Sunday, December 20, 2015

Favorite comments of '15: R.Craigen and Anonymous and Anonymous

On Conversations on the Rifle Range 22: Tesselations, Border Crossings and Guess and Check

R. Craigen said...
...I think the very word "rote" has been abused and tormented into something that it never was before, by modern discourse.

Today when one says "rote learning" they generally mean "without understanding". But that is not what the word means, although some dictionaries now include that meaning. "Rote" means, essentially, "by repetition". That is, rote learning is that which is learned through repetition of some task. Think of words sharing a common root: "rotation", "rota", "rotary". It means to repeat something over and over.

Repetition ... is the basis of most memory-building. And memory is the seat of learning. So where there is no rote, there can hardly be much learning. An actor learns his or her lines by rote. Does this mean they do not understand those lines? You'll find few in the business who would agree with that conclusion. Athletes learn their competitive skills by rote ... repetition. Does this mean they have no understanding of the game? No, in fact most would tell you that "understanding", in a vacuum of those skills, is of little value. Same in mathematics.

Rote is not "understanding", or certainly not "complete understanding". But understanding is not complete even after years of excellent learning. Even as a professional mathematician I am continually learning my subject matter at a deeper level, even the elementary topics. I rankle at the suggestion that there is some royal road and down which teachers should supposedly lead students directly to understanding, prior to mastery of requisite skills. Plato understood well that there was no such road, and the situation is no different today. 
Anonymous said...
Before there was writing, the traditional cultures that we all are descended from accomplished most of their learning by demonstration, repetition and practice. Writing added the ability to catalogue learnings and have them for reference, but it did not invalidate the older forms of learning.
Anonymous said...
“Just like a first grader who memorizes the multiplication tables, he will never come to understand. It will be plug and crank for him, all the way.”

I take issue with this statement. It seems as though educators have a view of memorized knowledge that is only negative. It is as though they imagine all children who produce such knowledge to be pale and forced to sit inside by parents who make them do repetition for hours on end. Their performance of this knowledge being only a parlor trick with no depth. First, why will the child “never understand”? It seems inevitable that in fact even if he is just chanting or singing the facts, in the coming months or years he will continue to apply this knowledge to math problems and develop the same understanding as his peers. Likely he will go faster through the material as he can do problems without struggling to access the facts. Second it seems as though as much as this is denigrated, teachers know that this must happen at some point. A first grader who has this memorized is a victim of his parents distorted vision, but a fourth grader who has this memorized is just an ordinary child. Certainly as an adult when I think of 3x5 I rely on my memorized knowledge and never consider the concept of how that is achieved.

Also I don’t think it is true in all cases that a child could not understand. Multiplication is not that difficult to grasp. 2 groups of 3, equals 3 groups of 2, equals 2+2+2 or 3+3, all of this can be shown and explained fairly easily. We are abroad this year in a new school system and I noticed looking ahead in the first grade textbook, that multiplication is introduced toward the end of the year.

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