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中文题名:

 人教A版高中必修教材函数主线习题的数学抽象素养的表现研究    

姓名:

 韩文颖    

保密级别:

 公开    

论文语种:

 chi    

学科代码:

 045104    

学科专业:

 学科教学(数学)    

学生类型:

 硕士    

学位:

 教育硕士    

学位类型:

 专业学位    

学位年度:

 2023    

校区:

 北京校区培养    

学院:

 教育学部    

研究方向:

 学科教学(数学)    

第一导师姓名:

 马波    

第一导师单位:

 数学科学学院    

提交日期:

 2023-06-18    

答辩日期:

 2023-05-14    

外文题名:

 THE PERFORMANCE OF MATHEMATICAL ABSTRACTION LITERACY IN THE FUNCTIONS EXERCISES OF REQUIRED TEXTBOOK PUBLISHED BY PEP-A    

中文关键词:

 数学抽象素养 ; 函数主线 ; 习题 ; 人教A版教材    

外文关键词:

 Mathematical abstraction literacy ; Functions mainline ; Exercises ; Textbook published by PEP-A    

中文摘要:

为了贯彻党的十九大提出的教育方针以及目前我国正在实行“新课标、新教材、新高考”的教学改革,《普通高中数学课程标准(2017 年版2020年修订)》提出了数学学科的六大核心素养。其中,在六大核心素养中数学抽象排名首位。教材作为教师和学生学习的重要载体,那教材的数学抽象素养的表现如何?带着这样的问题,笔者选择人教A版数学教材函数主线习题作为研究对象,研究其在数学抽象素养上的表现,为使用该版本教材的教师在布置培养学生数学抽象素养的函数作业时提供参考。

本文依托《普通高中数学课程标准(2017 年版2020年修订)》,构建了涉及内容、水平、维度(情境与问题、知识与技能、思维与表达、交流与反思)的三维分析框架,对人教A版高中数学教材函数主线的习题进行编码,对数据进行量化分析,得出函数主线习题在数学抽象素养水平上的表现特点,习题在数学抽象素养的四个维度上是怎样表现的以及每一部分内容习题的数学抽象素养表现如下:

1.人教A版高中数学教材的函数主线习题能够集中体现数学抽象素养,在水平上的分布特点为:大多数的习题达到水平一,其余习题位于水平二,没有习题达到水平三。

2.人教A版高中数学教材的函数主线习题在数学抽象素养的四个维度上的表现特点为:全部习题在“情境与问题”、“知识与技能”以及“思维与表达”这三个维度上都有表现且大多数题目达到水平一,少数习题达到水平二,没有达到水平三的题目;在“交流与反思”这一维度上只有2.55%的题目有表现且达到水平一。

3.函数主线不同内容的习题在数学抽象素养水平以及维度上的表现不同。水平方面,五部分内容的水平分布大致与总体上一致,但其中“函数的应用”内容习题达到水平二的有43.24%,远超于其他部分。维度方面,五部分内容习题的相同表现特点为:在“情境与问题”、“知识与技能”以及“思维与表达”这三个维度上全都有表现,且都是大多数习题位于水平一,没有达到水平三的题目。不同的表现特点为:在“交流与反思”这一维度上,“指数函数与对数函数”、“函数的应用”这两部分内容的习题有表现,且全为水平一,其余三部分内容习题在该维度没有表现。

基于以上结论,本研究建议高中数学教师根据函数主题习题的数学抽象素养表现结合学生的实际情况布置作业,以培养学生的数学抽象素养;建议人教A版教材应适当在第三、四、五章的练习题、复习参考题部分增加“交流与反思”维度的习题,供教师和学生使用。

外文摘要:

In order to implement the educational policy proposed by the 19th National Congress of the Communist Party of China (CPC) and the teaching reform of "new curriculum standard, new teaching materials and new college entrance examination" currently being implemented in China. The General High School Mathematics Curriculum Standard (2017 Edition Revised 2020)  proposes six core qualities of mathematics. Among them, mathematics abstraction ranks first among the six core qualities. Teaching materials as an important vehicle for teachers and students to learn, then how does the performance of mathematical abstraction literacy of teaching materials. With such a question, the author chooses the main line of function exercises in the mathematics textbook of the Human Education A edition as the object of study to examine its performance on mathematical abstract literacy, so as to provide reference for teachers who use this edition of the textbook when assigning function assignments to develop students' mathematical abstract literacy.

Relying on the General High School Mathematics Curriculum Standards (2017 Edition Revised 2020), this paper constructs a three-dimensional analysis framework involving content, level, and dimensions (context and problems, knowledge and skills, thinking and expression, and communication and reflection), codes the exercises of the function mainline in the high school mathematics textbook published by the PEP-A, and analyzes the data quantitatively to derive the performance of mathematical abstract literacy on the function mainline exercises The characteristics of how the part of the exercises performed on the four dimensions of mathematical abstract literacy not and the mathematical abstract literacy performance of each part of the content exercises are as follows:

1. The function exercises of the textbook published by the PEP-A can focus on mathematical abstraction literacy, and the distribution in levels is characterized by: most of the exercises reach level 1, the rest are located at level 2, and no exercises reach level 3.

2. The performance of function exercises of the textbook published by the PEP-A on the four dimensions of mathematical abstraction literacy is characterized by: all the exercises are characterized by "situations and problems", "knowledge and skills", and "thinking and expression". "In the dimension of "Communication and Reflection", only 2.55% of the questions had performance and reached Level 1.

3. Exercises with different content in the main line of functions differ in their level of mathematical abstraction literacy as well as in their dimensions. As for the level, the distribution of the five parts of the content is generally consistent with the overall level, but 43.24% of the "Application of Functions" exercises reached Level 2, which is much higher than the other parts. In terms of dimensions, the same performance characteristics of the five parts of the exercises are: all of them have performance in the three dimensions of "situations and problems", "knowledge and skills", and "thinking and expression". Most of the exercises are located in Level 1, but not in Level 3. The different performance characteristics are: in the dimension of "Communication and Reflection", the exercises of "Exponential and Logarithmic Functions" and "Application of Functions" are performed, and they are all at Level 1. Level 1, the remaining three parts of the exercises have no performance in this dimension.

Based on the above findings, this study suggests that high school mathematics teachers should assign assignments based on the mathematical abstraction literacy performance of function-themed exercises and students' actual situations in order to cultivate students' mathematical abstraction literacy; it is suggested that the "Communication and Reflection" dimension of exercises should be appropriately added to the textbook published by the PEP-A for teachers and students to use.

参考文献总数:

 49    

馆藏号:

 硕045104/23012    

开放日期:

 2024-06-18    

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