# 2015~2019年高考数学全国卷和江苏卷的比较研究A Comparative Study Based on the National Volume (Mathematics) and Jiangsu Volume (Mathematics) from 2015 to 2019

DOI: 10.12677/CES.2021.91024, PDF, HTML, XML, 下载: 55  浏览: 95

Abstract: On April 23, 2019, the new college entrance examination plan of Jiangsu Province was released, in which it was pointed out that mathematics subjects will no longer be set independently by Jiangsu Province, but will return to the national college entrance examination and adopt the national volume in a unified way. Widespread concern from all over the country has been aroused because of the promulgation of this plan, and it is also a huge challenge for teachers who have adapted to Jiangsu volume for many years. Therefore, according to the requirements of the new college entrance examination plan, this paper takes the National Volume I (Science Mathematics) and Jiangsu Volume (Science Mathematics) in 2015~2019 as the research object, compares and analyzes the similarities and differences between the two types of test papers from three aspects: the content of investigation, the ability requirements and the overall difficulty. The results are as follows: there are some differences between the national volume and Jiangsu volume in the degree of emphasis and the form of investigation of the content of investigation; the national volume pays more attention to the ability of calculating and solving than Jiangsu volume; the national volume pays more attention to spatial imagination than Jiangsu volume and both the national volume and Jiangsu volume pay attention to the investigation of basic knowledge and main contents.

1. 引言

2. 研究设计

2.1. 研究对象

2.2. 研究工具

2.2.1. 考察内容的分类

Table 1. Classification of investigation contents

2.2.2. 能力要求的分类

Table 2. Classification of competence requirements

2.2.3. 整体难度的框架

Table 3. Framework of overall difficulty

${d}_{i}=\frac{{\sum }_{j}{n}_{ij}{d}_{ij}}{n}\left(\underset{j}{\sum }{n}_{ij}=n,i=1,2,3,\cdots \right)$

2.3. 数据处理与整理

(2019年全国I卷，1)已知集合 $M=\left\{x|-4$N=\left\{x|{x}^{2}-x-6<0\right\}$，则 $M\cap N=$ ( )

A. $\left\{x|-4 B. $\left\{x|-4

C. $\left\{x|-2 D. $\left\{x|2

3. 研究结果与分析

3.1. 考察内容的比较与分析

$\omega \left(全国卷\right)=\frac{考察内容所占分值}{140}×100%$$\omega \left(江苏卷\right)=\frac{考察内容所占分值}{180}×100%$

Table 4. The proportion of each knowledge unit in the national volume and Jiangsu volume from 2015 to 2019

Figure 1. Broken line chart of the proportion of each knowledge unit in 2015 national volume and Jiangsu volume

Figure 2. Broken line chart of the proportion of each knowledge unit in 2016 national volume and Jiangsu volume

Figure 3. Broken line chart of the proportion of each knowledge unit in 2017 national volume and Jiangsu volume

Figure 4. Broken line chart of the proportion of each knowledge unit in 2018 national volume and Jiangsu volume

Figure 5. Broken line chart of the proportion of each knowledge unit in 2019 national volume and Jiangsu volume

1) 江苏卷集合与常用逻辑用语、函数与导数、三角函数、立体几何相比全国卷总体偏多，全国卷向量、概率与统计、其他相比江苏卷总体偏多，不等式差距不大，数列、平面解析几何无规律；

2) 全国卷立体几何一般与空间向量联系在一起综合考察；

3) 全国卷集合与常用逻辑用语、数列、其他均以基础小题(选择题或填空题)呈现，江苏卷有时会以解答题甚至压轴题出现；

4) 全国卷各内容分值占比相对江苏卷较均衡、考察较全面，二者解答题题型固定，但考察内容不尽相同：全国卷解答题(17~21)的考察内容一般固定为：三角函数、立体几何、概率与统计、平面解析几何、导数与函数五大部分；江苏卷I卷中解答题(15~20)的考察内容一般分为三角函数、立体几何、实际应用题(涉及立体几何、函数与导数、平面解析几何等的综合应用题)、平面解析几何、函数与导数、数列六大部分，II卷中必做题(22~23)考察内容并不固定；

5) 全国卷着重对函数与导数、平面解析几何、三角函数的考察，其对应分值占比ω五年来(2016~2019年)均位列前5。

3.2. 能力要求的比较与分析

$\omega \left(全国卷\right)=\frac{能力要求所占分值}{140}×100%$$\omega \left(江苏卷\right)=\frac{能力要求所占分值}{180}×100%$

Table 5. Proportion of capacity requirements of national volume and Jiangsu volume in 2015~2019

Figure 6. Broken line chart of the proportion of capacity requirements of national volume and Jiangsu volume in 2015

Figure 7. Broken line chart of the proportion of capacity requirements of national volume and Jiangsu volume in 2016

Figure 8. Broken line chart of the proportion of capacity requirements of national volume and Jiangsu volume in 2017

Figure 9. Broken line chart of the proportion of capacity requirements of national volume and Jiangsu volume in 2018

Figure 10. Broken line chart of the proportion of capacity requirements of national volume and Jiangsu volume in 2019

1) 江苏省逻辑思维能力的占比更高，相比全国卷更注重逻辑思维能力的考察；

2) 全国卷空间想象能力、运算求解能力、数据处理能力的占比更高，相比江苏卷更注重这三方面能力的考察；

3) 二者逻辑思维能力和运算求解能力占试卷总分值比例均较大，且所有能力要求的对应分值占比排序相同：逻辑思维能力 >= 运算求解能力 > 空间想象能力 > 创新应用意识 > 数据处理能力。

3.3. 整体难度的比较与分析

Table 6. The difficulty coefficient model of each difficulty factor of the overall difficulty of national and Jiangsu papers in 2015~2019

Figure 11. Radar chart of overall difficulty of national volume and Jiangsu volume in 2015

Figure 12. Radar chart of overall difficulty of national volume and Jiangsu volume in 2016

Figure 13. Radar chart of overall difficulty of national volume and Jiangsu volume in 2017

Figure 14. Radar chart of overall difficulty of national volume and Jiangsu volume in 2018

Figure 15. Radar chart of overall difficulty of national volume and Jiangsu volume in 2019

1) 全国卷运算水平普遍偏高，江苏卷推理能力、知识含量普遍偏高，背景因素、是否含参、思维方向总体差距不大，认知水平无明显规律；

2) 江苏卷整体难度与全国卷差异不大。

3.4. 研究结果

1) 全国卷知识内容的侧重程度和考察形式与江苏卷有一些差异。

2) 根据统计结果：全国卷运算水平普遍偏高，全国卷运算求解能力的占比更高，因此全国卷较江苏卷更加注重运算求解能力的考察。

3) 能力考查的分析中发现全国卷空间想象能力要求普遍高于江苏卷，这说明全国卷较江苏卷更加注重空间想象的考察。

4) 全国卷和江苏卷都注重基础知识和主干内容的考察。

4. 教学建议

1) 进行教学调整，教学内容可以有所侧重

2) 注重运算求解能力的培养

① 注重公式等一系列运算基础知识和能力的教学；

② 传授灵活的运算技巧，锻炼学生用宏观的视角看待运算对象，有时候看似繁琐的运算其实只需几步变形或换元就能变为简单的运算，要求学生敏锐地捕捉到式中隐藏的关系和条件，需要一定程度和规模的训练；

③ 注意符号运算能力的培养；

④ 展示典型例题的过程示范，明晰一般步骤及其对应的依据，这样可使学生养成规范的运算习惯和清晰的运算思路，这对于解决一般难度的试题有着很显著的作用，同时也能大大地提高运算的准确率；

⑤ 督促学生养成验算和检查的良好习惯，提高运算合理性和精确性，学生在运算过程中容易粗心，因此要特别强调验算的重要性，做到每一步有理、每一环有据，精力集中、认真演算，切忌想当然。

3) 注重空间想象能力的培养

4) 注重基础知识和主干内容的教学

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