Research of Educational Approach Which Lets Learners to Understand Algebraic Ideas and Methods Deeply

让学习者深入理解代数思想和方法的教育方法研究

• 批准号: 17500611
• 负责人: NISHIZAWA Hitoshi
• 金额: $ 1.75万
• 依托单位: Toyota National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500611/
• 关键词: Algebra; Deep Understanding; Algebraic Expression; Graphic Expression; Linguistic Expression

Although black box approach seems to have popularity in high-school mathematics learning in Japan, it certainly devalues the learning of not only mathematics but also engineering subjects that use mathematics. If teachers encourage their students to use a formula as a convenient tool to solve mathematical problem without teaching the hidden mechanism enough, the students tend to memorize it blindly and use it as a black box. They use it in the examination effectively and forget it in several months. After that, there remains only vague memory that they have learnt something. In such a learning style, the simple use of technology might cause disaster because it only increases the effectiveness of black boxes.After surveying the low performance of our students in linear algebra, the authors have confirmed the cause as black box approach in their learning of abstract ideas. In the lessons of linear algebra, too many formulas were learnt without understanding the background mechanism and possible applications in the real world. There were few modeling, numerical confirmations, and linguistic explanations of the relations between symbolic & numerical representation and graphic objects. As the result, large number of students applied black box approach especially in linear algebra.This research tries to show the importance of linguistic explanation in avoiding black box approach by describing the authors' recent attempt to connect symbolic expressions and graphical representations in linear algebra through linguistic explanation with the help of technology. The further focus on linguistic explanation we have, the lesser black box approach the students apply in their learning, we believe.

虽然黑箱法在日本高中数学学习中似乎很受欢迎，但它确实贬低了数学的学习，也贬低了使用数学的工程学科的学习。如果教师鼓励学生把公式作为解决数学问题的方便工具，而没有充分教授隐藏的机制，学生往往会盲目地记忆公式，并把它当作一个黑匣子。他们在考试中有效地使用它，几个月后就忘记了。在那之后，他们只剩下模糊的记忆，他们学到了一些东西。在这种学习方式下，简单地使用技术可能会造成灾难，因为它只会增加黑箱的有效性。在调查了我们的学生在线性代数中的低表现后，作者证实了他们在学习抽象概念时使用黑箱方法的原因。在线性代数的课程中，有太多的公式是在不了解背景机理和在真实的世界中可能的应用的情况下学习的。对于符号和数字表征与图形对象之间的关系，几乎没有建模、数字确认和语言解释。本研究通过描述作者最近在线性代数中通过语言解释和技术的帮助来连接符号表达式和图形表示的尝试，试图表明语言解释在避免黑箱方法中的重要性。我们相信，我们对语言解释的进一步关注，学生在学习中应用的黑箱方法就越少。

项目成果

WebMathematica-based Introductory System of Mathematical Experiments

Web基于Mathematica的数学实验入门系统

• 发表时间: 2006
• 期刊: Proc. 8^<th> International Mathematica Symposium (IMS06) (CD-ROM)
• 作者: H.Nishizawa;T.Yoshioka
• 通讯作者: T.Yoshioka

Departing from Black Box Approach in Linear Algebra with the Help of a Web-System

借助网络系统摆脱线性代数中的黑盒方法

• 发表时间: 2008
• 期刊: Proc. 7^<th> IASTED International Conference on Web-Based Education (WBE2008) (CD-ROM)
• 作者: 大塚正雄;H. Nishizawa
• 通讯作者: H. Nishizawa

Flexible Solving Strategies in Algebra Remain in the Long Term

从长远来看，代数中的灵活求解策略仍然存在

• 发表时间: 2005
• 期刊: Proc. 10^<th> Asian Technology Conference in Mathematics (ATCM2005)
• 作者: H.Nishizawa;T.Yoshioka;H. Nishizawa
• 通讯作者: H. Nishizawa

A Graphical Explanation of Fundamental Vector Operations for Engineering Students

为工科学生提供基本向量运算的图解

• 发表时间: 2007
• 作者: H.Nishizawa;T.Yoshioka;H. Nishizawa
• 通讯作者: H. Nishizawa

WebMathematica-based Introductory System of Mathematical Expressions

基于WebMathematica的数学表达式入门系统

• 发表时间: 2006
• 期刊: Proc. 8^<th> International Mathematica Symposium (IMS06) (CD-ROM)
• 作者: H. Nishizawa;T. Yoshioka;H. Nishizawa;H. Nishizawa
• 通讯作者: H. Nishizawa