论文部分内容阅读
《数学课程标准》把数列视为反映自然规律的基本数学模型,要求在教学中通过日常生活中的实例,了解数列的概念和几种表示方法,特别指出要体现数列是一种特殊函数(离散函数),通过列表、图像、通项公式表示数列,把数列融于函数之中。函数思想是中学阶段学生所接触到的最重要的数学思想方法之一。数列作为一种特殊的函数,更是与函数思想密不可分,任何数列问题都蕴含着函数的本质及意义,具有函数的一些固有特征。因此我们在数列教学中,应充分利用其函数本质,以函数的概念、图象、性质为纽带,架起函数与数列之间的桥梁,揭示它们间的内在联系。而函数、方程和不等式三者密不可分,等差数列和等比数列作为两类特殊数列,自然有着千丝万缕的联系。
The Mathematical Curriculum Standard treats a sequence as a basic mathematical model that reflects the laws of nature and asks for an understanding of the notion of sequence and several representations of teaching through the examples in daily life. In particular, it is pointed out that the sequence is a special function (Discrete Function), through the list, image, general formula series, the series into the function. Function thinking is one of the most important mathematical thinking methods that middle school students come across. As a special function, the sequence is closely related to the function thought. Any series of questions contain the essence and meaning of the function, and have some inherent features of the function. Therefore, we should take full advantage of the nature of its functions in sequence teaching, take the concept, image and nature of the function as a link, set up a bridge between the function and the sequence, and reveal the intrinsic connection between them. The function, equation and inequality are inseparable, and the arithmetic sequence and the geometric sequence are two kinds of special sequences. They are inextricably linked.