Teacher's Guide for Mathematics Education

Meaning of
"What/Why to Teach"

understand what practical strategies they are implicitely or explicitely using in his class

knowledge of mathematics

"What are the subjects in the unit? "

The meaning of this title is "What are the subjects in the unit, from a higer standpoint of mathematics?"

Here we are to write such a content as becomes to be an answer to the following kind of questions :
- Show me precisely the reasoning which proves "nnnnn x 10 = nnnnn x 10 for any nnnnn".
- What is the "addition" of the natural number ?
- Show me precisely the reasoning which proves "m x n = n x m for any natural number".
- Why both the "addition" of the natural number and the "addition" of the rational number are called "addition". In order that an operation can be called "addition", what conditions does it require to satisfy ?
- What is "number" ?
- Why both the natural number and the rational number are called "number". In order that an entity can be called "number", what conditions does it require to satisfy ?
"Where should learners reach ?"

I think there is no room for you to misunderstand this title.

"Why to Teach"

Here we are to write such a content as becomes to be an answer to the following kind of questions :

For examle,

Teacher	:	Why is it necessary for students to learn "nnnnn x 10 = nnnnn x 10 for any nnnnn" ?
You	:	Because it is one of the formula we (implicitely) use in the calculation of, for example, "458 x 7212". Like this : ...... By the way, it is a good exercise for you to pick up all formula which you are, in the logical sense, implicitely using in the calculation of "458 x 7212".
Teacher	:	Please show me all the formula I, in the logical sense, use in the calculation of "458 x 7212".
You	:	Ok, look this .....