1. paul and john
treemiesters
balloonhands
noo wayy
laughing
most of our way
through the monotony
and when that doesn’t work
i’m locked into the bathroom
singing beulah land

2. burning walnuts
for the pesto
twice

3. sheet tray of potatoes
450 degrees
meets bare arm
shock of heat
pink patching and spreading across skin

4. the undeniable
mathematical
and scientific approach
to poetry
including charts and
computations

5. how quick
sun slips
stopping
halfway there
to fetch bike light
from bag
to be seen
in the thick dark

6. the poem
that killed
the whole room
with sister in the last stanza
i don’t need to tell you
what she’s doing
in the doorway
at the rescue missison

7. this is not a love affair
but i am tortured and passionate

8. the essay
that refuses
to write itself

9. gelato for dinner
kitchen laughter for dessert

10. scalloped hanky
of so many feathers
tucked into
back right pocket

I regularly watch the Science Friday video podcast. This week they had an interesting piece on potamology (OK, I just learned that word and wanted to use it in my post: potamology is the scientific study of rivers). The podcast showcased the work Christian Braudrick and Bill Dietrich of University of California, Berkeley, who achieved what had not been done before; they were able to create a meandering river in a laboratory setting.

Such rivers lazily snake back and forth through a gently sloping field. They change shape over time by continually eroding the outer bank of each curve and depositing silt on the inner bank. Occasionally two bends in the river come together, changing the topology of the river, and ultimately leaving behind an oxbow lake.

In passing, the narrator mentioned a very interesting mathematical fact about meandering rivers. It turns out that the size of a river cannot be determined by its shape on a map. In particular, if you looked at an aerial snapshot of a meandering river, you would not be able to tell whether it is the Amazon or a small neighborhood stream! I had to investigate this stunning fact.

It appears that nature forces certain geometric relations on the features of the river. Let denote the length of a meander (the “wavelength”) and be the width of the river (see my drawing below). The curves in a meander are roughly circular (rather than sinusoidal, for example). Let denote the radius of curvature of a bend.

It turns out that these variables are almost always related in the following way:

.

I was stunned to learn this. What a beautiful fact. To see a remarkable scatterplot of the first relationship, see Figure 12.16 in The environment: principles and applications, By Chris C. Park (p. 374).

From what I can tell, the observation dates back to a 1960 paper by Luna Leopold, the Chief Hydrologist of the USGS.

I have no idea why there is a linear relationship between these variables, but it seems to me that if you know that such a relationship exists and you knew one of the constants, then you could estimate the other one. For example, suppose you knew that . In each cycle, a river winds clockwise around one circle of radius , then counterclockwise around another circle of radius . In doing so it will produce a wavelength of roughly .

[Images by:prefers salt marsh (CC BY-NC-ND 2.0), petercastleton (CC BY 2.0), molas (CC BY-NC-SA 2.0), stuant63 (CC BY-NC 2.0)]

1-2-3-4

The National Bureau of Economic Research has released their report on whether (and how) No Child Left Behind (NCLB) has helped increase student achievement. They used NAEP data and compared states that had accountability testing in place prior to NCLB with those that did not when the law was passed. It turns out that math seems to have held the greatest opportunity for change:

We find that NCLB generated large and statistically significant increases in the math achievement of 4th graders (effect size = 0.22 by 2007) and that these gains were concentrated among white and Hispanic students, among students who were eligible for subsidized lunch, and among students at all levels of performance. We find more moderate positive effects in 8th grade math achievement. These effects are concentrated at lower achievement levels and among students who were eligible for subsidized lunch. In contrast, our results suggest that NCLB had no impact on reading achievement among either 4th or 8th graders.

While the findings are great news for some kids, the authors make clear that these results also illustrate that, in fact, lots of kids are still behind. And, of course, the report does a good job describing what has happened but not why (the authors suggest the next directions for follow-up research).

If reading this kind of research is your thing, note that the report has a comprehensive review of the literature on this topic.

Welcome to Rose Home School :: Growing Smarter Roses. This blog will be maintained by mammarose and daddyrose. We are proud parents who plan to home school, and we are getting ready now.

Rose Homeschool :: Growing Smarter Roses will be a blog all about everything we can find and do and create and share about home schooling, and all around making sure your child is open to learning anything and everything. Our home school blog will begin with preschool education and development and grow over time to eventually offer curriculum up to 12th grade and college prep. However, at the time of the creation of this blog, we are the parents to an 8 month old, so we are not exactly focused on higher levels of education just yet, though it isn’t far off, promise.

Our category structure (at this time, subject to change and grow as this blog grows and develops) is:
ABCs & 123s | Art & Craft Projects | Coloring Pages
Game, Song & Exercise | Math | Misc. | Spelling & Reading

These will grow and populate quickly, so enjoy the flow of shared knowledge, and may you have a wonderful journey in educating your child. We hope we are able to help you along the way!

So, I had this math test today… I so failed it. I had this HUGE nervous breakdown this morning too. OH MY GOSH. BOYS. GAH.

Lame math test.

I created three little math lessons in Scratch. In order to capture them with Jing, I had to put in a “wait 10 sec block.” I finally accomplished my goals, though!
The lessons are my way of trying to explain the different quadrants so that kids can figure out how to create better using Scratch. Oh, and I had to use tinyurl.com to shorten the long links that Jing gave me!
First one: http://tinyurl.com/ykkknlj
Second one: http://tinyurl.com/yz8wyo8
Third one: http://tinyurl.com/ygcgta8

I wrote before how to compute the expected number of coin tosses needed to throw a head:
http://bbzippo.wordpress.com/2009/11/05/expected-number-of-coin-tosses/

I mentioned that I didn’t have a rigorous solution for N heads in a row, and I was asked to at least present a non-rigorous one.
Ok, let’s say we know the expectation to get N heads in a row and it equals to E(N). Now we want to compute E(N+1). How many tosses on average do we need to turn N heads into N+1 heads? With the probability 1/2 you need only 1 additional toss. But if you fail to throw a head with that one toss, you need to start over and end up tossing the coin E(N+1) times on average, plus that 1 time that gave you a tail.
So E(N+1) = E(N) + 1/2 + 1/2*(E(N + 1) + 1)
Or E(N+1) = 2*E(N) + 2
Since we know E(1) = 2 then E(2) = 6, E(3) = 14, etc.
It’s not difficult to come up with a non-recursive formula:
E(N) = 2*(2^N – 1)

Why is this solution not rigorous? Because you can’t manipulate expectation values like this without saying a lot of additonal blah-blah about your random variables being independent or dependent, and the expectation being a linear function, maybe about Markov chains, etc.

There are many examples of classroom games for practicing math facts with speed. But here’s a version that keeps students active, yet is simple enough for teachers to assess everyone individually. The kids call it Rocket Math, though different from the curriculum published  by D. Crawford. This is a game.

Students get in two lines. Head each line with a chair for the “pilots”.  Reveal a flash card to the pilots and have them call out the answer. The student who first calls out the correct answer gets to take the other pilot to their “wing”. The next two are up. Eventually, the rocket will become unbalanced and be taken down by the winning team!

I’ve noticed that students aren’t over-competitive with this game because they come up to challenge a different person most of the time. If anything, they get a general sense of whether they need to practice their facts in comparison to others in class. Years ago, I had a girl who struggled in math and was initially defeated in each play of Rocket Math only to come back after a long weekend with every fact down pat and ready to show it. Memorizing math facts is a task that is more representative of perseverance or “book smarts” than the ability to solve higher-order algorithms.

After watching the 3-minute video, you can see that teacher has a strong grasp on a few typical assessments:
1. Which students can state multiples of 2, 1 and 0 with automaticity?
2. Which students know their facts, but struggle under pressure?
3. Which students count their multiples to get an answer?
4. Which students struggle with confidence?
5. Which students watch the pilots while waiting in line to get extra exposure?
6. Which students miss the same fact repeatedly?

I have used “Jumping Calculator” and “Rocket Math” as primary practice of facts in the classroom. The result is total buy-in from students, as well as kinesthetic, visual and auditory presentation. Most important, the games are quick and free up time in the classroom to teach math as a language and subject. It’s nice to not spend 1/3 of the year on memorizing basic facts!

MATH APPS:

Basic Math

Cost: Free

Description: Offers basic addition, subtraction, multiplication, and division problems with three answer choices.

Application: Good for very low level math, not so good for high school

Brain Blaze Divide

Cost: Free

Description: Offers division problems by level-1-12. six answer choices per problem, and shows a progress screen with areas that need work.

Application: Good app for high schoolers to test basic division skills

Pop Math Lite

Cost: Free

Description: You must choose the bubbles with corresponding values, so you must choose bubble 1 (1+1) and bubble 2 (2) in order to advance.

Application: Fun app, also good to test basic math skills

iMath Test Lite

Cost: Free Demo/ the free version doesn’t do much but could be worth the investment for the full app

Description: Tests more complicated multiplication, division, addition and subtraction skills.

Application: Good for high school

Please note I would be away for Thanksgiving so I might not tweet as much. But before I do, here are the tweets of the week.

Test prep companies are catering to a new demographic: 3 & 4 year olds http://bit.ly/6G8iPP | I think this is a little ridiculous. Just let the kids be kids. They have a lot of schooling and test prep ahead of them.

Student assaulted during Kick A Jew Day http://bit.ly/90mVDM & Red-haired boy beat up on Kick a Ginger Day http://bit.ly/7Mso9l | I find both of these instances very disturbing. How could kids be so cruel? Here is the bigger problem (regarding the Kick A Jew Day). “But one grandparent said he just chalks it up to kids being kids. ‘Personally I think it’s a non issue,’ said Raymond Brusca.” Bullying should not be accepted as a fact of life. This is when you can’t let kids be kids.

White House Begins Campaign to Promote Science and Math Education http://bit.ly/578Zur | We definitely need more Bill Nyes or Mythbusters, people who make science and math cool and exciting and Obama is absolutely right. Scientists and engineers should be recognized for their achievements and viewed like role models like athletes do right now. I guess what I’m envisioning is kind of like those Intel commercial lately which show scientists like Ajay Bhatt (one of the people responsible for the USB) as rock stars. People do respond to efforts like that. Again going back to the Intel example, they couldn’t keep up with the high demand to give away Ajay Bhatt t-shirts and had to raffle them off and without a doubt is one of Intel most successful marketing efforts. I don’t know how much people in going into science and math fields because of that but it is a start. Society has made the most progress when the scientists and engineers’ innovations are encourage and celebrated.

Have a great Thanksgiving and as always you can follow me at my twitter account, (@gmatlinks).

I found the following quote from John von Neumann in a book as a motto (I don’t remember which one, maybe David Joyner’s Adventures in Group Theory, but need to check):

Young man, in mathematics you don’t understand things. You just get used to them.

I liked this very much. My girlfriend (she’s a math teacher and also doing a PhD on teaching math) liked it too. So we were happy to see that quote…

…Then few months later the quote came up again in a discussion, and I realized that we had two different interpretations of it. Her take:

• This is how (rather badly) math is taught nowadays. We teach mechanistic algorithms and the pupils do not need to know why do the recipes work as long as they can carry out the calculation, they get good marks.

My take:

• As you dig deeper into math or go higher into the thin air of extreme abstraction (choose your favourite metaphor) the mathematical objects are no longer directly grounded in our everyday 3D physical bodily experience. You can understand number 3, just 3 sheeps or 3 fingers, easy, but how about generalised reciprocities in number theory? No matter how abstract the objects are, if you meet them regularly, they become good friends and you don’t care about their ontological status, they become part of your world.

So who is right? What did the old master mean?

Little investigation reveals that it was said to a young physicist who complained when having difficulties understanding a mathematical method… Still, both explanations seem possible.

A friend of ours once described baseball as a “statistics generating device“.  What with at bats, hits, runs, RBIs, wins, losses, saves, ERA, putouts, assists, errors, etc.  there is no shortage of data you can collect from your average baseball game.  Countless hours are spent arguing over “Was Willie Mays faster than Mickey Mantle?” or “Who was a better hitter: Barry Bonds or Babe Ruth?“

No Contest.

Invented by Bill James, Sabermetrics is the use of statistics to analyze players/teams in baseball (and other sports).  In the last 10 years it has become popular to use this mathematical analysis (instead of just experience and gut feelings) to decide things like which players to hire and fire.  Some teams swear by this approach, but it’s also controversial since sabermetricians argue that things like RBI aren’t very important in studying players.

This

Wednesday, December 2nd at 5pm in PHSC 1105

John Paul Cook, a grad student in the OU math department, will talk about some of the math and history behind sabermetrics.  He has promised that you don’t need to know about baseball or statistics!  He also claims that some of the same mathematics can be used to study other sports (maybe he’ll tell us why the OU football team has been stinking it up this year!).

As always, Free Pizza!

Also, the flyer is here.

Sabermetrics not Sabertoothmetrics

The following piece of news, in my humble opinion, deserves more mention in the math blogosphere than it has garnered so far. At the center of the story is an Iranian student of mathematics, Mahmoud Vahidnia, who was invited to a meeting between Iran’s Supreme Leader Ayatollah Ali Khamenei and the country’s scientific elite on Oct 28, 2009. An excerpt from a Guardian report on what transpired during a (perhaps, routine) question and answer session:

“I don’t know why in this country it’s not allowed to make any kind of criticism of you,” he told Iran’s most powerful cleric, who has the final say in all state matters. “In the past three to five years that I have been reading newspapers, I have seen no criticism of you, not even by the assembly of experts [a clerical body with the theoretical power to sack the leader]. I feel that if this doesn’t happen this situation will lead to discord and grudge.”

Vahidnia, who achieved nationwide recognition two years ago by winning Iran’s annual mathematics Olympiad, made his remarks at a meeting between Khamenei and the country’s scientific elite. They came after the supreme leader asked at the end of a question-and-answer session if anyone else wanted to speak. He chose Vahidnia after seeing him being pushed down by officials when he stood to ask a question.

Referring to the post-election crackdown sanctioned by Khamenei, he asked: “Wouldn’t our system have a better chance of preserving itself if we were using more satisfactory methods and limited the use of violence only to essential circumstances?”

I discovered the above piece of news “accidentally” via the Colbert Nation.  The Associated Press also did a report. I wonder if our Iranian readers (if there is any!) could furnish more information on this.

7-1 & 7-2:  Do on p. 191-192 # 26-38.  Show work for all.

1. Today, we will review addition and subtraction math facts.
2. Play Rock Hopper at http://www.eduplace.com/kids/hmm/swfs/rockhopper_grade3.html.
3. Take the practice quiz here: http://www.eduplace.com/kids/hmm/practice/templates/rules.jsp?ID=hmm07_ep/gr3/0407&GRADE=3&UNIT=2&CHAPTER=4&LESSON=7&UNIT_TITLE=Addition%20and%20Subtraction&CHAPTER_TITLE=Add%20Whole%20Numbers 

Most people I talk to support “sustainability” and “social justice” goals. Ecology teaches us that we need to frame these human aspirations in relation to the biological capacity of the earth: the energy, and resources that support our burgeoning populations and economies.

As human society sets out to achieve ecological sustainability and social justice on earth, we face two serious challenges: One, humanity already over-consumes the biological capacity of the planet; and secondly, humanity suffers from a vast gap between rich and poor.

Free-market fundamentalists claim we’ll close this gap, and restore the planet, by growing our economies, perhaps with “green” jobs, but this business-as-usual approach fails to account for ecological reality.

Do the Math

According to data compiled by the UN, the Global Footprint Network, and Dr. William Rees at the University of British Columbia, total human consumption already exceeds the earth’s capacity by 30 percent. This is known as biological “overshoot.” The UN estimates that most natural services to human societies – forests, fish, fresh water, and clean air – are now declining annually. As human population and consumption grow, our collective overshoot increases.

Meanwhile, the wealthy 15 percent use about 85 percent of the resources – the total energy and materials, the “stuff,” that Earth provides. The “wealthy” includes anyone who has a home, job, transport, access to education, hot showers, convenient fuel, and food every day: people in the so-called “developed” world. If you have those things, you live among the wealthy 15 percent, who use most of the world’s resources.

There is more to social change than the biophysical numbers, but any serious ecologist or justice advocate needs to know how resource overshoot limits our choices to achieve sustainability and social equality. Let’s do the math.

Nature’s rules

Start with these facts:

1. Total human consumption =

130% of Earth’s capacity

2. The rich 15% use 85% of the stuff;

while the poor 85% use 15% of the stuff

If we define the sustainable, equitable consumption per person as “1 unit” of stuff, the facts above mean that an average 100 people use 130 “units.” To be sustainable, the total consumption of 100 people needs to be 100 “units” of stuff. And to achieve social justice, each person would use 1 unit. But of course, that’s not how our world works.

Total human consumption of a 100 average people equals 130, not 100, and since the rich 15 use 85% of everything, they use 110 units (130 X 85%). The poor 85, meanwhile, use the other 20 units of stuff.

Therefore:

The average rich person uses:

110/15   =    7.333  units of stuff

The average poor person uses:

20/85    =    0.235  units of stuff

How are we doing? Not too well. The average person in the developed nations consume 30-times more than the average working poor, dispossessed, and starving multitudes. And meanwhile, we already use more energy and materials than Earth can annually supply.

So if we want a world of ecological sustainability and social justice, then we must face some difficult facts. To start with, humanity must consume less stuff.

We must reduce the total human consumption for 100 average people from 130 to 100, and then, we must share those 100 units of stuff that the earth can provide.

If we were able to achieve that, then everyone would simply use 1 “unit,” the ecologically sound, socially equitable amount of energy and materials. As we know, in our current situation, we consume more than the earth’s capacity and the rich take almost everything.

Another way to understand this is to imagine humanity as a family of seven people, that earns $100,000 per year but spends $130,000, and one member of the family alone spends $110,000. This family is going broke because one person, 15% of the family, is pigging out.

Dysfunctional? Yes.

Sustainable? No.

Reality bites

By these figures, we see that to achieve sustainability and social justice, the rich would have to consume about 1/7 of what they currently consume. If that happened, the world’s poor could increase their consumption by about 4-times.

That’s the straightforward, biological and physical reality we now face.

Under our current economic system, achieving sustainability and social justice might appear impossible. However, using less and sharing represent nothing more than common decency, the sort of behaviour we supposedly teach our children.

We hear from our alleged leaders, of course, that this is politically and logistically impractical. So, instead, we labour under the delusion that we’ll make the world “equitable” by growing all the economies until the poor, developing countries achieve greater wealth. We’ll make our economies “sustainable” by creating “green” products, hybrid cars, and renewable energy.

If the earth was an infinite storehouse and could provide infinite sinks for our garbage, that would be a reasonable plan. But the earth is not infinite. It remains unequivocally finite.

And Nature doesn’t really care about our social theories, economic presumptions, or our whining about wanting more. Humanity is now like a clever but obsessive adolescent, who must be warned: “Sorry, this will sound really annoying, but there are real limits to your freedom to consume.”

Suppose we soften the blow for the rich world, the spoiled child of humanity. We could live within the earth’s capacity if the rich simply cut their consumption in half and the poor could then double their current consumption. Here is how that would work, by the numbers:

The average rich person would use 3.67 units of stuff, instead of 7.33. And then, the average poor person could use 0.53 units of stuff (slightly more than double), instead of 0.235. This equation alone would feed the 1-billion starving, and end world hunger.

Our equation for 100 average people would then look like this:

Rich consumption:

15   X   3.67   =   55 units of stuff

Poor consumption:

85   X   0.53  =   45 units of stuff

Total  =  100 units of stuff for 100 average people.

In this scenario we would be sustainable and the world’s poor could grow their economies to the point of doubling their use of energy and resources.

If we achieved this simple change in human consumption patterns, we could exist within the carrying capacity of the Earth.

Is this difficult to imagine? Is it fair? The ratio between the average rich and poor would then be about 7-to-1, far more equitable than the current 30-to-1 ratio. To achieve this, the rich only have to give up half their consumption. That could be achieved primarily by eliminating wastefulness, planned obsolescence, plastic packaging, exotic holidays in jet airplanes, and the most wasteful of all human inventions: cars.

Growth fundamentalists will grumble at this because they imagine a world in which they can look forward to being richer, consuming more, not less. However, biophysical reality sets the limits. We do not get to rewrite the laws of biology and physics for our own convenience.

Two problems remain

Even if humanity could make this simple change – the rich cut consumption by half, the poor double their consumption, and we achieve sustainability – we still face two problems.

First of all, we currently add 75 million new people to the planet every year. What stuff are they going to use?

To live decent lives, these new humans would need the infrastructure services roughly equal to a nation such as France, Germany, or Egypt. And then again, every year.

Human population growth proves to be both an ecological and social justice issue. The planet is finite. I’m mystified that some people find this so difficult to accept. Since we have already reached biological overshoot, human population growth pushes us farther out over the cliff.

For example, we now face declining oil and fish yields, but few people realize that oil and fish yields per capita peaked in the 1970s, thirty years ago. Each day, as we add more people and degrade our ecosystem, the average human – regardless of stock market paper wealth – becomes biophysically poorer.

Like the over-spending family, having a new baby every year, and spending more, while degrading their assets, every year we have less to go around and more mouths to feed.

To achieve sustainability and social justice, we must stabilize human population. We are breaking the back of the natural world with our insistence on endless growth of both population and consumption.

Fortunately, we could stabilize human population with three simple and socially beneficial policies worldwide: Women’s rights, contraception, and education.

The second challenge we face is that we share this planet with millions of other species. These non-human earthlings possess a right to life and habitat as much as we do. Furthermore, humanity relies on the benefits of biological diversity and symbiosis within the ecosystem.

We cannot design human culture to devour every last niche of the planet, every river and forest, the last corner of the ocean and stretch of grassland. We need to preserve every acre of wilderness that still exists on the earth.

Living within Earth’s budget

Growth is not evil, it just isn’t permanent.

In nature, all growth stops. New organisms may replace the old, diversity can increase, but there exist no cases in nature of endless growth. As Dr. Albert Bartlett at the University of Colorado points out, “After maturity, continued growth is either obesity or cancer.” In a finite world, we cannot grow ourselves out of overshoot.

Years ago, Canadian master ecological logger, Merv Wilkinson, came to our small, island community in British Columbia to show us how he had managed to earn a living for over 50 years, selectively logging the forest he grew up in, and still retain a healthy forest with more standing timber than the day he started logging. As we walked through the woods, he explained the nuances of soils, natural seeding, tree growth rates, cutting rates, and selection criteria for harvest. Then, he stopped, thought for a moment, and said: “It’s simple really: Just cut below the annual growth rate.”

That is now the lesson for humanity on a global scale. We simply have to learn to live within the capacity of our single island in space, planet Earth. To achieve this, the wealthy must find peace with a lower-consumption lifestyle.

Rex Weyler

You can respond to “Deep Green” columns at my Ecology, where I post portions of this column and dialogue with readers.

(o)(o)

Episode 2 is almost in! We have two more parts to go, coming in the next two weeks. For those of you who want to catch up on the story, here are the first three in order for your viewing pleasure:

Part 1 Estroade

Part 2 Reading Aloud

Part 3 Mommy Jogs

yeaaaaahhhhh happy holidays, ya’ll. do you like likes to be thankful. see you soon.