本文選題：大陸 + 臺灣　； 參考：《河南大學》2015年碩士論文

【摘要】：臺灣《大學入學指定科目考試(數學考科)》(簡稱“臺灣指考”)與大陸《普通高等學校招生全國統一考試數學》(簡稱“大陸高考”)功能類似,其數學甲、數學乙試卷分別對應于大陸的理科、文科試卷,故本文選擇2005-2014十年間大陸高考理科、文科數學和臺灣指定科目考試數學甲、數學乙共四十套試卷為研究對象,從橫向和縱向兩個方面,比較兩岸高考數學在考試形式、試卷結構、知識模塊分值比重上的異同,并對這些異同產生的原因從兩岸數學教材和課程標準(綱要)上進行了對比分析。有如下結論:(1)兩岸高中數學課程文件在框架結構方面相差不大,不同點在于大陸《標準》還有前言,臺灣《綱要》則設立了核心能力、時間分配等項目。另外,臺灣《綱要》是分《必修綱要》和《選修綱要》兩部分來闡述,大陸《標準》中有關必修課程和選修課程,只在內容標準部分分開敘述,而其它部分的要求則一致,并沒有分開。(2)兩地的數學課程均采取了必修與選修相結合的方式。在必修課程內容的選擇方面,大陸與臺灣的目的與標準是一致的。在選修內容設計上,臺灣針對建議學習對象的不同,分為四類:標準課程、基礎課程、統整課程和進階課程,大陸的選修課程僅相當于臺灣的標準課程,顯然臺灣在課程設計上要比大陸更加多樣化。(3)臺灣教材包含的知識點數量明顯多于大陸教材。兩岸高中數學教材對知識內容的安排上各有側重:大陸教材重視傳統數學內容的選擇,注重大眾的數學學習,側重基礎數學的講解;臺灣教材更重視現代化數學內容的選擇,與大學教育相聯系。臺灣《綱要》強調課程要注重與大學數學的銜接,而大陸《標準》中未涉及課程的時代性、前瞻性與銜接性。(4)臺灣指考數學的試題題型較之大陸更為豐富和多樣,包含多選題,相同點是都有單選題、填空題和解答題。其中,臺灣的單選為五選一型,大陸為四選一型。大陸高考客觀題比例維持恒定,相較之下臺灣指考無論在單選題還是客觀題(單選+多選)上,波動都很大,無明顯規律可循。(5)大陸高考數學理科、文科試卷在題型和題量上保持完全一致,折線圖呈現直線。臺灣指考數學試卷的題量較為穩定,但無明顯規律。兩岸試卷題量的差別對應于考試時長的不同:臺灣考生要在80min的時間內完成11-13道題目,滿分100;大陸考生要在120min的時間內完成22道題目,滿分150。(6)臺灣指考考試時長的限制,僅占大陸數學考試時間的53%,故在知識容量和知識點覆蓋率上遠低于大陸,這就對臺灣在試題的“知識交匯程度”提出了較高的要求。(7)大陸對“函數與導數”模塊的重視程度要高于臺灣,另外,內地不論文理,均側重于函數性質與圖形的抽象研究,而臺灣更注重生活應用,特別是數學乙,只要求簡單函數的簡單應用,不做復雜抽象的分析。(8)大陸理科在“三角”部分的比重不算很高;文科在此部分的變化比較有特點,大致可以認為其比重以兩年為一組,呈現“此消彼長”的態勢。臺灣數學甲中,“三角”部分并非每年都涉及,但一旦有相關題目,所占比重都很高,數學乙則對“三角”不作要求。(9)大陸理科從2008年至今,對“概率與統計”部分的考查保持穩定。臺灣不管數學甲、乙,都對基于排列組合的概率分析有較高的要求。相對數學甲而言,數學乙對“機率統計”要求更高,考查的力度也更大。(10)大陸理科和文科中對“解析幾何”的考查往往是兩道小題、一道大題的形式,分值均在22分及以上。臺灣數學甲中考查分值的波動很大;數學乙中,對“解析幾何”的考查出現“點斷”式的空缺總體來說要求較低。(11)大陸無論理科還是文科中,數列題是每年的必考題之一,屬于重點內容。臺灣數學甲、乙都出現了大片的空白。這與臺灣的考試范圍有關,數列知識往往在學測中考查,指考很少涉及,且試題多集中在級數和極限上。所以,臺灣在“數列”領域與大陸側重點不同。(12)大陸理科和文科在對“立體幾何”部分的考查上基本保持同步,十年來考查的比重波動不是很大。臺灣數學甲中,波動較大,無明顯規律和模式;數學乙則對此部分不作要求,最近七年均未出現相關試題。筆者就以上分析,得出以下粗淺的建議:大陸高中數學教材內容可適當延拓;大陸必修課程與選修課程可并重;借鑒臺灣的考試資訊模式;大陸試題在體現數學應用性可加強;大陸理科、文科可增大區分。
[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.
【學位授予單位】：河南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6

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