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在数学教学中,概念教学的难度大、要求高,稍不留意即出错误。本文拟对几个常见的典型病例进行试诊。病例1“两腰相等的三角形叫做等腰三角形。”诊断:在一般的三角形中,只把围成它的三条线段都称作“边”,而未定义“腰”。只在等腰三角形中才定义“腰”——等腰三角形中相等的两边叫做两腰。“腰”既是在“等腰三角形”的基础上定义的,现又反过来用“腰”定义“等腰三角形”,就犯了“循环定义”(也称“逻辑循环”)的错误。治疗:正确的定义应是:“两边相等的三角形叫做等腰三角形。”
In mathematics teaching, the concept of teaching difficult, demanding, a little bit of attention that is wrong. This article is intended to test a few common typical cases. Case 1 “An equal triangle on both sides is called an isosceles triangle.” Diagnosis: In a general triangle, only the three segments that enclose it are called “sides”, and “waist” is not defined. The “waist” is defined only in the isosceles triangle - the two sides equal in the isosceles triangle are called the two lumbar regions. “Waist” is defined on the basis of “isosceles triangles”. In turn, the definition of “isosceles triangle” by “waist” in turn makes the mistake of “circle definition” (also called “logic circle”). Treatment: The correct definition should be: “The equal triangles on both sides are called isosceles triangles.”