我国大陆与台湾近十年高考数学的比较研究

发布时间：2018-05-20 06:27

本文选题：大陆 + 台湾　；参考：《河南大学》2015年硕士论文

【摘要】：台湾《大学入学指定科目考试(数学考科)》(简称“台湾指考”)与大陆《普通高等学校招生全国统一考试数学》(简称“大陆高考”)功能类似,其数学甲、数学乙试卷分别对应于大陆的理科、文科试卷,故本文选择2005-2014十年间大陆高考理科、文科数学和台湾指定科目考试数学甲、数学乙共四十套试卷为研究对象,从横向和纵向两个方面,比较两岸高考数学在考试形式、试卷结构、知识模块分值比重上的异同,并对这些异同产生的原因从两岸数学教材和课程标准(纲要)上进行了对比分析。有如下结论:(1)两岸高中数学课程文件在框架结构方面相差不大,不同点在于大陆《标准》还有前言,台湾《纲要》则设立了核心能力、时间分配等项目。另外,台湾《纲要》是分《必修纲要》和《选修纲要》两部分来阐述,大陆《标准》中有关必修课程和选修课程,只在内容标准部分分开叙述,而其它部分的要求则一致,并没有分开。(2)两地的数学课程均采取了必修与选修相结合的方式。在必修课程内容的选择方面,大陆与台湾的目的与标准是一致的。在选修内容设计上,台湾针对建议学习对象的不同,分为四类:标准课程、基础课程、统整课程和进阶课程,大陆的选修课程仅相当于台湾的标准课程,显然台湾在课程设计上要比大陆更加多样化。(3)台湾教材包含的知识点数量明显多于大陆教材。两岸高中数学教材对知识内容的安排上各有侧重:大陆教材重视传统数学内容的选择,注重大众的数学学习,侧重基础数学的讲解;台湾教材更重视现代化数学内容的选择,与大学教育相联系。台湾《纲要》强调课程要注重与大学数学的衔接,而大陆《标准》中未涉及课程的时代性、前瞻性与衔接性。(4)台湾指考数学的试题题型较之大陆更为丰富和多样,包含多选题,相同点是都有单选题、填空题和解答题。其中,台湾的单选为五选一型,大陆为四选一型。大陆高考客观题比例维持恒定,相较之下台湾指考无论在单选题还是客观题(单选+多选)上,波动都很大,无明显规律可循。(5)大陆高考数学理科、文科试卷在题型和题量上保持完全一致,折线图呈现直线。台湾指考数学试卷的题量较为稳定,但无明显规律。两岸试卷题量的差别对应于考试时长的不同:台湾考生要在80min的时间内完成11-13道题目,满分100;大陆考生要在120min的时间内完成22道题目,满分150。(6)台湾指考考试时长的限制,仅占大陆数学考试时间的53%,故在知识容量和知识点覆盖率上远低于大陆,这就对台湾在试题的“知识交汇程度”提出了较高的要求。(7)大陆对“函数与导数”模块的重视程度要高于台湾,另外,内地不论文理,均侧重于函数性质与图形的抽象研究,而台湾更注重生活应用,特别是数学乙,只要求简单函数的简单应用,不做复杂抽象的分析。(8)大陆理科在“三角”部分的比重不算很高;文科在此部分的变化比较有特点,大致可以认为其比重以两年为一组,呈现“此消彼长”的态势。台湾数学甲中,“三角”部分并非每年都涉及,但一旦有相关题目,所占比重都很高,数学乙则对“三角”不作要求。(9)大陆理科从2008年至今,对“概率与统计”部分的考查保持稳定。台湾不管数学甲、乙,都对基于排列组合的概率分析有较高的要求。相对数学甲而言,数学乙对“机率统计”要求更高,考查的力度也更大。(10)大陆理科和文科中对“解析几何”的考查往往是两道小题、一道大题的形式,分值均在22分及以上。台湾数学甲中考查分值的波动很大;数学乙中,对“解析几何”的考查出现“点断”式的空缺总体来说要求较低。(11)大陆无论理科还是文科中,数列题是每年的必考题之一,属于重点内容。台湾数学甲、乙都出现了大片的空白。这与台湾的考试范围有关,数列知识往往在学测中考查,指考很少涉及,且试题多集中在级数和极限上。所以,台湾在“数列”领域与大陆侧重点不同。(12)大陆理科和文科在对“立体几何”部分的考查上基本保持同步,十年来考查的比重波动不是很大。台湾数学甲中,波动较大,无明显规律和模式;数学乙则对此部分不作要求,最近七年均未出现相关试题。笔者就以上分析,得出以下粗浅的建议:大陆高中数学教材内容可适当延拓;大陆必修课程与选修课程可并重;借鉴台湾的考试资讯模式;大陆试题在体现数学应用性可加强;大陆理科、文科可增大区分。
[Abstract]:Taiwan "the designated subject examination of university entrance examination (mathematics examination section) >" (referred to as "Taiwan examination") is similar to the function of the national unified examination mathematics of the mainland of the mainland ("the national college entrance examination" for short). Its Mathematics A and Mathematics B are respectively corresponding to the science of the mainland and the examination papers of the liberal arts, so this article chose the mainland college entrance examination in 2005-2014 and ten years. There are forty sets of test papers in liberal arts and Taiwan designated subjects and Mathematics B as the research object. From two aspects of horizontal and vertical, the similarities and differences of the examination form, the structure of examination papers and the proportion of knowledge modules are compared between the two sides of the cross straits college entrance examination, and the reasons for these similarities and differences are advanced from the cross-straits mathematics teaching materials and the curriculum standard (outline). The following conclusions are made: (1) there is little difference in the frame structure of the high school mathematics curriculum documents between the two sides of the Taiwan Straits. The different points lie in the continental < standard > and the preface, the Taiwan < outline > to set up the core competence, the time distribution and so on. In addition, the Taiwan < outline > is divided into the compulsory program > and the elective outline > in the standard > in the continental < standard >. The required courses and elective courses are described separately in the standard part of the content, while the requirements of the other parts are unanimous. (2) both the two places have taken a combination of compulsory and elective courses. In the choice of the required courses, the purposes and standards of the mainland and Taiwan are consistent. In the design of the elective content, Taiwan is divided into four categories: standard courses, basic courses, integrated courses and advanced courses. The elective courses in the mainland are only equivalent to the standard courses in Taiwan. Obviously, Taiwan is more diversified than the mainland. (3) the number of knowledge points contained in the Taiwan textbook is obviously more than that of the mainland textbooks. The teaching materials have different emphasis on the arrangement of knowledge content: the mainland textbooks attach great importance to the selection of traditional mathematical content, pay attention to the mathematics learning of the masses and focus on the explanation of basic mathematics; the textbooks of Taiwan pay more attention to the selection of modern mathematics content and the connection with the university education. The curriculum of the Taiwan outline > strong tune should pay attention to the connection with the university mathematics, and the mainland < The standard > does not involve the times, foresight and cohesion of the curriculum. (4) the test questions in Taiwan are more abundant and diverse than the mainland, including the multiple selection questions, and the same points are all single, fill and answer questions. Among them, the single election of Taiwan is the one type and the big land is four. The proportion of the objective questions in the mainland college entrance examination is maintained constant. There is great fluctuation in both the single and objective questions (single election + multi selection) in Taiwan, and there is no obvious rule to follow. (5) the mathematics science and science of the mainland college entrance examination, the examination papers of the liberal arts are all consistent in the type and quantity, and the line diagram is straight. The quantity of the test papers in Taiwan is more stable, but there is no obvious law. The volume of test papers on both sides of the Taiwan Straits The difference corresponds to the difference in the length of the exam: the Taiwan examinee should complete 11-13 questions in the time of 80min, full score 100; the mainland examinee should complete 22 questions in the time of 120min, the full score (6) of the exam time limit, only 53% of the time of the continental mathematics examination, so it is far lower in the knowledge capacity and knowledge coverage rate than in the mainland, This puts forward higher requirements for the "degree of convergence of knowledge" in Taiwan. (7) the importance of the mainland to the "function and derivative" module is higher than that of Taiwan. In addition, the mainland, regardless of the arts and Sciences, lays particular emphasis on the abstract study of the properties of the functions and figures, and in Taiwan, the rebirth application, especially the Mathematics B, only requires simple functions. Single application, not complicated abstract analysis. (8) the proportion of the Continental Science Department in the "triangle" part is not very high; the changes in the section of the liberal arts are characteristic. It is generally considered that the proportion of the section is two years as a group, showing the trend of "this trend." in Taiwan Mathematics A, the "triangle" part is not involved every year, but once there are related questions. The proportion of the Mathematics B is not required for the "triangle". (9) the science of science and technology in mainland China has maintained stability from 2008 to the present. No matter in Mathematics A or B, there is a high requirement for the probability analysis based on the permutation and combination. (10) the examination of "analytic geometry" in the science and liberal arts of the mainland is often two small questions, and the form of a big question is 22 and more. The fluctuation of the score of the Taiwan mathematics examination is very large; in Mathematics B, the "point break" vacancy is generally low for the analysis of "analytic geometry". 11) the number list is one of the most important questions in the mainland, whether science or liberal arts, which is one of the key questions of every year. Taiwan Mathematics A and B have a large blank. This is related to the examination scope of Taiwan. The number of series of knowledge is often examined in the test, and the test is seldom involved, and the test questions are concentrated on the series and limit. So, Taiwan is in the series. The focus of the field is different from that of the mainland. (12) the science and arts of Continental Science and arts have basically kept synchronizing on the examination of the "stereoscopic geometry" part. In the last ten years, the fluctuation of the specific gravity is not very large. In Taiwan Mathematics A, the fluctuation is large and there is no obvious law and mode; Mathematics B is not required for this part, and the relevant test questions have not appeared in the last seven years. On the basis of the above analysis, the following shallow suggestions are made: the content of high school mathematics textbooks in mainland China can be extended properly; continental compulsory courses and elective courses can be attached equal weight; the examination information model of Taiwan is used for reference; the mainland test questions can be strengthened in the embodiment of mathematical application; the Continental Science Department and the liberal arts can increase the distinction.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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