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论文独创声明和学术诚信承诺 本人向河南大学提出硕士学位申请。本人郑重声明所呈交的学位论文是本人在导师的指 导下独立完成的,对所研究的课题有新的见解。据我所知,除文中特别加以说明、标注和致谢的地方外,论文中不包括其他人已经发表或撰写过的研究成果,也不包括其他人为获得任何教育、科研机构的学位或证书而使用过的材料。与我一同工作的同事对本研究所做的任何贡献均已在论文中作了明确的说明并表示了谢意。 在此本人郑重承诺所呈交的学位论文不存在舞弊作伪行为,文责自负。 学位申请人(学位论文作者)签名 201 年 月 日 关 于学位论文著作权使用授权书 本人经河南大学审核批准授予硕士学位。作为学位论文的作者,本人完全了解并同意河南大学有关保留、使用学位论文的要求,即河南大学有权向国家图书馆、科研信息机构、数据收集机构和本校图书馆等提供学位论文(纸质文本和电子文本)以供公众检索、查阅。本人授权河南大学出于宣扬、展览学校学术发展和进行学术交流等目的,可以采取影印、缩印、扫描和拷贝等复制手段保存、汇编学位论文(纸质文本和电子文本)。 (涉及保密内容的学位论文在解密后适用本授权书) 学位获得者( 学位论文作者)签名 201 年 月 日 学位论文指导教师签名 201 年 月 日 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。 关键字 大陆,台湾,对比研究,高考试卷 ABSTRACT Taiwan university entrance examination subjects math-test specified and the national high school mathematics exam have similar function.So this paper choose science and liberal arts mathematics from 2005-2014,ten years college entrance examination and Taiwan specified subjects that is math A and math B, forty sets of paper in total as the search object. It compares the similarities and differences the examination in the mathematics examination paper structure, the proportion of knowledge module scores from the crosswise and longitudinal two aspects.The following conclusions are obtained 1 In the framework structure mathematics curriculum documents of cross-strait high school have no big difference. The only difference is the “standard“. There are forewords in mainland. While the ?Outline? in Taiwan established the core competence and time allocation. In addition, Taiwan “Outline“ is divided into two parts to elaborate, the compulsory outline and elective outline. However the compulsory courses and elective courses in mainland standard only narrate the contents, but the other part is consistent with the requirements of others, and not be separated. 2Taiwan “Outline“ emphasized that curriculum should focus on the interface, and the university mathematics teaching material, pay attention to cohesion in integration and connection. While the mainland “standard“ doesn?t involve contemporaneity, forward-looking and cohesion of the course. 3Both mathematics curriculum adopt the way of the combination of the compulsory and elective. In the choice of the compulsory course content, the objective and standard between Taiwan and mainland is consistent. In the elective content design,Taiwan aims at the difference of learning objects, dividing the curriculums into four categories standard curriculum, basic curriculum, integrated curriculum and advanced curriculum. That truly realized “different students learn different math; everyone gets different development in mathematics“. The eletive course in mainland is the equivalent of the standard course in Taiwan. Obuiously,Taiwan?s course design is more diverse than that of mainland. ( 4) The textbooks of Taiwan contain more knowledge points than mainland textbooks. The arrangement of knowledge content on both sides of the high school mathematics textbooks have different emphases. The mainland textbooks attach great importance to the choice of the traditional mathematics teaching material, pay attention to mathematics learning for all, and focus on the explanation of basic mathematics. Taiwan textbooks pay more attention to the modern mathematics content selection, associating with University education. As for modern mathematics, progression and series, derivative and its application, elementary linear algebra these three aspects in Taiwan textbook is more important.While the preliminary algorithm is more special. There is no knowledge unit in Taiwan textbooks. As for the traditional mathematics, complex number and the complex plane, triangle function solutions and trigonometry in Taiwan appear to be more important, but there is only three points in coordinate system and the parameters in the equation. ( 5) The test length is 120min in mainland and the full mark is 150, corresponding to an average of 1.25 points/min;The time in Taiwan is 80min and the full mark is 100, corresponding to average out of 1.25 points/min. The style of the questions of the math test in Taiwan is more than the rich and diverse, including multiple choice.The same is that both have single choice, gap filling and short answer question. Among them, Taiwan is five select one type but the mainland is four choose one. In the college entrance examination in mainland, the proportion of objective questions remains constant. In contrast to Taiwan both in single answer and objective questions multiple-choice sigle-choice fluctuates wildly.There is no obvious regularity. 6 Science and liberal arts mathematical in the college entrance examination papers maintain consistency in types and quantities. The line graph shows linear. The quantity of Taiwan mathematics examination questions is more stable but no obvious rules. The corresponding to different quantity of cross-strait papers at exam time is different Taiwan candidates should complete 11 to 13 problems in 80min but the mainland examiner should finish 22 questions in 120min. 7Whether Chinese college entrance examination or Taiwan mathematics test, knowledge examination are very broad, paying attention to the examination of key knowledge module. However, because of examination time limit, the math exam time accounts for only 53, so the capacity of knowledge and knowledge coverage rate are far lower than that of the mainland, which puts higher requirement level“ on the Taiwan in the item of “knowledge interchange. 8 The degree of attention to “function and derirative” module is higher than Taiwan. In addition, no matter science or art, the mainland focuses on the abstract research of the function properties and graphics,.While Taiwan pays more attention to the life application, especially in Mathematics B, only requring a simple application of simple functions, not analyzing the complex abstract. 9The proportion of the “triangle” in the science part is not high. Changes in this part have more characteristics. It can be roughly considered that the proportion in two years is a group, showing a “shift“ in the situation. In mathematics A in Taiwan, the “triangle” is not every year related to, but once there is relevant topics, the proportion is very high. Maths B is not required to “triangle“. 10 2008 to now, the research on “probability and statistics“ remains stable in mainland.Taiwan no matter mathematics A or mathematics B, has a higher requirement of analysis based on permutation and combination. Comparing with Math A,Math B has higher requirements on “probability and statistics“. The strength of examination is also great. 11In continental Science and arts the test of the analytic geometry examination has two s two questions and one problem. The scores are all above 22 points. The scores of Taiwan mathematical A have large fluctuations; In mathematics B, the test on the “analytic geometry“ examine appears “point break“ type vacancies. Generally speaking, the requirements are low. 12Series title is almost involved every year. It is the key content. In Taiwan no matter Mathematics A or Mathematics B, there are large areas of blank. This is related to the Taiwan examination scope. Sequence knowledge often appears in measurement science, but it rarely involved in Taiwan Math test, and it concentrates more on the series and limit. So, Taiwan and the mainland have different priorities about “series“. 13Science and arts maintain “solid geometry“ test, the fluctuation is not great in ten years. Taiwan mathematical A, the changes over the years are great, there is no obvious rules and patterns. This part of Mathematics B is not required. It hasn?t appeared in recent seven years. On the above analysis the author draws the following suggestions the mainland high school mathematics textbook content can be appropriately extended; the required courses and elective courses can be equal; use the test ination model of Taiwan for reference; test can strengthen embodied in the application of mathematics, the arts and science can increase the partition. KEY WORDSContinental,Taiwan,comparative study,college entrance examination papers 目 录 摘 要 ..................................................................... I ABSTRACT ................................................................. IV 目 录 .................................................................. VIII 第 1 章 绪论 ............................................................... 1 1.1 研究背景 .......................................................... 1 1.2 研究意义 .......................................................... 2 1.2.1 理论价值 ..................................................... 2 1.2.2 实践意义 ..................................................... 2 1.3 研究方法与设计 .................................................... 3 1.3.1 研究问题 ..................................................... 3 1.3.2 研究设计 ..................................................... 3 1.3.3 研究方法 ..................................................... 3 1.4 文献综述 .......................................................... 5 1.4.1 课程标准的比较研究现状 ....................................... 5 1.4.2 国内外不同版本数学教材的比较研究现状 ......................... 6 1.4.3 高考数学试卷的比较研究现状 ................................... 8 第 2 章 大陆与台湾课程标准(纲要)的比较 .................................. 11 2.1 大陆与台湾数学课程改革背景 ....................................... 11 2.2 台湾普通高级中学必 /选修科目“数学”科课程纲要 ................ 11 2.2.1 必修科目 .................................................... 12 2.2.2 选修科目 .................................................... 14 2.3 大陆与台湾课程标准(纲要)异同点分析 ............................. 14 2.3.1 大陆标准与台湾纲要框架结构异同点 .................... 15 2.3.2 大陆标准与台湾纲要课程基本理念异同点 ................ 16 2.3.3 大陆标准与台湾纲要课程目标异同点 .................... 17 2.3.4 大陆标准与台湾纲要必 /选修课程内容标准异同点 ......... 18 第 3 章 大陆与台湾高中数学教科书知识点的比较 .............................. 21 3.1 台湾教材多于大陆的数学知识点 ..................................... 22 3.2 大陆教材多于台湾的数学知识点 ..................................... 24 第 4 章 大陆与台湾近十年高考数学试卷的比较 ................................ 32 4.1 考试形式 ......................................................... 33 4.2 题型及所占分值、题量分析 ......................................... 33 4.2.1 大陆与台湾“选择题”所占分值比重比较 ........................ 33 4.2.2 大陆与 台湾“填空题”所占分值比重比较 ........................ 35 4.2.3 大陆与台湾“解答题”所占分值比重比较 ........................ 36 4.2.4 大陆与台湾“题量”变化比较 .................................. 36 4.3 考查知识模块所占分值分析 ......................................... 37 4.4 六大主干知识走向 ................................................. 40 4.4.1 模块一“函数与导数” ........................................ 40 4.4.2 模块二“三角” .............................................. 41 4.4.3 模块三“概率与统计” ........................................ 42 4.4.4 模块四“解析几何” .......................................... 43 4.4.5 模块五“数列与级数” ........................................ 44 4.4.6 模块六“立体几何” .......................................... 44 4.4.7 “六大主干知识”分值比 例 .................................... 45 第 5 章 结论与建议 ........................................................ 48 5.1 结论 ............................................................. 48 5.1.1 课程标准(纲要)层面 ........................................ 48 5.1.2 教材知识点层面 .............................................. 49 5.1.3 试卷题型及所占分值层面 ...................................... 50 5.1.4 试卷题量层面 ................................................ 51 5.1.5 试卷各知识模块所占分值层面 .................................. 51 5.2 建议 ............................................................. 55 5.2.1 大陆高中数学教材内容可适当延拓 .............................. 55 5.2.2 大陆必修课程与选修课程可并重 ................................ 55 5.2.3 借鉴台湾的考试资讯模式 ...................................... 55 5.2.4 大陆试题在体现数学应用性可加强 .............................. 56 5.2.5 大陆理科、文科可增大区分 .................................... 56 5.3.值得注意的问题 ................................................... 56 结束语 ................................................................... 58 参考文献 ................................................................. 60 附录 A ................................................................... 62 致 谢 .................................................................... 64 第一章 绪论 1 第 1 章 绪论 1.1 研究背景 台湾是中国不可分割的一部分,由于历史原因与大陆阻隔多年。两地在政治制度、文化与意识形态的价值取向等因素的不同,使得其在课程教育的规范和要求有着比较大的差异。近年来,在两岸关系逐步改善和经济方面合作愈加紧密的同时,文化上的交流也日趋活跃,因此,关注台湾的教育、对两岸基础教育进行比较和分析,对我们来说有着与时俱进的必要性。 数学是基础学科,是自然科学与社会科学领域的一门工具学科,在整个教育系统中起着重要作用,很大程度上联系着一个国家的科学发展水平,所以数学教育历来备受关注和重视。台湾在学习西方数学教育方面的起步比大陆要早,并且落实的更加到位。因此从某种程度上来说,了解台湾的高中数学教育,是大陆向世界其它先进国家学习的一个自然过渡。 高考,是一种纸笔考试,以 能力考核为主,主观和客观题兼有,对难度和速度都有严格要求的常模参照性考试。 1大学入学考试即高考,是两岸高等院校的入学选拔性考试,是考生选择和进入高等院校的资格标准,对学生成绩的评价、国家的教育发展、人才选拔,以及社会流动和分层有着不可替代的作用。台湾现行的是始于 2002 年的大学多元入学方案,与大陆每年的普通高等学校招生全国统一考试在功能、形式、流程上有很多相似之处,也有很大差别。 当然,无论何种类型的考试,试卷内容都对其发挥着关键的导向作用 。 从一个国家或地区最重要的考试试卷内容中,我们不仅可以看出其教育目的 ,更可以看出其对待传统文化的态度,对学生思维能力、性格修养、思想境界的要求和政治意识形态力量介入的程度。 2高考试卷一直扮演着十分重要的角色,因此研究海峡两岸十年来高考数学试题的命制、内容、结构等,汲取其精华,具有重要的意义,能进一步探索大陆地区的中学数学教育改革之路。 2003 年 3 月,我国进行了第八次新课程改革,它在课程目标、课程设置、课程实施、1 教育部考试中心 ,高考数学考 试能力考查与题型设计 [M].北京 高等教育出版社 ,199948-49 2 夏蕾 .海峡两岸大学入学考试语文试卷比较研究 [D].扬州大学 ,2008.
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