高一学生图式语言转换能力调查研究

发布时间：2018-11-03 09:14

【摘要】：数学语言是数学知识和思维的载体,是进行数学交流的有效工具,甚至可以说“数学教学就是数学语言的教学”。数学语言按其表现形式可分为文字语言、符号语言和图式语言三种类型。在解决问题的过程中,往往需要进行不同形式语言的转换,而数学语言转换能力也是数学能力的重要标志。21世纪,人们已经进入了一个“读图”时代,学生应该具备一定的读图、作图和用图的能力,具备一定的图式语言转换能力是现代社会对所有学生的要求。为了了解高一新生图式语言转换能力的现状,笔者通过对文献的分析研究制定出相应的测试题,并走访邯郸市不同层次的多所学校进行了预测试,最终选定四所学校的209名高一学生作为样本进行了正式测试。问卷主要从将图式语言转换为文字语言、将图式语言转换为符号语言以及图式语言自身的转换三个方面来测试,并在问卷调查后对个别学生、教师进行了访谈来弥补问卷调查的不足。经整理分析最终得出高一学生图式语言转换能力在以下几方面相对较差:将图形语言转换成文字语言、将图像语言转换成符号语言、图表语言内部的转换。具体结论如下:(1)绝大多数学生数学语言表达能力较弱,出现表述不清、用词不准确、表述冗长等现象;(2)大多数学生读图能力较差,不能理清图中各元素的相互位置关系以及所包含的数量关系,不能将图形的形状和数量关系结合起来进行描述;(3)大多数同学对特殊函数的图像在形的方面有一定的掌握,但是对它们隐含的一些数量关系不是很明确;(4)绝大多数的学生符号应用意识差,不了解符号语言的几何意义;(5)一半学生用图的意识薄弱,忽视图中文字和符号语言的描述,导致理解出现偏差;(6)学生的作图能力较差,仅有极少数学生能够正确规范的做出图形;(7)学生将图形语言转换为图像语言的能力相对稍强。针对高一新生图式语言转换能力的现状,提出高中阶段提高学生图式语言转换能力的教学建议,有关加强学生读图训练的具体策略:(1)培养学生的读图兴趣,提高学生的读图能力;(2)丰富学生读图的素材,提高学生读图能力。有关加强学生作图训练的具体策略:(1)教师应重视基础图形的教学,;(2)课堂上,教师应该给学生展示作图的机会;(3)教师应该培养学生良好的作图习惯。有关加强学生用图训练的具体策略:(1)在图式语言的基础上发展其它形式的数学语言;(2)教师在平时教学中重视图式语言;(3)注重概念教学,精讲概念的含义。
[Abstract]:Mathematical language is the carrier of mathematics knowledge and thinking, it is an effective tool for mathematical communication, and it can even be said that "mathematics teaching is the teaching of mathematical language". Mathematical language can be divided into three types according to its manifestation: literal language, symbolic language and schematic language. In the process of solving problems, it is often necessary to change different forms of language, and the ability of mathematical language conversion is also an important symbol of mathematical ability. In the 21st century, people have entered an era of "reading pictures". Students should have the ability to read, draw and use drawings, and the ability of schema language conversion is the requirement of all students in modern society. In order to understand the current situation of schema language conversion ability of freshmen in Senior one, the author made the corresponding test questions through the analysis and study of the literature, and visited many different schools in Handan City to carry out prediction tests. A sample of 209 freshmen from four schools was selected for formal testing. The questionnaire is mainly tested from three aspects: transforming schema language into literal language, transforming schema language into symbolic language and transforming schema language into schema language itself. Teachers conducted interviews to make up for the deficiencies of the questionnaire survey. After finishing and analyzing, it is concluded that the ability of schema language conversion is relatively poor in the following aspects: converting graphics language into text language, image language into symbolic language, and internal transformation of chart language. The specific conclusions are as follows: (1) the majority of students' mathematical language expression ability is weak, the expression is not clear, the words are not accurate, the expression is long and so on; (2) most students have poor ability to read pictures and can not clearly understand the relationship between the position and quantity of each element in the graph, and can not combine the shape and quantity of the graph to describe it; (3) most of the students have a certain grasp of the image of the special function in shape, but some of the implicit quantitative relationships are not very clear; (4) most of the students have poor awareness of the application of symbols and do not understand the geometric meaning of symbolic language. (5) half of the students have weak consciousness of using pictures and ignore the description of characters and symbolic languages in pictures, which leads to the deviation of understanding. (6) students' ability of drawing is poor, only a few students can make graphics correctly and normatively; (7) students' ability of converting graphics language to image language is relatively strong. In view of the present situation of schema language conversion ability of freshmen in senior high school, the author puts forward some teaching suggestions on how to improve students' schema language conversion ability in senior middle school. The specific strategies for strengthening students' reading ability are as follows: (1) cultivating students' interest in map reading; Improve students' reading ability; (2) enrich students' reading materials and improve students'reading ability. The specific strategies for strengthening students' drawing training are as follows: (1) teachers should attach importance to the teaching of basic graphics (,; (2), teachers should show students the opportunity of drawing, and (3) teachers should cultivate students' good drawing habits. The specific strategies to strengthen the training of students' drawing: (1) to develop other forms of mathematical language on the basis of schematic language; (2) to attach importance to schema language in normal teaching; (3) to pay attention to the teaching of concepts and to elaborate on the meaning of concepts.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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