| Research Abstract |
1. Factors affecting Difficulty
(1) Multiplication : The mental multiplication was difficult as the multiplicand or the multiplier became larger, and it was shown that the problem containing 5 as easy. For the multi-digit multiplication, the difficulty was related to the number of digits involving the product, the frequency for a need to carry over, the existence, number and location of 0, type of a partial product, and the difficulty of the mental multiplication and one figure addition.
(2) Addition : One figure addition was difficult as the augend or the addend became laager. When they contained 5 or the same number, it was easy. It was shown that the size of a number is comparatively difficult for 4. As for the multi-digit addition, the number of digits involved the augend or the addend, the frequency for a need to carry over, and the existence, number and location of 0 were related to the difficulty.
(3) Subtraction : One figure subtraction was as follows. When there was nothing carry
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ing down, it was easy that the minuend, subtrahend, or remainder contained 0, 5, or 10, and difficult, that the minuend was large (except for 10), or the subtrahend or the remainder was a middle size number (except for 5). It was difficult that the subtrahend was large for the carrying down case. As for multi-digit subtraction, the number of digits involved the subtrahend or the remainder, location and frequency for a need to carry down, and the existence, number and location of 0 were related to the difficulty.
(4) Division : The factors affecting the difficulty of the multi-digit division were a type of basic operation, the existence of residual, the existence and type of carrying over and down, how depending on which 0 appears and its type and frequency for a need to correct.
2. The Categorizations of Multi-digit Arithmetic and Its Structure of Difficulty
It was categorized on the basis of the factors affecting the difficulty about each arithmetic, and tables and figures were created.
3. Creation of Teaching Materials
About all the types obtained by 2, a fixed number of concrete problems for a child learning were generated.
4. Development of Instruction Support System
The program of an instruction support system was created. Less
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