程序性知识课程设计的新视角:算理贯通,算法统整  

A New Perspective on Procedural Knowledge Curriculum Design:Arithmetic Coherence and Algorithmic Integration

作　　者：巩子坤[1] 张希 金晶 史宁中[3] Gong Zikun;Zhang Xi;jin jing;Shi Ningzhong(Jin Hengyi Honors College,Hangzhou Normal University,Hangzhou Zhejiang 311121,China;School of Science,Hangzhou Normal University,Hangzhou Zhejiang 311121,China;School of Mathematics and Statistics,Northeasi Normol University,Changchun Jilin 130024,China)

机构地区：[1]杭州师范大学经亨颐教师教育学院 [2]杭州师范大学理学院,杭州311121 [3]东北师范大学数学与统计学院,长春130024

出　　处：《课程．教材．教法》2021年第6期89-95,共7页Curriculum，Teaching Material and Method

摘　　要：程序性知识课程设计的关键是解决“算理贯通、算法统整”问题,而“分数运算算理贯通、算法统整”是关键中的关键。从公理、定义、运算律和性质出发,基于“演绎推理”,推演分数加、减、乘、除运算的算理,以不变的算理来推导万变的算法,实现分数运算内部算理的一致性,从而实现分数、小数运算算理的一致性。同时,基于“计数单位”,推导分数运算的算法,以不变的算法来统整有理数的运算,实现分数运算与整数、小数运算前后算法的一致性。然后,以分数除法中“一个数除以分数”为例,重构利于学生理解算理、统整算法的教学设计,例说上述两个一致性是如何实现的。最后给出程序性知识课程设计的建议。The key to the design of a procedural knowledge curriculum is to solve the problem of“arithmetic coherence and algorithmic integration”,and“arithmetic coherence and algorithmic integration in fraction operations”is the key to this.The arithmetic of addition,subtraction,multiplication and division of fractions is deduced from axioms,definitions,laws and properties,based on“deductive reasoning”,to achieve consistency in the internal arithmetic of fractions and thus in the arithmetic of fractions and decimals.At the same time,the algorithm of fraction operations is derived based on the“counting unit”,and the algorithm of rational numbers is unified by the unchanging algorithm,thus achieving consistency between the algorithms of fraction operations and those of integers and decimals.Then,using the example of“dividing a number by a fraction”in fraction division,we reconstruct a design that facilitates students’understanding of arithmetic and unifies the algorithm,illustrating how these two consistencies are achieved.Finally,suggestions are given for the design of procedural knowledge lessons.

关 键 词：程序性知识 算理贯通 算法统整 演绎推理 

分 类 号：G623.5[文化科学—教育学]