新课标小学数学教科书中的算理知识及其掌握研究

发布时间：2018-08-10 17:31

【摘要】：算理知识是在解决数学问题的过程中,技能操作的程序和步骤背后的原理与依据。义务教育数学课程标准(2011年版)明确提出:课程内容不仅包括数学结果,也包括数学结果的形成过程和蕴含的数学思想方法,它的选择要有利于学生体验与理解、思考与探索,从而培养学生问题解决的能力。研究主要从两方面进行:首先,利用文本分析法对新课标小学数学教科书(2012年版)中的算理知识进行系统化分析;其次,以小学数学教师为研究对象,通过实证研究的方法调查其对算理知识掌握程度,同时对影响小学数学教师算理知识掌握程度的因素进行分析。根据研究,将小学数学教科书中的算理知识按呈现方式及呈现层次分类。呈现方式分别为教科书正文呈现、阅读材料呈现与习题呈现三类,呈现层次分别为教科书中全部呈现、部分呈现与未呈现三类,分别对每一类进行具体分析。依照此分类及各维度知识的比例编写测试卷,对新疆乌鲁木齐市47名小学数学教师进行测试,对教师的掌握程度及影响因素进行分析。研究的主要结果为以下几点。(1)对教科书中的算理知识进行梳理分类,用图片的形式呈现教科书中的内容,分析教科书中对算理的呈现形式。按照呈现层次对每类算理知识进行具体分析,得出算理的由来。(2)根据测试结果的统计,小学数学教师对算理知识的掌握程度并不理想,测试卷总平均分为55.57。按呈现方式分类时,在教科书阅读材料中呈现的算理知识掌握程度最弱,在习题中呈现的算理知识掌握程度较好;按呈现层次分类时,教科书中部分呈现的算理知识掌握程度最弱,全部呈现及未呈现的算理知识掌握程度较好。(3)根据测试结果与个案分析,发现对小学数学教师算理知识掌握的影响因素分别为教科书中算理知识呈现形式、教师学历、教龄、职称及任教年级等。(4)教科书中算理知识呈现形式是影响教师算理知识掌握程度的主要因素。在教师学历方面,大专学历教师各部分算理知识平均得分均低于本科学历教师。在教师教龄与职称方面,随着教龄与职称的增长,测试卷平均分大体呈递增趋势。在任教年级方面,任教高年级段的教师得分明显高于于其他教师。
[Abstract]:The knowledge of calculation is the principle and basis behind the procedures and steps of skill operation in the process of solving mathematical problems. The mathematics curriculum standard of compulsory education (2011 edition) clearly points out that the curriculum content includes not only the mathematics result, but also the forming process of the mathematics result and the mathematics thought method contained therein. The choice of the curriculum should be beneficial to the students' experience and understanding, thinking and exploration. So as to cultivate students' ability to solve problems. The research is mainly carried out from two aspects: first, the text analysis method is used to systematize the knowledge of calculation in the new curriculum standard primary school mathematics textbook (2012 edition); secondly, the primary school mathematics teachers are taken as the research objects. Through the method of empirical research, the author investigates the degree of mastery of mathematical knowledge, and analyzes the factors that affect the degree of mastery of mathematical knowledge of primary school mathematics teachers. According to the research, the mathematical knowledge in primary school mathematics textbooks is classified according to presentation mode and presentation level. The presentation methods are textbook text presentation, reading material presentation and exercise presentation, presentation levels are all presented in the textbook, partial presentation and non-presentation of three types, respectively, for each type of specific analysis. According to this classification and the proportion of knowledge in each dimension, 47 primary school mathematics teachers in Urumqi, Xinjiang were tested, and their mastering degree and influencing factors were analyzed. The main results are as follows: (1) sorting out and classifying the knowledge of calculation in textbooks, presenting the contents of textbooks in the form of pictures, and analyzing the forms of presentation of reasoning in textbooks. According to the level of presentation of each kind of knowledge of calculation specific analysis, the origin of reasoning. (2) according to the results of the test statistics, primary school mathematics teachers to master the degree of knowledge of calculation is not ideal, the average test paper is divided into 55.57. When classifying according to presentation, the degree of mastery of mathematical knowledge presented in textbook reading materials is the weakest, and the degree of mastery of mathematical knowledge presented in exercises is better; when classifying according to presentation level, Part of the textbook presents the weakest degree of knowledge in the knowledge of calculation, all presented and not presented, the degree of mastery of the knowledge of calculation is better. (3) according to the test results and case analysis, It is found that the factors influencing the mastery of mathematical knowledge in primary school mathematics teachers are the presentation form of mathematical knowledge in textbooks, teachers' educational background and teaching age. Professional title and teaching grade. (4) the form of knowledge presentation is the main factor that affects teachers' knowledge of calculation. In terms of teachers' qualifications, the average scores of each part of the teachers with junior college qualifications are lower than that of teachers with undergraduate degrees. In terms of teachers' teaching age and professional title, the average score of test paper increases with the increase of teaching age and professional title. In terms of teaching grade, the score of teachers in senior grades was significantly higher than that of other teachers.
【学位授予单位】：新疆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G623.5

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