کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
360876 | 1436036 | 2009 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes exercises about it. The paper focuses on how Isaac developed an understanding of this concept, how he evaluated whether a mathematical assertion is true or false, how he generated counterexamples to disprove a statement, and the general role examples play for him in concept development and understanding.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: The Journal of Mathematical Behavior - Volume 28, Issues 2–3, June–September 2009, Pages 200–208
Journal: The Journal of Mathematical Behavior - Volume 28, Issues 2–3, June–September 2009, Pages 200–208
نویسندگان
Keith Weber,