关于高中立体几何教学中空间想象能力的培养
摘要
在高中的立体几何的教学中,使学生系统地掌握空间图形的基本性质,一些简单的多面体的画法及两体积公式,发展学生的空间想象能力和逻辑思维能力,培养学生进一步应用这些知识发现问题﹑分析问题﹑解决问题的思维能力和认知能力是教学的最终目的.但多年来影响立体几何教学的突出问题恰是学生的空间想象能力差,空间感建立缓慢甚至无法形成.造成学生提起立体几何就“谈虎色变”,可以说学生的空间想象能力对于立体几何教学是至关重要的,同时也决定了立体几何教学的成败.本文旨在针对这一问题,在查阅了大量的文献和深入调查学生产生问题的事实基础上,从培养学生画图,识图和辩图能力;强化常见几何体的点、线、面的位置关系;反复挖掘基础知识;基本概念等方面入手,结合课堂教学实践,不断改进教学策略和方法,最后通过实验数据统计结果进行比较分析、研究,提出了培养学生空间想象能力的几点体会与建议.
In the high school three-dimensional geometry teaching, our goal is to let the students systematically grasp the nature of spatial image, some simple polyhedron drawing skills and two volume formulas, so as to develop the students’spatial imagination ability and logical thinking ability. We are aiming at training the students to apply these knowledge further to finding, analyzing, and solving the problem. Because the power of thought and cognition is the ultimate objective of teaching.
But for many years, what has mostly affected the three-dimensional geometry teaching is exactly that the students lacking in sense of space develop spatial imagination ability slowly, some even unable to form it.
So the students feel terrible when someone mentions the three-dimensional geometry. We can say the student's spatial imagination ability is very important and at the same time it determines the three-dimensional geometry teaching. This thesis is for the purpose of solving the above problems. On the foundations of consulting the massive literature and investigating the students, I attempt to train the students to draw and distinguish the figures, strengthen the position relations between points, lines and sides in common geometric figures and dig into basic concept. Combined with teaching practice, I unceasingly improve the teaching strategy and method. Finally, I come up with several inspiration and thoughts about how to improve the students’space imagination ability by comparing, analyzing and studying the experimental data.
In the high school three-dimensional geometry teaching, our goal is to let the students systematically grasp the nature of spatial image, some simple polyhedron drawing skills and two volume formulas, so as to develop the students’spatial imagination ability and logical thinking ability. We are aiming at training the students to apply these knowledge further to finding, analyzing, and solving the problem. Because the power of thought and cognition is the ultimate objective of teaching.
But for many years, what has mostly affected the three-dimensional geometry teaching is exactly that the students lacking in sense of space develop spatial imagination ability slowly, some even unable to form it.
So the students feel terrible when someone mentions the three-dimensional geometry. We can say the student's spatial imagination ability is very important and at the same time it determines the three-dimensional geometry teaching. This thesis is for the purpose of solving the above problems. On the foundations of consulting the massive literature and investigating the students, I attempt to train the students to draw and distinguish the figures, strengthen the position relations between points, lines and sides in common geometric figures and dig into basic concept. Combined with teaching practice, I unceasingly improve the teaching strategy and method. Finally, I come up with several inspiration and thoughts about how to improve the students’space imagination ability by comparing, analyzing and studying the experimental data.
引文
(1)谭国华. 新课程标准高考对数学能力考查的形式与要求[J]中学数学研究,华南师范大学出版社,2006(9):8-10.
(2)高中立体几何内容研究及启示[J]中学数学教与学(湖南科学技术出版社),2006(10):38-41.
(3)李燕杰,李晓东,宋士波.更新观念,完善学生空想象能力的培养[J].数学教育报,1996,5(4):57-60.
(4)米山国藏.数学的精神、思想和方法[M].成都:四川教育出版社,1986.
(5)邵光华.数学思想方法与中学数学[M].北京:北京师范大学出版社,2005.
(6)周春荔.数学教育学[M] 北京:首都师范大学出版社, 2001.
(7)鲁正火,等.数学教育研究概论[M].北京教育科学出版社,1998.
(8)周珍,连四清,周春荔.中学生空间图形认知能力发展与数学成绩关系的相关性研究[J].数学教育学报,2005,14(1):57-58 .
(9)张思明.中学数学建模教学的实践与探索[M].北京:北京教育出版社,1998.
(10)熊宜勤. 实施因材施教的理论与实践[J]. 广西高教研究,2000(4):83-87.
(11)张劲松.浅谈高中数学新课程中“立体几何”部分的内容与要求[J].中学数学教与学(湖南科学技术出版社),2006(10):36-37.
(12)刘华祥主编.中学数学教学论[M]武汉:武汉大学出版社.
(13)杨冠夏 .《从立体几何入门教学看数学语言》中学数学月刊[J]苏州大学出版社 2007.2.
(14)李明振. 认知方式及其与学生数学思维灵活性的关系研究[J]. 心理发展与教育,1994(3):16-20.
(15)林崇德.学习与发展[M].北京:北京师范大学出版社,1999.473.
(16)唐殿强等. 高中生认知方式与学业成绩关系研究[J]. 辽宁教育研究,2002(12):13-18.
(17)钱丽娟《,高中数学实验教学的探索与实践》高中数学教与学[J]2006.
(9):4-5.
(18)李正银,刘景昭.STS 教育观下数学教学策略探讨[J].数学通讯,2000
(13):4-6.
(19)周军. 教学策略[M].北京:教育科学出版社,2003.10-11,258-265.
(20)周丽丽,《直观几何》及对我国几何课程改革的启示[J]数学教育学报,2001,10.
(21)杨高全.数学教学策略研究[J].湖南教育学院学报,200(11):97-100.
(22)李晓文等.教学策略[M].北京:高等教育出版社,2004.198-201.191.
(23)严士毽,张奠宙,王尚志.普通高中数学课程标准(实验)解读[M].南京:江苏教育出版社,2004.318-319.
(24) 张维中.文化视野中的数学与数学教育[M]。北京:人民教育出版社,2005,11-28.
(25)易竹贤,关于初、高中数学课程衔接问题的探讨[J]中学数学教与学,中国人民大学出版社.2006(11):34-37.
(26) 王延文,王光明.数学能力研究导论[M].天津:天津教育出版社.1999:146.
(27)叶一舵。男女生的学习心里差异[M].福州;福州教育出版社,1985
(28)傅安球。男女心理差异与教育[M].郑州:河南教育出版社,1987.
(29) 闫承利 . 素质教育课堂优化策略 [M]. 北京:教育科学出版社,2003.20-25.
(30)罗增儒.中学数学课例分析[M].西安,陕西师范大学出版社,2001.
(31)沈文选.中学数学研究与中学数学教育[J].中学数学,2002(1).
(32)朱水根,王延文等.中学数学教学导论[M]. 北京:教育科学出版社,1998.196..
(33)张奠宙.中国数学双基教学的理论与实践[M].上海教育出版社 2006.6
(34)周根龙.试论数学教学反思[J].数学教育学报,2003(1).
(35)沈文选.数学教师专业化与教育数学研究[J].中学数学,2004(2).
(36) 徐英俊,教学设计[M].教育科学出版社,2001.
(2)高中立体几何内容研究及启示[J]中学数学教与学(湖南科学技术出版社),2006(10):38-41.
(3)李燕杰,李晓东,宋士波.更新观念,完善学生空想象能力的培养[J].数学教育报,1996,5(4):57-60.
(4)米山国藏.数学的精神、思想和方法[M].成都:四川教育出版社,1986.
(5)邵光华.数学思想方法与中学数学[M].北京:北京师范大学出版社,2005.
(6)周春荔.数学教育学[M] 北京:首都师范大学出版社, 2001.
(7)鲁正火,等.数学教育研究概论[M].北京教育科学出版社,1998.
(8)周珍,连四清,周春荔.中学生空间图形认知能力发展与数学成绩关系的相关性研究[J].数学教育学报,2005,14(1):57-58 .
(9)张思明.中学数学建模教学的实践与探索[M].北京:北京教育出版社,1998.
(10)熊宜勤. 实施因材施教的理论与实践[J]. 广西高教研究,2000(4):83-87.
(11)张劲松.浅谈高中数学新课程中“立体几何”部分的内容与要求[J].中学数学教与学(湖南科学技术出版社),2006(10):36-37.
(12)刘华祥主编.中学数学教学论[M]武汉:武汉大学出版社.
(13)杨冠夏 .《从立体几何入门教学看数学语言》中学数学月刊[J]苏州大学出版社 2007.2.
(14)李明振. 认知方式及其与学生数学思维灵活性的关系研究[J]. 心理发展与教育,1994(3):16-20.
(15)林崇德.学习与发展[M].北京:北京师范大学出版社,1999.473.
(16)唐殿强等. 高中生认知方式与学业成绩关系研究[J]. 辽宁教育研究,2002(12):13-18.
(17)钱丽娟《,高中数学实验教学的探索与实践》高中数学教与学[J]2006.
(9):4-5.
(18)李正银,刘景昭.STS 教育观下数学教学策略探讨[J].数学通讯,2000
(13):4-6.
(19)周军. 教学策略[M].北京:教育科学出版社,2003.10-11,258-265.
(20)周丽丽,《直观几何》及对我国几何课程改革的启示[J]数学教育学报,2001,10.
(21)杨高全.数学教学策略研究[J].湖南教育学院学报,200(11):97-100.
(22)李晓文等.教学策略[M].北京:高等教育出版社,2004.198-201.191.
(23)严士毽,张奠宙,王尚志.普通高中数学课程标准(实验)解读[M].南京:江苏教育出版社,2004.318-319.
(24) 张维中.文化视野中的数学与数学教育[M]。北京:人民教育出版社,2005,11-28.
(25)易竹贤,关于初、高中数学课程衔接问题的探讨[J]中学数学教与学,中国人民大学出版社.2006(11):34-37.
(26) 王延文,王光明.数学能力研究导论[M].天津:天津教育出版社.1999:146.
(27)叶一舵。男女生的学习心里差异[M].福州;福州教育出版社,1985
(28)傅安球。男女心理差异与教育[M].郑州:河南教育出版社,1987.
(29) 闫承利 . 素质教育课堂优化策略 [M]. 北京:教育科学出版社,2003.20-25.
(30)罗增儒.中学数学课例分析[M].西安,陕西师范大学出版社,2001.
(31)沈文选.中学数学研究与中学数学教育[J].中学数学,2002(1).
(32)朱水根,王延文等.中学数学教学导论[M]. 北京:教育科学出版社,1998.196..
(33)张奠宙.中国数学双基教学的理论与实践[M].上海教育出版社 2006.6
(34)周根龙.试论数学教学反思[J].数学教育学报,2003(1).
(35)沈文选.数学教师专业化与教育数学研究[J].中学数学,2004(2).
(36) 徐英俊,教学设计[M].教育科学出版社,2001.