ارتقای تفکر تابعی: شناسایی طرحواره های پیش نیاز دانش آموزان پایه ی هفتم در تعمیم الگوهای شکلی دومتغیره

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه ریاضی و آمار، دانشکده علوم پایه، واحد تهران مرکزی، دانشگاه آزاد اسلامی

2 گروه ریاضی، دانشکده علوم پایه، ,واحد تهران مرکزی، دانشگاه آزاد اسلامی،

3 گروه ریاضی، دانشکده علوم پایه، دانشگاه خوارزمی، تهران، ایران

چکیده

الگوهای شکلی ظرفیتی بی‌نظیر برای ارتقای تفکر تابعی دارند. این تحقیق با هدف شناسایی طرح‌واره‌های پیش‌نیاز در تعمیم الگوهای شکلی دو متغیره به انجام رسید. روش جمع آوری داده‌ها کمی- کیفی بود. جامعه-ی آماری تحقیق، تعداد 493 دانش‌آموز از شهرستان ملکان (آذربایجان شرقی) بود که تعداد 220 دانش‌آموز به عنوان نمونه انتخاب شدند. با استفاده از تحلیل خود مفهوم، پیشینه‌ی تحقیق و تجربیات محقق تجزیه تکوینی مقدماتی که شامل طرح‌واره‌های پیش نیاز در تعمیم بود، تدوین گردید. سپس آزمونی شامل 7 تکلیف بر اساس چارچوب عمل-شیء-فرآیند- طرح‌واره (APOS) طراحی شد. روایی آزمون توسط متخصصین آموزش ریاضی و معلمین مجرب تایید شد. با استفاده از تجزیه و تحلیل پاسخ‌های دانش‌آموزان بر اساس چارچوب APOS و اجرای سه چرخه‌ی تحقیق با روش تدریس فعالیت گروهی- بحث کلاسی- تمرین درخانه (ACE)، با 19 دانش‌آموز ، تجزیه تکوینی نهایی شد و نقائص دانش‌آموزان در طرح‌واره‌های پیش‌نیاز استدلال، فضای سه‌بعدی R3 و متغیر در تعمیم الگوهای شکلی دو متغیره، شناسایی و کدگذاری شدند. با شناسایی سازه‌های ذهنی دانش‌آموزان در تعمیم الگوها، مسیر یاددهی و یادگیری آن، هموارتر خواهد شد.

چکیده تصویری

ارتقای تفکر تابعی: شناسایی طرحواره های پیش نیاز دانش آموزان پایه ی هفتم در تعمیم الگوهای شکلی دومتغیره

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Enhancing Functional Thinking: Identifying the prior schemas of seventh grade students in Generalization of two-variable figural patterns

نویسندگان [English]

  • Robabaeh Afkhami 1
  • Nasim Asghary 2
  • Ali Reza Medghalchi 3
1 Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of mathematics, Islamic Azad University, Central Branch, Tehran, Iran
3 Department of Mathematics, Kharazmi Univercity, Tehran,Iran
چکیده [English]

The figural patterns have a unique capacity to enhance functional thinking. The aim of this study is to identifying the prior schemas in generalization of two-variable figural patterns .The data collection method was quantitative and qualitative. The statistical population of the study were consisted of 493 students from Malekan township (East Azarbayjan) and 220 students were selected as sample. Using the self-concept analysis, background and experiences of researcher, initial genetic decomposition was developed. Then, a test of 7 task (46 question) was designed based on Action-Object-Process- Schema (APOS) framework. The validity of the test was confirmed by three experts in mathematics education and four experienced teachers. Internal coordination of questions was confirmed with Cronbach's alpha of 0.68. Using the analysis of students' responses to this test based on the APOS framework and doing three cycles of the research were conducted with the teaching method of Activity-Class discussion-Exercise(ACE), with 19 volunteer students, genetic decomposition was finalized and defects of student in reference schema , R3 schema and variable schema as prior schemas in generalization of two-variable figural patterns were identified and encoded. Identifying the mental constructs of students in generalizing patterns, will make it easier to better teaching and learning.

کلیدواژه‌ها [English]

  • Functional Thinking
  • Generalization
  • APOS Theory
  • Two-variable figural pattern

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