Education Personal: algebra homeschooling math
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Homeschooling My Daughter For My Own Benefit — Math
My kid is 7. She doesn’t need to know algebra.
I am 54. I don’t need to know it either. So why am I studying it?
It’s not that big a time commitment. I have no tests to pass.
But as I thought about my hope for daughter to grow up fully numerate and unintimidated by math-y stuff, I realized that I had to get over my own intimidation in the face of math, which (despite having a whole family full of supernumerate math-lovers) I hated in school.
So I decided to map my own ignorance, with the help of various library books and Khan Academy videos.
How much of the algebra I was exposed to in high school stuck to me? Damned little, apparently. How much of my own incompetence is due to ignorance and/or incompetence? How much of it is due to lingering emotional responses from math trauma in school?
Recently I’ve been playing with lines and slopes. I have absolutely no recollection of ever learning y-b = m (x – a) or anything that looks like it, so my engagement with the formula and its constituents doesn’t seem to have emotional content (unlike, say, quadratics, which are associated in my mind with a terrible homework fight I had with my father somewhere in 9th grade).
The first thing I notice is now many simple mistakes are available for me to make at every step of the way. It is going to take many many iterations before this process is internalized in my (so to speak) mental muscle memory. I am intellectually aware of what’s required to calculate the slope of a given line — but the actual physical process of writing the numbers down in the right positions vis-a-vis one another is fraught with complications.
As a music teacher I’ve got an advantage over some other folks: I never had any musical talent, so I had to build my musicianship from the molecular level up, making every mistake possible. It looks like the same process is happening with math.
Music teachers with “talent” are often ignorant of two key factors in developing mastery: number of repetitions and size of learning increment. It’s not enough to repeat something until your student does it right — once it’s been done right is the time to begin repetitions! And it’s not enough to increment the learning in steps suitable to your own learning style — it’s essential to figure out the increments your student requires, which may be much smaller than what you needed.
My algebra increments are very small. Fortunately, I’m patient. Yesterday I did three or four slope formulas, some several times. I made mistakes in calculating the initial slope; I transposed x and y in my head; I reversed + and – signs; I simply wrote down a 3 where I meant to write a 2. Each of these and more sent me in different wrong directions — since I didn’t figure out what I’d done until later. And that was just in the initial calculation. Once I began trying to plug these numbers into the y-b = m (x – a) formula, a whole new collection of mistakes emerged.
You know what? I’m interested in the mistakes. Getting it right is not the objective here; the “goal” is to figure out as many different ways of getting it wrong as I can.
The fact that my daughter sees me doing this at the breakfast table is a bonus for the homeschooling process. I’m doing it because I’d like to get over my own anxieties.
Education environment Personal Politics: Arctic atmospheric CO2 carbon emissions
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Year 3, Month 6, Day 10: You Thought Y2K Was Gonna Be Bad? Try CO24C.
The world’s air has reached what scientists call a troubling new milestone for carbon dioxide, the main global warming pollutant.
Monitoring stations across the Arctic this spring are measuring more than 400 parts per million of the heat-trapping gas in the atmosphere. The number isn’t quite a surprise, because it’s been rising at an accelerating pace. Years ago, it passed the 350 ppm mark that many scientists say is the highest safe level for carbon dioxide. It now stands globally at 395.
So far, only the Arctic has reached that 400 level, but the rest of the world will follow soon.
Upfucked ungood. Sorry, kids. Good luck with your lives; you’re gonna need it. Sent May 31:
As kids, we clustered around the driver’s seat when the odometer on our family car turned over; Dad would decelerate a bit and we’d call off fractions of a mile. All those zeros were tangible proof of how far we’d traveled. Sometimes we’d celebrate (ice-cream!).
Now we get to watch as another and considerably more ominous number scrolls by. When CO2 is measured at 400 parts per million in the atmosphere over the Arctic, though, it’s nothing to celebrate. Scientists agree that the survival of our civilization hinges on keeping concentrations of this greenhouse gas below 350 ppm, a landmark we crossed decades ago.
While we always came home at the end of a family drive, it now looks as though industrial humans may have driven too far. The Earth we grew up on is irreversibly behind us, thanks to the past century’s profligate consumption of fossil fuels. No cheering this time.
Warren Senders
environment India Politics: archaeology history monsoons sustainability
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Year 3, Month 6, Day 9: Great God a’Mighty, That’s Moose Turd Pie!
More on the Harappans, this time from the Calcutta Telegraph:
“The link between a weakening monsoon and the fate of the Harappan civilisation should now be considered as settled,” said Ronojoy Adhikari, a physicist with the Institute of Mathematical Sciences, Chennai, a research team member.
“We can now almost rule out every other hypothesis that has ever been proposed for the decline of urbanism in the Harappan heartland,” said Adhikari, who used statistical tools to analyse changing urban patterns in the region from 7000 BC to 500 BC.
Adhikari and his colleagues from Pakistan, Romania, the UK, and the US combined evidence from archaeology, geology, and satellite photos to develop a chronology of landscape changes in the region spanning nearly 10,000 years.
Their analysis shows that the emergence of settlements coincided with a steady weakening of the monsoon that began about 5,000 years ago. The Harappans took advantage of a window in time during which a weakening monsoon encouraged settlements.
“It was a kind of a Goldilocks civilisation,” said Liviu Giosan, a geologist and principal of the study at the Woods Hole Oceanographic Institution in the US. “During periods of heavy rains, the floods were too wild for people to settle near rivers, it was too dangerous.”
As the monsoon rains weakened, a gradual decrease in the intensity of floods stimulated the intensive agriculture and encouraged urbanisation about 4,500 years ago. But the continued decline in monsoon rainfall began to drive people to wetter regions upstream and eastward.
“As rivers became increasingly drier, going east became an escape route,” Giosan told The Telegraph. The archaeological record shows that settlements shifted eastward, but the region did not support crop surpluses that the Harappans had enjoyed in their river valleys.
“They forgot their (Harappan) script, and concentrated on survival,” Giosan said.
Archaeologists believe it might have been during these times of decline that the Harappan civilisation developed one of its great legacies — the double-cropping system with kharif and rabi crop rotations that survives in the subcontinent even today.
Generic…but good! Sent May 30:
While differences outweigh similarities in any comparison of our own industrialised civilisation with that of the ancient Harappans, there is much to be learned from the emerging story of a vibrant urban culture that met its doom in the forces of environmental transformation.
The climate crisis that now threatens us is of our own creation; our rapid and unthinking consumption of fossil fuels has unleashed an essentially instantaneous shift away from the relative climatic calm of the past ten or twelve thousand years, to a new state of increasing extremity, violence and irregularity. One wonders if the Harappan citizens (like so many of us modern humans) assumed that the forces of nature are inherently benign? Did they avoid thinking about their vanishing monsoons until it was too late for their cities to survive?
Will future archeologists similarly speculate on our culture’s fate in the aftermath of a runaway greenhouse effect?
Warren Senders
environment India Politics: denialists history sustainability
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Year 3, Month 6, Day 8: The Indus Near!
The slow eastward migration of monsoons across the Asian continent initially supported the formation of the Harappan civilization in the Indus valley by allowing production of large agricultural surpluses, then decimated the civilization as water supplies for farming dried up, researchers reported Monday. The results provide the first good explanation for why the Indus valley flourished for two millennia, sprouting large cities and an empire the size of contemporary Egypt and Mesopotamia combined, then dwindled away to small villages and isolated farms.
The Harappan civilization, named after its largest city, Harappa along the upper Indus River, evolved beginning about 5,200 years ago and reached its height between 4,500 and 3,900 years ago, stretching across what is now Pakistan, northwest India and Eastern Afghanistan. An urban society with large cities, a distinctive style of writing and extensive trade that reached as far as Mesopotamia, the society accounted for about 10% of the Earth’s population at its height and rivaled Egypt in its power. Unlike Egypt and Mesopotamia, however, the Harappans did not attempt to develop irrigation to support agriculture. Instead, they relied on the annual monsoons, which allowed the accumulation of large agricultural surpluses — which, in turn, allowed the creation of cities. The civilization was largely forgotten by history until the 1920s, when researchers finally began studying it in depth.
OK, it’s a bit of a stretch, but it felt good to write this. Sent May 29:
The ancient Harappans had it good for a long time. The annual monsoons provided ample water for their crops, ensuring food enough to sustain their civilization for well over a millennium. What did the Harappan people think when the seasonal rains began to get irregular? Were priests lavishly paid to perform elaborate incantations in the hopes of restoring the no-longer-idyllic climate? Did traveling storytellers tell their listeners that everything would be just fine, that the monsoons had always been undependable? Was there a bitterly polarized political standoff between those who recognized that things were changing and those who steadfastly refused to accept the facts?
Of course, their culture was regional, not global — and their demise was not self-triggered through profligate consumption of fossil fuels. But future anthropologists will surely puzzle over industrial civilization’s apathetic and uncomprehending response to global climate change. Are we all Harappans today?
Warren Senders
environment: economics media irresponsibility sustainability
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Year 3, Month 6, Day 7: Well, I Guess You “Win” That Round.
Peter Passell offers a well-constructed argument in the Minneapolis Star-Tribune:
Climate change, we are often told, is everyone’s problem. And without a lot of help containing greenhouse gas emissions from rapidly growing emerging market countries (not to mention a host of wannabes), the prospects of avoiding disaster are small to nil.
Now you tell us, retort policymakers in the have-less countries: How convenient of you to discover virtue only after two centuries of growth and unfettered carbon emissions.
Since you were the ones to get us into this mess, it’s your job to get us out. (The United States’ what-me-worry posture on climate change does not, of course, make the West’s efforts to co-opt the moral high ground any more convincing.)
This clash of wills is a bit more nuanced than that, but not much. Almost all the net growth in greenhouse gas emissions for the last two decades – and more than half the total emissions today – is coming from the developing world.
What’s more, most of the cheap opportunities for reducing emissions are to be found in the same countries. But as a matter of equity, it’s hard to argue with “you’ve had your turn, now it’s ours.” And it’s equally hard to see how the stalemate will be resolved before the world goes to hell in a plague of locusts (in some places, literally).
The comments are full of stupid denialists who have not, apparently, taken the trouble to read the article. Shocked, I tell you. Shocked. Sent May 28:
Any approach to an equitable assignment of responsibility for mitigating the impact of climate change is doomed to fail as long as citizens of the developed world find it easier to reject the existence of the greenhouse effect entirely. In the world’s poorest and least developed countries, climate-change denialism is an unaffordable luxury; it is only the economically privileged who are free to indulge in careless wishful thinking under the guise of “skepticism.”
Ask any rural agriculturist whether the climate has changed; the answer will be immediate and unequivocal. An Indian farmer facing the consequences of a vanishing monsoon is immune to the persuasions of a petroleum-sponsored news program.
Yes, poor countries need to invest in economic growth along with sustainable technology — but rich countries cannot claim moral ascendancy as long as their citizens prefer to reject the evidence of science in favor of thinly disguised arguments of convenience.
Warren Senders
environment Politics: carbon emissions corporate irresponsibility greenhouse gases
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Year 3, Month 6, Day 6: The Longest Moustache…
The Miami Herald runs an AP story from Neela Banerjee about our giant carbon-emission numbers:
WASHINGTON — Emissions of heat-trapping carbon dioxide reached an all-time high last year, further reducing the chances that the world could avoid a dangerous rise in global average temperature by 2020, according to the International Energy Agency, the energy analysis group for the world’s most industrialized states.
Global emissions of carbon-dioxide, or CO2, from fossil-fuel combustion hit a record high of 31.6 gigatonnes in 2011, according to the IEA’s preliminary estimates, an increase of 1 Gt, or 3.2 percent from 2010.
The burning of coal accounted for 45 percent of total energy-related CO2 emissions in 2011, followed by oil (35 percent) and natural gas (20 percent).
According to the vast majority of climatologists, the rapid rise of carbon dioxide in the atmosphere because of industrialization over the last 150 years has led to an increase in global average temperature by about 1 degree Celsius.
Yay, us. Sent May 27:
Most world record attainments are occasions for pride. The fastest, the strongest, the furthest, the most powerful. But the news that 2011 set a record for global carbon emissions is no cause for celebration.
It’s not just that post-industrial humans have pumped more CO2 into the atmosphere than ever before, but that we’ve known for decades about the likely consequences of a runaway greenhouse effect — thereby making 2011’s accomplishment a world record for willful ignorance as well as destructive pollution.
The huge quantities of greenhouse gases we’ve set loose indicate not just our burgeoning fossil-fuel consumption, but of our inability to clean up the waste products of our profligate lifestyle. Another landmark achievement: whether it’s turning oil into disposable plastic containers, or burning gasoline in our idling vehicles, we’re number one when it comes to converting the Carboniferous era’s ancient sunlight into toxic trash. Notify the Guinness Book of Records!
Warren Senders
environment Politics: economics idiots responsibility sustainability
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Year 3, Month 6, Day 5: It Wasn’t Me Who Made Him Fall / No, You Can’t Blame Me At All…
The Worcester Telegram (MA) runs an AP story on the squabbling teenagers of the international community:
BONN, Germany — Another round of U.N. climate talks closed Friday without resolving how to share the burden of curbing man-made global warming, mainly because countries don’t agree on who is rich and who is poor.
China wants to maintain a decades-old division between developed and developing countries, bearing in mind that, historically, the West has released most of the heat-trapping gases that scientists say could cause catastrophic changes in climate.
But the U.S. and Europe insisted during the two-week talks in Bonn that the system doesn’t reflect current economic realities and must change as work begins on a new global climate pact set to be completed in 2015.
“The notion that a simple binary system is going to be applicable going forward is no longer one that has much relevance to the way the world currently works,” U.S. chief negotiator Jonathan Pershing said.
Fools. Sent May 26:
If there’s anything more depressing than the continual accumulation of bad news on climate change, it’s the endless cycle of avoidance and denial on the part of the world’s richest nations. For decades we’ve watched the same spectacle: those countries which have prospered economically through their profligate consumption of fossil fuels are also the ones resisting any moves toward responsibility for the messes they’ve created. Meanwhile, the world’s poorest nations — also, of course, the smallest contributors to the planetary greenhouse effect — are the good citizens of the international community, committing themselves to further reductions in CO2 emissions even as the United States dithers and blusters.
Coupled with this is the predictable chorus of catcalls directed at those who point out the obvious fact that infinite growth on a finite planet is impossible. The first president Bush once stated, “The American way of life is non-negotiable.” Why not?
Warren Senders
environment Politics: Bonn climate conference economic injustice economy
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Year 3, Month 6, Day 4: Yo-Ho-Ho And A Bottle Of Domaine de la Romanee-Conti Romanee-Conti Grand Cru!
Well. Who could ever have expected this:
BONN, Germany — U.N. climate talks ran into gridlock Thursday as a widening rift between rich and poor countries risked undoing some advances made last year in the decades-long effort to control carbon emissions that scientists say are overheating the planet.
As so often in the slow-moving negotiations, the session in Bonn bogged down with disputes over technicalities. But at the heart of the discord was the larger issue of how to divide the burden of emissions cuts between developed and developing nations. Developing nations say the industrialized world – responsible for most of the emissions historically – should bear the brunt of the emissions cuts while developed nations want to make sure that fast-growing economies like China and India don’t get off too easy. China is now the world’s top polluter.
“There is a total stalemate,” said Artur Runge-Metzger, the chief negotiator for the European Union.
The negotiations in Bonn were meant to build on a deal struck in December in Durban, South Africa, to create a new global climate pact by 2015 that would make both rich and poor nations rein in emissions caused by the burning of oil and other fossil fuels. But on the next-to-last day of two weeks of talks there was little sign of progress, as different interpretations emerged on what, exactly, was agreed upon last year.
“There is distrust and there is frustration in the atmosphere,” Seyni Nafo, spokesman for a group of African countries, told The Associated Press.
Sociopaths. Sent May 25:
The sickness of America’s economy is uncannily mirrored by the sickness of the planet: the very wealthy and powerful resist regulation, deny responsibility for their actions, and spurn any policies that would impact their profitability.
On Wall Street, unregulated banks gamble money that never existed to begin with, turning to our government to bail out their losses, while at the Bonn climate conference, it’s the nations that triggered global climate change in the first place that are vehemently rejecting the kind of robust, systemic transformation that climate scientists tell us is essential for the survival and prosperity of our species in the coming centuries.
Just as “pirate capitalists” reward themselves for the destruction of our nation’s once vibrantly interdependent economy, great multinational oil corporations reap rich returns while plundering the ecological systems upon which all Earthly life depend. Economic and environmental injustice, it turns out, are one and the same.
Warren Senders
Year 3, Month 6, Day 3: Can’t You Speak Nicely?
The Boston Globe reports on some disturbing statistics — but not disturbing enough:
An additional 150,000 or more Americans could die by the end of this century due to excessive heat caused by climate change, according to a report released Wednesday by the Natural Resources Defense Council.
The New York-based advocacy group, which based its findings on other studies, projects that Midwestern cities will bear the brunt of hotter summers, with 19,000 additional deaths by the end of the century in Louisville, 17,900 in Detroit, and 16,600 in Cleveland. The Midwestern cities are more vulnerable because of their greater temperature swings, lack of air conditioning and green space, and the types of buildings.
The report estimates an additional 5,715 people will die in Boston by the end of the century because of the increased heat.
I’m running all over the place; this letter’s nothing I’m going to point to with pride later on. Sent May 24:
The statement forecasting an extra 150,000 American deaths over the next ninety years due to climate change will undoubtedly be used to mislead the public: those with vested interests in minimizing the threat of global climate change can simply do some arithmetic to back up a claim that fewer than 2000 extra deaths a year is nothing to get excited about.
But the scary numbers aren’t those referring to the people who succumb to months of uninterrupted hundred-plus degree days, which is what the NRDC report quantifies. What happens to our food supply when agricultural yields plummet in the extreme heat? When electrical supplies begin to fail due to unplanned-for demand? When our water supply proves inadequate?
And, of course, those numbers only refer to the USA. How many deaths can we expect worldwide? How many millions of climate refugees, some in the most geopolitically unstable parts of the world?
Warren Senders
Ornette Coleman…
…has a few things for us to hear:
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When I turned fifteen, I was living in my grandmother’s apartment in Lincoln, Massachusetts. My brother and parents were in Toronto for the year.
On that birthday, knowing of my burgeoning interest in jazz, my parents gave me the Smithsonian Collection of Classic Jazz — a 6-lp box set with a lot of wonderful music.
And the last side of the last disc had three pieces by Ornette. And I was well and truly hooked.