Wednesday, February 28, 2007

I Would Have Watched If I Had Known

But nobody told me! Thank goodness for YouTube.

Blog Slurping: Archiving Your Blog

This came in e-mail today and even though it is commercial (but free) software, I thought it worthy of posting. For Mac and PC. Clipped from
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The Connecticut River: The Comerford Development at Fifteen Mile Falls

As seen at scenic pullover on I-91 northbound, Barnet, Vermont
The Connecticut River, starting at the International Boundary, flows 380 miles to the Atlantic Ocean. In its course the river falls 1640 feet. In 1928, the New England Power Association started a two-year project to build one of the largest hydroelectric developments in the country. The dam is located in the towns of Monroe, NH and Barnet, VT and is 275 miles above the river's mouth. When dedicated on September 30, 1930 President Herbert Hoover pressed a button at the White House to start the first of four generating units.

This marker commemorates 75 years of continual operation of this project and is dedicated to the builders, operators, and neighbors of this first Fifteen Mile Falls Development.
(continued on other side)
Vermont Division for Historic Preservation -- 2006

(continued from other side)
The dam has earth embankments, a concrete gravity spillway and intake section, steel penstocks, and powerhouse. The reservoir has a surface area of 1093 acres at elevation of 650 feet above sea level and extends seven miles upstream. The dam is 2,253 feet long with a maximum height of 170 feet. The dam can pass flows through hydraulic operated sluice gates, flash boards, and stanchion bays as well as the turbines. The discharge capacity at full pond would be 99,000 cubic feet of water per second.

The powerhouse contains four turbines, at a combined rating of 216,800 horse power and the 162,300 kilowatts is enough to power 162,300 homes. At the present time hydroelectricity accounts for five percent of New England's power needs.


digital zoom


Rachmaninov Had Big Hands


Puzzling Week: Left and Right Queues

It has always been speculated that the left queue of most attractions at Walt Disney World tend to progress faster than the right queue. On the new Rock’N’Roll Coaster, cast members allow 50 guests into the left and 10 guests into the right queue immediately at park opening. Every minute after that 10 guests are added to the left queue and 12 guests are added to the right queue.

How long will it take to move the same number of guests to move through both queues?

How many guests will go through the left and right queues after one hour? How many guests will go through the left and right queues after a twelve-hour day?


Puzzling Week: The Tortoise and the Hare

The time has come to clear the hare’s bad name as a lazy show-off whose arrogance leads to spoiled opportunities. In fact, it is the conduct of the tortoise that deserves our scrutiny, for this leather-skinned reptile is nothing but a cheat! Recently uncovered information proves that the tortoise’s celebrated come-from-behind victory over the speedier hare was a resul tof shrewd deceit, not praiseworthy persistence.

Years after the famous footrace, the hare challenged the tortoise to a rematch on roller blades. The hare was able to skate at a rate of 15 miles per hour (mph) while the tortoise could skate at the rate of only 12 mph. Knowing he was slower, the tortoise made up a lame excuse for being given a 27-mile head start in the 165 mile race. These are the basic facts of the story.

Who won the race? Was the head-start fair? Explain your reasoning.


Puzzling Week: Speeding Tickets

In Massachusetts the fine for speeding is a flat fee of $100 plus $5 for each mile per hour above the 55mph speed limit. In Vermont the fine for speeding is a flat fee of $50 and $10 for each mile per hour above the 65mph speed limit.

If you were stopped for speeding right on the border between Massachusetts and Vermont, and stopped by both a Vermont and a Massachusetts trooper, which state would you like to be fined by?

Explain your reasoning.


Tuesday, February 27, 2007

The Connecticut River

Wells River, VT

Wells River, VT

Barnet, VT

Barnet, VT

Nearly my entire life I have had a thing for the Connecticut River. Until I moved to Vermont I have always lived near it. I have watched it flood as I rode my bike through the fields and meadows on its banks. I have learned the historic signifigance of it in Connecticut.

But in Vermont I know practically nothing about it. I need to return to learning more. A dream of mine is to spend time exploring the origins of this river as it rises out of the Three Connecticut Lakes in New Hampshire. I also have a dream to canoe down the entire length.

So here and there in the future in this blog I will add posts about what I learn about the river. And I will make plans to fulfill those dreams.


Cats Tuesday: Cat Symmetry

Cicking on most of the photos in this post will open a new window so that you can see the full-size image.

I teach mathematics to middle school students in public school and also to college students (which is why I am always late on Tuesday visits to everyone's blog: my algebra class is on Tuesday night after working all day!).

Symmetry is a topic in the middle school and I spent one vacation week playing with paint programs and photos of my Possum (of the kitten fight last week) and Scout (one of Amy's beagle dogs) learning how to show facial symmetry.

In each of the following sets of photographs, the original photo is in the middle. The left photo of each set shows each face with two left halves and the right photo shows two right halves.

I like how they all came out. I then continued with photos I grabbed from the web of Denzel Washington and Tyra Banks. I have included instructions for any of you who would enjoy playing with this. Just click the "read more" at the bottom.

One flickerite who saw these said that she has done them but she used quadrants (top/left; top/right; bottom/left; bottom/right) and the results were wild! I haven't had a spare moment to do that yet!

Thank you for reading this rather long post! Since public school is on vacation, I may get to see your posts during the day today! Happy blogging!

Here is Symmetry Amy (my middle daughter):

To do this yourself (I have cut and pasted portions of the paper I wrote):

In the April issue of Mathematics Teacher I found a wonderful article Fostering Mathematical Inquiry with Explorations of Facial Symmetry by Michael Todd Edwards. I immediately grabbed my digital camera and played! What follows here is a synopsis of his article. I offer my commentary at the end.

Collect photos of famous people (models, celebrities). The photos should only be head-on shots of faces. Scan or download the photos into a folder on your computer. You can use Word, AppleWorks, Paint and even PowerPoint for this study.

Cut the left side of the face. Duplicate it. Flip it horizontally and place it on top of the right side of the face. Align both sides.

The more symmetrical the face, the less change you will see in the new photo. The less symmetrical the face, the more change you will see.

Print copies for students to explore reflection symmetry. They will connect corresponding right and left side facial features with line segments. They will measure the line segments. They will then attempt to find patterns in the quadrilaterals that they have made.

Do attractive faces have similar types of quadrilaterals with similar sides? Are ratios involved? Study the angles of the quadrilaterals. Can you write an algorithm for "beauty"? What is "beauty"?

Students simply love looking at these photos and want to make them of themselves. Of course, parental permission would need to be obtained for that to happen. There are other questions to explore: What qualities in an infant's face make us feel protective towards them? What types of animal faces give us positive feelings?

I am very concerned about the emphasis on beauty in this exploration. It is a valid topic to explore, but be very careful in public school. Too many of our children, especially our girls, have negative feelings about their beauty and worth. Keep the discussion strictly mathematical and discuss symmetry. The students to whom I have shown this work only want to see the symmetry and think nothing of beauty. There is more than enough material in discussions of symmetry to fascinate us.
Tyra Banks

Denzel Washington

Monday, February 26, 2007

Math Anxiety Research

Researchers: Math anxiety saps working memory needed to do math

February 20, 2007
SAN FRANCISCO, California (Reuters) -- Worrying about how you'll perform on a math test may actually contribute to a lower test score, U.S. researchers said on Saturday.

Math anxiety -- feelings of dread and fear and avoiding math -- can sap the brain's limited amount of working capacity, a resource needed to compute difficult math problems, said Mark Ashcraft, a psychologist at the University of Nevada Las Vegas who studies the problem.

"It turns out that math anxiety occupies a person's working memory," said Ashcraft, who spoke on a panel at the annual meeting of the American Association for the Advancement of Science in San Francisco.

Ashcraft said while easy math tasks such as addition require only a small fraction of a person's working memory, harder computations require much more.

Worrying about math takes up a large chunk of a person's working memory stores as well, spelling disaster for the anxious student who is taking a high-stakes test.

Stress about how one does on tests like college entrance exams can make even good math students choke. "All of a sudden they start looking for the short cuts," said University of Chicago researcher Sian Beilock.

Although test preparation classes can help students overcome this anxiety, they are limited to students whose families can afford them.

Ultimately, she said, "It may not be wise to rely completely on scores to predict who will succeed."

While the causes of math anxiety are unknown, Ashcraft said people who manage to overcome math anxiety have completely normal math proficiency.

Science News Online

Week of June 30, 2001; Vol. 159, No. 26
Math fears subtract from memory, learning

Bruce Bower

By about age 12, students who feel threatened by mathematics start to avoid math courses, do poorly in the few math classes they do take, and earn low scores on math-achievement tests. Some scientists have theorized that kids having little math aptitude in the first place justifiably dread grappling with numbers.

That conclusion doesn't add up, at least for college students, according to a study in the June Journal of Experimental Psychology: General. On the contrary, people's intrusive worries about math temporarily disrupt mental processes needed for doing arithmetic and drag down math competence, report Mark H. Ashcraft and Elizabeth P. Kirk, both psychologists at Cleveland (Ohio) State University.

Math anxiety exerts this effect by making it difficult to hold new information in mind while simultaneously manipulating it, the researchers hold. Psychologists regard this capacity, known as working memory, as crucial for dealing with numbers.

"Math anxiety soaks up working-memory resources and makes it harder to learn mathematics, probably beginning in middle school," Ashcraft says.

He and Kirk ran three experiments, each with 50 to 60 college students. Experiments included roughly equal numbers of male and female students who cited low, moderate, or high levels of math anxiety on a questionnaire.

In the first experiment, Ashcraft and Kirk found that students with a high level of math anxiety enrolled in fewer math courses, received lower math grades, and scored worse on working-memory tests involving numbers than their peers did.

Math anxiety's disruptive effects on working memory appeared in the next experiment. In a series of trials, students first saw a set of letters to be remembered. They were then timed as they performed a mental addition problem. After solving it, volunteers tried to recall the letters they had seen.

High-math-anxiety students scored poorly on both tasks but especially on the mental addition. Their performance hit bottom on problems that involved carrying numbers, such as 47 + 18. However, when permitted to use pencil and paper during trials, they did as well as students without math worries did, indicating an underlying math competence.

The third experiment found that high math anxiety translates into poorer performance on an unconventional number-manipulation task that also taxed working memory. In some trials, for instance, students had to add 7 to each of four numbers that they briefly viewed, one at a time, and then verbally report the transformations in the proper order.

Earlier studies have found that math anxiety temporarily boosts heart rate and other physical indicators of worry, notes psychologist David C. Geary of the University of Missouri in Columbia. Psychological therapies that reduce math worries improve math performance, he adds.

"Ashcraft's study is the first solid evidence that math-anxious people have working-memory problems as they do math," Geary says.


Ashcraft, M.A., and E.P. Kirk. 2001. The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General 130(June):224.

Further Readings:

Miyake, A. 2001. Individual differences in working memory: Introduction to the special section. Journal of Experimental Psychology: General 130(June):163.


Mark H. Ashcraft
Department of Psychology
Cleveland State University
Cleveland, OH 44115

David C. Geary
Department of Psychological Sciences
University of Missouri
210 McAlester Hall
Columbia, MO 65211-2500

Elizabeth P. Kirk
Department of Psychology
Cleveland State University
Cleveland, OH 44115

From Science News, Vol. 159, No. 26, June 30, 2001, p. 405.


Sunday, February 25, 2007

Southwest Views of Barton Mountain

Viewed from the southwest on I-91. There are three "humps": the large on on the right, the middle and the small one on the left. I live beneath the middle hump under the cliffs. There is a cell tower hidden in the trees on the summit. Elevation: 2,235 feet (681.228 meters).

Naturally, as soon as I drove away I found a better view point 1/8 mile up the highway. But there was some traffic today, so I will go back another day for the better shots.

In this next photo I have crudely drawn a triangle. The cell tower is at the top, the cliffs are at the bottom. I am below the cliffs but you can't see highway from the house so you can't see my land here.


Highest Elevation on I-91

Interstate 91 runs from New Haven, CT to Derby Line, VT on the Canadian border.
1856 feet or 565.7088 meters
Sheffield, Vermont
Between exit 24 (Wheelock/Sheffield) and exit 25 (Barton, Vermont)


Saturday, February 24, 2007

My New Favorite Chocolate

Helene subs quite a bit in school and one day the topic came to chocolate. Her son lives in Belgium and sends chocolate home to her. The next time she subbed, she brought in a bar of this dark chocolate. It is great! Creamy and truly dark. Very rich, though, so my stomach hurt because I had too much.

Both of these pictures of the labels link to the manuafacturer's web site. For my gifts, you can google for an online retailer. Price is no object!

From the Jacques site:
In 1982, Jacques Chocolaterie was acquired by Stollwerck. To keep pace with the growing success of its products, the factory was repeatedly expanded, the last time in 2004.

At the end of the 19th century, when Belgium was in industrial and commercial euphoria, Antoine Jacques founded Jacques Chocolaterie in 1896.

In 2005, Jacques – whose key visual is a knight – and Callebaut – Barry Callebaut’s traditional brand for consumer products in Belgium – were merged to combine the best of two worlds: the name awareness of Jacques with the recognized quality of Callebaut inside. The result is a strong brand for anyone with a sweet tooth, distinguished by authenticity, a pioneering spirit and conviviality.


Friday, February 23, 2007

Photo Hunters: Soft

I can't explain why this is soft to me. But Mother-Daughter Night with the Women's Fellowship at church, held every April, is softness for me. Amelia and I have gone at least three times. She is my middle daughter and lives in Vermont. It's always a potluck supper and I fret for weeks about what we are going to bring (since I don't cook very well). But Amy always comes up with good and easy ideas that are the first dish to be finished.

Every woman got one of these tiny Beanie Baby type ducks on the first supper we went to. We had a Mary Kay party after the potluck. We were nearly on the floor laughing at each other with the things we were doing with the makeup! This duck has a special place in my heart. One day I will proudly have all three daughters at that dinner with me!

To make the image softer I used picnik (a free online photo editor) and GIMP. I don't know what I'm doing with either app, so I just kept clicking buttons until I had something I liked! I'm looking forward to seeing what other ideas people have for "soft"! Thank you for stopping by. Have a wonderful and peaceful week!


Thursday, February 22, 2007

Puzzling Week: Petals Around the Rose

Polar bears, they come in pairs.
They sit around the hole in the ice
like petals around a flower.

How many polar bears do you see? 10
How many fish do you see? 8
How many plankton do you see? 74

How many polar bears do you see? 6
How many fish do you see? 6
How many plankton do you see? 93

So have you figured out how it's figured out?

NCTM's Illumination site has a wonderful lesson for this puzzle.

Nope! No spoiler here!
Tradition requires me to never post the solution.
After you figure out the answers, can you derive any equations to solve this puzzle for any combination of dice tossed?

When you solve the puzzle, you deserve membership in the Polar Bear Club!


Wednesday, February 21, 2007

Booking Through Thursday: Writing in Books, Part Two

A couple weeks ago, we asked about how you take care of your books, with one of the questions asking whether you write in your books. Well, what about books that are meant to be written in? Like, say, a journal or diary? Do you keep one? Obviously, if you're answering this, you have a blog--do you just let your blog be your journal? Or do you also keep one for private stuff also?
Journals are a women's tradition. If our American history texts were written from these sources, our country would most likely be different. Our foremothers from the Mayflower (the foremothers about which I have the most knowledge) kept journals. They had agreements with one another that upon the death of one, another would come to their home, find the journal and destroy it (usually by fire, which leaves no trace).

Journals are confidential. I would categorize blogs as public commentary: writing that we don't mind others read. People reading my blog can easily conclude what my political and religious beliefs are. But they won't be reading my journal.

I keep journals periodically: during tremendous times of stress or during transitional times. They are in several hand written books. When I lived in Connecticut I had a network of friends to whom I vowed to destroy their journals upon their death. They gave me the same vow to destroy my journals, unread, on my death.

We also swore that my move to Vermont would never destroy our bonds of friendship, but it did. But Sue, my friend since 5th grade, is in Vermont. She can now function as my "journal-burner" and I can do so for her, continuing our centuries old feminine tradition.

Thank you for stopping by. I look forward to reading the discussion this week on this topic!


Tuesday, February 20, 2007

The Backhoes Are Out Again

Driving up to the college this afternoon, just like last week, I noticed that the backhoes had been out clearing the snow from the roads again. Pushing it back into the fields. The shoulders had already been plowed clear after the snowstorm last week. But now there is five or ten feet more cleared out. There is lots of room now for more snow.

The question: Why? I've been hearing rumors all week of a storm on Thursday. But the weather service says that only a clipper is coming through. Just 2-4 inches. That doesn't justify all this work. This bulldozing of snow was done in every town I traveled through today.

On my road a bulldozer is cutting out all the snowbanks from the village on up (and doing it at 9PM). I hope they come up here because my mailbox is still buried. Jon's plow can't possibly clear it out. I'm not getting any mail again and will have to race home tomorrow after school to pick it up at the post office.

The mountains of snow in the playground at school are humongous. It makes recess great fun for the kids. But they are trying to dig tunnels and caves in the piles and we can't allow that.

The kids are jumping off of shed roofs, house roofs, store roofs, trees. All for the great fun of landing in the feet deep piles of snow that cushion their falls. I have even heard of kids snowboarding off of their house roofs!

One pair of boys (from my homeroom, of course!) even took their sled off a cliff. It was super duper cool, they reported. The front of the sled rose up in front of them as they floated to the ground.

People are still shoveling off their roofs. I wish they would hire these kids to do it so that the kids could get their thrills safely. Sledding off of a mountain cliff seems a bit risky to me.


Monday, February 19, 2007

Cats Tuesday: Kitten Fight

I had been in Vermont helping my father the weekend after 9/11/01 when my sister brought a feral kitten to him. He did not want the cream tortie baby but I fell in love with her. I brought her home and named her Possum. Coincidentally Danielle had adopted Lester, a large ginger tabby kitten, on the same Saturday.

The following photographs chronicle their first meeting:

Poor Lester!

I made my first comic of this kitten fight. If interested, you can view it at meeyauw's Comics. Unfortunately, I misnamed Lester and called him Jasper. A new window will open when you click the link.

Thank you for coming by. Please remember I work late Tuesday nights so I won't be by to see your stories until later.


Stray Bars

Thank you again, Sue!


Students' View of Intelligence Can Help Grades

From National Public Radio - Morning Edition, Thursday, February 15, 2007. See . Our thanks to Greg Gierhart for bringing this piece to our attention.

Your Health: Students' View of Intelligence Can Help Grades
By Michelle Trudeau

A new study in the scientific journal Child Development shows that if you teach students that their intelligence can grow and increase, they do better in school.

All children develop a belief about their own intelligence, according to research psychologist Carol Dweck from Stanford University.

"Some students start thinking of their intelligence as something fixed, as carved in stone," Dweck says. "They worry about, 'Do I have enough? Don't I have enough?'"

Dweck calls this a "fixed mindset" of intelligence.

"Other children think intelligence is something you can develop your whole life," she says. "You can learn. You can stretch. You can keep mastering new things."

She calls this a "growth mindset" of intelligence.

Dweck wondered whether a child's belief about intelligence has anything to do with academic success. So, first, she looked at several hundred students going into seventh grade, and assessed which students believed their intelligence was unchangeable, and which children believed their intelligence could grow. Then she looked at their math grades over the next two years.

"We saw among those with the growth mindset steadily increasing math grades over the two years," she says. But that wasn't the case for those with the so-called "fixed mindset." They showed a decrease in their math grades.

This led Dweck and her colleague, Lisa Blackwell, from Columbia University to ask another question.

"If we gave students a growth mindset, if we taught them how to think about their intelligence, would that benefit their grades?" Dweck wondered.

So, about 100 seventh graders, all doing poorly in math, were randomly assigned to workshops on good study skills. One workshop gave lessons on how to study well. The other taught about the expanding nature of intelligence and the brain.

The students in the latter group "learned that the brain actually forms new connections every time you learn something new, and that over time, this makes you smarter."

Basically, the students were given a mini-neuroscience course on how the brain works. By the end of the semester, the group of kids who had been taught that the brain can grow smarter, had significantly better math grades than the other group.

"When they studied, they thought about those neurons forming new connections," Dweck says. "When they worked hard in school, they actually visualized how their brain was growing."

Dweck says this new mindset changed the kids' attitude toward learning and their willingness to put forth effort. Duke University psychologist, Steven Asher, agrees. Teaching children that they're in charge of their own intellectual growth motivates a child to work hard, he says.

"If you think about a child who's coping with an especially challenging task, I don't think there's anything better in the world than that child hearing from a parent or from a teacher the words, 'You'll get there.' And that, I think, is the spirit of what this is about."

Dweck's latest book, Mindset: The New Psychology of Success, gives parents and teachers specific ways to teach the growth mindset of intelligence to children.


Sunday, February 18, 2007

What is this???

What is this???, originally uploaded by meeyauw.

This is so scary! It's on the attic ceiling (roof?). It looks like a vampire bat took a mouse up there, sucked it dry and left it! I can't stand this and need to know what it is!

Uploaded by meeyauw on 18 Feb '07, 11.02pm EST.


Happy Valentine's Day!

Happy Valentine's day!, originally uploaded by sirgawins.

I got a Valentine from SirGarwins! I was included with dozens of others, but I was finally remembered! I don't know how Sir did this, but it's fantastic. He lives in eastern Europe.

Click on the photo and see if you can see my name (meeyauw)! I have added a note that you can see when you mouse over it on the flickr photo page.

Damn it. Some people just don't $%^ get it. Then a stranger from eastern Europe does.


Mystical Moose

mystical moose, originally uploaded by Steve took it.

Yes, I am flickr'ing tonight and some photos are simply too outstanding to ignore! I don't know where this photo was taken but it could have easily been here.


The Little Catepillar

DPP_0006, originally uploaded by beetlechickster.

You have to visit the large version of this photo at:


Time Graph: Solstice to Solstice

Time Graph: Solstice to Solstice, originally uploaded by jbum.

from the flickr photographer jbum:

I thought the winter solstice would be an appropriate time to make another one of these graphs, and here it is.

To build this graph I collected about 40,000 thumbnails of photos that have been tagged “Sunset”.

I positioned each thumbnail horizontally according to the day it was taken, and vertically according to the hour it was taken.

By making each photo translucent, I created a “hot spot” which shows when the most photos were taken, each day of the past year.

The bright band shows the approximate time of sunset for each day for most of the photographers (who are in the northern hemisphere). You can see that as the year progresses, the time of the sunset changes.

The deepest dip in the band corresponds to the summer solstice (about June 22), and the high parts on each end correspond to the winter solstices (about December 22).

The photos which are not in the bright area are anomolous for various reasons. They may not be photographs of the sunset or they may have incorrect time information in the metadata.

Uploaded by jbum on 23 Dec '06, 3.14am EST.


Collapsing Barns

A gaping hole is left in the barn owned by Denis and Claire Michaud, of Hardwick, after the roof collapsed under the weight of snow.
Caledonian Record

One of the disturbing consequences of the Valentine's Day Blizzard is collapsing barns. These cows survived but I have counted over 100 cows in the state who have died from the collapses or have been sent to slaughter because there was no place to house them when the barn was destroyed.

People with empty barns have been asked to donate space for homeless cows.