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在数学教学中加强新旧知识的联系,是減轻学生负担、提高教学质量的一项有效措施。本文提出一些初步的看法,与同志们共同研讨。 (一)理解与掌握教材的內在联系和相互关系我认为理解与掌握以下几种主要关系,对加强新旧知识的联系是有帮助的。 1.一般与特殊的关系。例如对函数来说,方程、数列、不等式等可视为函数的特例;而对方程来说,一次方程、二次方程等是它的特例。在中学教材的安排上,一般来说是由特殊到一般,有时是由一般到特殊。对某一部分教材来说,有时是先一般后特殊,而后又由特殊到一般。譬如在初中平面几何的“三角形”一章中,先研究三角形的一般概念,接着研究三角形的特殊部分——等腰三角形,而后研究一般三角形的有关重要定理(如全等定理)。最后研究特殊三角形的有关知识等。这样安排主要是为了便于学生接受。
To strengthen the connection between old and new knowledge in mathematics teaching is an effective measure to reduce the burden on students and improve the quality of teaching. This article puts forward some preliminary views and discusses with comrades. (I) Understanding and mastering the intrinsic connections and interrelationships of teaching materials I believe that understanding and mastering the following major relationships will help to strengthen the link between old and new knowledge. 1. General and special relationships. For example, functions, equations, sequences, inequalities, etc., can be regarded as special cases of functions. For equations, primary equations, quadratic equations, etc. are special cases. In the arrangement of secondary school textbooks, it is generally from special to general, and sometimes from general to special. For a certain piece of teaching material, it is sometimes general and special, and then special to general. For example, in the “triangle” chapter of the plane geometry of junior high schools, the general concept of triangles is first studied. Then the special part of the triangle, the isosceles triangle, is studied and then the important theorems of general triangles (such as the congruent theorem) are studied. Finally, study the relevant knowledge of special triangles. This arrangement is mainly for students’ acceptance.