几何画板应用于高中数学实验的教学研究
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摘要
数学有两个侧面,一方面数学是演绎科学:另一方面数学更像是一门实验性的归纳科学。在现今中学数学的教学中,数学作为演绎科学的角色得到很好的发展。数学作为培养学生逻辑思维能力的重要工具已得到广泛的共识,并且在应试环境下培养学生的思维能力更多地只是停留在解题能力上。这样中学数学教学就是在一条腿走路。数学作为一门实验性的科学它对学生的思维能力和创新能力的培养远比让学生会解几道题更为重要。在目前中学的实际教学中数学实验更多地停留在教学研究的层面上,并未深入师生和课堂。
本文是作者结合日常的高中教学实践从数学实验的理论概述和实验的实践设计两方面进行研究。通过理论上分析应用几何画板网络技术下的数学实验教相对传统教学而言的优点。通过实验研究和问卷调查分析数学实验教学对学生学习的影响。应用几何画板的高中数学实验是指:在高中课程标准中,为研究与获得某种数学理验证某种数学猜想,解决某种数学问题,实验者运用几何画板软件平台和一定的物质手段在数学思维的活动参与下,在思维的实验环境中或特定的实验条件下所进行的一种数学探索活动。而教师在这类现代数学教学实验研究中要恰当的运用数学实验,创设问题情景,引导学生参与实践、自主探索、合作交流,从而发现问题、提出猜想、验证猜想和创造性解决问题。
全文从四个方面探讨了应用几何画板的高中“数学实验”教学。
1、在高中开展“数学实验”教学是现代数学教育的要求和必然趋势。本部分笔者结合自身的教学实践经验和从国内外开展“数学实验”教学的情况对“数学实验”进行了认识,阐述了从教改与课改的需要、学生学与教师教的需要在高中进行“数学实验”教学的必要性,并分析了在高中开展“数学实验”教学的作用。
2、通过对几何画板软件的性能和特点的分析,阐述利用几何画板软件平台进行教学的可行性。《几何画板》是一个“个性化”的面向学科的工具平台。这样的平台能促进教学的课堂效果,也能帮助学生在实际操作中把握学科的内在实质,培养他们的观察能力和问题解决能力。
3、结合实际探讨了如何进行高中“数学实验”教学,它包括基本模式、目标、原则、类型和教学设计。开展对实验教学与未开展实验教学的班级进行学习成绩、学习兴趣、学习信念的统计、研究和分析。
4、通过对比实验数据分析,结合问卷调查、得出如下结论:
(1)几何画板在数学实验教学中的应用可以改变教师教学方法和改变学生的学习方式。几何画板进入课堂使数学教学过程发生了重要变化,改变了教师的教法,有效地促进了学生的学习。有些教学内容可以让学生亲自动手操作、观察、分析、发现,不必再用“老师讲学生听”的教学方式进行。新的教学模式出现了,学生由被动地听课变为动手实验去经历知识的发生和形成过程。有实验课题、实验目的、实验过程、实验结果,最后学生自己写实验报告。创设了数学背景,让学生由听数学,变成亲自动手做数学、探究数学,极大地调动了他们学习的主动性,使学生有了一个沟通几何图形与几何符号、几何语言的机会。
(2)应用几何画板的数学实验可以改善学生的学习态度,提高学生学习的兴趣,可增强后进生学习的信心,有利于学生学习成绩的提高。在实验课中应用几何画板数学软件不仅能方便地进行数值计算,而且能方便地进行数学表达式的化简、画图等工作。让学生用现代化的方法处理数学问题、发现问题,通过数学实验,学生获得真实、鲜明、生动的具体过程,促进学生动脑,动手,动口,积极主动参与,成为知识的发现者,从而主动建构数学概念,探索和验证数学规律,进而培养学生勇于探索和创新的人文素养。更重要的是,能让广大的学生确实体会到数学是有用的,培养他们在今后的学习和工作中,主动地用数学工具去分析和解决专业中的实际问题的意识和能力。
There are two aspects of Mathematics, Mathematics is one interpretation of science on the other hand is more like math a summary of experimental science. In today's Middle School Mathematics Teaching, Mathematics as a scientific interpretation of the role of well development. Training students as mathematical logic thinking ability has been an important tool for a wide range of consensus, in the test environment and cultivating more thinking ability of students to remain in the problem-solving capabilities. This is the Middle School Mathematics Teaching legs in a walk. Mathematics as a scientific experiment of its students thinking ability and ability to innovate than to the cultivation of several students, and that is more important . At the actual teaching of secondary school mathematics experiment more remain in the teaching and research level, not in depth and classroom teachers.
This thesis is to study the mathematic experiment from its two sides overview theory and practice design by combining daily senior high school teaching fulfillment. Theoretically, it analyzes the advantages of the Geometer's Sketchpad-based mathematic experiment teaching under network technology over the traditional teaching. The thesis analyze how mathematic experiment affects students' learning in the way of experiment study and questionnaire. The Geometer's Sketchpad-based mathematic experiment is a mathematical exploring activity in the senior high school curriculum standard that experimenters use the Geometer's Sketchpad and some matter means to conduct in the mathematical thinking way, in experimental environment of thinking or in the specially-appointed mathematical condition order to get a certain mathematical theory, check a certain mathematical guess, solve a certain mathematical problem. In modern experiment research, teachers should appropriately mathematical experiment, establish the problem scene, guide students to take part in practice, independently investigate and cooperate and intercourse so as to discover problems, put forward guess and verify guess and creatively solve problems.
The whole thesis probes into The Geometer's Sketchpad-based "mathematical experiment teaching in senior high schools from four sides.
1. Carrying out the "mathematical experiment" teaching in senior schools is requirement and the inevitable trend of the modern mathematical education. In thesis, I talk about the recognition of mathematical experiment by combining my own teaching experience and according to the study on mathematical experiment at home and abroad, expound the necessity of carrying out mathematical experiment according to the necessity of the teaching reform and the course reform, and analyze the function of carrying out mathematics experiment in senior high schools.
2. By analyzing the function and characteristics of the Geometer's Sketchpad software, this thesis expounds the possibility of using the Geometer's Sketchpad to teaching mathematics. The Geometer's Sketchpad is an individual tool facing to courses. This tool can improve classroom teaching result and also can help students to master the inside nature of courses in practice, cultivate their observation ability and their ability of solving problems and develop their thinking ability.
3. By combining the reality, this thesis probes into how to carry out mathematical experiment in senior high schools, including basic mode, target, principle, type and teaching design. This thesis carries on the covariance, research and analysis about study result and study interest and study conviction between the class which opens an exhibition experiment teaching and the one which doesn't open an exhibition experiment teaching.
4. This thesis makes conclusions as follows by analyzing experiment data, combining questionnaire, individual case interview:
(1) The application of the Geometer's Sketchpad in the mathematical experiment teach can change teaches' teaching ways and change students' learning ways. The Geometer's Sketchpad's getting into classrooms changes the mathematical teaching process, changes teachers teaching methods and effectively improves students' learning. Students can operate, observe, analyze, and discover some contents of courses in person. It is not necessary to us teaching method of "the teacher speaking and the students listening". The new teaching mode appears. Students turns from passively listening to carrying on experiment in person experiences the occurrence and formation process of knowledge . There is an experimental topic, an experimental purpose and an experimental process and finally students fill in an experimental report. It establishes a mathematical background, lets students turn from listening to mathematics to doing mathematics and investigating mathematics in person, which greatly stimulate the active for studying. Students have a chance to communicate with geometry graph, geometry signs geometry language.
(2) The Geometer1 s Sketchpad-based mathematic experiment can improve students' learning attitude, raise students' learning interest and strengthen the poor study students' confidence and it is beneficial to the improvement of students' scores. The application of the Geometer's Sketchpad software in experimental classes can not only carry on a number calculation expediently, can also easily carry on a mathematical expression simplification and drawing can let students use a modern method to deal with mathematical problems, discover problems. By doing mathematical experiment, students can acquire a true, fresh and clear and vivid concrete process, urge students to use brains, use hands and speak and become the finder knowledge so that they can actively construct mathematical concept, investigate and verify mathematical regulation, and then cultivate humanistic quality. More importantly, it can let students really realize that mathematics is useful. It can cultivate their consciousness and ability of using mathematical tools to analyze and solve the actual problems of their majors in future study and jobs.
本文是作者结合日常的高中教学实践从数学实验的理论概述和实验的实践设计两方面进行研究。通过理论上分析应用几何画板网络技术下的数学实验教相对传统教学而言的优点。通过实验研究和问卷调查分析数学实验教学对学生学习的影响。应用几何画板的高中数学实验是指:在高中课程标准中,为研究与获得某种数学理验证某种数学猜想,解决某种数学问题,实验者运用几何画板软件平台和一定的物质手段在数学思维的活动参与下,在思维的实验环境中或特定的实验条件下所进行的一种数学探索活动。而教师在这类现代数学教学实验研究中要恰当的运用数学实验,创设问题情景,引导学生参与实践、自主探索、合作交流,从而发现问题、提出猜想、验证猜想和创造性解决问题。
全文从四个方面探讨了应用几何画板的高中“数学实验”教学。
1、在高中开展“数学实验”教学是现代数学教育的要求和必然趋势。本部分笔者结合自身的教学实践经验和从国内外开展“数学实验”教学的情况对“数学实验”进行了认识,阐述了从教改与课改的需要、学生学与教师教的需要在高中进行“数学实验”教学的必要性,并分析了在高中开展“数学实验”教学的作用。
2、通过对几何画板软件的性能和特点的分析,阐述利用几何画板软件平台进行教学的可行性。《几何画板》是一个“个性化”的面向学科的工具平台。这样的平台能促进教学的课堂效果,也能帮助学生在实际操作中把握学科的内在实质,培养他们的观察能力和问题解决能力。
3、结合实际探讨了如何进行高中“数学实验”教学,它包括基本模式、目标、原则、类型和教学设计。开展对实验教学与未开展实验教学的班级进行学习成绩、学习兴趣、学习信念的统计、研究和分析。
4、通过对比实验数据分析,结合问卷调查、得出如下结论:
(1)几何画板在数学实验教学中的应用可以改变教师教学方法和改变学生的学习方式。几何画板进入课堂使数学教学过程发生了重要变化,改变了教师的教法,有效地促进了学生的学习。有些教学内容可以让学生亲自动手操作、观察、分析、发现,不必再用“老师讲学生听”的教学方式进行。新的教学模式出现了,学生由被动地听课变为动手实验去经历知识的发生和形成过程。有实验课题、实验目的、实验过程、实验结果,最后学生自己写实验报告。创设了数学背景,让学生由听数学,变成亲自动手做数学、探究数学,极大地调动了他们学习的主动性,使学生有了一个沟通几何图形与几何符号、几何语言的机会。
(2)应用几何画板的数学实验可以改善学生的学习态度,提高学生学习的兴趣,可增强后进生学习的信心,有利于学生学习成绩的提高。在实验课中应用几何画板数学软件不仅能方便地进行数值计算,而且能方便地进行数学表达式的化简、画图等工作。让学生用现代化的方法处理数学问题、发现问题,通过数学实验,学生获得真实、鲜明、生动的具体过程,促进学生动脑,动手,动口,积极主动参与,成为知识的发现者,从而主动建构数学概念,探索和验证数学规律,进而培养学生勇于探索和创新的人文素养。更重要的是,能让广大的学生确实体会到数学是有用的,培养他们在今后的学习和工作中,主动地用数学工具去分析和解决专业中的实际问题的意识和能力。
There are two aspects of Mathematics, Mathematics is one interpretation of science on the other hand is more like math a summary of experimental science. In today's Middle School Mathematics Teaching, Mathematics as a scientific interpretation of the role of well development. Training students as mathematical logic thinking ability has been an important tool for a wide range of consensus, in the test environment and cultivating more thinking ability of students to remain in the problem-solving capabilities. This is the Middle School Mathematics Teaching legs in a walk. Mathematics as a scientific experiment of its students thinking ability and ability to innovate than to the cultivation of several students, and that is more important . At the actual teaching of secondary school mathematics experiment more remain in the teaching and research level, not in depth and classroom teachers.
This thesis is to study the mathematic experiment from its two sides overview theory and practice design by combining daily senior high school teaching fulfillment. Theoretically, it analyzes the advantages of the Geometer's Sketchpad-based mathematic experiment teaching under network technology over the traditional teaching. The thesis analyze how mathematic experiment affects students' learning in the way of experiment study and questionnaire. The Geometer's Sketchpad-based mathematic experiment is a mathematical exploring activity in the senior high school curriculum standard that experimenters use the Geometer's Sketchpad and some matter means to conduct in the mathematical thinking way, in experimental environment of thinking or in the specially-appointed mathematical condition order to get a certain mathematical theory, check a certain mathematical guess, solve a certain mathematical problem. In modern experiment research, teachers should appropriately mathematical experiment, establish the problem scene, guide students to take part in practice, independently investigate and cooperate and intercourse so as to discover problems, put forward guess and verify guess and creatively solve problems.
The whole thesis probes into The Geometer's Sketchpad-based "mathematical experiment teaching in senior high schools from four sides.
1. Carrying out the "mathematical experiment" teaching in senior schools is requirement and the inevitable trend of the modern mathematical education. In thesis, I talk about the recognition of mathematical experiment by combining my own teaching experience and according to the study on mathematical experiment at home and abroad, expound the necessity of carrying out mathematical experiment according to the necessity of the teaching reform and the course reform, and analyze the function of carrying out mathematics experiment in senior high schools.
2. By analyzing the function and characteristics of the Geometer's Sketchpad software, this thesis expounds the possibility of using the Geometer's Sketchpad to teaching mathematics. The Geometer's Sketchpad is an individual tool facing to courses. This tool can improve classroom teaching result and also can help students to master the inside nature of courses in practice, cultivate their observation ability and their ability of solving problems and develop their thinking ability.
3. By combining the reality, this thesis probes into how to carry out mathematical experiment in senior high schools, including basic mode, target, principle, type and teaching design. This thesis carries on the covariance, research and analysis about study result and study interest and study conviction between the class which opens an exhibition experiment teaching and the one which doesn't open an exhibition experiment teaching.
4. This thesis makes conclusions as follows by analyzing experiment data, combining questionnaire, individual case interview:
(1) The application of the Geometer's Sketchpad in the mathematical experiment teach can change teaches' teaching ways and change students' learning ways. The Geometer's Sketchpad's getting into classrooms changes the mathematical teaching process, changes teachers teaching methods and effectively improves students' learning. Students can operate, observe, analyze, and discover some contents of courses in person. It is not necessary to us teaching method of "the teacher speaking and the students listening". The new teaching mode appears. Students turns from passively listening to carrying on experiment in person experiences the occurrence and formation process of knowledge . There is an experimental topic, an experimental purpose and an experimental process and finally students fill in an experimental report. It establishes a mathematical background, lets students turn from listening to mathematics to doing mathematics and investigating mathematics in person, which greatly stimulate the active for studying. Students have a chance to communicate with geometry graph, geometry signs geometry language.
(2) The Geometer1 s Sketchpad-based mathematic experiment can improve students' learning attitude, raise students' learning interest and strengthen the poor study students' confidence and it is beneficial to the improvement of students' scores. The application of the Geometer's Sketchpad software in experimental classes can not only carry on a number calculation expediently, can also easily carry on a mathematical expression simplification and drawing can let students use a modern method to deal with mathematical problems, discover problems. By doing mathematical experiment, students can acquire a true, fresh and clear and vivid concrete process, urge students to use brains, use hands and speak and become the finder knowledge so that they can actively construct mathematical concept, investigate and verify mathematical regulation, and then cultivate humanistic quality. More importantly, it can let students really realize that mathematics is useful. It can cultivate their consciousness and ability of using mathematical tools to analyze and solve the actual problems of their majors in future study and jobs.
引文
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