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学生解决问题的思维活动,是一个由思维过程和思维结果组成的两面体。 在教学过程中,一些教师常常只重视学生解决问题的思维结果,而忽视其思维过程的研究,例如,解题时,只要求学生做对了就行,很少注意研究学生的思维方式和技巧。这种做法是欠妥当的,为什么这样说呢?举一个大家熟悉的例子。德国数学家高斯上小学时,他的数学教师给班上出了这样一道题:“计算1+2+3……+100=?”高斯和大多数同学计算的结果一样,都是5050。单从计算结果来看,高斯和他的这些同学在解决该问题上应该说是属于同一水平。但仔细研究一下两者的思维过程(解题过程),便会发现情况并非如此。同学们解题时用的是依次逐个相加的方法,而高斯用的是(1
Student thinking activities to solve the problem, is a two-dimensional body composed of the thinking process and the result of thinking. In the process of teaching, some teachers often only attach importance to students 'problem-solving thinking and neglect the research of their thinking process. For example, when solving a problem, they only ask the students to do the right thing and rarely pay attention to the students' ways of thinking and skills. This practice is not proper, why do we say this? Let us give you a familiar example. When a German mathematician Gauss was in elementary school, his math teacher put the question to the class: “Calculate 1 + 2 + 3 ... + 100 =?” Gauss, like most of his classmates, calculated 5050. From the calculation results alone, Gaussian and his classmates should be said to be on the same level in solving this problem. However, if we carefully examine the thinking process (problem solving process) of both, we will find that this is not the case. Students solve the problem is used in turn one by one method, and Gaussian use of (1