Frazz by Jef Mallett for June 21, 2023

Concepts don’t always agree with the finished products.

That would make Caulfield the eternal fifth-grader.

The only things that I learned by rote in school were … hmm. Well, the addition tables in (3rd?) grade and the times tables in (5th?) grade. And then I memorized the “important three” trig equations: sine = 1/cosecant, cosine = 1/secant and cosine²θ +sine²θ = 1 … oh yeah, and “opposite over hypotenuse = sine” in high school. That allowed me to generate all the others at need. I did horribly on history tests, though I kind of enjoyed the material. How the heck can I remember the name of the king who did something and when? I have enough trouble with the color of General Washington’s white horse or the date of the war of 1812.

Repetition fixes the information in the mind. Practice teaches the hands how to do the task.

Knowing how something is done and being able to do it quickly and well are two very different things.

I have many college students that “know the concept” but refuse to do the work. Personal Discipline should be a part of education but alas….

In Japan, schools run year round with a six week break in July/August and one or two week breaks at other times in the school calendar.

“If you are acquainted with the principle, what do you care for a myriad instances and applications?”—Thoreau on newspapers

Caulfield can ‘see’ the answers, but, like many sharp students, doesn’t want to be required to or can’t ‘show the work.’ But guessing isn’t a reliable factor. while ‘showing the work’ means one has mastered the process and can repeat it as needed.

Some kids would never get out of school but would still be able to live good, productive lives.

I was regarded as lazy in school because I understood the concept after three problems and found the next thirty mindlessly boring. I hated math. I became a math teacher.

Speaking as a person who struggled with homework for the same reason, it is also important to develop the skills of self-discipline and follow-through.

Caulfield, we already have a janitor at this school, and he’ll probably never retire.

Muscle memory. Physical, and mental exercise.

A doctoral candidate in mathematics at the Massachusetts Institute of Technology had been working for days on a particularly knotty problem but was making no headway. Desperate for insight, he showed up 15 minutes early for a seminar being conducted by brilliant mathematician Norbert Wiener and wrote the problem on the blackboard. Other students started to arrive and were murmuring among themselves about how completely opaque the path to a solution would be when Dr. Wiener himself walked in. He paused on the way to the front of the room and stared at the problem. Everyone was dead silent as the clock ticked along for over 15 minutes. Finally Wiener stepped forward, picked up a piece of chalk, and wrote the answer underneath the problem.

This was of no help to the original student, however, since he needed insight as to the methodology, so he asked “Dr. Wiener, isn’t there another way to go about that?”. Wiener paused for a moment in thot and then said, “Why, yes, I believe there is.” Another 10 minutes went by as he again stared at the problem intently, then he once more he picked up the chalk and wrote the same answer underneath the first.

And that, my children, is the difference between a genius and you and me!

I once tried to read a book on math by myself.   I soon found that I needed other students to slow me down enough to absorb one lesson before I dumped the next on top of it.

Okay, I’ve got that, don’t need to do any more exercises.

Okay, I’ve got that, don’t need to do any more exercises.

Okay, I’ve got that, don’t need to do any more exercises.

What the flim flam is this chapter talking about?

(sigh) That was my problem. I did pretty well in school, mostly by test scores. Had a problem with rote homework assignments. Now I wish I had worked on those. It’s one thing to know the concepts and how to do things, it’s another to be able to quickly and easily apply them, and for that you need to practice, practice, practice.

I beat the 100-years war and the Seven-Mile bridge (in the Keys) really messed up your mind.