高中数学教学中开展探究性学习的实践研究
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摘要
近年来，我国新的基础教育课程改革已将变革学习方式、倡导探究性学习放在了突出的地位，强调在学科领域，要为学生创设探究性学习的空间。我国新颁布的《数学课程标准(实验)》设立了“数学探究”“数学建模”等学习活动，力求通过各种不同形式的自主学习、探究活动，让学生体验数学发现和创造的历程，发展他们的创新意识。本文以此为指针，联系高中数学教学的实际，探讨了探究性学习方式在高中数学教学中的应用和实践，在实践的基础上提出了课堂教学、实习作业、研究性课题学习中开展探究性学习的步骤，试图为高中数学教学开展探究性学习探索一条实践之路。
本文的主要结论有：
(1)课堂教学是开展探究性学习主要阵地，在课堂教学的不同环节中可以选择合适的探究内容：
①在新授课中，从知识的发生、发展中探求概念、法则形成的过程；
②在例习题课中，通过对例习题进行引申、推广、拓展，探究问题的变式和结论的推广；
③在复习课上，从知识的最近发展区探求概念的延伸和思维方法的综合；
④在应用课上，从问题的现实背景中探求数学模型。
探究性学习的课堂教学模式可总结为如下四个操作程序：
①教师创设问题情境，引导学生探究；
②学生开展主动探究活动(提出问题——假设、猜测结论——检验、推证结论)；
③学生展示、交流探究结果，师生、生生总结评价；
④意义建构，纳入知识体系。
(2)实习作业是一个实践性的课题，对于实习作业的探究性教学模式可以总结为如下五个操作程序：
①确定内容，明确要求；②成立小组，明确分工；
③制定方案，实施方案；④验证结论，形成成果；
⑤小组交流，师生评价。
(3)研究性课题的教学关键在于要为学生创设一个适于探究的情景，研究性学习课题的教学模式可以总结为如下六个操作步骤：
①教师向学生介绍课题内容；②学生组成研究小组，明确责任分工；
③分组讨论，制定研究方案；④按小组分工实施方案；
⑤探究结论，形成成果；⑥小组交流，师生共同评价。
In recent years, the basic curriculum reform of our country has placed reforming learning mode and research-based study in conspicuous place, laying emphasis that students should have time in their academic studies. The curriculum standard for mathematics set by the ministry of education of our country requires school to give students activities such as " mats research" and " mathematical modeling" for the purpose the students may have opportunities of experiencing the process of discovering maths laws and develop their creativity. The purpose of this theses is to research research-based study mode in senior high school mathematics teaching and the things related such as classroom teaching procedures, homework based on practical problem solving, and on the basis of the research, put forward the procedures for research-base study in classroom teaching, homework based on practical problem solving, trying to seek a approach for carrying out research-based study mode in senior high school mathematics teaching.
Main conclusions of this theses:
(1)The classroom teaching is the basic means of carrying out research-based study , and in different stages of the classroom teaching students may choose different things to research, such as:
①In teaching-new-knowledge classes, students can research how a maths concept or a principle is formed.
②In doing-exercise classes, students may research the variations of a problem or how to make use of a conclusion by studying maths problems.
③In teaching review classes, research how to expand a concept or use a concept comprehensively.
④In teaching applying classes, seek a maths model from the background of maths problem.
The classroom teaching mode fro research-based study can be summarized as the following teaching modes:
①The teacher creates a problem for students to research.
②Students actively find a problem to research( finding a problem, imagining a conclusion and trying to prove the conclusion.
③Students give a presentation of their result of their research. The teachers and students give a summary and assessment.
④Students construct their knowledge meaningfully and systematically.
(2) The homework based on practical problem solving is a practical project. The research on it can be summarized as the following five teaching modes:
①Knowing the content of the homework and requirements.
②Forming groups and dividing the work on the homework.
③Making the plan for carrying out the homework.
④Proving the conclusion and getting the result.
⑤Presenting their research and giving assessment.
(3) The key for carrying out research-based teaching is to create a problem-solving situation for students. The teaching mode can have following procedures:
①The teachers make the students know what to research.
②Forming groups and dividing the work on the research.
③Having group discussions and making the plan for the research.
④Carrying out the research in groups.
⑤Trying to get a conclusion for their research.
⑥Presenting their research result and the teachers and students assess their work together.
本文的主要结论有：
(1)课堂教学是开展探究性学习主要阵地，在课堂教学的不同环节中可以选择合适的探究内容：
①在新授课中，从知识的发生、发展中探求概念、法则形成的过程；
②在例习题课中，通过对例习题进行引申、推广、拓展，探究问题的变式和结论的推广；
③在复习课上，从知识的最近发展区探求概念的延伸和思维方法的综合；
④在应用课上，从问题的现实背景中探求数学模型。
探究性学习的课堂教学模式可总结为如下四个操作程序：
①教师创设问题情境，引导学生探究；
②学生开展主动探究活动(提出问题——假设、猜测结论——检验、推证结论)；
③学生展示、交流探究结果，师生、生生总结评价；
④意义建构，纳入知识体系。
(2)实习作业是一个实践性的课题，对于实习作业的探究性教学模式可以总结为如下五个操作程序：
①确定内容，明确要求；②成立小组，明确分工；
③制定方案，实施方案；④验证结论，形成成果；
⑤小组交流，师生评价。
(3)研究性课题的教学关键在于要为学生创设一个适于探究的情景，研究性学习课题的教学模式可以总结为如下六个操作步骤：
①教师向学生介绍课题内容；②学生组成研究小组，明确责任分工；
③分组讨论，制定研究方案；④按小组分工实施方案；
⑤探究结论，形成成果；⑥小组交流，师生共同评价。
In recent years, the basic curriculum reform of our country has placed reforming learning mode and research-based study in conspicuous place, laying emphasis that students should have time in their academic studies. The curriculum standard for mathematics set by the ministry of education of our country requires school to give students activities such as " mats research" and " mathematical modeling" for the purpose the students may have opportunities of experiencing the process of discovering maths laws and develop their creativity. The purpose of this theses is to research research-based study mode in senior high school mathematics teaching and the things related such as classroom teaching procedures, homework based on practical problem solving, and on the basis of the research, put forward the procedures for research-base study in classroom teaching, homework based on practical problem solving, trying to seek a approach for carrying out research-based study mode in senior high school mathematics teaching.
Main conclusions of this theses:
(1)The classroom teaching is the basic means of carrying out research-based study , and in different stages of the classroom teaching students may choose different things to research, such as:
①In teaching-new-knowledge classes, students can research how a maths concept or a principle is formed.
②In doing-exercise classes, students may research the variations of a problem or how to make use of a conclusion by studying maths problems.
③In teaching review classes, research how to expand a concept or use a concept comprehensively.
④In teaching applying classes, seek a maths model from the background of maths problem.
The classroom teaching mode fro research-based study can be summarized as the following teaching modes:
①The teacher creates a problem for students to research.
②Students actively find a problem to research( finding a problem, imagining a conclusion and trying to prove the conclusion.
③Students give a presentation of their result of their research. The teachers and students give a summary and assessment.
④Students construct their knowledge meaningfully and systematically.
(2) The homework based on practical problem solving is a practical project. The research on it can be summarized as the following five teaching modes:
①Knowing the content of the homework and requirements.
②Forming groups and dividing the work on the homework.
③Making the plan for carrying out the homework.
④Proving the conclusion and getting the result.
⑤Presenting their research and giving assessment.
(3) The key for carrying out research-based teaching is to create a problem-solving situation for students. The teaching mode can have following procedures:
①The teachers make the students know what to research.
②Forming groups and dividing the work on the research.
③Having group discussions and making the plan for the research.
④Carrying out the research in groups.
⑤Trying to get a conclusion for their research.
⑥Presenting their research result and the teachers and students assess their work together.
引文
[1] 陈旭远 《研究性学习的理论与实践》 东北师范大学 www.cydj.net.cn/jinxiu/xinxijiaoyu/dianjiaojiaoyan/jiaoshilundao/yan.ppt
[2] 杨亚玺 《普通高中数学实施研究性学习的教学实践与探索》 湖南师范大学 2003．3
[3] 张奠宙 李士铸 李俊编著 《数学教育学导论》 高等教育出版社 2003．4
[4] 中华人民共和国教育部制定 《普通高中数学课程标准(实验)》 人民教育出版社 2003．499999933
[5] 《现代汉语词典(2002年增补本)》 商务印书馆 2002．5
[6] National Research Council 《The National Science Education Standards Washington DC: National Academy Press 1996
[7] 美国国家研究理事会 严守戢等译 《美国国家科学教育标准》 科学技术文献出版社 1999
[8] 任长松 《探究式学习》 教育科学出版社 2005．2
[9] 数学课程标准研制组编写 《普通高中数学课程标准(实验)解读》 江苏教育出版社 2004．4
[10] 蔡上鹤 戴佳珉主编 全日制普通高级中学教材(人教版)教案系列丛书数学第一册(下)《教案》 人民教育出版社 2004．12
[11] 戴在平主编 《开放题——数学教学的新模式》 上海教育出版社 2002．1
李亦菲 《探究性学习》 中国教育报 2000．11．18
李亦菲 杨宝山 《探究学习与研究性学习的四个误区》 中国教育学刊
霍益平 张人红 《研究性学习的特点和课程定位》 原载《课程 教材 教法》(京) 2000．11
霍益萍 《研究性学习：实验与探索》 广西教育出版社
钟启泉 崔允漷 张华主编 《〈基础教育课程改革纲要(试行)〉解读》 华东师范大学出版社
文喆 《学习方式、传播方式与课堂教学改革》 人民教育 2000(12)
张华 《论“研究性学习”课程的本质》 教育发展研究 2001(5)
教育部 《全日制普通高中“研究性学习”实施指南(试行)》
彭贤智主编 《以学生为主——当代教育改革新思潮》 山东教育出版社
郑毓信、梁贯成 《认识科学，建构主义与数学教育》 上海教育出版社
[2] 杨亚玺 《普通高中数学实施研究性学习的教学实践与探索》 湖南师范大学 2003．3
[3] 张奠宙 李士铸 李俊编著 《数学教育学导论》 高等教育出版社 2003．4
[4] 中华人民共和国教育部制定 《普通高中数学课程标准(实验)》 人民教育出版社 2003．499999933
[5] 《现代汉语词典(2002年增补本)》 商务印书馆 2002．5
[6] National Research Council 《The National Science Education Standards Washington DC: National Academy Press 1996
[7] 美国国家研究理事会 严守戢等译 《美国国家科学教育标准》 科学技术文献出版社 1999
[8] 任长松 《探究式学习》 教育科学出版社 2005．2
[9] 数学课程标准研制组编写 《普通高中数学课程标准(实验)解读》 江苏教育出版社 2004．4
[10] 蔡上鹤 戴佳珉主编 全日制普通高级中学教材(人教版)教案系列丛书数学第一册(下)《教案》 人民教育出版社 2004．12
[11] 戴在平主编 《开放题——数学教学的新模式》 上海教育出版社 2002．1
李亦菲 《探究性学习》 中国教育报 2000．11．18
李亦菲 杨宝山 《探究学习与研究性学习的四个误区》 中国教育学刊
霍益平 张人红 《研究性学习的特点和课程定位》 原载《课程 教材 教法》(京) 2000．11
霍益萍 《研究性学习：实验与探索》 广西教育出版社
钟启泉 崔允漷 张华主编 《〈基础教育课程改革纲要(试行)〉解读》 华东师范大学出版社
文喆 《学习方式、传播方式与课堂教学改革》 人民教育 2000(12)
张华 《论“研究性学习”课程的本质》 教育发展研究 2001(5)
教育部 《全日制普通高中“研究性学习”实施指南(试行)》
彭贤智主编 《以学生为主——当代教育改革新思潮》 山东教育出版社
郑毓信、梁贯成 《认识科学，建构主义与数学教育》 上海教育出版社