数学教育における記号表現の問題(I) : 乗法の計算形式を例として

For the studies of some linguistic aspect of mathematical symbols in current arithmetic text-books, I will consider "the working form of calculating" (e. g. multiplication) as to an example in mathematical symbols. Because "the working form of calculating" is principal in school mathematics of primary school.
The working form of calculating is to be combined with process of calculating and its descriptive form.
In order to understand some characters of the working form, we should research into aspects of mathematics, semantic, and semiology of the working form.
For beginners and slow-learners of mathematics "the lattice form" of multiplication is familiar and comprehensive, still more easy to deal with it.
Therefore I wish "the lattice form" should be used in classroom.
If students understand principle of multiplication through the lattice form, they may take an interest in the advanced working form of calculating.
I point out some characteristic of the lattice form.
(1) The lattice form has an effect on geometric ideas, that is, this form is regulated by vertical, horizontal and diagonal.
(2) In a mental process, the above stated shape perhaps makes someone of them to feel suppression.
(3) But the form indicates simultaneously the process of thinking.
(4) Code A is simple and unitary. On the other side, the product (e. g. 3×4) by code A means 12 ones 12 tens, 12 hundreds,………as well as 12.