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中学数学教师从事的学术研究活动,其目的是为了提高中学数学教育的质量,研究的范围既包括初等数学,也包括中学数学教育的理论与实践。因此,初等数学研究是中学数学教育工作者学术研究活动的重要组成部分,其内容主要涉及初等数学专题的发现与探讨,数学思想方法论以及有关数学史的研究等等。 (一) 科学研究的实质是科学家发现问题和解决问题的活动。科学研究的起点应当是问题。正如爱因斯坦所指出的“提出一个问题比解决一个问题更为重要,因为解决问题也许仅是一个数学上或实验上的技能而已;而提出新的问题、新的理论,从新的角度去看旧问题,却需要有创造性的想象力,而且标志着科学的真正进步”。那么在初等数学领域中如何发现与捕捉问题呢?兹提及以下几点。
The purpose of the academic research activities of middle school mathematics teachers is to improve the quality of mathematics education in middle schools. The scope of research includes both elementary mathematics and the theory and practice of middle school mathematics education. Therefore, elementary mathematics research is an important part of the academic research activities of middle school mathematics educators. Its content mainly involves the discovery and discussion of elementary mathematics topics, the methodology of mathematics thinking, and the study of the history of mathematics. (a) The essence of scientific research is that scientists discover problems and solve problems. The starting point of scientific research should be a problem. As Einstein pointed out, “proposing a problem is more important than solving a problem, because solving a problem may only be a mathematical or experimental skill; and proposing new problems, new theories, and new perspectives. The old problem requires creative imagination and marks the real progress of science.” So how do you find and catch problems in the elementary mathematics field?