Critical thinking in Geometry

reply to post by davidgrouchy


i am not sure i understand you here. 80/10 is 8 as far as i know. there is no remainder.

Originally posted by delicatessen
i am not sure i understand you here. 80/10 is 8 as far as i know. there is no remainder.

Exactly.

I didn't understand it at first either.

The students are taught to answer the question how many clusters of 10's divides into 80. As cluster is a fuzzy term, any answer that is close to 8 equals a correct answer. They are taught that if they want a precise answer to use a calculator.

The justification behind this is that, bogging the students down in nitty gritty details is counter productive. The important thing is that they just understand the concept of division. The only real detail work is focused on how to imput a division problem into a calculator.

Maybe now it becomes clear why her grandfather started becoming very angry with me when I explained what they were teaching her. His first reaction was that this couldn't be true, and that I _must_ be missinformed. Like I said, a month later I got an appology from a very sad grandfather, who had lost some of his love of this country.

It seems like everytime I findout what's going on it's better if I just keep it to myself.

Sorry I forgot to address the specific issue of remainders.

Other sample problems were...

80 / 7

and

80 / 9

Correct answers, or I should say approved answers were 9, 10 or 11, in the first case, and 7, 8 or 9 in the second case. Just as long as the answer was "close." When I told her, "they didn't teach you how to carry the remainder? It's much easier. Here let me show you." And I started working it out. When she saw what I was doing, to carry the remainder, she stopped me and said. "I'll get in trouble if I do it that way."

She seemed sincere so I just helped her do the rest of her homework the way she was instructed.

But I dug into on my own later. It's called clustering, or clusters. Remainders not allowed.

I apologize if my last two posts are less than clear.
I'm becoming more emotionally distraught as I relive the experience.
I'll try to take up the subject again on the morrow.

I did a quick search and here is a news article from 2008
discussing what I'm talking about with long division
in New York.



Renegade parents teach old math on the sly

www.azcentral.com...

But in his fourth-grade class, long division wasn't on the agenda. As many parents across the country know, this and some other familiar formulas have been supplanted, in an increasing number of schools, by concept-based curricula aiming to teach the ideas behind mathematics rather than rote procedures.

Notice that the article uses the argument against the old method that the new method is "just another way of doing math" and that "more avenues" are more logical.

This seems to convince most parents. The very people who were not taught deductive reasoning with geometry, and don't have an absolute grasp on what emperical truth is. Additionally, while they state that it's just-another-way out of one side of their mouth, they are, in fact, not teaching the other-way. At all.

Oh, and wait until you see the New, new-math.
The egyptian method where a solution is not reduced to it's simplest form,
but remainders are retained in fraction form.

For instance.

5 / 2 = 2 and 1 over 2 or notationally 2 1/2

With this next generation an answer of 2.5 will get them "in trouble"

This is slated for the teaching of algebra.
The reasoning being that it is easier to intuitively work an equation when similar fractions appear on both sides.
That and irrational numbers and repeating decimals won't gum up the works.

reply to post by davidgrouchy


I appreciate this and could not agree with you more. Holistic critical thinking seems to raise more eyebrows than it should. My only addition to this discussion is that, in my view, the issue we face is not an increase in the human being's inability to think critically, but that it is an increase in the ability of the average person to make his/her inability to think critically a public reveal. 100 years ago, the average person was not involved in the public debate at any level. Most people in this society, and certainly in any other society, were not schooled in any form of critical thinking. They were taught a trade or they simply found work where it existed. A very small percentage of people had the advantage of a full education, and even fewer had the capacity to make their views known publicly.

I am of the opinion that the average human being still suffers from magically thinking, and always has. Critical thinking has always been anathema to the "wisdom of the common man". The only difference is that now days the intelligentsia is being forced to tailor their thinking to the marketplace of ideas that the common man has seized control of and refashioned for its own uses. If a professional thought leader doesn't submit to the "wisdom of the common man" then he/she ceases to be a professional thought leader, and that kind of economic reality definitely shapes the nature of thought within the marketplace of ideas. After all, in a free-market society, as the modern world has aggressively become, if thought can't survive commercially, then it can't survive at all.

Critical thinking survives and thrives, but it does so as fits and starts within small pockets of thinkers who spend the lion's share of their day working menial jobs, well outside the mainstream of knowledge exchange. They say that people get the government that they deserve. It's also true of the kind of truth they get.

Paraphrase...

People get the truth that they deserve.

Wow, now that's putting a fine point on it.

The thought is both repellant and frightfully plausible to me. My first instinct is to rally up a big counter thesis to what 'deserve' means, and start blaming all kinds of institutions, and corrupt business practices contaminating public education in a desire to have customers who are easily manipulated.

But that wouldn't be the whole truth would it. As some people do graduate with the ability to think critical in a geometric sense. Also parents should share some, if not a lot, of the blame for not being closely involved in what the children are being taught.

So yeah. I'm rolling that one around and starting to like the way it tastes better and better.

People get the truth that they deserve.

If a professional thought leader doesn't submit to the "wisdom of the common man" then he/she ceases to be a professional thought leader, and that kind of economic reality definitely shapes the nature of thought within the marketplace of ideas.

Also, this sentence is a thesis worthy of a degree in Economic Anthropology.
Too bad there is no such field to date.
It would simplify a lot of things if there were.

Interesting that this post appears right around the Illuminati geometry post. Critical thinking sure, but consider this:

It is a fact that Washington DC is laid out according to Masonic Geometric principals.
Every single aspect of the Swine Flu bandit seems to have been coded-the days, the addresses, even the amount of money he stole. Every aspect.
Mathematical and Geometric coding is used ritualistically by Freemasons.
You don't have to think at all to notice that it is much more than a coincidence that all of the bandits hits line up like that.
Maps and research into other things that the Illuminati have pulled, like JFK's assassination and Princess Di's "accident", are coded with the same geometry. It just requires people to find the right key. In the case of the other geometry post, the key is 4141.

That is critical thinking, not just posting a long, academic article trying to disprove what is clear as day to people that are awake enough to see it

I'm going to check out the "Illuminati geometry post" right now. Be back to comment after I'm more informed to what that thread is about.

[edit]

Ok, I found one posted by you, that predates my thread by one day. It was largely ignored, I'm sad to see. And the day after my thread a second one was started with a lot of pictures, and a lot more drama built into the paragraphs. It seems to be doing quite well. It looks to me like someone 'got' what you were saying, and remanufactured your post. The second one seems to be going quite strong with comments.

www.abovetopsecret.com...
Your post that predates mine.

www.abovetopsecret.com...
the one made after mine, that is more colorful.

As to the subjects in those posts, I'll comment on within the threads. I don't wish to drag that particular discussion into this thread.

My mother attended a 2 year medical lab technician program around 1938. Fast forward 50 years, she was shocked to find her 8 yr old grandson learning cell biology in a regular third grade classroom, at a level she hadn't learned until college.

Working through Geometry proofs or solving Algebra equations I think trains the brain to think logically. I think what happened in America, many citizens complained that memorizing basic number facts (such as 7+2=9 or 7x2=14) was too hard work, especially since the then new device, a calculator, could make knowing these facts obsolete, so they believed. Likewise fractions.Geometry proofs/solving equations just took too much effort! And unless students could translate effort into some kind of monetary reward, why bother to memorize, so they believed.

You mention your work with pipes. That is wonderful! Where would the world be without pipes!? And the people to repair them.

Come to think of it, practical Geometry is involved with pipes. And try to lay out a basketball court without Euclidean geometry. And even a rudimentary knowledge of non-Euclidean geo would help understand why airplanes fly the routes they do.

Yes, in an increasingly complex world specialization can be needed. But how fortunate you are to have a polymer physicist friend to talk to! We all don't need to know all the knowledge in the world; our true treasure is in meeting people with whom we can share the parts we either lack or for which we have a passion.

Formal education should be a starting point for knowledge. Informal education is what we should do the rest of our lives.

One of the foremost Topologist in the world is a friend of mine.
He just attended a conference in Tel Aviv over the summer and works with a fields medal winner,
in the development of a major breakthrough in Topology.

Anyway...

Back when he was teaching Math at the University of Alabama in Tuscaloosa
he was having a lot of trouble with the American students. He's Dutch by birth.
I was staying with him and we would talk about things like how a college degree
in America is equivalent only to a high school diploma in Europe, and things like that.

One day he comes home quite frustrated, as he is _trying_ to reach the students, but
his accent is a little thick, he has that classic wild haired geeky mathematician look and
he felt he was loosing them more and more. This was years ago, 1998 or 99, can't remember.

I said to him...
"Why don't you just stay up late and watch David Letterman. That way you'll be on the same wavelength
as your students."

He came home the next day so happy he was bouncing around. His gawky maleness had become an asset. He could reference things that the students had on their minds. And, most hilarious to me, he became a diehard Letterman watcher. So now when he's in America he watches two TV stations. C-Span, AND David Letterman.


David Grouchy

reply to post by davidgrouchy


A topologist friend! You really are truly blessed!

Letterman and C-SPAN...that would do

reply to post by davidgrouchy


Alright....

I am tracking a little better.

This thread deserves to show up on the recent threads list: I'm bumping it!

Yes, this is the kind of stuff that makes one want to weep.. I've envied the classical education of the early 20th century for a while now. At least I'm not the only ill educated buffoon though, which isn't much of a consolation for me or the carcass of Western civilisation.

Ugh... if you want to feel stupid, this thread is for you.