The Psychology of ArithmeticThorndike, Edward L. (Edward Lee)
Science
The Psychology of Arithmetic
Thorndike, Edward L. (Edward Lee)
Arithmetic -- Study and teaching
The common practice of either having no use made of pencil and paper or
having all computations and even much verbal analysis written out
elaborately for examination is unfavorable for learning. The demands
which life itself will make of arithmetical knowledge and skill will
range from tasks done with every percentage of written work from zero up
to the case where every main result obtained by thought is recorded for
later use by further thought. In school the best way is that which, for
the pupils in question, has the best total effect upon quality of
product, speed, and ease of production, reënforcement of training
already given, and preparation for training to be given. There is
nothing intellectually criminal about using a pencil as well as inner
thought; on the other hand there is no magical value in writing out for
the teacher's inspection figures that the pupil does not need in order
to attain, preserve, verify, or correct his result.
The common practice of having the final responses of all _easy_ tasks
given orally has no sure justification. On the contrary, the great
advantage of having all pupils really do the work should be secured in
the easy work more than anywhere else. If the time cost of copying the
figures is eliminated by the simple plan of having them printed, and if
the supervision cost of examining the papers is eliminated by having the
pupils correct each other's work in these easy tasks, written answers
are often superior to oral except for the elements of sociability and
'go' and freedom from eyestrain of the oral exercise. Such written work
provides the gifted pupils with from two to ten times as much practice
as they would get in an oral drill on the same material, supposing them
to give inner answers to every exercise done by the class as a whole; it
makes sure that the dull pupils who would rarely get an inner answer at
the rate demanded by the oral exercise, do as much as they are able to
do.
Two arguments often made for the oral statement of problems by the
teacher are that problems so put are better understood, especially in
the grades up through the fifth, and that the problems are more likely
to be genuine and related to the life the pupils know. When these
statements are true, the first is a still better argument for having the
pupils read the problems _aided by the teacher's oral statement of
them_. For the difficulty is largely that the pupils cannot read well
enough; and it is better to help them to surmount the difficulty rather
than simply evade it. The second is not an argument for oralness
_versus_ writtenness, but for good problems _versus_ bad; the teacher
who makes up such good problems should, in fact, take special care to
write them down for later use, which may be by voice or by the
blackboard or by printed sheet, as is best.
CHAPTER XIV
THE CONDITIONS OF LEARNING: THE PROBLEM ATTITUDE
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