Suppose you've paid for a child (or relative or employee or ...) to take 12 years of piano lessons. Then you discover that your protégé can only play scales on the piano, but cannot play any music.
This is the situation with our students whose 12 years of mathematics in Public or Private School are paid for by American citizens. (Yes, I said "Private", because the "religious" schools get significant tax-write-offs and the nonreligious ones get some, which must be made up in the "Federal Budget".) The most capable ones of them can "play the scales" -- perform correct arithmetic and algebraic calculations -- but they "cannot play the music" -- CANNOT APPLY THAT CALCULATION TO PROBLEMS.
Similarly, so many students who can read fiction and school texts CANNOT READ WORK INSTRUCTIONS!
I've been watching this for 62 years. (Elsewhere, I describe how I -- a former DROPOUT --completed a semester's work in 6 courses of Tulsa High School IN TWO WORKS -- motivated by TICKETS TO ALL MOVIE THEATERS IN TULSA IF I SATISFIED GRADUATION REQUIREMENTS BY A GIVEN DATE. This made me sceptical about American Educational Standards, and started my bird-doggin'.) In all that time, I've never read any good news in the newspapers or heard it on radio or TV. But I have read many accounts of American teen teams competing in Problem-Solving with teen teams from European countries and elsewhere. 8th Place; 10th; 12th; 15th; etsettery -- but never 1st!
No, Ophelia, don't give me that jazz about the Catholic Schools or the Jewish Schools or "Christian Schools". If they're so good, why don't they put in a team that beats all competition? I don't think their Educators are too modest to think of this, or shun the good publicity.
On one of my Web Pages, I've a quotation from Lester Thurow, MIT economist: "Americans people are not used to a world where ordinary production workers need mathematical skills." And Thurow gave a good example of this, involving well-paying jobs.
Before "The Computer Revolution", the "Number One Industry" was "Automobile". But this industry suffered periodically from "inventory flu". Too many cars were stored in inventory to be disposed up by retail sales. So workers on the assembling line and in auxiliary jobs had to be "laid off" until the inventory was significantly lowered.
In Japan, Toyota managers solved this problem which American managers considered unsolvable: JUST-IN-TIME INVENTORY. Pacing the various stages so that inventory-glut didn't happen! But this requirement every one essentially involved to perform calculations to see how to make this controlled process succeed. A manual was written for workers to read. Happily, Japanese high school graduates could understand the manual and do their part. So Justi-in-Time Inventory was a success.
Then Toyota established a manufacturing plant in North Carolina and tried to set up Just-in-Time Inventory there. Trouble! American high school graduates couldn't understand the translated manual, and couldn't do the operations when they were explained to them. American college graduates couldn't either. Toyota had to hired American graduate school students to do the work that Japanese high school students could do!
On another Website, I've a quotation from Ricard Bellmann, who created the powerful "Dynamic Programming" procedure. When, in the 50's, it was applied correctly by the Pentagon to defense systems under construction, no COST-OVERUNS OCCURRED. But that must have been bad news for some people, because I haven't heard of any applications of "Dynamic Programming" or a similarly effective controls, since the fifties. Anyway, Bellman said: "95% of the mathematics departments of North America have opted out of civilization." He meant that THEY DON'T CARE ABOUT APPLIED MATHEMATICS, which is one reason that our students can't do it. (One noted theoretical mathematician even said, "Applied Mathematics is bad mathematics.")
As a result of this, American corporations spend billions o dollars re-educating our "educated" students so that they can be of use. And whose really paying for that? You are. It's passed on to you and all of us. Every one who buys products or services is paying for this extra education! Talk about "double taxation" ....
Before running across this, I read, in The Mathematical Monthly of The Mathematical Association of America (concerned with high school and college mathematics), a reprint of a speech by the man assuming the Presidency of MAA. I'll explain the title, "England was Lost on The Playing Fields of Eton, A Parable for Mathematics".
In the very early 19th century, the Duke of Wellington (whose troops defeated the great Napolean in the Battle of Waterloo) was quoted as saying, "The Battle of Waterloo was won on the playing fields of Eton". Presumably, playing soccer, Rugby, etc., prepared officers for leading their men to this triumph. This has been quoted again and again, to vaunt the value of Sports in the Curriculum and in Society. But the media don't tell you the rest of the story. I have somewhere his correcive statement. The gist of it is that the Duke was tired of reporters asking him silly questions, so gave them as silly answer.
The meaning of this title was that 20th century English universities were not supporting Applied Mathematics, and this seemed to be the case in America. The speech noted one good engineering school where engineering students WERE NOT ALLOWED TO TAKE ANY COURSES IN THE MATHEMATICS DEPARTMENT of this school, but only in the Engineering Department. And young mathematics teachers who believed in Applied Mathematics had been hired to teach these courses.
And here's even an earlier story. In a January, Sunday Morning, New York Times, I read that the eminent mathematician, Solomon Lipschutz, had come out of retirement to teach a course in "Nonlinear Differential Equations" for American rocket engineers. At this time, America had not yet successfully launched a rocket. Either blew up on the Pad, or soon after launching. But the Soviets had many successes and an orbiting satellite. A good reporter asked Lipschutz about this. Lipschutz pointed out that Soviet mathematicians were adept in Nonlinear Differentials Equations; he believed this math helped them in their space work; but American engineering schools would not teach this subject. When asked what would solve this academic problem, Lipschutz uttered, "Only The Angel of Death!" -- meaning that when enough of these engineering profs were killed off, this course might get into American curricula.
I'll close with another true story. And I hope it worries you as much as it worries me.
A few years ago, The Mathematical Monthly, printed an alarming announcement: THE HALF-LIFE OF A COLLEGE MATHEMATICS CLASS IS ONE YEAR! That means that half of those studying math drop out each year.
This is worse than any epidemic or pandemic in recorded history. In the terrible "Black Plague" (or "Black Death"), peaking in 1248, half the people died in some regions. But this was not generally the case, and only for one year. But this math attrition apparently goes on year after year. For I've read no good report in the succeeding months and years.
I'll "spell it out for you". Consider 100 students entering a college to major in mathematics (not all in the same "class"). At the end of the Freshman year, only 50 are ready to start the Sophmore year. Then only 25 to start the Junior year. And only 6 graduate with a B.S. in Math (which a teacher should have to teach in Primary School, certainly in Middle School. Out of 100, 6%. But it's worse than that.
At the end of the First year of Grauate School, 3 left. At the end of of the Second year of Graduate School, to receive an M.S. in Mathematics (which you should have to teach High School Math), only 1 left out of 100. That person starts the Third year of Graduate School, with two years needed to obtain a doctorate -- but does not make it. 0% out of 100!
Do you realize what this means? Ask yourself, "What's the schoolin of those teach Mathematics in our schools?" There must be thousands of teachers out there who would not be allowed to teach Math only a few decades ago. The politicians and the Media must not want you to know about the situation, because there seems to be a coverup about it.
Are you ready to FACE THE MUSIC to demand that THEY LEARN TO PLAY THE MUSIC?
The same problem exists in relation to the other two "R's" of Education: Reading and Wroting.Student can read novels, short stories, drama, newsreports, but cannot read work instructions and must be trained for this.
They can write theme papers and letters, but cannot write proper work reports, and must be trained to do so.