09 فروردین 1403
فاطمه احمدپور

فاطمه احمدپور

مرتبه علمی: استادیار
نشانی: دانشکده مهندسی سیستم های هوشمند و علوم داده - گروه ریاضی
تحصیلات: دکترای تخصصی / ریاضی
تلفن: -
دانشکده: دانشکده مهندسی سیستم های هوشمند و علوم داده

مشخصات پژوهش

عنوان Students’ ways of understanding a proof
نوع پژوهش مقالات در نشریات
کلیدواژه‌ها
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مجله Mathematical Thinking and Learning
شناسه DOI
پژوهشگران فاطمه احمدپور (نفر اول) ، David Reid (نفر دوم) ، محمدرضا فدایی (نفر سوم)

چکیده

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.