In order to grasp a general principle by handling an instance of that principle,the general principle must be discerned by separating it from the specific instance in which it is embedded.But how can such a separation be brought about? This is actually the classical problem of general qualities and specific instances.The former are what dwell in Plato's world of pure ideas,whereas the latter are what populates our world.How can we tell the two apart? For example,how can we distinguish “threeness” from three apples,the idea of serendipity from a serendipitous event,or as in Gick and Holyoak's (1980) case the idea of simultaneously converging paths from destroying a tumor in the stomach by radiation?
As I have argued,in relation to the Greeno et al.(1993) and Lobato and Siebert (2002) studies,discernment or separation can hardly come about by focusing on one instance only,in which the general and the specific are completely inter-twined;the former implicit,the latter explicit.If there are two sufficiently different instances of the same principle,what is common (the principle) may possibly be discerned from what is different (the instances).The more different cases available to the learner,the greater the likelihood that the principle will be discerned as the primary,or only,thing common to all,because of the likelihood of ruling out what is different (Reeves ＆ Weisberg,1994).The likelihood of distinguishing the principle and its specific instantiation can also be enhanced by drawing learners' attention to the commonalities between the different instances.
The main point is that in order to discern the general principle to be used in the second problem,empirically at least two examples are needed.The traditional idea of transfer-learning something in Situation A (discerning a general principle) and using it in Situation B—is logically untenable.As all the transfer experiments quoted by Lave (1988) demonstrated,the first instance in which learners discern a principle may actually occur when they are dealing with Situation B rather than Situation A.From Lave's point of view,this can be seen as an example of local construction of the solution (i.e.,the solution does not exist prior to the problem being solved).From the point of view of my own line of reasoning,this is an example of the necessity of variation.Without different instances (at least two) the learner is most unlikely to become aware of the general principle.In fact,in a follow-up of their study,Gick and Holyoak (1983) showed that although learners had little success in abstracting (or separating) generalized solutions from single specific instances,they frequently managed to do so when dealing with two different instances.One could say,of course,that several examples make it possible for the learner to discern the general principle because the examples all embody the same general principle.It is true,provided the examples are different.Using the same example twice or several times instead would not do.