Layers of Understanding

"Ogres are like onions...we have layers" Theses are the famous lines of the Shrek. While it's not always green or funny, understanding and learning is in a way like onions and ogres. They have layers.

What do I mean by that?

When a child first learns something, it usually takes the form of rote method. They see it over and over again (or hear it or do it depending on their learning styles; see nav bar on the left) then start to imitate the new learning.

Let's follow a series of simple examples. Suppose Bobby is learning additions and subtractions.

As a start, he might see, hear, or feel that information and memorize it. By the way, in order for him to memorize it effectively, he has to accept it as a fact. If he isn't convinced that this new knowledge is the truth, it will be very hard for him (to say the least) to advance to understanding it later.

Of course, he could not believe it and still memorize it. That's exactly why memorizing is not understanding. It is merely like a computer repeating back a pre-programmed answer. It does not understand the answer. We can go on and on in a philosophical discussion on the meaning of understanding, and so on, but... let's not.

Anyways, so our Bobby has now accepted (through his own trials and errors maybe) that this is a fact and has memorized it. If someone were to ask him a straight forward question, he's sure to get the answer right.

But he still doesn't yet understand the concept. Teachers and books continue to give him different explanations and/or examples of the concept. With each new information, Bobby's knowledge starts to mushroom out and become an understanding.

He starts to see that this principle that he accepted as truth is really true and that there are multiple examples of it. He begins to see that the knowledge is not static, but is dynamic (that is, changing and moving; unlike a static example in his textbook). In other words, he begins to see that the principle that he memorized isn't only true in the example he memorized but can be applied to virtually anything and still make sense.

His realization that this concept is dynamic, he begins to see how this might have been used in other ways all around him. At the highest level, Bobby begins to form his own theories about the world using this newly attained understanding. In other words, he begins to synthesize new information and test out whether they are true or not. With each result that he sees, it will modify or solidify his current level of understanding, further enhancing his understanding of the grand concept.

Let's briefly go over the points again:

  1. Accept the fact as truth.
  2. Memorize the fact.
  3. Add layers of understanding. Knowledge becomes dynamic from static.
  4. Begins to see how it might have been used in other situations.
  5. Begins to synthesize his own theories of how the concept might be applied in other areas.

In all of these steps, keep in mind that each result or experience (e.g., lessons, books, diagrams, discussions, etc...) brings new layer of understanding. These new information will either support or disagree with his existing understanding.

And in each case, Bobby is forced to either modify or solidify his knowledge to incorporate the new information so that it is still held true at the end of the day.

With enough, this soon leads to a fully developed level of understanding and thus allows Bobby to start theorizing beyond what he was taught. He is able to use the base knowledge that he was taught as a springboard to launch further forward.

Suppose that initially, Bobby was always shown problems of addition and subtraction with apples. Soon, Bobby might have developed an untruthful (and not taught directly to him either) knowledge in his mind that these rules only apply to apples and nothing else.

When he is told later that these principles hold true even for oranges, the new information disagrees with his current existing understanding.

This is to be expected because his current understanding is limited and yet immature. But when he is shown enough examples that this indeed is true as well, he will modify his understanding of the concept to allow for the new information to be 'absorbed'.

This in the end, assuming that he isn't mislead, will form a much more fuller and stronger understanding that Bobby can use to propel himself forward in learning new and more advanced concept.

Quick, what's 6x7?

"education at play"

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