"...our current educational process was designed for rocket scientists that were in short supply 50 years ago. In other words, there are many facets to mathematics but in most of our educational institutions we are given one path from arithmetic to algebra to geometry to calculus. And should we falter anywhere along that path, we tend to stop and move away from the subject"

Calculus requires an understanding of geometry and algebra, each of which requires an understanding of mathematics. Now, it may be possible to vary the path as: Math-Geometry-Algebra-Calculus, but realistically there's not much difference, nor can there be much difference, in the path to calculus. And it's never been just 'rocket scientists' who need calculus. All of the hard sciences need some understanding of calculus, as do all fields of engineering. (Maybe computer science and software engineering folks don't need calculus themselves, but they usually need some familiarity with calculus since they design stuff that uses it.)

So that's really a false charge against a mathematics curriculum that has been around for a couple hundred years. It really rankles me when I see someone making a strawman argument or using a back-handed smear to make a point. You want to say that there are other ways to teach mathematics, or topics in mathematics that can be fun and useful and rewarding? Just say so. I've mentioned Vi Hart and her YouTube videos on this site a number of times. She's great and she talks a lot about (and demonstrates) really fun topics in Math.

As for the "should we falter anywhere along that path, we tend to stop and move away from the subject" comment -- my wife struggled with Math in high school, and took just the minimum needed for her BA and MA degrees in early childhood education. Years later, just for fun, she took evening courses in Trig and Calculus from the local junior college and earned straight 'A's.

What? Jackie Robinson????

Maths is part of rocket science, though. _{Or something...}

I for one have always had a rather strong distaste for the crap they call mathematics that they insist on teaching in school and college.

What exactly is the point of teaching loads of theoretical gobbledy goop that has near zero application in daily life while almost all forms of practical applied math that everyone needs and will use every day gets ignored? I do recall being told some lame excuse once that was something to the effect of perhaps knowing how to do theoretical mathematical would lead someone do discover the cure for cancer.

Really? I am supposed to believe that a abstract conceptual math theorem will cure/kill a invasive biological life form whereas having the knowledge of a biochemist with practical applied math skills and understandings of how cell biology works won't?

How many people do you know that have trouble doing basic applied math like balancing their check books or even just figuring out what their average MPG numbers are for the vehicles they drive or that can even figure out if their credit card company or bank is ripping them off on interest rates?

Anyone ever remember covering that math in high school? I do and it covered about one week total and that was it.

Had the same beliefs when I was just an engineer. Try going back to get your advanced degree in physics and watch how quickly that gobbledy goop math becomes essential. Physics is just applied gobbeldy goop math.

Similarly, my wife can't understand why we learn geometry and calculus in high school. (she is a nurse) I can't get through a couple days without using it. Depends on what you do if you need it or not.

Well then lets put it this way.

Statistically how many typical high school students are going to grow up to be advanced physicists and how many are going to grow up and never be able to handle basic math like keeping tack of the their own checking accounts or loan payments and worse?

Needs of the many here is what I am going for.

It is not the Math, it is the teaching of the math, that is an abomination. It is frequently taught by math (and physics) deficient teachers, with the help of schoolbooks displaying total inanity. And sowing confusion by embedding some numerical and such theoretical nuggets nobody ever needs and uses. And all the while the necessary foundation is not laid.

The first time I encountered that, was with my children. When I discovered, that they do not understand this, do not grasp that, I got mad as hell. On a 3 weeks florida vacation I promised them not to take more time, than a 1/2 hours between breakfast, and the opening of the pool. In those sessions they grasped and learned more math and physics, than 2-3 years high school. It is still with them.

Mind it, none of them was interested in math for math's sake. One is a financial adviser, one is a good biochemist, one is a good computer programmer. What I would call yeoman math users. Nothing fancy.

I on the other hand learned high math from excellent teachers, and needed it. They were clear, only what was needed, no bs.

Still, I found all High school math books to be revolting abuse of the students. Who needs the incessant offal of number theories mixed in?!? For example. I never did!

I have read many books from Richard Feynman. His no bs, barebones approach to difficult things suited me. In his later years he was roped into schoolbook evaluations. Reviewing many dozens, he found ALL of them offensive, debasing garbage.

One Example of Lucidity.

The (Foucault) pendulum directly proved, that the Earth globe turns.

Once you accept, that a suspended pendulum will keep swinging in the same plane, the physical proof is almost an afterthought.

You place it on the north pole, and the earth turns around this way in a day.

On the south pole, it will turn that way in a day.

On the equator it is not turning under the pendulum at all.

All other places fall somewhere inbetween.

NOW, DID I USE ANY MATH HERE AT ALL? I DID NOT NEED ANY!

This picture, and understanding will accompany you for life. If needed, detailed math can be looked up, or worked out with basic trigonometry. If needed.

I never needed it.

I agree that the teaching of math is a major problem. During one period of unemployment, I taught high school math for one year. Years later I still get stopped in the stores by students who tell me I was the best math teacher they ever had. At first I found this hard to believe. That teaching job was the hardest job I had ever had in my life! While doing it, I always felt inadequate. However, talking to these now grown kids, I keep hearing that what made me good was I would always tell them why this was important and where they could expect to see it in real life.

That was probably the best decision I had made that year. I work in the Real World, not Acedemia. I figured the one thing I could do for my students that the professional teachers couldn't do was to point out Real World applications. I kept it up during the year because of the positive feedback I got from my students. Positive feedback? Not anything verbal. Nothing like a "Thank you" or "Interesting lecture". I would look out over the class at all the heads face down toward the desks while I talk about simultaneous equations, everyone bored out of their skulls. Then, with these magic words, "That's how you do this. Now here is where you will use this once you get a job" all of those heads would pop up. Math isn't boring. High school and the life of a teenager are boring. The kids I worked with were yearning to get out of there and into the Real World. Anytime I started talking about Math in Life, they were interested.

"A man gotta know his limitations." The great existentialist philosopher, and peace supporter, Clint Eastwood.

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Those are words worthy to live by.

When I was a teen, I was in the metal shop one day a week, for two years. Good enough to "get" some things, good enough to be dangerous in others, and to know the difference, thanks to good and practical teachers.

So, one example.

I need to purchase a motor driven measuring gizmo components, and get it work for a trip to Outer Mongolia, and it got to work. What to do?

I know enough, what rpm and what torque is sensible. Do I need straight gear, slanted one, planetary, split pretensioned to avoid chatter, or don't care? I definitely look for a complete package: controller, motor, gear, coupler. I have no clue, what else I need, and what else is available strictly off-the-shelf. Then I contact a good broker, like CD4, and pay for their services. What I require, that the package be used in volume, and for a number of years. That information I pay for, as I need the best reliability, and I do not have the info, nor do I want to be the test case. I want rock solid performance. And, when (Murphy willing) the sh** still hits the fan, UPS will deliver an exact standard replacement in a week, even to Outer Mongolia.

Another example, closer to home.

I learned more from the late and great Bob Pease and Williams (no, not the music legend) about Analog Design, than I ever could in a school. It was, like sitting at the feet of violin virtuosos, and actually "getting" some of it. Both stressed time and again, that if you cannot lay it out on a napkin, your design (or theirs) is no good. They could (and did) teach semiconductor physics to physicists. They did that to me. The generation following, all refer to them, profitably.

They taught some of the "what" kind. But, their emphasis was on the "how" and "why', and how can you find them out for yourself. Then, how to prove them experimentally, first of all to yourself.

You see, modern industry is in the 21st century. But, the bulk of the schools are still stuck in the late 1700s / early 1800s, beginning Industrial Revolution, One Size Fits All, and All Advance in Lockstep, or Else, setup.

The young ones are bored out of their skulls with this inanity. And run rings around their elders with whatever good or ugly, but exciting stuff catches their fancy on the internet. Heck, I am not their generation numerically, but you bet your bippy, I am in spirit. I really needed to learn biochemistry, the brick and mortar was no help. So I did it without them, and now I do not need them, ever again.

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I do not ask you, to abandon principles. But, if you cling centuries old, outdated setups and rituals, why do you complain about being refused as worthless and left behind?