建立在理解基础上的记忆

前言众所周知,记忆是人类日常生活中不可缺少的一种行为模式,人类不论做什么都离不开记忆。比如乘法口诀容易记忆且琅琅上口。但从记忆方式上来讲,容易出现机械式记忆、死记硬背,往往忽视掉记忆的意义。当代数学教育强调的是学生的学习方式优化,数学学习中又特别提出针对学习、自主探究、动手实践以及和各种交流等探究式学习模式,这些学习方式都是建立在理解性记忆基础之上的。     

数学要记忆更要理解

数学要记忆还是要理解，这是个似乎不需要讨论的话题，或许平淡得让人不屑一顾，但事实告诫我们，相当数量的学生对数学学习靠记忆还是理解的认识存在两种偏激的倾向：数学依靠理解，不记也行；数学依靠记忆，会套则灵。这两种倾向无形中制约着学生思维的发展，这很值得我们思考。     

初中学生假性理解归因分析及其对策

“一听就懂,一做就错”是初中数学教学中普遍存在的一个现象——假性理解。假性理解指的是学生对概念或数学基本事实、定理、公式、法则、性质,只有机械的记忆和表面的理解,更没有形成能力。因此,对学生学习数学时假性理解的探讨,能更准确地评价、指导学生的学习,更合理地控制教学进程,提高学习能力。一、假性理解的归因分析     

数学概念的理解与记忆教学例谈

数学教学《大纲》中明确要求:小学数学中的概念、性质、法则、公式等,都是基础知识,必须使学生切实学好。培养和发展学生在理解的基础上的记忆,是数学教学的一项重要任务.记忆很重要,没有记忆就没法进行学习。记忆必须是在理解的基础上的记忆,切忌死记硬背。要想处理好这个关系,必须重视和加强概念教学,根据概念进行判断和推理,掌握算理和算法。     

浅谈数学教学中的理解与记忆

在中学生的数学学习中,在培养数学思维能力,强调合情推理、演绎推理的同时,我们也强调要促进学生对数学知识和方法的理解与记忆;课程标准在要求减轻学生的记忆内容的同时,也要求学生记住一些必要的数学知识和方法。由此可见,理解和记忆能力之重要。本文就如何将理解与记忆应用于数学教学中,谈谈自己的看法。     

运用信息技术促进学生数学理解

《普通高中数学课程标准》指出：“教师应帮助学生理解和掌握数学基础知识、基本技能”;“要注重对数学本质的理解和思想方法的把握,避免片面强调机械记忆、模仿以及复杂技巧”．数学理解是数学学习的关键,影响着学生数学情感的发展．促进学生的数学理解,是数学教学的一个重要任务．     

自学数学如何加深理解──自学杂谈之八

自学数学如何加深理解──自学杂谈之八钱宗仁理解记忆是人们公认的重要记忆方法，对于自学数学者来说，应该说是最主要最有效的记忆方法。学习数学达到理解可分为两个阶段。第一阶段是直接理解，即一般所说“懂”。判定一个人对所学某数学问题是否真懂了的一个常用方法，...     

学好数学也需要理解与记忆并重

<正>学习数学重在理解,而记忆是学好语文、英语等文科的必要因素,但为什么要学好数学也需要记忆呢?对于部分符合学生认识水平的知识当然应以理解为主,但有些数学知识相对于学生的认识水平具有超经验性、合情性和难以理解性,因而学生初学起来并不能较好地理解。对于这些知识,学生要在初步理解的基础上先记住并进行一定的训练,然后在     

理解之难

记忆以储存信息为特征,是学习的基础和前提;理解以编译信息、解释信息为特征,是学习的核心和关键.记忆对人类的学习固然重要,但理解对人类的学习更加重要.我们知道,没有理解的记忆一般被称作"机械记忆",其效果是很不理想的,除了极少数"白痴天才",大多数人也很难真正做到"机械记忆".记忆必须引入理解,因为理解才是学习的本质,也是学习的出发点和归宿.     

多元智能理论对理解性数学教学的启示

“学习数学只不过是套公式,如果题目中缺乏足够的条件,他们甚至不知道该用什么公式;如果他们忘记了公式,那就束手无策了,因为他们自己推导不出公式来,不理解公式的真正含义和来源,公式只不过是一堆要记忆的材料而已”。这是我国现行数学教育的某种写照,学习科学的特色就在于它强调理解性学习,因此数学理解成为最近数学教育研究的热点是顺应了这个趋势并切合了实际的需要,有许多的数学教育研究工作者和一线的数学教师纷纷从理论和实践两个方面进行了探索并取得了一定的成果。数学理解是复杂的身心活动,设计促进学生数学理解的教学活动要求教…     

A new perspective on memorization practices among East Asian students based on PISA 2012

Abstract

This study examined learning strategy use in mathematics among East Asian students in East Asian educational systems. By employing latent class analysis on the Programme for International Student Assessment (PISA) 2012 data, we found four classes of learning strategy types, namely memorization with metacognitive strategies (17.49%), metacognitive strategies with memorization (50.70%), elaboration only (10.33%), and metacognitive strategies with elaboration (16.47%). The results showed that the majority of the students in all seven East Asian educational systems belonged to the ‘metacognitive strategies with memorization’ class, and most students adopted more than one type of learning strategy when learning mathematics. Additionally, students who reported the use of metacognitive strategies along with either memorization or elaboration showed higher mathematics achievement. We conclude that the cognitive processes employed by students of East Asian backgrounds are more complex and nuanced than the previous perception that they relied heavily on memorization.     

正确把握学习中的理解

论述了有关理解的下述几个观点对指导学生学习是有利的:1、理解是有层次之分的,学习的过程是一个不断加深理解的过程;2、应从实际出发去强调理解;3、理解与记忆是相互渗透、相互促进的;4、训练既有赖于理解,又有助于理解.     

Universals and specifics in learning strategies: Explaining adolescent mathematics, science, and reading achievement across 34 countries

We examined whether strategies of memorization, transfer through elaboration, and metacognition accounted for reading, science, and mathematics achievement across 34 countries. 158,848 fifteen-year-olds completed a reading literacy test and a questionnaire. Of these students, 88,401 completed a science test, and 88,590 completed a mathematics test. We analyzed the data using multi-level regressions of Rasch-estimated test scores and modeled differences across countries and across schools. Students who reported using memorization strategies often scored lower in all subjects. Transfer through elaboration was not significantly linked to any achievement scores. Lastly, students reporting greater use of metacognitive strategies often scored higher. Compared to students in individualistic societies, to achievement scores of students in collective cultures were linked more strongly to schoolmates' use of metacognitive strategies and less strongly to their own use of metacognitive strategies. These results highlight how cultural contexts can moderate the links between adolescents' learning strategies and their academic achievement.     

Facilitating Learning Events Through Example Generation

This study deals with the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of instances of the concept. Data were collected in spring of 1995 through interviews with 11 third and fourth year undergraduate mathematics students. We discuss the data from the perspective of the student's concept image and introduce the notion of learning event to indicate when a student communicates and applies a new understanding of a concept. We infer that the students in our study who employed an example generation learning strategy were more effective in attaining an initial understanding of the new concept than those who primarily employed other learning strategies such as definition reformulation or memorization.This revised version was published online in September 2005 with corrections to the Cover Date.     

关于数学建构性教学的认识和思考

数学教学应是建构地学与教的统一，建构观下的数学知识应包含数学经验知识和建构策略知识，相关地，数学学习和教学应有两种不同的类型，“建构主义”应成为指导数学教学的行动纲领，建构主义不排斥其它学习理论，建构性教学并非数学建模数学。     

理解数学享受数学

只有真正理解数学内在的应用价值、文化价值、智力价值和本质含义，确定它在学校课程中占有的重要地位。才能使教师的教育理念得以升华。儿童享受到数学学习的快乐。     

Understanding mathematical literacy: The contribution of research

Amid the current ‘math wars’ in the United States, research evidence is being both demanded and attacked by all sides. A recent study designed to synthesize the literature on mathematics learning and to provide research-based recommendations, advice, and guidance developed an elaborated view of mathematical literacy, termed mathematical proficiency in the study report. Mathematical proficiency can serve as a focus for both research and practice, avoiding the extreme positions with respect to the goals of mathematics learning that are so often found in disputes over school mathematics. The study also demonstrated how research could be synthesized so that evidence from research might be used more productively for changing school mathematics in ways that would yield greater mathematical literacy for all.     

Conceptual Understanding of Definite Integral with GeoGebra

This study aimed to determine the effect of a computer-assisted instruction method using GeoGebra on achievement of prospective secondary mathematics teachers in the definite integral topic and to determine their opinions about this method. The study group consisted of 35 prospective secondary mathematics teachers studying in the mathematics education program at a state university in Turkey. The study was carried out using an embedded design, and the Definite Integral Knowledge Test and an opinion form were used for data collection. Upon analyzing the data, the computer-assisted instruction method using GeoGebra was found to positively contribute to the success of teaching the definite integral topic. Prospective teachers stated that this method should be used in math courses as it creates a fun and interesting environment with dynamic learning elements, provides visualization and opportunities to learn mathematics through practice and exercises, enables thorough understanding and explication of skills, and makes way for conceptual learning instead of memorizing. Furthermore, this study was found to facilitate conceptual learning of the relationship between the lower sum, upper sum and Riemann sum.     

Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States

This study investigates Chinese and U.S. teachers’ cultural beliefs concerning effective mathematics teaching from the teachers’ perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis on student understanding with concrete examples, and the sample of Chinese teachers put more emphasis on abstract reasoning after using concrete examples. The U.S. teachers highlight a teacher’s abilities to facilitate student participation, manage the classroom and have a sense of humor, while the Chinese teachers emphasize a teacher’s solid mathematics knowledge and careful study of textbooks. Both groups of teachers agree that memorization and understanding cannot be separated. However, for the U.S. teachers, memorization comes after understanding, but for Chinese teachers, memorization can come before understanding. These differences of teachers’ beliefs are discussed in a cultural context.