Transformation As It Relates to Conservation and Infinity

 

 

Transformation is a mental structure necessary to be able to conserve.

Piaget investigated and wrote about it as it relates to conservation.
You may recall studies of interviewing children and asking them
to draw the position of a pencil from the moment it left a hand and until it hit the ground.

He found it took several years for children to construct the idea that the pencil was in an infinite number of positions starting from the hand and ending on the floor.

 

Other areas where the idea of transformation across values is applicable is the concept of variables. Being able to visualize how a variable change results in a range of possibilities which can sometimes be infinitely continuous.

The same structure might be applied to moral issues of right and wrong. Take a moral issue and define it with this mental construct with an extreem of rightness and wrongness ranging from a continuum of totally wrong, say for example when the pencil is in the hand, to totally right, the pencil on the floor. Example when is it okay to tell a lie? On the contimuam from okay on issues of - do you like the shirt, dinner, ... to Do you swear to tell the whole truth....

Another example is science. It takes the view that the pencil is never on the floor. There are no 100% right answers, everything is tentative. However, there are certain events or objects where we believe some facts or inferences (theories, laws) are closer to the ground than others (99.9%). For example with the seasons. Scientist are pretty much in agreement that the Earth's distance from the Sun doesn't vary enough to cause the seasons. And that the directness of the rays does vary enough to cause the seasons. However, even those ideas are tentative and open to reevaluation if new evidence is discovered.

While this idea is not too difficult for adults to understand it is difficult for young people as they are still constructing or assimilating a variety of ways to apply transformations. Then to compound the problem is what seems to be a human obsession of wanting to classify everything as right or wrong; black or white; ying or yang. Of course it isn't easy for teachers either when we are forced to evaluate tentative answers.