高中数学人教A版新旧教科书数列部分的比较研究

【作者】 王倩；

【导师】 罗新兵；

【作者基本信息】 陕西师范大学 ， 教育硕士（专业学位）， 2021， 硕士

【摘要】 随着新版高中数学教科书在全国的普及,将有更多省市的高中数学教师面临从旧版教科书向新版教科书的过渡。如何把握新教科书编写的变化对于教师来说是一个非常重要的问题。数列在数学教学中占有重要地位,它是许多数学知识联系的交汇点,与函数、算法、微积分等知识之间都有紧密联系,更是学习高等数学的重要基础。本文拟对2019年出版的人教A版高中数学新教科书与2004年版旧教科书数列部分在内容结构、知识系统和训练系统上的共同点和不同点进行研究,试图发现新旧教科书在数列内容编写上的传承和变化,进一步对数列内容的教师教学、学生学习和教材编写提出相应的建议。本文采用了文献研究法、内容分析法、比较研究法和统计分析法,运用了综合难度模型,对新旧教科书数列部分的内容结构、知识系统和训练系统进行了定性与定量结合的比较分析。其中内容结构包括两版教科书数列部分的位置信息、体例设计、栏目设置、章前引言、正文结构、旁白、拓展栏目和章末小结;知识系统包括数列部分的目录、知识点的选取、内容比例、知识点密度、知识点呈现以及数列知识与其他知识之间的联系;训练系统包括新旧教科书数列部分的例题、习题的数量和综合难度。在内容结构上比较发现:(1)新教科书数列部分的位置变为选修,对其的学习放在了简单方程、不等式、复数和统计概率等之后,体现了数列的难度;(2)章头部分删除了节题名,不如旧教科书直观;(3)用“归纳”栏目替代了“观察”栏目,“思考”和“探究”两个栏目的界限变得模糊,这些栏目设置的数量变多,让课堂中师生的互动效果更好;(4)将等差数列的概念和等差数列的前n项和公式放在了同一节,等比数列的概念和等比数列的前n项和公式放在了同一节,数学归纳法与数列其他部分的内容放在了同一章;(5)概念的引入上更多地联系了实际,同时也采用了一定的数学文化,便于学生理解知识;(6)旁白变为用不同的颜色区分不同的类型,同时图片类型不再是单调的灰、绿、白,给人以简洁明快、鲜艳活泼的感受;(7)删除了数列在科技、生活中应用的拓展栏目,增加了与中国古代数学家有关的数列典故,减弱了数列应用于实际的作用效果,增强了学生对中国文化的认同感;(8)小结中对知识结构的联系更加紧密,难度有所增加,便于活跃学生思维。在知识系统上比较发现:(1)新教科书目录标题总量减少;(2)新教科书对“等差数列的递推公式”、“等差数列的性质”、“首尾相加法”、“等差数列的前n项和公式的图像”四个知识点进行了详细的叙述;(3)知识点密度降低,篇幅增多,更加重视知识的形成过程;(4)在呈现知识点的实例上有很大改变;(5)新教科书在正文中直接给出数列与函数的关系,没有设置涉及算法的程序,设置了涉及微积分的例题。在训练系统上比较发现:(1)新教科书题目的数量大大增多,涉及的题型更全面;(2)对题目中的背景和应用要求降低,在体现数列在现实生活的作用上程度降低;(3)题目的探究和运算难度较大,比较重视对学生理论推理和运算能力的培养;(4)涉及多个知识点的题目比例增多,更加注重培养学生对综合知识的运用。基于上述研究结论提出如下建议:(1)教学建议包括:合理安排教学内容和时间;重视知识的生成过程;适当补充教学内容;增强知识之间的联系。(2)学习建议包括:充分结合教科书上的实例理解数列的相关概念;结合函数知识学习数列;提高运算能力;在学习中举一反三。(3)教材编写建议包括:在章头增加节题名;适当增加探究栏目;适当增加数列在实际中运用的题型;在例题中增加程序题型。更多还原

【Abstract】 With the popularization of new high school mathematics textbooks in the country,more senior high school mathematics teachers in many provinces and cities will face the transition from the old edition to the new one.How to grasp the changes in the preparation of new textbooks is a very important problem for teachers.The sequence of numbers plays an important role in mathematics teaching.It is the intersection of many mathematical knowledge,and has close relationship with functions,algorithms,calculus and other knowledge,and is also an important basis for learning higher mathematics.This paper intends to study the common points and differences between the new textbook of human education a and the number of old textbooks in 2004.It tries to find the inheritance and change of the new and new textbooks in the compilation of the series content,and further puts forward corresponding suggestions for the teaching,students’ learning and textbook compilation of the series contents.By using literature research method,content analysis method,comparative analysis method and statistical analysis method,and using the comprehensive difficulty model,this paper makes a qualitative and quantitative comparative analysis of the content structure,knowledge system and training system of the number sequence part of the new and old textbooks.The content structure includes the location information,style design,column setting,introduction before the chapter,body structure,narration,extended column and summary at the end of the chapter;the knowledge system includes the contents of the series,the selection of knowledge points,the content proportion,the density of knowledge points,the presentation of knowledge points and the relationship between series knowledge and other knowledge;the training system includes The number and comprehensive difficulty of the examples and exercises in the series of new and old textbooks are analyzed.In terms of content and structure,we find that:(1)the position of the number sequence in the new textbook has become elective,and the learning of it has been put after simple equations,inequalities,complex numbers and statistical probability,which reflects the difficulty of the number sequence;(2)the section title has been deleted in the first part of the chapter,which is not as intuitive as the old textbook;(3)the column of "observation" has been replaced by the column of "induction","thinking" and"exploration" The boundaries of the two columns become blurred,and the number of these columns becomes more,so that the interaction between teachers and students in the classroom is better;(4)put the concept of arithmetic sequence and the first n terms and formulas of arithmetic sequence in the same section,the concept of arithmetic sequence and the first n terms and formulas of arithmetic sequence in the same section,and the content of mathematical induction and other parts of arithmetic sequence in the same chapter;(5)The introduction of the concept is more practical,but also uses a certain mathematical culture,which is convenient for students to understand knowledge;(6)the narration is changed to use different colors to distinguish different types,and the picture type is no longer monotonous gray,green,white,giving people a simple,bright and lively feeling;(7)the expansion column of the application of sequence in science and technology and life is deleted,The number series allusions related to ancient Chinese mathematicians are added,which weakens the practical effect of number series application,and enhances students’ sense of identity with Chinese culture;(8)the knowledge structure in the summary is more closely related,and the difficulty is increased,which is convenient for students to activate their thinking.In the knowledge system,we find that:(1)the total number of titles in the new textbook catalogue decreases;(2)The new textbook gives a detailed description of four knowledge points:"recurrence formula of arithmetic sequence","properties of arithmetic sequence","addition of head and tail","first n terms of arithmetic sequence and image of formula";(3)The density of knowledge points decreased,the space increased,and more attention was paid to the formation process of knowledge;(4)There are great changes in the examples of presenting knowledge points;(5)In the text of the new textbook,the relationship between sequence and function is given directly.There is no program related to algorithm,but examples related to calculus.In the training system,it is found that:(1)the number of new textbook topics is greatly increased,and the types of topics involved are more comprehensive;(2)the requirements for the background and application of the topics are reduced,and the degree of reflecting the role of sequence in real life is reduced;(3)the exploration and operation of the topics are more difficult,and more attention is paid to the cultivation of students’theoretical reasoning and operation ability;(4)multiple knowledge is involved With the increase of the proportion of questions,more attention should be paid to the cultivation of students’ comprehensive knowledge.Based on the above research conclusions,the following suggestions are put forward:(1)teaching suggestions include:reasonable arrangement of teaching content and time;emphasis on the generation process of knowledge;appropriate supplement of teaching content;strengthening the connection between knowledge.(2)Learning suggestions include:fully understand the related concepts of sequence with examples in textbooks;learn sequence with function knowledge;improve the operation ability;take one against three in learning.(3)Suggestions for textbook compilation include:adding section titles at the beginning of chapters;appropriately adding inquiry columns;appropriately increasing the types of number series used in practice;and adding procedural types in examples.更多还原