Are certain algorisms more efficient and economical than
others? In which form should a pupil learn his addition com-

6
binations, 4 -|- 6 = 10 or -|- 4 ? In the case of long division should

10

it be 45)67836(, or 45)67836?

Is it wise to use several different algorisms for a single
process, when it is possible to use but one? In other words
does not a multiplication of algorisms increase the amount of
memorization of forms required of the child ? In division instead
of having three algorisms, one for the combinations 6^3 = 2,
another for short division 3 )45735, and a third for long division
345)45735. would it be any better to have a similar form through-



General Subjects for Experiment 63

out for easy identification of the three processes as fundamentally
one, thus

_2 15245 132

3)6, 3)45735, 345)45735

345



1 123
1035



885
690

195
and in connection with all this what weight should be given to
Professor Smith's objection that the universal custom of the
business world does not recognize the first two forms of this
latter set?

Shall the attempt to get rapidity of calculation be preceded
by the attempt to get absolute accuracy, the quickening of the
work being left until certainty of command over combinations
is assured? Or shall rapidity in handling combinations and
manipulations be a parallel activity? Take for example the at-
tempt to have the children attack the successive combinations
in column addition with a definite rhythm, the teacher pointing
to each successive stage, or chorus work being utilized with the
quickest students setting the pace?

Does motor activity accompanying a process of memorization
of combinations require fewer repetitions than where no special
provision is made for motor activity? How far does it help
to repeat the numbers aloud ? to write them on paper ? to manipu-
late objects when the combination is being learned?

How far can rhythm be used in memorizing combinations or
tables ? Does the use of rhythm decrease the number of repeti-
tions required for mastery? How much?

Bibliography : On the general question consult the works of
Professor Young and the author. On the special question of
number games consult the following:

Johnson, G. E., Education by Plays and Games. Pedagogical Semi-
nary (Oct. 1894), Vol. III. This work contains a list of five hundred
games for children.
