نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی ریاضیات تربیتی، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران.

2 استادیار گروه ریاضی، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران

3 استاد گروه سنجش و اندازه‏گیری، دانشگاه علامه طباطبایی، تهران، ایران

چکیده

هدف از پژوهش حاضر، بررسی نحوه ساخت مفهوم متغیر و عبارت‌های جبری، در کتاب درسی ریاضی پایه هفتم، بر اساس نظریه‌های ساخت مفهوم Sfard (1991) و Tall and Gray (1994) است. این تحقیق، با رویکرد تفسیری از نوع کیفی است. روش مورداستفاده، روش تحلیل محتوا است. ازنظر هدف در گروه تحقیقات کاربردی و ازنظر جمع‌آوری و کنترل متغیرها در گروه تحقیقات غیرآزمایشی قرار دارد. فصل سوم کتاب ریاضی پایه هفتم، شامل 4 بخش الگوهای عددی، عبارت‌های جبری، مقدار عددی یک عبارت جبری و معادله است که این پژوهش به بررسی روند ساخت مفاهیم جبری در دو بخش متغیر و عبارت‌های جبری، می‌پردازد. یافته‌های پژوهش نشان می‌دهد که آموزش این دو مفهوم به‌گونه‌ای است که فرصت آموزشی لازم برای مرحله فشرده‌سازی (مرحله دوم ساخت مفهوم) پیش‌بینی نشده است و این مرحله، اغلب حذف شده است. همچنین در روند آموزشی، فرصت عبور از مرحله فشرده‌سازی به مرحله شی انگاری (مرحله سوم) فراهم نشده است. بنا بر نظریه گری و تال، ساخت مفهوم در مرحله رویه مانده و به مرحله آخر یعنی درک مفهوم نرسیده است؛ بنابراین با توجه به نظریه‌های ساخت مفهوم، مراحل درک ساختاری و مفهومی برای متغیر و عبارت‌های جبری در نگارش کتاب درسی پیش‌بینی نشده است.

کلیدواژه‌ها

عنوان مقاله [English]

Content Analysis the Process of Constructing Variable and Algebraic Expressions Concepts of 7th Grade’s Mathematical Book

نویسندگان [English]

  • Fatemeh Zahra Heidari 1
  • Nasim Asghari 2
  • Ali Delavar 3

1 Ph.D. Student in Mathematics Education, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Assistant Professor, Department of Mathematics Education, Central Tehran Branch, Islamic Azad University, Tehran, Iran

3 Professor, Department of Educational Measuring, Allameh Tabataba’i University, Tehran, Iran

چکیده [English]

This research examined the construction of algebraic concepts in the 3rd chapter of the 7th-grade mathematics textbook, utilizing Sfard’s and Tall’s theoretical frameworks. Content analysis was employed to achieve the research’s goal of understanding the process by which algebraic concepts are developed in the context of the specified curriculum. This particular research design is considered to be qualitative and focused on the development of educational content, rather than empirical in nature. This study, in terms of its purpose and design, falls under the applied research and non-experimental groups respectively. The chapter in question covers four sections, namely numerical patterns, algebraic expressions, numerical values of algebraic expressions, and equations. This study investigated the process of constructing algebraic concepts, specifically variables and algebraic expressions, utilizing the theoretical frameworks of Sfard and Tall. The research findings suggest that the educational process of algebraic concepts in the textbook tends to follow an accelerated timeline which skips or overlooks the condensation stage (the second stage in the concept development process) and quickly transitions to the reification stage (3rd point in the concept development process). In some instances, the entire condensation stage may even be bypassed, leading to insufficiently developed and understood mathematical concepts and subsequent learning difficulties. Additionally, the research findings are consistent with the theories of concept development proposed by Gray and Tall. Specifically, the construction of the concept has remained at the procedural stage and has not reached the final stage. As such, it is evident that the students have not developed a structural understanding of variables and algebraic expressions.

کلیدواژه‌ها [English]

  • algebra
  • variable
  • algebraic expressions
  • Sfard's theoretical
  • Gray & Tall theoretical
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