Page 216 - Deep Learning

The Growth of Competence 199

A task strategy might yield a correct answer and yet be inefficient. Well-
documented examples can be found in children’s arithmetic. At a certain age,
children respond to simple addition problems like 5 + 3 = ? by counting out five
fingers and then continuing to count out three more to arrive at the right answer
(one, two, three, four, five, six, seven, eight – eight is the answer). At a somewhat
later age, children discover that counting out the first addend is unnecessary,
and they begin with the larger addend and count up (five; five, six, seven eight –
eight is the answer). This shortcut can be discovered via analyses of execution
traces of past task solutions: Every solution that begins counting at unity passes
through the larger addend along the way. A mechanism that detects and deletes
repetitious and redundant steps is sufficient to detect such shortcuts. Shortcut
detection only applies when there is a shortcut to be detected. 63
Even in cases when there is no shortcut to be detected, strategy execution
64
can be optimized by extracting statistical regularities from the environment.
The latter are typically learned implicitly. For example, reaction times to words
that occur with high frequency in normal discourse are shorter than reaction
times to low-frequency words. This helps optimize reading, because the high-
frequency words, by definition, need to be accessed more often. This type of
optimization occurs late during practice, because the extraction of statistical
regularities requires large amounts of experience. Estimates of word frequen-
cies cannot be stable until the person has been reading for a while.
if a person is called upon to answer a question or solve a problem many
65
times, he will eventually remember the answer. This form of optimization
replaces computation with information storage. Like other forms of optimiza-
tion, it requires extended experience. implicit information about frequency of
occurrence is needed to identify tasks for which it is more efficient to memorize
the answers than to compute them as needed. Shortcut detection and optimiza-
tion via statistical regularity extraction and memory-based responding probably
account for much of the speed-up that occurs after a task has been mastered.

The Nine Modes Theory
to summarize, there are nine different types of information that might be
available in practice scenarios: verbal instructions issued by a coach or tutor;
prior declarative knowledge about the task environment; already mastered
strategies for analogous tasks; models, demonstrations and solved examples;
outcomes from unselective search; positive feedback; negative feedback;
execution histories; and statistical regularities in the environment. Each type
of information can be used to adapt, improve or speed up a cognitive skill.