This report aims to analyze the series of abilities to learn, which arrive at (G), from the point of view of the formative-process of the ability (G). At first, the following models of the series were set, (1) Uni-serial model A_m→A_m-1→…→A_i+1→A_i→A_i-1…→A_2→A_1→G (1) where A_i is ability in uni-series and it is called equal weight element. G is the goal of the series. A_i is higher than A_i+1 (2) Substitutive-serial model [figure] where A_l (l=1, 2, k-1, k+1, …, m) is equal weight element. A_ki (i=1, 2) is called substitutive element. A_1 is equivalent to G. 83) Multi-serial model [figure] (3) Secondly, the substitutive series (2) is analyzed as follows. Suppose that a_i* is the item of achievement test measuring the ability A_i in series (2), then the response patterns of pupils to the achievement test are represented with (a_1, a_2, ……, a_m) where a_i=1 or 0 1 is correct anser for item a_i* 0 is wrong answer for item a_i* Let number of response patterns in (a_1, a_2, ……, a_m), which had a_i=1, represent with R (a_i), then according to scalability of series (2), [figure] Let f (a_1, a_2, …, a_m) be degree of achievment, obtained by the pupi;s who had response pattern (a_1, a_2, …, a_m), on the goal (G) and let Q (a_i) define as follows, Q (a_i)=Σf (a_1, a_2, …, a_i-1, a_i=1, a_i+1, …, a_m)/R (a_i)-Σf (a_1, a_2, …, a_i-1, a_i=0, a_i+1, …, a_m)/R^^- (a_i) (5) where Σ is sum of all combination, on the conditioning series (2), in (a_1, a_2, …, a_i-1, a_i+1, …, a_m) a_l=1 or 0, (l=1, 2, …, i-1, i+1, …, m) R^^- (a_i) is number of response patterns in (a_1, a_2, …, a_m) which had a_i=0 [figure] Actually, substitutive elements have characterlike equal weight element from (a_1, a_2, …, a_m=1) to (a_1=0, a_2=0, …, a_k-3=0, a_k-2=1, a_k-1=1…, a_m=1) in scalogram, and additional elements (A_l1, A_l2, …, A_lp), which do not belong in the series (2), are mixed in the actual data. From the avobe point of view, formulas (4) ; (6) are refined as follows. [figure] [figure] Thus, application formulas (7) ; (8) substitutive series of abilities can be approximately abstracted from actual data.