基于数学教育观的“理解”之理解

The Understanding of "Understanding" Based on the View of Mathematics Education

"理解"是解释学的核心概念。基于哲学解释学的理解观,我们认为,理解本质上是以概念和关系为核心的意义复原、生成过程和存在方式,而存在方式就是认知过程与结果的相互融合。它具有主体性、相对性、差异性、循环性等基本特征。关于"理解"含义的认识与把握,对研究确定数学质量标准、数学教师专业标准以及提高数学教学质量起着关键性的作用。数学知识的系统性、严密性决定了知识之间的复杂的内在联系,要善于从整体上、本质上掌握相互关系,通过举例说明或讲故事、数学语言翻译、系统讲授、合理评价和反思等表现形式,采取梳理、综合、分类、对比、转化等方法不断提升理解者的理解水平。教师的智慧表现于教学过程,不仅要注重学习者的理解形成的过程,还要关注思考过程、探究过程中的理解。

＂Understanding＂ is the core concept of hermeneutics.Based on concept of philosophical hermeneutics of understanding theory,we think,understand is meaning recovery,the building process,and existence with concepts and relationships at the core.In addition,existence is the integration of cognitive processes and result.It has subjective,relative,difference,circulation and other basic features.Recognizing and securing the meaning of understanding plays a key role in research and enact the quality standards of mathematics,mathematics teacher professional standards and improve the quality of teaching mathematics.Systematic and rigorous of mathematical knowledge determine the complex intrinsic contact of knowledge,teacher should be good at grasping the relationship by the whole and nature idea,through the form of expression,examples or stories,mathematical language translation,systemic teaching,a reasonable evaluation and reflection,taking the methods of pectination,synthesis,classification,comparison,conversion and so on to improve the understanding levels of students.Teacher＇s wisdom is reflected in the teaching process,not only focus the learner＇s understanding formation process,but also concern about the understanding in the thought process and explore process.