高中数学新课程关于概率的教学误区及对策
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摘要
随机思想成为人们生存的必需的基本素质之一。由于概率研究的对象是不确定现象,与传统的教学内容有着极大的不同,因此传统的教育观念和教学方式就显得有些苍白,如何搞好概率的教学是数学教育界亟需解决的问题。国家教育部在基础教育改革中,于2003年4月颁布的《普通高中数学课程标准(实验)》(以下简称《标准》)里,较多地增加了概率统计的内容与课时,在编排顺序上也作了较大变动,这些变化体现了数学课程改革的基本理念。
本文根据作者,在高中新课程教材的一个多轮回的教学实践和多年的教学经验,首先分析了高中新课程数学设置概率内容的基本理念、教育价值及教学要求。其次,针对当前高中新课程中概率教学过程中存在的问题进行了分析研究,对其概念和方法应用产生的误区进行概括,并通过正反例将问题得以澄清。再次,以科学的数学教育理念为指导,以教与学对应的原理为核心,以提高教学效果为目标,提出了在教学过程中纠正误区的五个方面对策。最后,结合新课程概率初步内容的改革实验,对概率的教学提出了一些教学建议。总之,本文的研究可以增进对新课程的了解,对授课的教师和学习该课程的学生都有一定的指导意义。
高中新课程概率教学中还有很多值得进一步研究的方面,例如在培养学生认知和思维能力、基于现代教育技术的高中概率教学模式等方面还需作进一步深入研究。
Random mathematics consciousness is becoming a basic cultivation of people. But what probability research is an uncertain object, it is quite different from those in traditional teaching material, so the traditional education concept and teaching method is unconvincing. So how to teach probability in senior high school is an urgent problem to the mathematics’area. During basic educational reform, Ministry of Education in China issued High School Mathematics New Curriculum Standard (Try line) (Standard for short below) in April, 2003 , added more contents and periods about probability statistics and changed a lot in the order of arrangement, which reflects the basic ideas in mathematics curriculum reform.
Based on teaching practices of many high school new curriculum textbooks and years of teaching experience, the author first analyzes the basic ideas, educational values and teaching requirements of putting probability into high school new curriculum mathematics. Secondly, the author analyzes and studies the problems with probability teaching in high school new curriculum, summarizes the erroneous zones of its concept and ways of application and clarifies the problems by pro and con examples. Thirdly, guided by scientific mathematic educational ideas, centered on principles related to teaching and learning, aiming at making the teaching more effective, the author puts forward five aspects of countermeasures in correcting the erroneous zones during teaching. Finally, based on the experimental reform of the contents of probability, the author comes up with some teaching suggestions on probability teaching. In a word, the thesis can make others have a better knowledge of the new curriculum and benefit both teachers when they are teaching and students when studying the curriculum.
In the teaching of probability in high school new curriculum, there are more aspects worth further studying, For example, deeper studies are necessary on how to train students’abilities in cognition and thinking or the models of high school probability teaching based on modern educational technology.
本文根据作者,在高中新课程教材的一个多轮回的教学实践和多年的教学经验,首先分析了高中新课程数学设置概率内容的基本理念、教育价值及教学要求。其次,针对当前高中新课程中概率教学过程中存在的问题进行了分析研究,对其概念和方法应用产生的误区进行概括,并通过正反例将问题得以澄清。再次,以科学的数学教育理念为指导,以教与学对应的原理为核心,以提高教学效果为目标,提出了在教学过程中纠正误区的五个方面对策。最后,结合新课程概率初步内容的改革实验,对概率的教学提出了一些教学建议。总之,本文的研究可以增进对新课程的了解,对授课的教师和学习该课程的学生都有一定的指导意义。
高中新课程概率教学中还有很多值得进一步研究的方面,例如在培养学生认知和思维能力、基于现代教育技术的高中概率教学模式等方面还需作进一步深入研究。
Random mathematics consciousness is becoming a basic cultivation of people. But what probability research is an uncertain object, it is quite different from those in traditional teaching material, so the traditional education concept and teaching method is unconvincing. So how to teach probability in senior high school is an urgent problem to the mathematics’area. During basic educational reform, Ministry of Education in China issued High School Mathematics New Curriculum Standard (Try line) (Standard for short below) in April, 2003 , added more contents and periods about probability statistics and changed a lot in the order of arrangement, which reflects the basic ideas in mathematics curriculum reform.
Based on teaching practices of many high school new curriculum textbooks and years of teaching experience, the author first analyzes the basic ideas, educational values and teaching requirements of putting probability into high school new curriculum mathematics. Secondly, the author analyzes and studies the problems with probability teaching in high school new curriculum, summarizes the erroneous zones of its concept and ways of application and clarifies the problems by pro and con examples. Thirdly, guided by scientific mathematic educational ideas, centered on principles related to teaching and learning, aiming at making the teaching more effective, the author puts forward five aspects of countermeasures in correcting the erroneous zones during teaching. Finally, based on the experimental reform of the contents of probability, the author comes up with some teaching suggestions on probability teaching. In a word, the thesis can make others have a better knowledge of the new curriculum and benefit both teachers when they are teaching and students when studying the curriculum.
In the teaching of probability in high school new curriculum, there are more aspects worth further studying, For example, deeper studies are necessary on how to train students’abilities in cognition and thinking or the models of high school probability teaching based on modern educational technology.
引文
[1]李俊.中小学概率的教与学[M].上海:华东师范大学出版社,2003.
[2]中华人民共和国教育部.普通高中数学课程标准(试验)[M].北京:人民教育出版社,2003(4).
[3]金美月等.高中数学教师概率统计知识状况调查研究[D].沈阳:辽宁师范大学.2008.
[4]Green D R. Probability Concepts in 11-16 Year Old Pupils[M].2nd Education. Centre for Advancement of Mathematical Education in Technology, University of Loughborough,1982.
[5]Williams J S, Amir G S. 11-12 year old children's informal knowledge and its influence on their formal probabilistic reasoning. ERIC ED 387256. 1995.
[6]Konold,C.(1991).Understanding students’beliefs about porbabiliy. In:von Glasersefeld E.ed.Radieal Constructivsim in Mathematics Education. Dordrecht:Kluwer. 139~156.
[7]Fischbien,E and Gazit,A. Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics. 1984:1-24.
[8]Garham A.Jones, Cynthia W.Langral,Carol A.Thornton and A.Timothy Mogill Aframework for assessing and nurturing young children's thinking in probability.Educational Studies in Mathematics, 1997:101-125.
[9]Collis ,K, F and Biggs, J, B(1991).Developmental determinants of qualitative of school leaning .In G. Evans(Ed),learning and teaching cognitive skills(p185-207) Melbourne.
[10]张奠宙.迟到的收获[J].中学数学,2003(1).
[11]马萍等.高一学生统计素养现状的调查研究[D].上海:华东师范大学,2008.
[12]陈嫣、涂荣豹.关于随机性数学意识的培养[J].数学教育学报,2002(2).
[13]张文忠,但冰如.概率统计中的反例[M].成都:成都科技大学出版社,1991.
[14]杨宗磐.概率论入门[M].上海:科学出版社,1981:3.
[15]复旦大学.概率论[M].北京:人民教育出版社,1979.
[16]华东师范大学数学系.概率论与数理统计教程[M].北京:高等教育出版社,1983:46.
[17]胡迪鹤,刘文等(译).概率论及其应用[M].北京:科学出版社,1973:121-123.
[18]【瑞士】皮亚杰著,王宪钿等译.上海:发生认识论原理[M].商务印书馆,1981.
[19]张德然,茹诗松.高中概率统计教学中随机性数学思维的培养[J].课程·教材·教法,2003:9.
[20]【美】波利亚著,李志尧等译.数学与猜想[M].北京:科学出版社,2002:62.
[21]【美】斯蒂恩编,胡作玄等译.站在巨人的肩膀上[M].上海:上海教育出版社,2000.
[22]郑毓信,肖柏蓉,熊萍.论数学思维与方法论[M].成都:四川教育出版社,2001.
1.数学课程标准研制组.普通高中数学课程标准(实验)解读[M].南京:江苏教育出版社,2004.
2.叶尧城.高中数学课程标准教师读本[M].武汉:华中师范大学出版社,2003.
3.喻平.数学教育心理学[M].桂林:广西教育出版社,2004.
4.魏宗舒等.概率论与数理统计[M].北京:高等教育出版社,1983.
5.张奠宙.数学教育研究导引[M].南京:江苏教育出版社,1994.
6.张奠宙,李士绮,李俊.数学教育学导论[M].北京:高等教育出版社,2002.
7.章建跃.中学生数学学科自我监控能力[M].上海:华东师范大学出版社,2003.
8.李玉琪.中学数学教学与实践研究[M].北京:高等教育出版社,2001.
9.李玉琪.数学教育概论[M].北京:中国科技出版社,1994.
10.陆书环,傅海伦.数学教学论[M].济南:科学出版社,2004.
11.马忠林.数学方法论[M].南宁:广西教育出版社,2003.
12.马军英.概率论与数理统计学习指导与习题全解[M].济南:山东科学技术出版社,2005.
13.傅海伦.数学·科学与文化的殿堂[M].西安:陕西科学技术出版社,2004.
14.杨小微.教育研究方法[M].北京:人民教育出版社,2006
15.张饴慈.“新课标”理念下高中概率和统计内容的定位和教学[J] .数学通报,2005(6).
16.黄海平.浅谈《概率统计》教学中数学思想方法的运用[J].广西教育学院学报,1999 (4).15.
17.徐速.国内数学学习心理研究的综述[J] .心理科学通讯,2003.
18.饶汉昌.让中学生接触概率统计的思想方法[J].数学通讯,1999(12).
19.赵小平.借鉴外国经验改进概率教学[J].数学教学,2000(3).
20.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).
21.郑毓信,谢明初.“双基”与“双基教学”;认知的观点[J].中学数学教学参考,2004(6).
22.赵欣庆.对一个概率问题的两个误解[J].中学生数学,2005(3).
23.赵欣庆.概率学习札记[J].高中数学教与学,2005(6).
24.赵欣庆.抛掷硬币试验程序与概率定义教学[J].高中数学教与学,2005(8).
25.蔡上鹤.高三数学“概率与统计”章教学问答[J].中学数学教学参考,2003(8).
26.蔺云.哲学文化视下概率统计课的育人功能[J].数学教育学报,2002(11).
27.张德然,茹诗松.高中概率统计教学中随机性数学思维的培养[J].课程·教材·教法, 2003(9).
28.孔凡海.新教材“概率”必修部分教学的几点建议[J].中学数学教学参考,2003(4).
29.张丹.新课程理念下的统计与概率教学[J].数学通报,2005(1).
30.张奠宙.中学教材中的“数学文化”课例[J].数学教学,2002(4).
31.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).
32.杨慧娟.中美课程标准第三学段统计与概率教学目标的比较研究[J].中学数学, 2003(8).
33.王建波.从频率的角度理解概率的意义[J].中学生数理化,2005(12).
34.王柱元.对高中概率教学的几点思考[J].中学数学,2005(7).
35.王红蔚,汤慧龙.从一次调查谈中小学进行概率教育的必要性[J].数学教学,1998(4).
36.张怡慈.“新课标”理念下高中概率和统计内容的定位和教学[J].数学通报,2005(6).
37.翁泽群.古典概率问题解法探讨[J].数学通报,1997(8).
38.张耘,戴宇.古典概率教学浅析[J].数学教学通讯.2004(12).
39.钟志华.对高中新课程中概率教学的认识[J].数学教育学报,2006(15).
40.张文辉,王光明.数学认知理解的研究综述[J].曲阜师范大学学报,2005(1).
41.杨文泽.“统计与概率内容标准研讨”学习辅导[J].云南教育,2003(23).
42.俞求是.频率与概率[J].中学数学教学参考,2002(11).
43.转引自网站:2008年山东省高中教师新课程全员培训. http://portal.sdteacher.gov.cn
[2]中华人民共和国教育部.普通高中数学课程标准(试验)[M].北京:人民教育出版社,2003(4).
[3]金美月等.高中数学教师概率统计知识状况调查研究[D].沈阳:辽宁师范大学.2008.
[4]Green D R. Probability Concepts in 11-16 Year Old Pupils[M].2nd Education. Centre for Advancement of Mathematical Education in Technology, University of Loughborough,1982.
[5]Williams J S, Amir G S. 11-12 year old children's informal knowledge and its influence on their formal probabilistic reasoning. ERIC ED 387256. 1995.
[6]Konold,C.(1991).Understanding students’beliefs about porbabiliy. In:von Glasersefeld E.ed.Radieal Constructivsim in Mathematics Education. Dordrecht:Kluwer. 139~156.
[7]Fischbien,E and Gazit,A. Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics. 1984:1-24.
[8]Garham A.Jones, Cynthia W.Langral,Carol A.Thornton and A.Timothy Mogill Aframework for assessing and nurturing young children's thinking in probability.Educational Studies in Mathematics, 1997:101-125.
[9]Collis ,K, F and Biggs, J, B(1991).Developmental determinants of qualitative of school leaning .In G. Evans(Ed),learning and teaching cognitive skills(p185-207) Melbourne.
[10]张奠宙.迟到的收获[J].中学数学,2003(1).
[11]马萍等.高一学生统计素养现状的调查研究[D].上海:华东师范大学,2008.
[12]陈嫣、涂荣豹.关于随机性数学意识的培养[J].数学教育学报,2002(2).
[13]张文忠,但冰如.概率统计中的反例[M].成都:成都科技大学出版社,1991.
[14]杨宗磐.概率论入门[M].上海:科学出版社,1981:3.
[15]复旦大学.概率论[M].北京:人民教育出版社,1979.
[16]华东师范大学数学系.概率论与数理统计教程[M].北京:高等教育出版社,1983:46.
[17]胡迪鹤,刘文等(译).概率论及其应用[M].北京:科学出版社,1973:121-123.
[18]【瑞士】皮亚杰著,王宪钿等译.上海:发生认识论原理[M].商务印书馆,1981.
[19]张德然,茹诗松.高中概率统计教学中随机性数学思维的培养[J].课程·教材·教法,2003:9.
[20]【美】波利亚著,李志尧等译.数学与猜想[M].北京:科学出版社,2002:62.
[21]【美】斯蒂恩编,胡作玄等译.站在巨人的肩膀上[M].上海:上海教育出版社,2000.
[22]郑毓信,肖柏蓉,熊萍.论数学思维与方法论[M].成都:四川教育出版社,2001.
1.数学课程标准研制组.普通高中数学课程标准(实验)解读[M].南京:江苏教育出版社,2004.
2.叶尧城.高中数学课程标准教师读本[M].武汉:华中师范大学出版社,2003.
3.喻平.数学教育心理学[M].桂林:广西教育出版社,2004.
4.魏宗舒等.概率论与数理统计[M].北京:高等教育出版社,1983.
5.张奠宙.数学教育研究导引[M].南京:江苏教育出版社,1994.
6.张奠宙,李士绮,李俊.数学教育学导论[M].北京:高等教育出版社,2002.
7.章建跃.中学生数学学科自我监控能力[M].上海:华东师范大学出版社,2003.
8.李玉琪.中学数学教学与实践研究[M].北京:高等教育出版社,2001.
9.李玉琪.数学教育概论[M].北京:中国科技出版社,1994.
10.陆书环,傅海伦.数学教学论[M].济南:科学出版社,2004.
11.马忠林.数学方法论[M].南宁:广西教育出版社,2003.
12.马军英.概率论与数理统计学习指导与习题全解[M].济南:山东科学技术出版社,2005.
13.傅海伦.数学·科学与文化的殿堂[M].西安:陕西科学技术出版社,2004.
14.杨小微.教育研究方法[M].北京:人民教育出版社,2006
15.张饴慈.“新课标”理念下高中概率和统计内容的定位和教学[J] .数学通报,2005(6).
16.黄海平.浅谈《概率统计》教学中数学思想方法的运用[J].广西教育学院学报,1999 (4).15.
17.徐速.国内数学学习心理研究的综述[J] .心理科学通讯,2003.
18.饶汉昌.让中学生接触概率统计的思想方法[J].数学通讯,1999(12).
19.赵小平.借鉴外国经验改进概率教学[J].数学教学,2000(3).
20.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).
21.郑毓信,谢明初.“双基”与“双基教学”;认知的观点[J].中学数学教学参考,2004(6).
22.赵欣庆.对一个概率问题的两个误解[J].中学生数学,2005(3).
23.赵欣庆.概率学习札记[J].高中数学教与学,2005(6).
24.赵欣庆.抛掷硬币试验程序与概率定义教学[J].高中数学教与学,2005(8).
25.蔡上鹤.高三数学“概率与统计”章教学问答[J].中学数学教学参考,2003(8).
26.蔺云.哲学文化视下概率统计课的育人功能[J].数学教育学报,2002(11).
27.张德然,茹诗松.高中概率统计教学中随机性数学思维的培养[J].课程·教材·教法, 2003(9).
28.孔凡海.新教材“概率”必修部分教学的几点建议[J].中学数学教学参考,2003(4).
29.张丹.新课程理念下的统计与概率教学[J].数学通报,2005(1).
30.张奠宙.中学教材中的“数学文化”课例[J].数学教学,2002(4).
31.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).
32.杨慧娟.中美课程标准第三学段统计与概率教学目标的比较研究[J].中学数学, 2003(8).
33.王建波.从频率的角度理解概率的意义[J].中学生数理化,2005(12).
34.王柱元.对高中概率教学的几点思考[J].中学数学,2005(7).
35.王红蔚,汤慧龙.从一次调查谈中小学进行概率教育的必要性[J].数学教学,1998(4).
36.张怡慈.“新课标”理念下高中概率和统计内容的定位和教学[J].数学通报,2005(6).
37.翁泽群.古典概率问题解法探讨[J].数学通报,1997(8).
38.张耘,戴宇.古典概率教学浅析[J].数学教学通讯.2004(12).
39.钟志华.对高中新课程中概率教学的认识[J].数学教育学报,2006(15).
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