This is particularly true in mathematics.
My first introduction to this fact came in the fifth grade. The teacher (a woman - name not recalled) demanded that we not put loose leaf papers into our math books and gave warning that if she did find them there she would exact a penalty of one complete rendition of the times tables ... from 1-12 ... for each improperly placed paper.
One day, some weeks later, the day of reckoning came. She ordered all books placed on top of the desk and proceeded to examine each for the forbidden filler. 1 here, 3 there, 0 for you "Good kid", 5 again, 2, 7 ... on down the rows handing out the dreaded tasks to each miscreant. 5, 4, 0, 7, 2, ... hmmm ... 57 for you sir.
In the subsequent week of my pencil pushing punishment, I came to know the tables in a way which gave me an edge for the remainder of my school life. I came to appreciate this "favor". At the time it was simply miserable.
What value is there in simply writing something over and over?
The value lies in concentration. While writing the same thing fails, of itself, to integrate data, it does cause one's mind to focus on the particular matter for one cannot write with a pen or pencil and daydream at the same time. Each entry in the task is slightly different than the former and a mistake requires a rewrite ... and ... the work was actually checked for authenticity (spot checked). Though I tried to automate the process, I was unable to write and watch TV at the same time.
What I was able to do is notice from time to time, regularities and interesting relationships between numbers, primes, divisors, shortcuts, etc. In other words, the material began to integrate because of the demand to focus on the subject.
Another effect of rote memorization is the freeing up of mental CPU cycles to do other tasks. If I know some equations, say the trigonometric functions, from rote memory, I needn't spend time thinking about that aspect of a given mathematical problem. If the context is known from memory, one can focus on the relevant particulars at hand.
A student should probably spend half of his learning time just grinding out paper after paper full of data.
A Good Teacher will say:
"OK, you little bastards ... Start copying this page of facts. Copy it one hundred times ... or ... until your grubby little hands fall off. And I'm gonna' check to make sure you do it."The kids will resent this and moan and groan. But a few years down the line, they will appreciate it mightily. I guarantee it.
Does anyone really think that this won't work? How could you possibly fail at something as simple a S.A.T. mathematics after rote-writing the entire math FAQ 100 times? Remember, I don't mean do this only ... just half the time. The rest of the time you do integrated "thought" problems utilizing the now automated tools.