The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
Thus, by the mere action of frequency of connection, r_{1} is connected
with _a_; the bonds from _a_ to anything except r_{1} are being
counteracted, and the slight bonds from anything except _a_ to r_{1} are
being counteracted. The element _a_ becomes predominant in situations
containing it; and its bond toward r_{1} becomes relatively enormously
strengthened and freed from competition.
These three processes occur in a similar, but more complicated,
form if the situations _a_ + _b_, _a_ + _g_, etc., are replaced by
_a_ + _b_ + _c_ + _d_ + _e_ + _f_, _a_ + _g_ + _h_ + _i_ + _j_ + _k_,
etc., and the responses r_{1} + r_{2}, r_{1} + r_{7}, r_{1} + r_{12},
etc., are replaced by r_{1} + r_{2} + r_{3} + r_{4} + r_{5} + r_{6},
r_{1} + r_{7} + r_{8} + r_{9} + r_{10} + r_{11}, etc.--_provided the_
r_{1}, r_{2}, r_{3}, r_{4}, etc., _can be made singly_. In so far as any
one of the responses is necessarily co-active with any one of the others
(so that, for example, r_{13} always brings r_{26} with it and _vice
versa_), the exact relations of the numbers recorded in schemes like
schemes I, II, and III on pages 172 to 174 will change; but, unless
r_{1} has such an inevitable co-actor, the general results of schemes I,
II, and III will hold good. If r_{1} does have such an inseparable
co-actor, say r_{2}, then, of course, _a_ can never acquire bonds with
r_{1} alone, but everywhere that r_{1} or r_{2} appears in the preceding
schemes the other element must appear also. r_{1} r_{2} would then have
to be used as a unit in analysis.
The '_a_ + _b_,' '_a_ + _g_,' '_a_ + _l_,' ... '_a_ + _B_' situations
may occur unequal numbers of times, altering the exact numerical
relations of the connections formed and presented in schemes I, II,
and III; but the process in general remains the same.
So much for the effect of use and disuse in attaching appropriate
response elements to certain subtle elements of situations. There are
three main series of effects of satisfaction and discomfort. They
serve, first, to emphasize, from the start, the desired bonds leading to
the responses r_{1} + r_{2}, r_{1} + r_{7}, etc., to the total
situations, and to weed out the undesirable ones. They also act to
emphasize, in such comparisons and contrasts as have been described,
every action of the bond from _a_ to r_{1}; and to eliminate every
tendency of _a_ to connect with aught save r_{1}, and of aught save _a_
to connect with r_{1}. Their third service is to strengthen the bonds
produced of appropriate responses to _a_ wherever it occurs, whether or
not any formal comparisons and contrasts take place.
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