高中生概率学习状况研究
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摘要
新课程中已经明确提出:概率可以给人们提供另一种有效而且非常适用的思维方式一找出客观事物的统计规律性与随机现象的客观规律性。因此,概率的基础知识已经成为一个未来公民的必备常识,现在,概率和确定性科学一样,已成为我们认识和改造自然、社会的一种不可缺少的科学方法,掌握概率能够帮助我们有效的解决现实世界中的许多问题,认识到概率的思维方式和确定性思维方式的差异,这就是随机观念。这种充满辩证思想的新观念和认识客观世界的新视角,是学生应该建立的观念,也是概率教学的主要目标。
论文主要包括三个部分。
第一部分是第一章、第二章和第三章,主要阐述研究的背景、研究的问题、研究的意义、国内外的相关研究和本论文所采取的研究方法。
第二部分是第四章。
第四章从四个方面研究高中生概率学习状况。第一方面考查学生对频率定义和古典定义掌握情况,研究结果表明:学生学习了概率内容之后,仍然还存在对概率概念的错误理解;学生对概率的古典定义理解的还不透彻,具体做题时容易忘记古典定义的两大特征,在确定样本空间时容易出现错误。
第二方面考查学生辨析概率概念情况。涉及到的概念有不可能事件、可能事件、必然事件,概率模型有:等可能事件、互斥事件、对立事件、相互独立事件、n次独立重复事件,研究结果表明:对概率各种模型理解既不深刻,又不全面,抓不住概念的本质,甚至混淆。学生对概率问题中概率模型的判定和识别也不准确。已经学过概率的高三学生仍然存在预言结果的倾向,在两步概率计算问题上,系统学习过概率计算的高三应届学生更容易犯“简单复合法”,他们的主观概率意识更强。
第三方面考查学生利用概率值进行决策情况,即给定概率值时学生决策情况;给定一个结果对学生决策的影响;实际生活中学生利用概率知识进行判断的意识和能力。研究结果表明:学生对概率的应用了解很少,他们缺乏把所学知识联系、运用于生活实际、将亲身经历的实际问题抽象成数学模型并进行解释与应用的能力,在实际生活中缺乏利用概率知识进行判断和决策的意识。
第四方面研究学生解2008年高考概率题情况,研究结果表明:学生在做概率与其他章知识结合在一起的综合题型时,由于这类题往往与实践联系紧密,学生在阅读理解方面存在严重的困难。
论文的最后一部分是第五章和第六章,第五章主要呈现了本文的主要结论,第六章是关于高中概率教学的思考和建议以及一个教学案例。
The new curriculum has been clearly put forward:the probability can give an effective and very useful way of thinking to find a statistical regularity of objective things with the objective law of random phenomena.Therefore,the probability of the basic knowledge has been to become a citizen must have knowledge of the future,and now,probability and certainty of science,as has become us to understand and transform the natural,social an indispensable scientific methods,can help us grasp the probability of effective settlement of the real world many of the issues,recognizing that the probability of thinking and different ways of thinking uncertainty,and this is the concept of random. This is full of dialectical thinking of new ideas and understanding of the objective world and the new perspective,students should be established the concept of probability is the main objective of teaching.
Papers mainly includes three parts.
The first part is the first chapter,ChaptersⅡandⅢ,mainly on the background to the study,study,study the meaning of the relevant domestic and foreign research and this paper,the approach adopted.
The second part is in chaptersⅣ.
ChapterⅣstudies from high school students learning probability.The first test students on the frequency of the classical definition and the definition of informed,research results show that:the probability of learning content is still there on the probability of wrong interpretation of the concept; students to the classical definition of the probability of less than a thorough understanding of the specific topics do easy to forget that when the classical definition of the two major characteristics,in determining the sample space prone to error.
The second area to examine the situation of the students the concept of probability analysis.Related to the concept of impossible events,may events, an inevitable event,probabilistic model are:the potential events,mutually exclusive events,opposite events,the events are independent of each other, n independent duplication events,research results show that:the probability of various models for understanding neither profound nor comprehensive,can not grasp the essence of the concept,and even confusion.Students probabilistic model of the probability of the problem and identify the judge nor accurate.
Having studied the probability of three students still tend to predict the outcome,in the two-step the issue of probability calculation,the system studied the probability calculation of three year students to have a better offense, "Jane composite Law",and their stronger sense of subjective probability.
The third area to examine the probability of the value of students to use decision-making situation,that is,the probability of a given value of student decision-making situation;given the students a result of the impact of the decision-making;real life,the probability of secondary school students to use knowledge to determine the awareness and ability.The results show that:the application of the probability of students rarely understand that they lack the knowledge to contact the practical application of life,will experience the practical problems into a mathematical model of abstract interpretation and application and the ability,in real life,lack of access to to determine the probability of knowledge and awareness of decision-making.
The fourth area study students solution entrance probability title in 2008, the study results show that:the probability of students are doing with other chapter combines comprehensive knowledge questions,as a result of such practice and practice are often closely connected,students in reading comprehension there serious difficulties.
The last part of paper is chaptersⅤandⅥ,ChapterⅤpresents the main conclusions of this article.ChapterⅥis a high probability on the Teaching and recommendations as well as a teaching case.
论文主要包括三个部分。
第一部分是第一章、第二章和第三章,主要阐述研究的背景、研究的问题、研究的意义、国内外的相关研究和本论文所采取的研究方法。
第二部分是第四章。
第四章从四个方面研究高中生概率学习状况。第一方面考查学生对频率定义和古典定义掌握情况,研究结果表明:学生学习了概率内容之后,仍然还存在对概率概念的错误理解;学生对概率的古典定义理解的还不透彻,具体做题时容易忘记古典定义的两大特征,在确定样本空间时容易出现错误。
第二方面考查学生辨析概率概念情况。涉及到的概念有不可能事件、可能事件、必然事件,概率模型有:等可能事件、互斥事件、对立事件、相互独立事件、n次独立重复事件,研究结果表明:对概率各种模型理解既不深刻,又不全面,抓不住概念的本质,甚至混淆。学生对概率问题中概率模型的判定和识别也不准确。已经学过概率的高三学生仍然存在预言结果的倾向,在两步概率计算问题上,系统学习过概率计算的高三应届学生更容易犯“简单复合法”,他们的主观概率意识更强。
第三方面考查学生利用概率值进行决策情况,即给定概率值时学生决策情况;给定一个结果对学生决策的影响;实际生活中学生利用概率知识进行判断的意识和能力。研究结果表明:学生对概率的应用了解很少,他们缺乏把所学知识联系、运用于生活实际、将亲身经历的实际问题抽象成数学模型并进行解释与应用的能力,在实际生活中缺乏利用概率知识进行判断和决策的意识。
第四方面研究学生解2008年高考概率题情况,研究结果表明:学生在做概率与其他章知识结合在一起的综合题型时,由于这类题往往与实践联系紧密,学生在阅读理解方面存在严重的困难。
论文的最后一部分是第五章和第六章,第五章主要呈现了本文的主要结论,第六章是关于高中概率教学的思考和建议以及一个教学案例。
The new curriculum has been clearly put forward:the probability can give an effective and very useful way of thinking to find a statistical regularity of objective things with the objective law of random phenomena.Therefore,the probability of the basic knowledge has been to become a citizen must have knowledge of the future,and now,probability and certainty of science,as has become us to understand and transform the natural,social an indispensable scientific methods,can help us grasp the probability of effective settlement of the real world many of the issues,recognizing that the probability of thinking and different ways of thinking uncertainty,and this is the concept of random. This is full of dialectical thinking of new ideas and understanding of the objective world and the new perspective,students should be established the concept of probability is the main objective of teaching.
Papers mainly includes three parts.
The first part is the first chapter,ChaptersⅡandⅢ,mainly on the background to the study,study,study the meaning of the relevant domestic and foreign research and this paper,the approach adopted.
The second part is in chaptersⅣ.
ChapterⅣstudies from high school students learning probability.The first test students on the frequency of the classical definition and the definition of informed,research results show that:the probability of learning content is still there on the probability of wrong interpretation of the concept; students to the classical definition of the probability of less than a thorough understanding of the specific topics do easy to forget that when the classical definition of the two major characteristics,in determining the sample space prone to error.
The second area to examine the situation of the students the concept of probability analysis.Related to the concept of impossible events,may events, an inevitable event,probabilistic model are:the potential events,mutually exclusive events,opposite events,the events are independent of each other, n independent duplication events,research results show that:the probability of various models for understanding neither profound nor comprehensive,can not grasp the essence of the concept,and even confusion.Students probabilistic model of the probability of the problem and identify the judge nor accurate.
Having studied the probability of three students still tend to predict the outcome,in the two-step the issue of probability calculation,the system studied the probability calculation of three year students to have a better offense, "Jane composite Law",and their stronger sense of subjective probability.
The third area to examine the probability of the value of students to use decision-making situation,that is,the probability of a given value of student decision-making situation;given the students a result of the impact of the decision-making;real life,the probability of secondary school students to use knowledge to determine the awareness and ability.The results show that:the application of the probability of students rarely understand that they lack the knowledge to contact the practical application of life,will experience the practical problems into a mathematical model of abstract interpretation and application and the ability,in real life,lack of access to to determine the probability of knowledge and awareness of decision-making.
The fourth area study students solution entrance probability title in 2008, the study results show that:the probability of students are doing with other chapter combines comprehensive knowledge questions,as a result of such practice and practice are often closely connected,students in reading comprehension there serious difficulties.
The last part of paper is chaptersⅤandⅥ,ChapterⅤpresents the main conclusions of this article.ChapterⅥis a high probability on the Teaching and recommendations as well as a teaching case.
引文
1.中华人民共和国教育部制订.全日制普通高级中学学数学教学大纲[M].北京:人民教育出版社.2002,4
2.全日制普通高级中学教科数学第二册(下)[M].北京:人民教育出版社.2003,10
3.全日制普通高级中学教科书数学第三册选修(Ⅱ)[M].北京:人民教育出版社.2004,6
4.教育部.普通高中数学新课程标准(试验修订版)[M].北京:人民教育出版社.2003
5.李俊.中小学概率的教与学[M].上海,华东师范大学出版社.2003,5
6.陈希孺.概率论与数理统计[M]。安徽:中国科学技术大学出版社.2002,3
7.[美]波利亚.怎样解题[M].上海科技教育出版社.2002,p79.[美]波利亚著.怎样解题—数学方法的新面貌[M].上海:上海科技教育教育出版
3.中华人民共和国教育部制订.全日制普通高级中学学数学教学大纲[M].北京:人民教育出版社.2002,4
9.全日制普通高级中学教科数学第二册(下)[M].北京:人民教育出版社.2003,10
1O.全日制普通高级中学教科书数学第三册选修(Ⅱ)[M].北京:人民教育出版社.2004,6
11.教育部.普通高中数学新课程标准(试验修订版)[M].北京:人民教育出版社.2003
12.李俊.中小学概率的教与学[M].上海,华东师范大学出版社.2003,5
13.[美]波利亚.怎样解题[M].上海科技教育出版社.2002,p79.
14.[美]波利亚著.怎样解题—数学方法的新面貌[M].上海:上海科技教育教育出版社,2002
15.全美数学教师理事会,美国学校教育的原理和标准[M].人民教育出版社,蔡金法等译,2004.12
17.邹植民,李定武.概率论与数理统计[M].湖南师范大学出版社.2002
18.曹和翰.中学数学教学概论[M]北京师范大学出版社.2003
19.钱佩玲,邵光华著.数学思想方法和中学数学[M].北京师范大学出版社,1999
2O.张奠宙.数学教育学导论[M].北京:高等教育出版社.2003
21.郑君文,张恩华著.数学学习论[M].南宁:广西教育出版社.2003
22.宋礼民,刘原.概率论与数理统计[M].武汉:中国地质大学出版社,2002
23.张奠宙,宋及庆.教学教育概论[M].北京:高等教育出版社.2005,4
24.吴惠红.中学生对概率值的理解.[D].华东师范大学出版社.2004,5
25.郭宝珠.对学生在高中阶段概率学习中常见错误的分析.[D].东北师范大学出版社.2006.6
26.程伶俐.中学教学教师对概率概念及其教学的认识.[D].华东师范大学出版社,2006,10
27.郭明贵.关于概率概念的教学研究.[D]华中师范大学出版社,2006,5
28.吕建生.生活先于课程将统计概率推倒学生的面前[J].数学通报,2003,10
29.张饴慈.”新课标”理念下高中概率和统计[J].数学能报.2005.第44卷第6期
30.林大祥.初等概率教学浅探[J].数学能报,1996,第三期
31.罗建宁.瞿高海.从结构化观看数学教材中”集合论””数理逻辑””概率论”的关系[J]数学通讯,2003(17)
32.王柱元.对高中教学概率教学的几点思考[J].中学教学.2005,7
33.廖永.概率论发展简史[J].2008,6,5
34.钟志华.对高中新课程中概率教学计课的育人功能,数学教育报[J],2002,(5)
35.蔺云.哲学与文化视角下概率统计课的育人功能.教学教育学报[J].2002(5)
36.李俊.对学生”无法比较可能性”回答的理由剖析[J].数学教学,2003(6)
37.蔡上鹤.高三数学”概率与统计”教学问答[J].中学教学参考,2003,8
38.张丹,新课程理念下的统计与概率教学[J].数学通报.2005,1
39.舒元生.在概率统计教学中如何渗透中学数学思想方法[J].中学数学研究,2005,7
40.赵欣庆.对一个概率问题的两个误解[J].中学生数学,2005,3(月上)
41.Mets GN.The Assessment Challenhe in Statistics Education[M].Amsterdam:The InternationalStaistial Institute Press.1997.223-238
42.Lecoutre Mp.Cohnitive models and problem spaces in“purely random”situations[J].Educational Studies in Mathematics.23:557-568
43.GarfieldJB.Reflections on the past 15years[J].Teaching Statistics 1995,17
44.Green DR.1983a.schoolpupils probability concepts.Teaching Statistics,5(2):34-42
45.Watson.J M,Moritz J B.1998.Longitudinal Development of Chance Measurement.Manuscript
46.Konold,C.Understanding students'beliefs about probability.Radical Constructivism in Mathematics Education,139-156.1991
47.NCTM,Principles and Standards for School.Mathematics(Grade 9-12).2000.
2.全日制普通高级中学教科数学第二册(下)[M].北京:人民教育出版社.2003,10
3.全日制普通高级中学教科书数学第三册选修(Ⅱ)[M].北京:人民教育出版社.2004,6
4.教育部.普通高中数学新课程标准(试验修订版)[M].北京:人民教育出版社.2003
5.李俊.中小学概率的教与学[M].上海,华东师范大学出版社.2003,5
6.陈希孺.概率论与数理统计[M]。安徽:中国科学技术大学出版社.2002,3
7.[美]波利亚.怎样解题[M].上海科技教育出版社.2002,p79.[美]波利亚著.怎样解题—数学方法的新面貌[M].上海:上海科技教育教育出版
3.中华人民共和国教育部制订.全日制普通高级中学学数学教学大纲[M].北京:人民教育出版社.2002,4
9.全日制普通高级中学教科数学第二册(下)[M].北京:人民教育出版社.2003,10
1O.全日制普通高级中学教科书数学第三册选修(Ⅱ)[M].北京:人民教育出版社.2004,6
11.教育部.普通高中数学新课程标准(试验修订版)[M].北京:人民教育出版社.2003
12.李俊.中小学概率的教与学[M].上海,华东师范大学出版社.2003,5
13.[美]波利亚.怎样解题[M].上海科技教育出版社.2002,p79.
14.[美]波利亚著.怎样解题—数学方法的新面貌[M].上海:上海科技教育教育出版社,2002
15.全美数学教师理事会,美国学校教育的原理和标准[M].人民教育出版社,蔡金法等译,2004.12
17.邹植民,李定武.概率论与数理统计[M].湖南师范大学出版社.2002
18.曹和翰.中学数学教学概论[M]北京师范大学出版社.2003
19.钱佩玲,邵光华著.数学思想方法和中学数学[M].北京师范大学出版社,1999
2O.张奠宙.数学教育学导论[M].北京:高等教育出版社.2003
21.郑君文,张恩华著.数学学习论[M].南宁:广西教育出版社.2003
22.宋礼民,刘原.概率论与数理统计[M].武汉:中国地质大学出版社,2002
23.张奠宙,宋及庆.教学教育概论[M].北京:高等教育出版社.2005,4
24.吴惠红.中学生对概率值的理解.[D].华东师范大学出版社.2004,5
25.郭宝珠.对学生在高中阶段概率学习中常见错误的分析.[D].东北师范大学出版社.2006.6
26.程伶俐.中学教学教师对概率概念及其教学的认识.[D].华东师范大学出版社,2006,10
27.郭明贵.关于概率概念的教学研究.[D]华中师范大学出版社,2006,5
28.吕建生.生活先于课程将统计概率推倒学生的面前[J].数学通报,2003,10
29.张饴慈.”新课标”理念下高中概率和统计[J].数学能报.2005.第44卷第6期
30.林大祥.初等概率教学浅探[J].数学能报,1996,第三期
31.罗建宁.瞿高海.从结构化观看数学教材中”集合论””数理逻辑””概率论”的关系[J]数学通讯,2003(17)
32.王柱元.对高中教学概率教学的几点思考[J].中学教学.2005,7
33.廖永.概率论发展简史[J].2008,6,5
34.钟志华.对高中新课程中概率教学计课的育人功能,数学教育报[J],2002,(5)
35.蔺云.哲学与文化视角下概率统计课的育人功能.教学教育学报[J].2002(5)
36.李俊.对学生”无法比较可能性”回答的理由剖析[J].数学教学,2003(6)
37.蔡上鹤.高三数学”概率与统计”教学问答[J].中学教学参考,2003,8
38.张丹,新课程理念下的统计与概率教学[J].数学通报.2005,1
39.舒元生.在概率统计教学中如何渗透中学数学思想方法[J].中学数学研究,2005,7
40.赵欣庆.对一个概率问题的两个误解[J].中学生数学,2005,3(月上)
41.Mets GN.The Assessment Challenhe in Statistics Education[M].Amsterdam:The InternationalStaistial Institute Press.1997.223-238
42.Lecoutre Mp.Cohnitive models and problem spaces in“purely random”situations[J].Educational Studies in Mathematics.23:557-568
43.GarfieldJB.Reflections on the past 15years[J].Teaching Statistics 1995,17
44.Green DR.1983a.schoolpupils probability concepts.Teaching Statistics,5(2):34-42
45.Watson.J M,Moritz J B.1998.Longitudinal Development of Chance Measurement.Manuscript
46.Konold,C.Understanding students'beliefs about probability.Radical Constructivism in Mathematics Education,139-156.1991
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