操作延展性练习教学——在两种推理交互作用中发展数学新知识  

To Manipulate the Exercise Teaching of Ductility and Malleability:Developing New Mathematical Knowledge in the Interaction of Two Kinds of Reasoning

作　　者：顾丽英 邓德巍 GU Li-ying;DENG De-wei(Wuxi Xinzhou Primary School,Jiangsu Wuxi 214112,China;Hongze Experimental Primary School of Huai’an City,Jiangsu Huai’an 223100,China)

机构地区：[1]无锡市新洲小学,江苏无锡214112 [2]淮安市洪泽实验小学,江苏淮安223100

出　　处：《数学教育学报》2022年第3期50-55,93,共7页Journal of Mathematics Education

基　　金：江苏省教育科学“十一五”规划重点项目——发生认识论与数学的抽象度分析法(C-c/2001/02/007);江苏省教学研究“十三五”立项课题——基于ELLI框架的多元文化背景下儿童学习力培养研究(2019JK13-L038)。

摘　　要：在宏观背景和教育大环境相对不变的情况下,改进教学方法是提高教学质量的根本措施.各种教学方法层出不穷,其种类和定义也更加具体确切,更加专业.延展性教学就是一种.延展性是源于物质的一种物理属性,指可锤炼可压延的程度,这里把它拟人化地用于数学教学,以锤炼一个人的数学品质与能力,借以高标准地提高学生的数学核心素养.在回顾与分析这种教学方法的特点与模式之后,把它纳入到认知心理学及教育学研究的“三象一作”数学认知过程,由无锡市新洲小学等学校展开延展性练习教学.教师精心设计教学过程,通过一些典型教例,把“语言传递、直接感知、实际训练、引导探究、活动欣赏”等几种常用方法融为一体,在合情推理与演绎推理交互作用中延伸与拓展数学思维活动,发展数学知识.通过统计分析,学生数学推理能力有显著提高.实践证明数学课堂的延展性教学这种教学方法在小学数学教学中是可行的和有效的.其努力方向是:针对不同学生的认知基础和认识方式的差异,教学设计中还必须为学生提供和呈现多样化策略的应用与选择.延展性教学的进一步诠释过程中,对数学教学的终极目标也作了一点思考.Under the condition that the macro background and educational environment remain relatively unchanged,improving teaching methods is the fundamental measure to improve teaching quality.Various teaching methods emerge in an endless stream,and their types and definitions are more specific,more precise,and more professional.Ductility teaching is one of them.Ductility is a physical property derived from matter,which refers to the degree to which it can be tempered and calendared.Here,it is used in mathematics teaching to temper a person’s mathematical quality and ability,so as to improve students’mathematics competencies to a high standard.After reviewing and analyzing the characteristics and models of this teaching method,it was incorporated into the“three images and one work”mathematical cognitive process of cognitive psychology and pedagogy research.This ductility and malleability teaching practice was carried out by Wuxi Xinzhou Primary School and other schools.Teachers carefully design the teaching process,through some typical teaching examples,integrate several common methods such as“language transmission,direct perception,practical training,guided inquiry,and activity appreciation”,extend the interaction between plausible reasoning and deductive reasoning,expand mathematical thinking activities,and develop mathematical knowledge.Through statistical analysis,students’mathematical reasoning ability has been significantly improved.Practice has confirmed that the teaching method of extension teaching in mathematics classroom is feasible and effective in primary school mathematics teaching.The direction of its efforts is:in view of the differences in the cognitive basis and cognitive methods of different students,the teaching design must also provide and present the application and selection of diverse strategies for students.In the process of further interpretation of ductility teaching,some thoughts are also made on the ultimate goal of mathematics teaching.

关 键 词：“三象一作”过程 延展性练习教学 合情推理能力 逻辑推理能力 终极目标 

分 类 号：G447[哲学宗教—心理学]