【作者】 彭泽华；

【导师】 昌国良；

【作者基本信息】 湖南师范大学 ， 课程与教学论， 2009， 硕士

【摘要】 在数学学习中,由于数学的高度抽象性和概括性,特别是使用了高度概括的形式化语言,容易使学生造成表面的形式理解,而不能很好的掌握数学知识的实质。因此,数学学习中更需要进行抽象概括,只有通过逐步地从具体到抽象的概括,才能使学生真正的掌握数学知识,因此数学概括能力是学习数学所必须的能力,是学习数学的前提条件。一些研究表明高中阶段是学生的数学概括能力的又一显著的变化期,并且逐步趋于成熟,故高中生数学概括能力的发展比较重要。国内外关于数学概括能力的研究,主要是研究数学概括能力在数学能力中的地位,多以实证研究为主。高中生数学概括能力包括对数学符号、关系、结构、运算与推理、数学思想方法的概括能力,具有过程性和多样性等特点。影响高中生数学概括能力发展的内部因素包括学生的智力因素和非智力因素,外部因素包括教师、学校、家庭和社会四个因素。学生的学习方法、教师的教学方法以及教材的编排,是发展高中生数学概括能力有效路径。通过实证研究,本文发现通过改进学习方法和教学方法,发展高中生数学概括能力是可能的。更多还原

【Abstract】 In mathematics, students tend to stay on the surface, seldom the hardcore, due to its abstraction and generality, especially when special formal words are used. Therefore, it is required in the learning that students have the ability to summarize the universal links through massive facts and Generalization be a must, a prerequisite which shall be met in the first place. Some studies have shown that the time spent in the senior high school is a remarkable period during which the ability of generalization varies dramatically and comes to a steady state eventually. So the generalization ability to high school students is essential, which is this essay trying to explore.The studies of generalization ability in mathematics are mainly focus on its status in mathematics ability both domestic and abroad, and most of them are empirical researches. The mathematical generalization ability of senior high students, which include the generalization ability in mathematical symbols, relations, structures, computing and reasoning, mathematical thought and method, has the characteristics of process and diversity. The internal factors that influence the development of the ability include intelligence factors and non-intelligence factors, and the external factors include the teacher, the school, the family and the society. Learning methods of students, teaching methods of teachers and the layout of materials are both effective way to develop the mathematical generalization ability of senior high students. At last in the empirical research on teachers and students, this paper finds that it is likely to make remarkable progress in the generalization of mathematics for senior high students through improvement of teaching and learning methods.更多还原