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1.缘起在高三复习的一次阶段性检测中,有如下一道填空题:设f(x)是定义在R上的函数,若对任意x,f(x)满足:(1)f(x+3)≤f(x)+3,(2)f(x+2)≥f(x)+2,(3)f(3)=1,则f(2013)=____题中所给的条件,是用不等式组的形式,来描述一系列特殊点的函数值,具有周期性的变化规律.抽象性较强,有一定的难度.但从考试结果来看,却并非如此(全班50人,47人答对).因此,笔者的直觉,部分学生在解答中可能存在着某些非理性的因素.学生是如何分析的?使用的什么方法?是独特而深刻的思维
1. Origin In a high school review of a phased test, there is a following fill in the blank: Let f (x) be a function defined on R, if for any x, f (x) satisfy: (1) f F (x) = f (x) +2, (3) f (3) = 1, then f The condition is to describe the function values of a series of special points in the form of inequality groups, with the regularity of periodic variation, with strong abstraction and a certain degree of difficulty, but this is not the case from the test results (class 50 People, 47 correct answer.) Therefore, the author’s intuition, some students may have some irrational factors in the solution.How do students analyze? What method is used? It is a unique and profound thinking