论数学素质及其发展

作者：吴慧君、公绪杰

国籍：中国

出处：沈阳电力高等专科学校学报第2卷第1期

中文译文：

论数学素质及其发展

摘要：人类已经进入了信息时代,数学及其应用的发展对社会的发展所起的作用空前地加强了。这篇论文从两个方面论述了数学素质的重要性,一个是精确的定量思维和准确的定性思维,另一个是数学在解决实际问题中的应用,同时还论述了怎样培养数学素质。

关键词：数学;素质;教育

素质是一个人拥有的内在东西，它是一个人的精神、知识、能力、语言、行动等的综合，没有任何一个特征可以概括一个人的素质，它可以随着时间的推移以某种模式表现出来。在学校教学中，各学科都有一个共同的任务，那就是培养学生的素质，但各学科都有自己的重点，其他学科不能代替数学教学在培养学生素质过程中的作用。在基础教学阶段，数学学习可以使学生养成数学思维的习惯，形成观察世界和处理数学问题的能力。

我国正处于以经济建设为中心，构建社会主义摇篮和经济框架的时期，数学所发挥的社会功能及其应用将与以往有很大的不同。这就要求我们不仅要掌握必要的数学知识和技术，而且要在数学教学中获得与数学有关的良好素质。

一、 精确的定量思维和准确的定性思维

有研究者指出：定量思维是指人们从事实中获得问题，将其抽象为数学模型，从模型中获得答案或近似答案，然后对其进行检验，必要时修改模型以更好地接近事实，最后将该问题编成软件，使其得到更广泛和更方便的应用。这场讨论是对人类活动中所包含的数学活动的最好描述。我们可以从中得出，在解决问题的过程中，定量思维从开始到结束都存在。从某种意义上说，学习数学的主要作用是形成计算的思维，培养按规定步骤计算的习惯，和培养设计新程序的能力。

计算包括按照规律进行精确计算、心算和近似计算。它可以训练推理能力，培养按部就班的操作技巧，养成有规律的行动习惯。计算还可以提高把握整体事物的能力，探究事物的本质，通过选择适当的计算方法和判断结果的合理性来准确理解数据的特性。事实上，从逻辑推理中获得的结果只是计算的一小部分，更重要的是计算方法的构建、设计、选择，以及对定理的理解和应用。计算是一个数学实验的过程，它包括了丰富的数学实践，可以让我们深刻理解数学的真谛，是训练定量思维和定性思维的最佳途径之一。

二、 利用数学解决实际问题的意识

数学来自于现实，它是对现实进行抽象后的符号表达，是从数学的角度通过逻辑推理和计算获得和体现物质的特征。数学应用的重要性可以从技术发达的国家得到证明，这些国家的管理者、军事家和政治家在数学方面并不比相应的中国人强，但他们可以在行政和管理方面自觉地使用数学。例如，在花费大量资金和物质资源之前，他们肯定会邀请数学家来处理生产和管理方面的实际问题。贝尔实验室聘请了许多数学家，他们同样也很重视数学在军事方面的应用。据说在海湾战争中，在美国下令转移庞大的军事和后勤系统之前，他们已经制定了一个具有数百万变量的线性规划。所以甚至有人说：“如果第二次世界大战是一场物理战争，那么海湾战争就是一场数学战争。”人们可以从提供的信息中联想到数学理论，应用数学理论处理所面临的问题，我们可以得到不同数学理论之间实际的内在联系，这种联系可以使人们了解另一个领域。将数学与模型联系起来的思想是这方面的典型代表，建立不同数学理论之间的联系是数学应用的另一种模式。

三、 结论

现在提倡素质教育是一个正确的理念。虽然我们在古代取得了卓越的成就，但我们从13世纪开始就落后了。然而，近代中国数学借鉴了国外的数学，使得我们在数学上取得了很大的成就，但是这与我们的文化并不能很好地协调。人们对数学的意识是相当漠不关心的，所以我们不得不提倡数学素质的发展。

附：外文原文

On the Quality of Mathematics and Its Development

Wu Huijun Gong Xujie

（Communication Class 981 . Shen yang Electric Power Institute )

Abstract We have entered the era of information. The importance of mathematics and its application to the developing of society is unprecedently strengthened. This paper states the importance of nurturing mathematics quality mainly in two parts, one is definite quantitative thought and accurate qualitative thought., and the other is the importance played by mathematics in handling practical problems. It also tells how to nurture the quality of mathematics.

Key words mathematics; quality; education

Quality is something internal that one owns, it is a synthesis of ones spirit, knowledge, ability. words, actions and so on. Theres no single characteristic can summarize mans quality. It can be ex- pressed in some pattern along with time. In school instruction, disciplines have a common task, which is to develop students quality, but each has its own emphasis. Others cannot replace the mathematical instruction s action iii the procession of ones quality developing. During the stage of basic instruct ion, the study of mathematics can make students nurturing the habit of thinking mathematically. forming the ability of observing the world and handling the matter in mathematics.

Our country is now in the period of taking coco- nomic developing as the center of our work. build- Ing the framework of socialist basket economy. The funk ion of society played by mat chat ices and its application will be instant lee deferent from what it was before. It requires us not only to master nieces- sari mat lemmatical knowledge and tech nick, but al- so to gain good quality connected with mathematics during the instruction of mat hepatics.

1. Definite quantitative thought and accurate qualitative thought

Some researchers pointed out; quantitate ivy though it is that people gain problem from the fact, abstract it into mat hem at ices model. get the answer or approximate answer from the model then check it. modify the model to press close to the fact better when it is necessary y, finally make up software of the matter to make wider and more convenient ap- plication. This discussion is to lie best description to the activity y of mat heat ices contained in people s ac- trivet is. We can see from it. that quantitative t Hough t exists from the beginning to the end during the course of set to link the matter. From some points, the main Inuit ion of set undying mathematics is to form the thought of computation. to north urea the habit of calculating according to the required procedure and to nurture the ability y of designing new procedure.

Calculation includes acc urate calculating accord- Ing to the regulation, calculating by heart, and ap- proximate computation. It can train the skill of in-

refence, nurture the technique of operation according to the procedure, form the habit of acting regularly. And it can raise the ability of holding matters as a whole, investigating the essence of matter, under- standing the character of data accurately by choosing

surely invited the mathematicians to deal with the practical problems in production and administration. A lot of mathematicians are employed in BELL lab. They also lay emphasis on the application of math- mastics in military affairs.

the proper calculation and judging the rea-son ability of the result. In fact, the result gained from logical

to transfer

before the USA ordered

War,

a huge and rear service system. They had work

deduction is a very small part of calc elation. Whats out a linear programming millions of variables.

more important is the construction, designing, choos

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