形式化方法在高中算法教学中的应用研究

Research on Application of Formal Methods in High School Algrithmic Teaching

国家教育部制定的高中新课程标准将算法初步作为高中数学课程的必修内容,算法与程序设计也首次纳入到选修课之列。全国大部分普通高中均按新课标开展教学实验,不少省份还把算法内容纳入高考。同时现有算法初步和算法与程序设计教材在介绍算法与算法设计方法时,无法说清楚算法设计的过程;在教学实践中,这一问题更加突出。这给高中生学习、理解及掌握算法和算法设计方法带来很大的困难。本文从新课程实验教材中及数学高考题中选取两个问题,用支持算法程序形式化开发的PAR(Partition And Recur)方法与PAR平台,从待求解问题的精确功能描述出发,经过一系列等价数学变换,最后得到正确的算法和程序。实践说明PAR方法与PAR平台可以在高中算法教学及学生能力评测中发挥建设性作用。

The algorithm is adopted initially as a required course of high school mathematics curriculum content by ministry of education high school curriculum standards,the algorithm and program design goes into the list of elective courses for the first time.The new curriculum in most high school teaching is experimented,and many provinces incorporate it in the College Entrance Examination.Meanwhile the existing teaching materials of algorithms and the algorithms and procedures are designed for introducing algorithms and algorithm design method,can not make clear the process of algorithm design,in teaching practice,this problem is acute.It makes high school students hard to learn,understand and mastering the method and algorithm design.This paper selects two issues from new curriculum teaching materials and mathematics test questions of College Entrance Examination,supporting by PAR,to solve the problem from the exact function description,through a series of equivalent mathematical transformation,finally gets the right algorithm and procedures.The practice shows that PAR method and PAR platform in high school teaching and evaluating student ability can play a constructive role.