高中共建学生数学思维特点的实证研究
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摘要
数学思维教育是21世纪数学教育的核心。数学是与思维联系紧密的科学,是思维的科学。在数学教学中,要求学生通过自己的思维来学习,这是普通教育首要的教学目的和要求。学生学习数学,不仅要掌握教学大纲所规定的数学实践知识、技能和能力,而日.要掌握数学思维的方法,促进思维的发展。现代数学教学把发展学生的思维提到了相当高的地位、形象的把数学喻为“思维的体操”,这是因为数学是一门以论证方式建立的学科,要实现逻辑论证,必须经过不懈的努力,学习数学的那种精神,对所有学习者都是有益的。
本文立足于教学实践,以鞍山市第一中学高三共建班学生为被试对象,通过课堂教学观察、教学实录、试卷剖析、个别答疑等对学生在问题解决中呈现的思维特点进行研究和分析,对共建班中的男生、女生、数学优等生、数学困难生进行了分类,了解他们在逻辑思维、形象思维、直觉思维三方面的水平差异,探索优化学生数学思维的教学策略,从而促进他们数学的学习。研究中采用了问卷、观察、访谈、测验等科学手段。
Maths thinking education is the centre in 21 century .Maths is a science very close to thinking,a science of thinking . Abstract: So as to mathematic teaching, requiring students study overpass their thinking, this is chiefly teaching aim and reques. Students must mastery neat only episteme and ability, which didactical outline stipulates, but also ways and means mathematic thinking, that can develop their thinking. Modern mathematics teaching has raised it to a fairly high position that it develops students'ability of thought, and it compares mathematics to”the gymnastic of thought ".This is because mathematics is the subject that is established by demonstration .To realize logic demonstration,we must persevere and study those spirit of mathematics via unremitting efforts,which is helpful for all the learners.
This paper stands in teaching practice.I experiment on the students of seven classes in the Middle School of anshan .The students are from the liberal arts of high 3. Through classroom teaching observation and the anatomy of test papers,individual answers to the questions raised by the students etc, I make a study of thought characteristics that have appeared in problem solution study .1 classify the students into several groups,such as ,schoolgirls and schoolboys,mathematics high-class livelihood and students having difficulty with mathematics in liberal arts to have some idea of their horizontal discrepancy in the aspect of logic thought, thinking in images and intuition thought 3 and explore optimization student mathematics thought to promote the study of their mathematics. In research,I have adopted questionnaire and observation,visit to talk,the scientific means such as test.
本文立足于教学实践,以鞍山市第一中学高三共建班学生为被试对象,通过课堂教学观察、教学实录、试卷剖析、个别答疑等对学生在问题解决中呈现的思维特点进行研究和分析,对共建班中的男生、女生、数学优等生、数学困难生进行了分类,了解他们在逻辑思维、形象思维、直觉思维三方面的水平差异,探索优化学生数学思维的教学策略,从而促进他们数学的学习。研究中采用了问卷、观察、访谈、测验等科学手段。
Maths thinking education is the centre in 21 century .Maths is a science very close to thinking,a science of thinking . Abstract: So as to mathematic teaching, requiring students study overpass their thinking, this is chiefly teaching aim and reques. Students must mastery neat only episteme and ability, which didactical outline stipulates, but also ways and means mathematic thinking, that can develop their thinking. Modern mathematics teaching has raised it to a fairly high position that it develops students'ability of thought, and it compares mathematics to”the gymnastic of thought ".This is because mathematics is the subject that is established by demonstration .To realize logic demonstration,we must persevere and study those spirit of mathematics via unremitting efforts,which is helpful for all the learners.
This paper stands in teaching practice.I experiment on the students of seven classes in the Middle School of anshan .The students are from the liberal arts of high 3. Through classroom teaching observation and the anatomy of test papers,individual answers to the questions raised by the students etc, I make a study of thought characteristics that have appeared in problem solution study .1 classify the students into several groups,such as ,schoolgirls and schoolboys,mathematics high-class livelihood and students having difficulty with mathematics in liberal arts to have some idea of their horizontal discrepancy in the aspect of logic thought, thinking in images and intuition thought 3 and explore optimization student mathematics thought to promote the study of their mathematics. In research,I have adopted questionnaire and observation,visit to talk,the scientific means such as test.
引文
[1]刘华祥.中学数学教学论.[M].武汉:武汉大学出版社, 2003 年 8 月
[2]王跃华.杨晶为伟.谈中学数学思维品质的培养.[J].沈阳教育学院学报.2004.4 月
[3] 张奠宙. 数学教育学导论. [M].北京:高等教育出版社,2003 年 8 月
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[7]曹时武.高中文科学生的数学认知特点及施教策略.2006 年
[8]罗增儒.例说数学解题的思维过程[J].中学数学教学参考.2002 年 5 期
[9]钱佩玲.中学数学思想方法.[M].北京师范大学出版社.2000 年 11 月
[10]邵志芳.思维心理学.[M].华东师范大学出版社.2001 年
[11]候宪胜.师范生在数学学习过程中思维特点的实证研究研究生论文.[D].2002
[12]李盛华.同样的立体感,不一样的图形.[J].数学教学.2005 年 11 月
[13] 赵艳玫. 高中文科学生数学思维特点实证研究论文 .[D].
[14]唐大友.高中数学优等生数学思维特点的实证研究.毕业论文.[D].
[15]赵汪.培养学生创造性思维习惯的教学点滴 .[J].中学数学,1999.
[16] 童其林.利用解题后的“再思考”,培养学生的思维品质.[J].数学通讯.1998.8
[17]雷文阁.浅谈中学数学思维品质极其培养.山东教育学院学报 .[J].2001.5
[18]李宏.普通中学男女生立体几何学习差异的研究.数学教育学报.[J].2000.2
[19]刘勇.高考专题复习系列讲座.平面解析几何.[J].数学通讯.2007 年 3 月
[20]郑观宝.方程 x1 + x2 + x3 + x4 +???+ xm = n的正整数解的个数及其应用.[J].2006 年第 18 期[21]中学数学研究.华南师范大学,广东省数学学会.2005 年 1-12 期
[22]数学通讯..[J].2005 年 1-12
[23]张顺燕.数学教育与数学文化.[J].数学通报.2005 年 1 期
[24]黄安成.数学悟性与《立体几何》.[J].数学通报.2005 年 1 期
[25]陶兴模.数学复习课的基本策略 .[J].数学通报.2005 年 4 期
[26]徐明杰.浅谈空间想象能力的培养.[J].数学通报.2005 年 6 期
[27]罗增儒,赵婧一.由考题谈垂直.[J].中学数学教学参考.2007 年 3 月
[28]罗增儒.数学解题学引论.[M]..陕西师范大学出版社,1997.
[29]于鹤玲:选择恰当教法 解除教学困扰[J],教育探索,2005(6)
[30]郑俊盛:提高差生数学水平的若干措施[J],中学数学研究,2000(5)
[31]张奠宙:中学数学教材教法(再版序) [M],华东师大出版社,1994.
[32]前苏联克鲁捷斯基.中小学学生数学能力心理学.[M]
[33].G·Wallace J·M Kallffman. Eaching children with learning problems Charles E·Merrill publicly company 1978
[34].Docked Children’s Learning Difficulties blacker well publishers 1993:A cognitive, Approach.
[35]S Leigh Nataro.A Comparative Study of Geometry Curricula.The Mathematics Teacher,2003(7).
[36].Kendal. Correct Mathematics as an Educational Task, 1973
[37]Clements M A.and Nerida F. 1996.Ellerton:Mathematics Education Research:Past , Present and Future UNESCO.
[2]王跃华.杨晶为伟.谈中学数学思维品质的培养.[J].沈阳教育学院学报.2004.4 月
[3] 张奠宙. 数学教育学导论. [M].北京:高等教育出版社,2003 年 8 月
[4]任樟辉.数学思维论. [M].广西教育出版社.2000 年
[5]陈登轩.数学创新思维特点探微[J].数学通讯.2001 年 19 期
[6] ]刘华为.培养思维调控力之拙见[J].中学数学教学参考.2000 年 3 月
[7]曹时武.高中文科学生的数学认知特点及施教策略.2006 年
[8]罗增儒.例说数学解题的思维过程[J].中学数学教学参考.2002 年 5 期
[9]钱佩玲.中学数学思想方法.[M].北京师范大学出版社.2000 年 11 月
[10]邵志芳.思维心理学.[M].华东师范大学出版社.2001 年
[11]候宪胜.师范生在数学学习过程中思维特点的实证研究研究生论文.[D].2002
[12]李盛华.同样的立体感,不一样的图形.[J].数学教学.2005 年 11 月
[13] 赵艳玫. 高中文科学生数学思维特点实证研究论文 .[D].
[14]唐大友.高中数学优等生数学思维特点的实证研究.毕业论文.[D].
[15]赵汪.培养学生创造性思维习惯的教学点滴 .[J].中学数学,1999.
[16] 童其林.利用解题后的“再思考”,培养学生的思维品质.[J].数学通讯.1998.8
[17]雷文阁.浅谈中学数学思维品质极其培养.山东教育学院学报 .[J].2001.5
[18]李宏.普通中学男女生立体几何学习差异的研究.数学教育学报.[J].2000.2
[19]刘勇.高考专题复习系列讲座.平面解析几何.[J].数学通讯.2007 年 3 月
[20]郑观宝.方程 x1 + x2 + x3 + x4 +???+ xm = n的正整数解的个数及其应用.[J].2006 年第 18 期[21]中学数学研究.华南师范大学,广东省数学学会.2005 年 1-12 期
[22]数学通讯..[J].2005 年 1-12
[23]张顺燕.数学教育与数学文化.[J].数学通报.2005 年 1 期
[24]黄安成.数学悟性与《立体几何》.[J].数学通报.2005 年 1 期
[25]陶兴模.数学复习课的基本策略 .[J].数学通报.2005 年 4 期
[26]徐明杰.浅谈空间想象能力的培养.[J].数学通报.2005 年 6 期
[27]罗增儒,赵婧一.由考题谈垂直.[J].中学数学教学参考.2007 年 3 月
[28]罗增儒.数学解题学引论.[M]..陕西师范大学出版社,1997.
[29]于鹤玲:选择恰当教法 解除教学困扰[J],教育探索,2005(6)
[30]郑俊盛:提高差生数学水平的若干措施[J],中学数学研究,2000(5)
[31]张奠宙:中学数学教材教法(再版序) [M],华东师大出版社,1994.
[32]前苏联克鲁捷斯基.中小学学生数学能力心理学.[M]
[33].G·Wallace J·M Kallffman. Eaching children with learning problems Charles E·Merrill publicly company 1978
[34].Docked Children’s Learning Difficulties blacker well publishers 1993:A cognitive, Approach.
[35]S Leigh Nataro.A Comparative Study of Geometry Curricula.The Mathematics Teacher,2003(7).
[36].Kendal. Correct Mathematics as an Educational Task, 1973
[37]Clements M A.and Nerida F. 1996.Ellerton:Mathematics Education Research:Past , Present and Future UNESCO.