The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
Figures 19 to 23 show no consistent plan for distributing practice.
With 5 × 5 (Fig. 19) the amount of practice increases from the first
treatment in grade 3 to the end of grade 6, so that the distribution
would be better if the pupil began at the end and went backward! With
7 × 7 (Fig. 20) the practice is distributed rather evenly and in small
doses. With 6 × 7 and 7 × 6 (Fig. 21) much of it is in very large doses.
With the divisions (Figs. 22 and 23) the practice is distributed more
suitably, though in Fig. 23 there is too much of it given at one time
in the middle of the period.
[Illustration: FIG. 19.--Distribution of practice with 5 × 5 in
the first two books of the three-book text E.]
[Illustration: FIG. 20.--Distribution of practice with 7 × 7 in
the first two books of text E.]
[Illustration: FIG. 21.--Distribution of practice with 6 × 7
or 7 × 6 in the first two books of text E.]
[Illustration: FIG. 22.--Distribution of practice with
72, 73 ... 79 ÷ 8 or 9 in the first two books of text E.]
[Illustration: FIG. 23.--Distribution of practice with
81, 82 ... 89 ÷ 9 in the first two books of text E.]
POSSIBLE IMPROVEMENTS
Even if we knew what the best distribution of practice was for each
ability of the many to be inculcated by arithmetical instruction, we
could perhaps not provide it for all of them. For, in the first place,
the allotments for some of them might interfere with those for others.
In the second place, there are many other considerations of importance
in the ordering of topics besides giving the optimal distribution of
practice to each ability. Such are considerations of interest, of
welding separate abilities into an integrated total ability, and of the
limitations due to the school schedule with its Saturdays, Sundays,
holidays, and vacations.
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