数学理解的三种基本形态及教学启示  

Three Basic Forms of Mathematical Understanding and Implications for Teaching

作　　者：徐彦辉[1] XU Yan-hui(College of Mathematics and Physics,Wenzhou University,Wenzhou 325035,China)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《宁波大学学报（教育科学版）》2022年第5期66-72,共7页Journal of Ningbo University(Educational Science Edition)

基　　金：浙江省高等教育“十三五”教学改革研究项目“新工科背景下数学类专业应用型人才培养模式的研究”(jg20180297)。

摘　　要：数学理解包括三种基本形态,即:记忆性理解、解释性理解和探究性理解,这三种数学理解分别对应着“记得、晓得和明得”三种不同的状态。三种数学理解对数学学习都是有价值的,但仅有记忆性和解释性理解是不够的,探究性理解才是数学教学的最终目标。实践中,不少水平不高的教师常常只能让学生达到记忆性理解,有一定水平的教师能让学生达到解释性理解,真正让学生达到探究性理解的教师并不是很多。教师要不失时机地促进学生数学理解层级的迭代升级,促使学生最终达到探究性理解,吴文俊院士数学学习的经验对把握数学理解的三种基本形态有借鉴和启迪意义。在课堂教学中引导学生从事生动活泼的数学探索性活动常常是一个相当艰难的过程,对教师的数学探究素质提出了较高的要求,教师应努力引导学生去探求数学知识的意义和发现的过程,促使学生数学探究性理解方式的养成。The three basic forms of mathematical understanding involve memory understanding, explanatory understanding and exploratory understanding that correspond to three states of “remembering, knowing and exploring”, being vital to mathematical understanding and learning. This means that students have to be upgraded from memory and explanatory understanding to the ultimate teaching goal of exploratory understanding. In practice, most instructions often allow students to achieve the memory understanding or the explanatory understanding while ignoring the exploratory understanding. This study argued that it is of great significance to examine the three basic forms of mathematical understanding by referring to Wu Wenjun’s experience of mathematics learning. It believed that mathematical teachers are supposed to direct students’ to be engaged in the lively mathematical exploratory activities as a great challenge in quality mathematics inquiring to foster students’ mathematical knowledge and process of discovering mathematics, and eventually develop the ultimate goal of exploratory understanding of mathematics.

关 键 词：数学理解 记忆性理解 解释性理解 探究性理解 

分 类 号：G40-032[文化科学—教育学原理]