های ابتکاری شباهت بیشتری داشته باشند تا به یک رَوِیه عمومی، مانند آنچه که در مباحثی مانند جبر یا آنالیز به چشم می‌خورد. این ویژگی موجب می‌شود که بسیاری از یادگیرندگان، با هدف به‌دست آوردن رویه‌های کلی، برای رده‌بندی مسئله‌های ترکیبیاتی تلاش کنند. مشاهدات تجربی نشان می‌دهد که معمولاً آنان در مسیر این تلاش، ابتدا مسئله‌های ترکیبیاتی را دسته‌بندی می‌کنند و سپس، یک فرمول برای هر حالت به‌خاطر می‌سپارند. مشکل زمانی آشکار می‌شود که تعداد حالت‌ها بیش از حدی است که یادگیرنده بتواند از آن‌ها، به‌عنوان رویه‌ای کارآمد استفاده کند. مطالعه حاضر، در ادامه پژوهشی در خصوص یادگیری مباحث ترکیبیات است که با هدف شناسایی چگونگی توسعه تفکر ترکیبیاتی انجام شده است. در این مقاله، استفاده از استدلال‌های ترکیبیاتی در آموزش، به‌عنوان آخرین گام شناخته شده در تفکر ترکیبیاتی، مورد مطالعه قرار گرفته است. 

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