Category: math and politics/philosophy

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Hey, you droogs,

There was an interesting post on the Whallah! blog about an article in the Associated Press, concerning the education of math teachers in public schools.

Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)

Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.

(more…)math ed math education math pedagogy multiplication public schools

The previous post was about the value of learning conceptually before you start practicing for skill.

There is an alternative argument that argues for the opposite. Many pedagogues try to plead the case that first you must teach the “basics” (meaning the basic skills, like the “multiplication facts”) before you can expect a child to acquire any meaning about it.

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While surfing some of the other math blogs in the blogosphere, I ran across a post in Michael Paul Goldenberg’s Rational Mathematics Education blog. Rational Math Ed is a gem of a blog, and is a must if you are a public school teacher or administrator.

In a recent post of his he mentions an article written by Paul Lockhart entitled, “A Mathematician’s Lament.” It was written in 2002, but has only gotten mass coverage recently, since it was featured on a post at the website of Keith Devlin.

For those of you who don’t know Keith Devlin, you are in for a treat. His writings are among the most lucid you will ever read about math. He makes very complicated things easy to understand. Please do yourself a great favor and visit his website.

You may have heard his lilting voice on NPR as “The Math Guy.” Devlin has also linked to Lockhart’s article, which is available as a free PDF download.

If you have any interest in math at all, even if you are not an educator, you will truly enjoy the enlightening thoughts that Lockhart shares with you. His appreciation, and enthusiasm for math, and teaching it are joy to read.

So take some time and revel in the passion Lockhart will enchant you with. Download the article now from the bottom of the post at Devlin’s site.

Please read both the Goldenberg and the Devlin essays about the article. They say everything I’d want to say, only better.

Photography by Santarosa, Justin Wong and Brian. Edited by Brian

(This was meant to be posted on Monday. Sorry about the lateness).

Many of us who struggle to learn math (yes, I am one of them) suffer from assorted challenges, like ADD, procrastination, lack of focus, depression, and other things that are or aren’t nameable.

That’s no big, deal, unless we chose to make it one. Every challenge is just that, a call to step up and beat it. So we constantly seek methods, systems and other tools to help us. That’s partly what makes a challenge fun - finding new, cool things that other people never think about.

Recently I was speaking with a friend of mine. He seems to get a lot done, and I always admired that about him. I mentioned that to him, and he seems to think that he doesn’t really. At least not naturally, anyway.

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Original photo by didbygraham

Q: When is a Compromise not a Compromise?
A: When it’s a Red Herring

We talked about “red herrings” in the previous posts about “The Case of the Missing Dollar.”

I occasionally do after-school presentations of MathMagic for the C.R.O.P. program in rural upstate New York. I’ve been participating in the program for years, as a local artist (magician). The program pays a very small honorarium, and a travel budget (Monday I drove 120 miles round-trip for peanuts) Most of the artists do it out of love of bringing their art to children who otherwise may never get exposed to it. It is a labor of love to all concerned, but it is a great mission.

The Creating Rural Opportunities Partnership (CROP) After School and Summer Program is a program which does just what it is named.

In it’s mission statement:

The goal of CROP is to provide intellectual development and opportunities for academic achievement for students grades K-8 with a strong focus on middle school.  In addition, CROP provides enrichment, health, wellness, life skills, recreational and cultural opportunities for 1260 middle school and primary grade students, community members and parents through a 21st Century Community Learning Center Partnership.

Over the last few years, funding for this excellent program has dwindled. Sound familiar? Art and after-school programs are typically among the first to get their throats cut when the government feels it needs to cut costs.
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Original Photo by Norsehorse Edited by Brian

Ah, I love it when readers beat me to the punch!

The comments to the original post pretty much sum up the paradox and it’s solution very well.

Khaled’s and Mark’s comments illustrate perfectly one of the things I wanted to point out about this puzzle. That point is:

Just because something is phrased a certain way is not reason to assume that that phrasing is the best way to represent the problem. And one way to critically examine the situation is to reframe it in a mathematical equation.

Khaled said, “Interesting how, once you assume that you can implicitly trust a given source, you can be led through any logic, or illogic, and have a lot of trouble pulling yourself back to a critical mindset.”

How true. Then Mark gave a good method to understand how to see where the paradox lies when he said, “I started to write an equation, because properly written equations can solve all counting problems, but then realized that this was pointless, because adding 2 dollars to the 27 dollars the guests paid did not reflect what happened.”

Exactly! The question was phrased to lead you to believe that because the facts were a certain way (which it accurately represented) you had to see it in a certain way (which was anything but accurate).

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Original Photo by Norsehorse Edited by Brian

There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this:

Three men go into a motel. The man behind the desk said that the room costs $30. So each man paid $10 and went to the room.

Later, the desk clerk realized that the room was only $25. So he sent the bellboy to the men’s rooms with five one-dollar bills.

The bellboy couldn’t figure out how to split five dollars evenly three ways, so he gave each man one dollar, and kept the other two for himself.

This meant that the three men had each paid $9 for their rooms, which makes a total of $27 dollars. Adding the two dollars that the bellboy kept would make a total of $29 dollars.

So where is the other dollar?

My advice to anyone trying to solve anything like this, or trying to think about anything at all, for that matter, is not to jump to conclusions.

Want to give it a try and add your thoughts in a comment? Go for it! I’m not asking for the solution, just some thoughts about the meaning of the puzzle - how it relates to life, logic, decision-making and understanding your world. I am not putting this up as a trivial puzzle.

My comments will be in the next post.

(Note: When I originally posted this, there were a few typos and other mistakes in it. If you busted your head over it till now, please accept my apologies. It should be correct now.)

(Or “The Seamus on Mitt Romney”)

Sometimes you read a story that just grabs you. I got one forwarded to me today that, at first glance, seems to have nothing to do with math. But since Math Mojo readers know that math is more meaningful than that stuff they shoved down your throat in school, I think you’ll appreciate this one. Bear with me.

In the summer of 1983, Mitt Romney took a vacation with his wife and five sons, to his parents’ cottage on the Canadian side of Lake Huron. The trip from Boston was twelve hours long.

According to an article in the Boston Globe by Neil Swidey and Stephanie Ebbert, Globe Staff, June 27, 2007:

“…Before beginning the drive, Mitt Romney put Seamus, the family’s hulking Irish setter, in a dog carrier and attached it to the station wagon’s roof rack. He’d built a windshield for the carrier, to make the ride more comfortable for the dog…

“… As the oldest son, Tagg Romney commandeered the way-back of the wagon, keeping his eyes fixed out the rear window, where he glimpsed the first sign of trouble. ”Dad!” he yelled. ”Gross!” A brown liquid was dripping down the back window, payback from an Irish setter who’d been riding on the roof in the wind for hours.

“As the rest of the boys joined in the howls of disgust, Romney coolly pulled off the highway and into a service station. There, he borrowed a hose, washed down Seamus and the car, then hopped back onto the highway. It was a tiny preview of a trait he would grow famous for in business: emotion-free crisis management.”

Yeah, otherwise known as “compassionate conservatism.” You know that to “conserve” means “to not use,” or “to use as little as possible.” To conserve your compassion for what? Your cronies? Your sons, who you conserve for your political agenda, but not to fight in a war that you support? Certainly not for your dog…
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While listening to “Morning Edition” on National Public Radio awhile ago, I heard a report about self-esteem in the workplace, and how Gen-Xers need constant praise for the simplest of accomplishments in order to feel appreciated.

Oh, my! The poor darlings are in the workforce now and now there are actually consulting firms that deal with how to keep the delicate little flowers happy, to retain them as workers, powered by constant praise, awards ceremonies and cookies and milk, I guess.

My first reaction was, “How idiotic. Just don’t hire the little turdblossoms in the first place, and the problem’s over.”

As usual, my first reaction is pretty useless. It seems that a great majority of gen-xers suffer from this self-esteem pathology, and if you aren’t going to hire gen-Xers, you are going to severely limit your pool of potential employees, some of whom may be genuinely talented for the job, despite their self-esteem problem.

So what do you do?

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(Continued from the previous three posts.)

the reader replied to my answer:

thank you professor for answering all of my future qustions, but u never answered my old answer though. What happens if i fail math 9 of coruse ill be end up in emath10 whats emath10 (doesn’t sound good though)Like do i get to go to collage but if u can’t answer that qustion ill ask someone else. Heres a qustion for you though what good paying job are there in this world without math like doesn’t require math because u told me everything involes math. but i am asking you to name some jobs thats don’t require math as a requirement. I am asking you all these qustions because i am scared the world might be a different place when i grow up so i am just prepareing for the future.

Professor Homunculus’s reply:

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