To Be Presented in the 11th Asian Technology Conference in Mathematics December 1216, 2006, Hong Kong SAR, China 

Importance of Linguistic Explanation in Mathematics Education, and the Support from Technologynisizawa@toyotact.ac.jp Takayoshi Yoshioka
Abstract Although Black box approach seems to have popularity
in highschool 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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