“REINVENTING” TECHNIQUES FOR THE ESTIMATION OF THE AREA OF IRREGULAR PLANE FIGURES: FROM THE EIGHTEENTH CENTURY TO THE MODERN CLASSROOM

Ioannis Papadopoulos

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“REINVENTING” TECHNIQUES FOR THE ESTIMATION OF THE AREA OF IRREGULAR PLANE FIGURES: FROM THE EIGHTEENTH CENTURY TO THE MODERN CLASSROOM

机译：估计不规则平面图形面积的“重新发明”技术：从十八世纪到现代教室

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The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such shapes. We claim that, when students deal for an adequate period with a succession of carefully designed tasks of the same conceptual basis—in our case that of the area of irregular shapes—then they “reinvent” problem-solving techniques for the estimation of their area, given that they have not been taught anything about these shapes. These techniques, in some cases, are almost the same as the abovementioned historical ones. In other cases, they could be considered to be an adaptation or extension of these.

机译：希腊基础教育的现代数学教科书中不存在不规则形状区域的问题。但是，这里有由18世纪著名的希腊学者为教育目的而写的书籍的集合，其中提出了一些有关估计此类形状的技术。我们声称，当学生在足够的时间里处理一系列相同概念基础的精心设计的任务时（在我们的例子中是不规则形状的区域），那么他们“重新发明”了解决问题的技术以估算其面积，因为尚未对这些形状进行任何教导。在某些情况下，这些技术与上述历史技术几乎相同。在其他情况下，可以将它们视为对它们的改编或扩展。

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来源
《International Journal of Science and Mathematics Education》 |2010年第5期|p.869-890|共22页
作者
Ioannis Papadopoulos;
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作者单位

Hellenic Ministry of Education—Primary Education, Ptolemeon 21 Str, 55535 Pylea, Thessaloniki, Greece;

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正文语种 eng
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area of irregular shapes; problem-solving techniques;

机译：不规则形状的区域;问题解决技术;

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“REINVENTING” TECHNIQUES FOR THE ESTIMATION OF THE AREA OF IRREGULAR PLANE FIGURES: FROM THE EIGHTEENTH CENTURY TO THE MODERN CLASSROOM

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