The unforgivable deficiencies of our math educational system
I am most certainly a product of our math educational system (or at least my math education is). I'm like a small valid sample of 'products' from the 'assembly line' that is our math educational system in America. And although I essentially was a math major at MooU (Michigan State) and was a very conscientious student (dedicated and disciplined), I consider that I barely understand math and its theoretical underpinnings. Is this my fault? Or something else? Is our math teaching system totally flawed? YES.
We don't introduce vital concepts early like we should.
Recently, you'll find an article written by me about Lebesgue measure and any connection to space/time. I'm 49 years old. I didn't encounter the vitally important concept of measure until I was around 35 years old when I was attending a graduate school in mathematics. For anyone in math, sciences, or engineering, they need to encounter this vital concept much earlier – say, sixth-grade or around 12 years old. Why? For the simple fact it's a core concept of our common number system and therefore relevant to any field depending on them .. Lebesgue measure surely is a 'deep mathematical concept' but.. That does not mean youth should not or cannot understand it.
Too much presentation/lecturing is performed in math.
Everyone knows that math is a 'hands on' field absolutely requiring practice to 'get it'. There is not one single math course on the planet that does not require some 'homework' or working problems. Math is learned by working problems. Early on, this means learning what basic operations 'do' and practicing them. Later on, we get more sophisticated and our problem solving repertoire hopefully increases so that we can solve a variety of math problems appropriately. Knowing when to use particular techniques is just as important as facility in applying those techniques themselves. This takes time and practice.
There's little or no caring mentoring in the current system.
This should have been my first point because of the glaring lack of mentors I've NOT experienced. I have no mentors / good teachers to compare against each other.. Perhaps I have one good teacher in math from both high-school and MSU – ONE. But even he refused to mentor appropriately. What do I mean by mentor? Encourage and inspire enthusiasm – love for math and math concepts.. With the right mentoring, I could have been a GREAT applied mathematician/scientist/engineer. Without mentoring, I'm 'floundering' and self-guided.
The pace and content are totally inappropriate.
This does not apply so much to high-school or earlier courses in math.. I particularly remember advanced calculus and graduate courses in analysis and other topics. Essentially, the students are trying to rush themselves to keep up with taking notes. They have no time/energy/attention for the actual content. This is deplorable and unforgivable. You're forced to read through your notes to try to understand the theorems and proofs taught in class. Attempting to perform homework only resulted in more confusion. I had no choice but to drop-out of the system at that time. Unforgivable.
The arrogance of academicians is ill-founded and inappropriate.
Other than snap-judgmentalness and vanity, arrogance is about the most repulsive human quality I can identify. Professors of mathematics and physics are about the most arrogant 'creatures' on the planet. Sheldon of Big Bang Theory is a parody but accurate portrayal of theoretical physicists. Both fields are very close conceptually and as sibling sciences. But the ego encountered in both is not DESIRED nor APPRECIATED. I can count on one hand – the humble professors in both fields I've encountered throughout my life.. This is unacceptable. Curb your ego-gorging. Wake up; grow up.
Proof motivation is NEVER addressed.
Rarely is a professor of mathematics actually trained in education. This is a critical fault of our educational system. But we can't blame that lack of training for the other critical fault of our system: I've never heard/seen an instructor attempt to deal with proof-motivation (how the particular proof they're about to cover was arrived at or developed to prove a particular theorem). If they expect us to memorize proofs then later somehow miraculously develop our own theorems and proofs, I don't see the connection. Math education in America basically SUCKS and does nothing to inspire young mathematicians, scientists, or engineers to be anything but cogs in the machine.
We don't train innovative/creative/curious scientists or engineers in America; we mass-produce robotic egotistical paper-pushers who do nothing but tow the line of the status quo. A perfect example is the LHC and 'the Higgs'.. A super-heavy transient particle is observed in a few decay schemes.. Because it fits their virtual boson-exchange and reductionist approach, 'the Higgs' is now labeled the 'source of mass'. Wow.. What vanity; what arrogance.. What narrow-mindedness.. And we have our 'wonderful' educational system to thank..
PS: math/physics textbooks seem to be deliberately obfuscating when they attempt to 'teach' something – especially at the 'higher' levels.. It's almost as if they're attempting to create an 'elite priesthood of mysteries' in both math and physics so that the only people who have the patience to unravel their complex deceptions will rise in their ranks.. I hate to bring in Satan at a time like this in the 'discussion' but.. It smacks of Satanic manipulation.