بررسی ویژگی های ساختار ریاضی، تطابق ریاضی و درجه انتزاع در بازنمایی های گرافیکی تولید شده دانش آموزان پایه چهارم
محورهای موضوعی : آموزش ریاضیفاطمه زارعی 1 , مجید حق وردی 2 *
1 - گروه ریاضی، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران
2 - گروه ریاضی، واحد اراک، دانشگاه آزاد اسلامی، اراک، ایران
کلید واژه: حل مساله , ساختار ریاضی, تطابق ریاضی, درجه انتزاع.,
چکیده مقاله :
هدف این پژوهش، بررسی ویژگی های بازنمایی های گرافیکی تولید شده (ساختار ریاضی، تطابق ریاضی، درجه انتزاع) دانش آموزان بر اساس چارچوب معرفی شده توسط اوت (2016) در حل مسایل کلامی ریاضی است. از اینرو به بررسی تاثیر چگونگی در نظر گرفتن ساختار ریاضی در بازنمایی های گرافیکی تولید شده توسط دانش آموزان و اینکه چگونه آنها از تطابق ریاضی با مسئله کلامی اطمینان حاصل می کنند و میزان درجه انتزاع آنها پرداخته شد. در این مطالعه از طرح ها و نقاشی های دانش آموزان به عنوان بازنمایی های گرافیکی استفاده گردید. در این پژوهش 124 دانش آموز پایه چهارم مدارس شهر تهران شرکت کردند. داده ها از طریق سه آزمون (پیش آزمون، پس آزمون و آزمون پیگیری) در فاصله دو روز متوالی جمع آوری شد و آزمون ها از 8 مساله کلامی طراحی شد. پس از پیش آزمون مداخله ای 4 هفته ای برگزار شده هر هفته به دانش آموزان یک مساله کلامی ریاضی داده شد و از آنها خواسته شد بر اساس مدل ککس (1999) بازنمایی گرافیکی برای آن ترسیم کنند که شامل همه مواردی بود که برای درک مساله لازم است. سپس از برخی دانش آموزان خواسته شد که بازنمایی خود را در کلاس ارایه دهند. پس از جمع آوری و تحلیل مستندات دانش آموزان، یافته ها نشان داد که دانش آموزان توجه بیشتری به ساختار ریاضی مناسب دارند. همچنین در تطابق ریاضی برای عملگرها، نمایش مقادیر و واحدها از نظر آماری قابل توجه بود اما دانش آموزان درجه انتزاع را نسبتاً ثابت نگه داشتند
The aim of this research is to investigate the features of generated-graphic representations (mathematical structure, mathematical matching, and degree of abstraction) of students in solving mathematic word problems based on the framework introduced by Ott (2016). Therefore, the effect of considering the mathematical structure in their self-generated graphic representations and how they ensure the mathematical matching with the word problems and what degree of abstraction were investigated. In this study, students' designs and drawings were used as graphic representations. In this research, participated 124 students of the fourth grade of schools in Tehran. The data was collected through three tests (pre-test, post-test and follow-up test) in two consecutive days and the tests were designed from 8 word problems. After the 4-week intervention pre-test, every week the students were given a mathematical word problem and they were asked to draw a graphic representation for it based on the model of Cox (1999) containing all the items that is necessary to understand the problem. Then, students were asked to present their representation in class. After collecting and analyzing students' documents, the findings of this research showed that students pay more attention to a mathematically appropriate structure. Also, in the mathematical matching for operators, the representation of values and units was statistically significant, but the students kept the degree of abstraction relatively constant.
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