Fig. 10.—Plan IV. A learning period with reviews of decreasing length at increasing intervals.
SAMPLE DISTRIBUTIONS
Let us rather examine some actual cases of distribution of practice found in school work and consider, not the attainment of the best possible distribution, but simply the avoidance of gross blunders and the attainment of reasonable, defensible procedures in this regard.
Figures 11 to 18 show the distribution of examples in multiplication with multipliers of various sorts. X stands for any digit except zero. O stands for 0. XXO thus means a multiplier like 350 or 270 or 160; XOX means multipliers like 407, 905, or 206; XX means multipliers like 25, 17, 38. Each of these diagrams covers approximately 3½ years of school work, or from about the middle of grade 3 to the end of grade 6. They are made from counts of four textbooks (A, B, C, and D), the count being taken for each successive 8 pages.[10] Each tenth of an inch along the base line equals 8 pages of the text in question. Each .01 sq. in. equals one example. The books, it will be observed, differ in the amount of practice given, as well as in the way in which it is distributed.
Fig. 11.—Distribution of practise with multipliers of the XX type in the first two books of the three-book text A.
Fig. 12.—Same as Fig. 11, but for text B. Following this period come certain pages of computation to be used by the teacher at her discretion, containing 24 XX multiplications.
These distributions are worthy of careful study; we shall note only a few salient facts about them here. Of the distributions of multiplications with multipliers of the XX type, that of book D (Fig. 14) is perhaps the best. A (Fig. 11) has too much of the practice too late; B (Fig. 12) gives too little practice in the first learning; C (Fig. 13) gives too much in the first learning and in grade 6. Among the distributions of multiplication with multipliers of the XOX type, that of book D (Fig. 18) is again probably the best. A, B, and C (Figs. 15, 16, and 17) have too much practice early and too long intervals between reviews. Book C (Fig. 17) by a careless oversight has one case of this very difficult process, without any explanation, weeks before the process is taught!