whichinvolvetheactionsofanimaginarysetof‘‘monsters,’’areshownintable
23.2. In the first puzzle, the monsters pass globes of various sizes back and
forth; in the second, they move themselves from globe to globe; in the third,
they change the sizes of the globe; and in the fourth, they change their own
sizes.
Ideally, because these problems are formally identical, people who have
solvedoneofthemshouldbehaveasiftheyhadsolvedthemall.Infact,thisis
not the case. There is a lot of transfer between problems that involve moving
either monsters or globes, and there is a lot of transfer between problems that
involve changing the sizes of either monsters or globes. But there is relatively
little transfer between move and change problems.
Failure of transfer is a frustrating reality in our classrooms. A statistics
teacheratCMUwhohadtaughtthePoissondistributiontothisclassthrougha
distance example was surprised that the next day his students could not apply
the distributionto anexample involvingtime.
Possible Responses to These Problems
The possibility that mastery of a field may take many years is an important
itemofmetacognitive knowledge thatwe oughtto teachto ourstudents.Some
students may be inappropriately discouraged by early setbacks because they
believe that failure indicates lack of talent rather than lack of knowledge.
Others, perhaps too well endowed with self-confidence, may believe that they
are destined to perform great acts of creativity with little or no effort on their
part. Some may even defend themselves against knowledge on the grounds
that it may spoil the purity of their individual spark. Students of either type
couldprofitbylearningthatlargequantitiesofknowledgemaybeessentialfor
skilledperformance intheir fields.
Table23.1
(continued)
Learningstrategies
Elaborative rehearsal
Notice hierarchical structure
Useoverlearning
Monitor ownlearning
Generateexamples
Use information inwordroots
Evaluation
Check results
Getexternalcriticism
General
Consolidate
Examine ownprocess
Time management skills
ThreeProblemsinTeachingGeneralSkills 561