Abstract
Piaget,J. & Inhelder,B. (1941/1985) have claimed that one acquires concepts of substance, weight, and volume in the following order.: conservation of substance→conservation of weight→conservation of volume. And validity of this claim was demonstrated by Lovell,K. & Ogilvie,E. (1960, 1961), Siegler,R.S. & Liebert,R.M. (1972), Brainerd,C.J. (1974, 1976, 1977), and Acredolo,C. & Acredolo,L.P. (1979, 1980). Especially Siegler,R.S. & Liebert,R.M. and Brainerd,C.J. are in a position called a Neo-Piagetian interpretation (i.e. Stage-Theory), and their versions identify with my views. Then from this viewpoint, conservation of substance, conservation of weight, and predominance of a measurement concept are regarded as a precondition to acquire conceptual knowledge in weight, which includes properties of equality, comparison, addition, and continuity.
According to Piaget,J. & Inhelder,B. (1941/1985), there exist 5 stages from nonconservation of substance to conservation of weight.: Stage I is in a condition to express nonconservation of substance, Stage IIA is in a condition to express a medium reaction between nonconservation and conservation of substance, Stage IIB is in a condition to express conservation of substance and show nonconservation of weight, Stage IIIA is in a condition to express a medium reaction between nonconservation and conservation of weight, and Stage IIIB is in a condition to express conservation of weight. Then aspects of these 5 stages are able to be drawn by equilibrium models of logical-mathematical cognition.
But the experiments in the preceeding researches are large-scale and inaequate for educational practices in consideration of the following reasons. That is, 1)whether investigative methods are comparatively simple and easy, 2)whether analyses of acquired datum are facile, and 3)whether it is simple for teachers to draw up plans of instruction on the grounds of analyses. Then in consideration of 1)-3), I developed 6 tasks on the grounds of the research of Piaget,J. & Inhelder,B. (1941/1985). The subjects are 149 third pupils of H elementary school in Kobe.
I have conducted Guttman's scalogram analysis (White,B.W & Saltz,E., 1957, pp81-99). The scalogram analysis follows the follwing procedure. 1)Tasks are ordered accrding to difficulty. (Table 1)
Table 1 Tasks ordered according to difficulty
2)A matrix is made up, with tasks in columns from left to right, put in increasing order of difficulty, and subjects in rows, from top to bottom, in increasing order of success. 3)This makes up a scalogram. A diagonal line proceeding stepwise,from top left to bottom right, separates the field of tasks passed, on the left, from the field of tasks failed, on the right. (Table2)
Table 2 A part of scalogram
The hierarchical nature of this scale is analyzed according to Guttman. Coefficients obtained were CR=0.91275 and MMR=0.6331. A coefficient of CR=0.90 is considered satisfactory, with MMR<0.80.PPR=(CR-MMR)÷(1-MMR)=0.76206. A coefficient> 0.70 is considered good. This shows that tasks formed a so-called 'perfect' hierarchical scale at the task level itself. Table3 is tasks ordered according to degree of success, then categorized levels and stages, namely, differentiation of levels and stages about conservation of weight.
Table 3 Differentiation of levels and stages about conservation of weight
