数学基本活动经验 研究：内涵与维度划分

Research on Mathematical Fundamental Activity Experience： Definition and Dimensions

数学基本活动经验与基础知识不同，知识可以传递，数学基本活动经验不能被传递，需要亲身经历和感悟；数学基本活动经验不同于数学能力，能力被人为细化，直接影响活动效率，数学基本活动经验更为综合，没有直接载体说明经验有无或强弱，但一定时间积淀的思维模式反映数学基本活动经验积累的结果。数学基本活动经验是经历和感悟了数学归纳推理和演绎推理后积淀的思维模式，最终建立一定的数学直观。维度划分体现数学基本活动的过程，概括为：观察、归纳猜想、表达、验证或证明。

Mathematical fundamental activity experience is different from mathematical knowledge. Knowledge can be passed on but the experience must be a combination of personal practice and comprehen sion. Mathematical fundamental activity experience is also different from mathematical ability. Ability can be divided into parts and has direct impact on the efficiency of activity， while the experience is more com- prehensive and can hardly be directly manifested as ＂existing/non-existing＂ or ＂strong/weak＂ ; but the re sults of long-term accumulation of mathematical fundamental activity experience can be represented by the mode of mathematical thinking. Mathematical fundamental activity experienee provides the basis for the formation of the individual's mode of mathematical thinking， which is the consequence of personal experi ence of the process of mathematical inductive and deductive reasoning over an extended period of time. The outcome of this process is the formation of mathematical intuition. The dimensions of mathematical funda- mental activity experience represent the process of mathematical fundamental activity including observa- tion， inductive guess， expression， and testing or verification.