To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Importance of Linguistic Explanation in Mathematics Education, and the Support from Technology

Hitoshi Nishizawa

Takayoshi Yoshioka
Electrical & Electronics Engineering
Toyota National College of Technology


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 his students to use a formula as a convenient tool to solve mathematical problem without teaching the importance to think the hidden mechanism, the students tend to remember it blindly and use it as a black box. They use it in examinations effectively and forget it in several months. After that, there remains nothing left. In such a learning condition, the simple use of technology might cause disaster because it only increases the effectiveness of black boxes. After surveying the lower performance of our students in linear algebra, the authors have confirmed the cause as such a black box approach in their learning, especially in linear algebra. In the lessons of linear algebra, too many formulas are taught without explaining the background mechanism and the possible applications in the real world. There are few modeling, confirmations, and linguistic explanations of the relation between symbolic & numerical representation and graphical representation. As the result, most of the students apply black box approach in linear algebra. This paper shows the importance of linguistic explanation in avoiding black box approach. It also describes the author's recent attempt to connect symbolic representation and graphical representation in linear algebra through linguistic explanation with a little help of technology. The further focus on linguistic explanation we have, the lesser black box approach the students apply in their learning.

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