Abstract
It is often observed that pupils who can solve one problem, cannot solve the other problems which have similar qualities. It is considered that
(1) The above phenomenon suggests that abilities of pupils to learn have multi-dimensional characteristics, and
(2) this multi-dimensional characteristics are provided the structure of abilities to learn.
This report aims to consider the method of analysis of structure of the ability to learn from the above points.
At first, we assume that one ability to learn (A) is constructed with sub-abilities (S1, S2,..., Sn), and each sub-ability S1, S2,...Sn is called the components of (A). Then, it was decided to abstract combination of components (Si) which construct the ability (A). If (Si)(i=1, 2,..., n) is components of abiliy (A), and if an achievement test which is constructed to measuure the ability (A) and sub-abilities (Si), is performed for pupils, combinations of minimum essential components for the ability (A) can be discovered by their response patterns of problems of the ability (A) and sub-abilities (Si). That is, if the response of the ability (A) changes from 1 to 0 when any one sub-ability (si) changes from 1 to 0, in one response pattern, then the combination of sub-abilities (si) is represented by (si) which is 1 in the response pattern, where 1 means a correct answer for an item, 0 means the wrong answer.
Secondary, I considered relations of the each sub ability si in the combination of (Si). If degree of cooperation between S1 and S2, S2 and S3 respectively is higher than degree of cooperation between S1 and S3, then this relation can be represenSted as follow,
S1-S2-S3
and when correlation coefficient between Si and Sj is. represented by R (Si, Sj), above relations are approximately as follow,
R (S1, S3) <R (S1, S2) R (S1, S3) <R (S2, S3) That is, relations of each. 51 which are included in the combination of (Si) are approximately represented by the generalization considered above.
Third, we can see various aspects (A1, A2,..., Am) with regard to the ability (A). And we can consider prior- experience (that which was already satisfactory experience to construct the ability (A)) and sub-abilities forming (A1, A2,..., Am) as the components (Si, S2,..., Sn) of (A). Then, the functional relation between aspect (A1, A2,..., Am) of (A) and its component (S1, S2,..., Sn) is represented by F (S1, S2,..., Sn) = (A1, A2,..., Am) Now let ψ (A1, A2,..., Am) represent the ratio of pupils who have some aspects (A1, A2,..., Am) of (A) to whole pupils, and let ψ (S1, S2,..., Sn) A1, A2,..., Am represent the ratio of pupils who have component (S1, S2,..., Sn) forming some aspect (A1, A2, Am) of (A) to pupils who have the aspec. t.(A1, A2,..., Am) of (A). Then, for adequate value (C1), it is considered that (A1, A2,..., Am) which satisfy C1 <ψ (Al, A2,..., Am) where approximate value of (C1) is _??_for each aspect (Ai) measured by alternative response item,
