The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
r_{1} is connected to _a_ by 6 repetitions. r_{2} and r_{not 2} are each
connected to _a_ by 1 repetition, but since they interfere, canceling
each other so to speak, the net result is for _a_ to have zero tendency
to call up r_{2} or r_{not 2}. r_{12} and r_{not 12} are each connected
to _a_ by 1 repetition, but they interfere with or cancel each other
with the net result that _a_ has zero tendency to call up r_{12} or
r_{not 12}. So with r_{22} and r_{not 22}. Here then the net result of
the six connections of _a_ _b_, _a_ _g_, _a_ _l_, _a_ _q_, _a_ _v_, and
_a_ _B_ is to connect _a_ with _r_, and with nothing else.
Case III. Contrasting Concomitants and Contrasting Element
Suppose now that the facts are as in Case II, but with the addition of
six experiences where a certain element which is the opposite of, or
very dissimilar to, _a_ is connected with the response r_{not 1}, or
r_{-1} which is opposite to, or very dissimilar to r_{1}. Call this
opposite of _a_, - _a_.
That is, we have not only
_a_ + _b_ responded to by r_{1} + r_{2},
_a_ + _g_ " " r_{1} + r_{not 2},
_a_ + _l_ " " r_{1} + r_{12},
_a_ + _q_ " " r_{1} + r_{not 12},
_a_ + _v_ " " r_{1} + r_{22}, and
_a_ + _B_ " " r_{1} + r_{not 22},
but also
- _a_ + _b_ responded to by r_{not 1} + r_{2},
- _a_ + _g_ " " r_{not 1} + r_{not 2},
- _a_ + _l_ " " r_{not 1} + r_{12},
- _a_ + _q_ " " r_{not 1} + r_{not 12},
- _a_ + _v_ " " r_{not 1} + r_{22}, and
- _a_ + _B_ " " r_{not 1} + r_{not 22}, as shown in
Scheme III.
Scheme III
_a_ opp. _b_ _g_ _l_ _q_ _v_ _B_
of _a_ (opp. of _b_) (opp. of _l_) (opp. of _v_)
r_{1} 6 1 1 1 1 1 1
r_{not 1} 6 1 1 1 1 1 1
r_{2} 1 1 2
r_{not 2} 1 1 2
r_{12} 1 1 2
r_{not 12} 1 1 2
r_{22} 1 1 2
r_{not 22} 1 1 2
In this series of twelve experiences _a_ connects with r_{1} six times
and the opposite of _a_ connects with r_{not 1} six times. _a_ connects
equally often with three pairs of mutual destructives r_{2} and
r_{not 2}, r_{12} and r_{not 12}, r_{22} and r_{not 22}, and so has zero
tendency to call them up. - _a_ has also zero tendency to call up any of
these responses except its opposite, r_{not 1}. _b_, _g_, _l_, _q_, _v_,
and _B_ are made to connect equally often with r_{1} and r_{not 1}. So,
of these elements, _a_ is the only one left with a tendency to call up
r_{1}.
Public-domain text, read in full here on John Shaqi.
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