The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
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!
[Illustration: FIG. 11.--Distribution of practise with multipliers
of the _XX_ type in the first two books of the three-book text A.]
[Illustration: 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.]
[Illustration: FIG. 13.--Same as Fig. 11, but for text C.]
[Illustration: FIG. 14.--Same as Fig. 11, but for text D.]
[Illustration: FIG. 15.--Distribution of practice with multipliers
of the _XOX_ type in the first two books of the three-book text
A.]
[Illustration: FIG. 16.--Same as Fig. 15, but for text B. Following
this period come certain pages of computation to be used by the
teacher at her discretion, containing 17 _XOX_ multiplications.]
[Illustration: FIG. 17.--Same as Fig. 16, but for text C.]
[Illustration: FIG. 18.--Same as Fig. 16, but for text D.]
Figures 19, 20, 21, 22, and 23 all concern the first two books of the
three-book text E.
Figure 19 shows the distribution of practice on 5 × 5 in the first two
books of text E. The plan is the same as in Figs. 11 to 18, except that
each tenth of an inch along the base line represents ten pages. Figure
20 shows the distribution of practice on 7 × 7; Fig. 21 shows it for
6 × 7 and 7 × 6 together. In Figs. 20 and 21 also, 0.1 inch along the
base line equals ten pages.
Figures 22 and 23 show the distribution of practice on the divisions of
72, 73, 74, 75, 76, 77, 78, and 79 by either 8 or 9, and on the
divisions of 81, 82 ... 89 by 9. Each tenth of an inch along the base
line represents ten pages here also.
Public-domain text, read in full here on John Shaqi.
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