初中方程内容的教材比较研究

发布时间：2018-08-06 15:17

【摘要】：在《全日制义务教育数学课程标准(2011年版)》颁布之后,各版本教材相继进行了新一轮修订,方程作为义务教育阶段数学教学的核心内容,具有重要研究价值,为更好的把握新版教材中的方程内容,本研究以人民教育出版社、北京师范大学出版社、江苏科学技术出版社,这三个版本教材为研究对象,对教材中方程及相关内容展开比较研究.通过对一元一次方程、二元一次方程组、分式方程、一元二次方程的系统研究,意在突出方程在初中学习中的整体性,本研究主要从教材中方程体系结构、呈现方式及教材特色这三方面展开比较,得到以下研究结论：对方程体系结构的研究,主要从方程体系与方程结构两个角度展开。首先,三个版本教材的方程体系相似性较强,都是按照一元一次方程、二元一次方程(组)、分式方程和一元二次方程的顺序展开,其中对二元一次方程组、分式方程、一次函数的学习顺序三个版本稍有不同,并且每部分内容课时安排也有差异；其次,对方程结构,通过横向与纵向的比较研究,发现三个版本教材对方程内容的呈现都采用了螺旋上升的结构形式,整体结构具有很强的相似性,各部分方程内容标题大致分为认识方程模型、求解方程和应用方程三大类,基本遵循了“问题情境→建立方程模型→求解、应用与拓展”的模式,各类方程的设计思路也基本一致,一方面体现了教材自身设计的一贯性,另一方面,也在一定程度上体现了现行教材的趋同性。对方程呈现方式的研究,主要从教材体例、栏目设置、问题素材这三个角度展开.首先,从教材体例角度分析,人教版教材结构体例形式最丰富,苏科版次之,北师版相对较简单；其次,从栏目设计角度分析,苏科版教材设置的栏目形式最丰富,但功能存在重叠,人教版栏目设置较丰富,缺少操作活动类栏目,北师版栏目设置相对简单；最后,从教材章前问题角度分析,三个版本在问题数量及背景方面都存在差别,对于教材例题习题的问题数量及素材选择也存在明显差异。对教材特色的研究,主要分析了各版本教材对数学思想方法的渗透,其中包含方程思想,化归思想,数形结合思想,分类思想,以及换元、降次、消元、配方等数学方法,各版本教材的设计具有一定特色。
[Abstract]:After the promulgation of the Mathematics Curriculum Standard for Full-time compulsory Education (2011 Edition), various editions of textbooks have been revised one after another. As the core content of mathematics teaching in compulsory education, the equation has important research value. In order to better grasp the equation content in the new edition of textbooks, this study takes the three editions of textbooks as research objects: people's Education Press, Beijing normal University Press, Jiangsu Science and Technology Publishing House. A comparative study of the equations and related contents in the textbook is carried out. Through the systematic research on the first order equation, binary first order equation group, divisional equation and quadratic equation, the purpose of this study is to highlight the integrality of the equation in junior middle school. By comparing the presentation methods and the characteristics of the textbooks, the following conclusions are drawn: the research on the structure of the equation system is mainly from the two angles of the equation system and the equation structure. First of all, the three versions of the textbook have strong similarity in equation systems, all of which are expanded according to the order of the first order equation, the binary first order equation, the fractional equation and the quadratic equation, among which, for the binary first order equation system, the fractional equation. The learning order of the first function is slightly different in three versions, and there are also differences in the class hours of each part of the function. Secondly, the structure of the equation is studied through the comparative study of horizontal and vertical. It is found that the contents of the equations are presented in spiral ascending form in the three editions of textbooks, and the whole structure is very similar. The contents of each part of the equations can be divided into three categories: the cognitive equation model, the solving equation and the applied equation. It basically follows the model of "problem situation establishing equation model solving, applying and expanding", and the design ideas of all kinds of equations are basically the same. On the one hand, it embodies the consistency of the design of the textbook itself, on the other hand, it shows the consistency of the design of the textbook itself, on the other hand, To a certain extent, it also reflects the convergence of existing textbooks. The research of equation presentation is mainly from three angles: textbook style, column setting and problem material. First of all, from the perspective of the style of teaching materials, the structure of teaching materials is the most abundant, the version of Su is the second, and the version of Northern teacher is relatively simple. Secondly, from the perspective of column design, the form of columns set up in the teaching materials of Suke edition is the most abundant. However, there is overlap in function, abundant column setup, lack of operating activity column, and relatively simple column setup in Beishi version. Finally, from the perspective of pre-chapter problems in textbooks, there are differences in the number and background of the problems in the three editions. There are also obvious differences in the number of questions and the selection of materials for the textbook sample exercises. The research on the characteristics of the textbook mainly analyzes the infiltration of each edition of the textbook to the mathematical thinking methods, including the thought of equation, the thought of transformation and reduction, the thought of combining numbers and shapes, the thought of classification, and the mathematical methods of changing, dropping, eliminating, formula, etc. The design of each edition of the textbook has certain characteristics.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【共引文献】