The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
We have _a_ + _b_ responded to by r_{1} + r_{2},
_a_ + _g_ " " r_{1} + r_{7},
_a_ + _l_ " " r_{1} + r_{12},
_a_ + _q_ " " r_{1} + r_{17},
_a_ + _v_ " " r_{1} + r_{22}, and
_a_ + _B_ " " r_{1} + r_{27}, as shown in
Scheme I.
Scheme I
_a_ _b_ _g_ _l_ _q_ _v_ _B_
r_{1} 6 1 1 1 1 1 1
r_{2} 1 1
r_{7} 1 1
r_{12} 1 1
r_{17} 1 1
r_{22} 1 1
r_{27} 1 1
_a_ is thus responded to by r_{1} (that is, connected with r_{1}) each
time, or six in all, but only once each with _b_, _g_, _l_, _q_, _v_,
and _B_. _b_, _g_, _l_, _q_, _v_, and _B_ are connected once each with
r_{1} and once respectively with r_{2}, r_{7}, r_{12}, etc. The bond
from _a_ to r_{1}, has had six times as much exercise as the bond from
_a_ to r_{2}, or from _a_ to r_{7}, etc. In any new gross situation, _a_
0, _a_ will be more predominant in determining response than it would
otherwise have been; and r_{1} will be more likely to be made than
r_{2}, r_{7}, r_{12}, etc., the other previous associates in the
response to a situation containing _a_. That is, the bond from the
element _a_ to the response r_{1} has been notably strengthened.
Case II. Contrasting Concomitants
Now suppose that _b_ and _g_ are very dissimilar elements (_e.g._, white
and black), that _l_ and _q_ are very dissimilar (_e.g._, long and
short), and that _v_ and _B_ are also very dissimilar. To be very
dissimilar means to be responded to very differently, so that r_{7}, the
response to _g_, will be very unlike r_{2}, the response to _b_. So
r_{7} may be thought of as r_{not 2} or r_{-2}. In the same way r_{12}
may be thought of as r_{not 12} or r_{-12}, and r_{27} may be called
r_{not 22} or r_{-22}.
Then, if the situations _a_ _b_, _a _g_, _a _l_, _a _q_, _a _v_, and
_a_ _B_ are responded to, each once, we have:--
_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}, as shown in Scheme II.
Scheme II
_a_ _b_ _g_ _l_ _q_ _v_ _B_
(opp. of _b_) (opp. of _l_) (opp. of _v_)
r_{1} 6 1 1 1 1 1 1
r_{not 1}
r_{2} 1 1
r_{not 2} 1 1
r_{12} 1 1
r_{not 12} 1 1
r_{22} 1 1
r_{not 22} 1 1
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