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抽象思维能力是人们认识事物本质的一种能力,并且是借以形成科学认识、揭示发展规律的一种重要的能力。抽象是“把事物共同的、本质的特征或联系抽取出来,而舍去个别的、本质的特征和联系的思维过程。”抽象思维能力并非数学所特有却是数学活动的第一大特征。高度抽象是数学的主要特征之一,教学活动中应着力培养学生从实际问题到数学问题的抽象,从特殊到一般的抽象,对事物本质属性的语言抽象能力,以及遵循学生抽象思维发展的规律水平,加强学生的抽象思维能力的培养。1.培养学生对概念、命题的抽象思维能力。概念是事物的本质属性在人脑中的反映,它是在抽象概念的基础上形成的思维形式,因此,新概念的学习是培养学生抽象概括能力的极好材料。在概念教学中,教师应该提供给学生丰富的、典型的、正确的实例,引导他们对这些实例进行分析、综合、比较、抽象和概括等一系列的思维过程。如圆、球、映射、函数等概念的教学都能充分体现概念的抽象思维过程。下面是学习初中函数概念的例子,一般可采用以下步骤。第一步,让学生分别指出下面例子中的变量以及变量之间的关系的表达式:
Abstract thinking ability is a kind of ability that people recognize the nature of things, and is an important ability to form a scientific understanding and reveal the law of development. Abstraction is the process of thinking that extracts common and essential features or relations of things, but discards individual and essential features and connections. "Abstract thinking ability is not unique to mathematics but is the number one characteristic of mathematical activity . High abstraction is one of the main characteristics of mathematics. Teaching activities should focus on cultivating students ’abstraction from practical problems to mathematical problems, from abstraction to general abstraction, linguistic abstract abilities to the essential attributes of things, and following the law of the development of students’ abstract thinking Level, strengthen the students’ abilities of abstract thinking. 1. Cultivate students’ abilities of abstract thinking on concepts and propositions. Concept is the reflection of the essential attribute of things in the human brain. It is a form of thinking formed on the basis of abstract concepts. Therefore, the study of new concepts is an excellent material for cultivating students’ abstract abilities. In concept teaching, teachers should provide rich, typical and correct examples to students, and guide them to analyze, synthesize, compare, abstraction and summarize a series of thinking processes. Such as the circle, the ball, the mapping, the function and so on the teaching of the concept all can fully reflect the abstract thought process of the concept. The following is an example of learning the concept of junior high function, the following steps can be generally used. The first step is for students to point out the variables in the example below and the expressions for the relationships between the variables: