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小学的中高年级、中学的初级阶段,正处在从具体形象思维向抽象逻辑思维过渡的阶段,这个阶段学生的抽象思维发生了“飞跃”或“质变”。具体地说,10—11岁开始,学生就能逐步分出概念的本质特性,能初步掌握比较科学的定义,能领会概念之间的逻辑关系,能独立进行一些简单的逻辑分析,并进行间接的推理。因此,可以说这一阶段正是发展学生形式逻辑思维的有利时期。小学数学内容,虽然有些能够反映辩证思维的某些规律,但却没在严格的推理论证。有很多内容还受到一定的局限。例如,加与减,可以说是相反的运算,两种运算相互依存;但在一定条件下可以相互转化就不好讲,因为还没有教过负数。从小学生的年龄特征来说,辩证思维比形式逻辑思维发展晚。因此,小学只能结合某些数学内容适当渗透一些唯物辩证观点的因素,给学生积累一些感性材料。比如,在小学数学中应用法则、公式、
The middle and high grades of primary schools and the primary stage of secondary schools are in the stage of transition from concrete image thinking to abstract logical thinking. At this stage, the abstract thinking of students has undergone “leap” or “quality change”. Specifically, starting from the age of 10 to 11, students can gradually separate the essential characteristics of the concept, can initially grasp the definition of more scientific, can understand the logical relationship between concepts, and can perform some simple logical analysis independently and indirectly. Reasoning. Therefore, it can be said that this stage is a favorable period for the development of students’ formal logical thinking. Primary school mathematics content, although it can reflect some of the laws of dialectical thinking, but it is not in the strict theoretical evidence. There is a lot of content that is subject to certain limitations. For example, addition and subtraction can be said to be the opposite operations. The two operations depend on each other; but it is not easy to convert them under certain conditions, because negative numbers have not been taught. From the perspective of pupils’ age characteristics, dialectical thinking develops later than formal logical thinking. Therefore, elementary schools can only infiltrate some factors of materialist dialectical perspectives with certain mathematics content and accumulate some perceptual materials for students. For example, applying rules and formulas in primary school mathematics