I recently came across an article in the Ayn Rand institute regarding a concept of teaching math in schools called “Whole math.” So I decided to research this a little further just to see what whole math really is.
Having gone to school many years ago, I never experienced this approach to math education. Math consisted of quantitatively working with absolutes and relatives, and reaching solutions in exact or otherwise accurate numerical results.
“Whole math” is a form of instruction that has kids develop their own methods of multiplying and dividing, ask questions of one another rather than of teachers, and learn that answers that are close to correct are good enough
Let’s hope none of the children who learn to use math this way ever work for NASA or the Department of Defense… or become scientists that discover new drugs…or build houses…or cars…hmm where is this going?
That’s a nice way to teach children to never be able to deal with reality.
Is someone playing a bad joke over there in America or what? I haven’t heard that much nonsense in a lifetime!
I got another one for you, let me paraphrase the introduction of a pre-calc text I was leafing through at the book store;
“Math is rendered boring to students by its rigid adherance to logic and proof. The concept of proof as an absolute is an out moded remnant of flawed 17th century thinking, proof instead depends on who and when you are.”
The book sought to teach mathematics through an examination of its non-essentials, without regard for truth, validity, or even correct answers.
“Math is rendered boring to students by its rigid adherance to logic and proof. The concept of proof as an absolute is an out moded remnant of flawed 17th century thinking, proof instead depends on who and when you are.”
Sure, “Pre-Calculus Mathematics in a Nutshell Geometry, Algebra, Trigonometry”
by George F. Simmons
It seems to be a popular seller, and there are a number of positive user reviews. Interesting that the author could make as clueless and horrific a statement of principle as that which you quoted, and yet put out a volume that might have some practical use.
Thanks for the quote and the reference. That is definitely one for the Horror File.
When I was in Algebra II, they introduced a mathematical entity called “Invisible numbers”. The creator was Rene Descartes. IS “invisible numbers” even valid?
Yes. Just a case of clarifying something that is real by using something that is not (such as the theorem stating that every polynomial of degree N has N zeros - though some of those zeros are imaginary because you cannot take the square root of -1)
When I was in Algebra II, they introduced a mathematical entity called “Invisible numbers”. The creator was Rene Descartes. IS “invisible numbers” even valid?
Though the use of “invisble” is not a proper translation of what Descartes said, he did use the term “false” to refer to negative roots of equations and he used the term “imaginary” to refer to the complex roots of such equations. I suspect that your book was referring to the “imaginary number” i, which is really a mathematical operator such that i*i = -1. This is a perfectly valid mathematical concept of method.
You have to be very careful when it comes to mathematics and physics in not treating some of the specialized terminology in too literal a way. “i” is not really “imaginary” and quarks do not have “charm,” as in being nice people.
You have to be very careful when it comes to mathematics and physics in not treating some of the specialized terminology in too literal a way. “i” is not really “imaginary” and quarks do not have “charm,” as in being nice people.
And there’s nothing immoral about irrational numbers.
I do not understand the point of your post. I previously wrote "and quarks do not have ‘charm,’ as in being nice people. " You seem to be repeating a good deal of what I said. Are you making a joke that I am just not getting, or do you have some point that I miss?
I was accepted into the California Academy of Math and Science for my high school years. While the science classes did have a progressive “environmentalist” angle they weren’t as bad as the math classes. To my dismay … we were used as guinea pigs for a new type of mathbook being developed called IMP (Interactive Mathematics Program). What IMP tries to do is teach the concepts without any basic formulas or foundations. It gives pendulum problems without teaching basic geometry or algebra. It gives calculus-required problems without introducing the Fundamental Theorem. It expects the students to work in groups…come up with their own “formulas” …and does not allow them to ask the teacher for any help. We always wondered why they even bothered hiring math teachers if all they did was read magazines at their desk. Also, no matter how smart a student is they cannot expect them to create formulas and identities which took brilliant geniuses years to come up with. Here is a link to their website:
Under “A Brief Description of IMP” there is a quote saying :
Dr. Webb has found that IMP students do as well as students in traditional mathematics classes on standardized tests such as the SAT. This is especially significant because IMP students spend about 25 percent of their time studying topics that are not covered on these tests.
I would suggest Dr. Webb find out if any of those students aren’t taking traditional math classes during their summer breaks at college campuses, which is what I had to do out of fear of getting behind in traditional math. Everyone at school hated this new progressive math program. We all complained about it to the administrators of the school. I recently found out that they now have elective courses which teach tradtional math along with these “IMP” classes at the school.
What is more worrying is that the IMP textbooks are now used in local unified school districts in Los Angeles.
It completely destroys the concept of passing along knowledge and building upon what those before you have discovered. If everyone used that sort of idea in every part of their lives men would be living in caves in the very near future.
" You seem to be repeating a good deal of what I said. Are you making a joke that I am just not getting, or do you have some point that I miss?