统计与概率的教材研究

发布时间：2018-04-20 21:21

本文选题：统计 + 概率　；参考：《华中师范大学》2015年硕士论文

【摘要】：这是一个信息爆炸的时代,网络和计算机科技的飞速发展使我们每天被各种各样、方方面面、随机变换的信息包围,如何筛选这些信息得到我们需要的,给我们的生活带来便利,然后通过恰当的处理,使之为我们所用是当前面临的一个难题.从数学的角度来看,就是如何收集、整理、分析数据并从中获取有价值的信息,作出合乎情理的决策,这是统计学的范畴；公民的日常生活由许许多多随机变换的事件构成,如何经过合理的剖析,恰当的了解这些事件来解决问题已经成为一个新时代人民的必需品,这是概率论的范畴.统计与概率的相关知识在我们每一个人的日常生活中得到了越来越普遍的应用,社会飞速发展,科技日新月异,对人才的要求也逐渐改变,义务教育阶段和普通高中阶段学生加强统计与概率的学习是十分必要的.数学在科学中的应用具有不可思议的有效性,它的结论常常被认为是真理,但是辩证唯物主义告诉我们真理是相对的,数学中的定理、公式等是相对真理,它们的成立是有一定的条件的,并不是“放之四海而皆准”的绝对真理,概率与统计进入中学在很大程度上帮助学生理解数学真理的相对性.概率研究的是具有不确定性的随机事件,这与学生长期接触的数、式、图形等确定性数学是不同的,随机事件本质上与辩证唯物主义发生认识论是相通的.本文首先分析了新课标下小学、初中及高中各个阶段统计与概率的目标要求和内容要求；接着从教材编写方式和呈现方式两方面具体全面的分析教材；最后研究了义务教育和普通高中阶段统计与概率的衔接性与系统性,结合皮亚杰认知发展理论和维果茨基的社会文化观,按照各个阶段学生的认知水平,给教师提出相应的教学建议.
[Abstract]:This is an era of information explosion, and with the rapid development of network and computer technology, every day we are surrounded by a variety of, all kinds of, random information, how to filter this information to get what we need. Bringing convenience to our lives and then dealing with them properly for our use is a current problem. From a mathematical point of view, how to collect, collate, analyze and extract valuable information and make reasonable decisions is a statistical matter; the daily life of citizens is made up of a lot of random events. How to properly understand these events to solve these problems has become a necessity for the people in a new era, which is the category of probability theory. The related knowledge of statistics and probability has been applied more and more commonly in the daily life of every one of us. With the rapid development of society and the rapid development of science and technology, the demand for talents has gradually changed. It is necessary for students in compulsory education and high school to strengthen the study of statistics and probability. The application of mathematics in science has inconceivable validity, its conclusion is often regarded as truth, but dialectical materialism tells us that truth is relative, theorems and formulas in mathematics are relative truth. There are certain conditions for their establishment, which is not the absolute truth of "letting the whole world fit". To a great extent, the entry of probability and statistics into the middle school helps students understand the relativity of mathematical truth. Probability studies random events with uncertainty, which is different from deterministic mathematics, such as numbers, formulas, graphs and so on, which students have been in contact with for a long time. In essence, random events are connected with dialectical materialist occurrence epistemology. This paper first analyzes the target requirements and content requirements of statistics and probability in each stage of primary, middle and senior middle schools under the new curriculum standard, and then analyzes the teaching materials from two aspects: the way of compiling textbooks and the way of presentation. Finally, the paper studies the connection and systematicness of statistics and probability in compulsory education and ordinary senior middle school, combining Piaget's cognitive development theory and Vygotsky's social and cultural view, according to the cognitive level of students in each stage. Put forward the corresponding teaching suggestion to the teacher.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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