The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
In many courses of study the order of systematic formation of the
multiplication table bonds is: 1 × 1, 2 × 1, etc., 1 × 2, 2 × 2, etc.,
1 × 3, 2 × 3, etc., 1 × 9, 2 × 9, etc. This is probably wrong in two
respects. There is abundant reason to believe that the × 5s should be
learned first, since they are easier to learn than the 1s or the 2s, and
give the idea of multiplying more emphatically and clearly. There is
also abundant reason to believe that the 1 × 5, 1 × 2, 1 × 3, etc.,
should be put very late--after at least three or four tables are
learned, since the question "What is 1 times 2?" (or 3 or 5) is
unnecessary until we come to multiplication of two- and three-place
numbers, seems a foolish question until then, and obscures the notion of
multiplication if put early. Also the facts are best learned once for
all as the habits "1 times _k_ is the same as _k_," and "_k_ times 1 is
the same as _k_."[8]
[8] The very early learning of 2 × 2, 2 × 3, 3 × 2, 2 × 4, 4 × 2,
3 × 3, and perhaps a few more multiplications is not considered
here. It is advisable. The treatment of 0 × 0, 0 × 1, 1 × 0, etc.,
is not considered here. It is probably best to defer the '× 0'
bonds until after all the others are formed and are being used
in short multiplication, and to form them in close connection
with their use in short multiplication. The '0 ×' bonds may well
be deferred until they are needed in 'long' multiplication,
0 × 0 coming last of all.
In another connection it was recommended that the divisions to 81 ÷ 9
be learned by selective thinking or reasoning from the multiplications.
This determines the order of bonds so far as to place the formation of
the division bonds soon after the learning of the multiplications. For
other reasons it is well to make the proximity close.
Public-domain text, read in full here on John Shaqi.
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