تاثیر دو رویکرد استدلالهای خلاق مبتنی بر ریاضی و الگوریتمی در یادگیری
محورهای موضوعی : علوم تربیتیزهره رشیدیان 1 , مجید حق وردی 2
1 - دانشجوی دکتری برنامه درسی، واحد اراک، دانشگاه آزاد اسلامی، اراک، ایران. zmath87z@gmail.com
2 - دانشیار آموزش ریاضی، گروه ریاضی، واحد اراک، دانشگاه آزاد اسلامی، اراک، ایران. Majid.Haghverdi@iau.ac.ir
کلید واژه: استدلال ریاضی, استدلال خلاق, استدلال الگوریتمی, یادگیری طوطیوار,
چکیده مقاله :
این مطالعه با بهرهگیری از چارچوب نظری )لایتنر ،2008)، به بررسی تأثیر دو رویکرد استدلالی متفاوت در یادگیری ریاضی میپردازد: استدلال الگوریتمی (AR) و استدلال خلاق مبتنی بر ریاضی. (CMR) چارچوب لایتنر با مرتبط ساختن استدلال به فرآیندهای تفکر، توانمندیهای دانشآموز و محیط یادگیری، منشأ و پیامدهای انواع مختلف استدلال را تشریح میکند. هدف اصلی این پژوهش، بررسی این فرضیه است که یادگیری ریاضی با استفاده از استدلال خلاق میتواند کارآمدتر و پایدارتر از زمانی باشد که دانشآموزان صرفاً از استدلال الگوریتمی استفاده می کنند و صرفا رویههای حل از پیش تعیین شده به آنها ارائه می شود. در این مطالعه تجربی، 91 دانشآموز پایه نهم به دو گروه تقسیم شدند: گروه AR که با فرمولهای از پیش تعیین شده آموزش دیدند (n=48) و گروه CMR که بدون راهنمایی مستقیم، دانش آموزان راهحلها را کشف و تولید میکردند (n=43). تکالیف مطالعه حاضر بر اساس روشی بود که قبلاً توسط بوئسن؛ لایتنرو پالم (2010) و پالم و همکاران (2011) بصورت توسعه یافته استفاده شد. نتایج این مطالعه نشان داد که اگرچه گروه AR در طول جلسه تمرین عملکرد بهتری داشت (p < .0001,r=0.77) اما در آزمون یک هفته بعد، گروه CMR به طور معناداری برتر بودp = .001)، (d = 0.7 تحلیل همبستگی نشان داد که برای گروه CMR، ارتباط قوی بین عملکرد تمرین و آزمون وجود دارد (r = .81, p < .0001)، در حالی که این ارتباط برای گروه AR معنادار نبود
Drawing upon the theoretical framework of Lithner (2008), this study investigates the impact of two different reasoning approaches on mathematics learning: Algorithmic Reasoning (AR) and Creative Mathematically-founded Reasoning (CMR). Lithner's framework explains the origins and consequences of different types of reasoning by connecting them to thought processes, student capabilities, and the learning environment.[2] The primary objective of this research is to examine the hypothesis that mathematics learning can be more efficient and sustainable when students utilize creative reasoning, as opposed to solely using algorithmic reasoning where they are only provided with predetermined solution procedures. In this experimental study, 91 ninth-grade students were divided into two groups: the AR group (n=48), which was taught using predetermined formulas, and the CMR group (n=43), where students discovered and generated solutions without direct guidance. The tasks in the present study were based on a methodology previously developed and used by Boesen, Lithner, and Palm (2010) and Palm et al. (2011). The results of this study indicated that although the AR group performed better during the practice session (p < .0001, r=0.77), the CMR group was significantly superior in the test administered one week later (p = .001, d = 0.7). A correlational analysis revealed a strong relationship between practice and test performance for the CMR group (r = .81, p < .0001), while this correlation was not significant for the AR group.
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