The Hazard of Using Calculators at School
Using calculators is a part of our modern way of life. Today it is not a problem for kids to get a calculator and put it into practice. Really, why must they toddle if they may ride a bike? On the face of it using calculators at school allows keeping away from many troubles.
By the help of a calculator we can carry out complicated mathematical operations quickly and accurately. Calculator proponents claim that calculators simplify tasks and allow students to spend less time on monotonous calculations and more time on understanding problems and determining the best methods for solving them; calculators allow students who would normally be turned off to math because of dissatisfaction or boredom to increase their mathematical understanding. Furthermore, every teacher of mathematics knows that there are graduating pupils in primary school who had not mastered the multiplication table, have difficulties with subtraction within the limits of 20 and so on. Give all of them calculators and they will obtain desirable result without sweating, puffing and having a dread of mistakes and therefore will become more confident about their math abilities.
But this good-looking picture is too charming to be a realistic one. There are several circumstances which make using calculators at school not so attractive. Firstly even a brand new modern calculator which has amazing computational power is a device only. Each calculator is as good and as accurate as its operator. To use it in proper way a pupil must know its manual well. Calculators of different kinds use different orders for carrying out mathematical operations, pressing keys, and their manuals have a bad habit to get lost. It is very easy to make simple mistakes when using one. You must think of the rough size of answers, so that you can see if an answer is sensible or not. To avoid mistakes you must repeat all calculations. If you get two different answers, then you must repeat all calculations for the third time.
Very often even advanced students make mistakes – pressing wrong buttons, forgetting to change a mode, rounding values too soon, forgetting to use brackets rightly … And what about bad achieving pupils? Can you imagine that a pupil who does not know what brackets are for can use them correctly? How can a kid who cannot mentally multiply 8 by 7 weighs up a result?
For advanced students a calculator is a comfortable vehicle, which helps him to reach their aim more rapidly and more easily, but in case of need they can go out of it and move themselves. And what is more they very often perform better without a calculator since in many cases mental computations are quicker, easier and more errorless then computations with calculator.
Whereas for bad achieving pupils a calculator is a motored wheel chair for cripples, without which they cannot move. They are afraid to carry out mentally simple arithmetical operations and waste precious time when pressing keys.
Besides that there is another significant hazard. A person who all the time uses a calculator gradually loses his/her mental computational skills. Very often even advanced pupils take calculators when they need to make simple computations which can be easily implemented in head. Their brains slowly but surely get accustomed to walking on crutches and became indolent to use mental computational abilities, whereas skills, which are not used, became forgotten very soon. In certain cases it leads to difficulties in math's learning.
Both my experience (32 years in the classroom) and my investigations (20 years of studies) shows that pupils with unsteady elementary mental computational skills (addition and subtraction within the limits of 20, multiplication and division within the limits of 100) have great difficulties while learning the other basic topics of arithmetic and algebra. In other words they are doomed to poor progress in school math. Even calculators cannot help them. If you want to see some figures and diagrams you can read my article "Influence of a Level of Elementary Mental Computation Skills upon Success in School Mathematics" at my web site www.simplar.boom.ru (reference – My Articles).
Do not think that I am trying to stop progress and calling to finish with any computing stuff at school. It is obvious that we can not manage without calculators today, but we must remember about simple mental computations and their significance for success or failure in math. I consider that it is necessary to lay emphasis once more – extensive using of calculators (especially at the first six or seven grades) leads to degeneration of pupils' mental computational skills and afterward to deterioration of their learning ability. This is the main hazard of using calculators at school.
Mercury- Messenger of the Gods (Planetary Series)
In our tour of the solar system, we should begin by exploring the innermost planet. A short distance from the inferno of our sun we find it, hurtling through space at 40 to 60 kilometers per second in its 88 day cycle around the sun. As we approach it we notice its similarity to a body much closer to Earth, our own moon. It too is heavily cratered, with no atmosphere (or only a trace of one) to protect its surface or erode signs of previous collisions. The sun as seen from this distance is approximately three times as large as from Earth, and we know this is going to be the most dominant force affecting our trip to this planet.
Now we have touched down and we take a quick look around. We know that the surface gravity of Mercury is 38% of Earth's, so if we weighed 200 pounds before, here we weigh only 76 pounds. Looking up at the sky we see a black, star-speckled sky dominated by the fiery globe of a sun almost three times larger than we are familiar with. There is only the faintest trace of an atmosphere, and the only way we even know it is there is the instrumentation we have with us. It will be totally useless to us. The sun beats down unabated in all its fury, and the temperature hovers around 800 degrees Fahrenheit. If we were on the night side the temperature would drop to -270 degrees. We would never survive her without space suits.
Bending down to inspect the surface we find a layer of dust similar to what astronauts found on the moon. This is the result of billions of years of meteor impacts, and also the extreme temperature differentials applied from a hellishly close sun. The processes which shaped this world across the eons were much different than the ones which shaped our home planet.
Around us are the pockmarks of craters, some mountain ranges, and a horizon much nearer than what we know at home.
Contrary to what astronomers once thought, there is actually a cycle of days here, but it is much different than anything we are used to. Mercury is not tidally locked with the sun, but tidal forces have slowed it to the point where its day is 58 of our days (indeed it will one day many years from now become locked one side to its huge neighbor). This means that Mercury's day is about three quarters as long as its year. This results in some very peculiar observations if we were to stay that long. We would observe the sun snake across the sky very slowly. In certain places on this world we would then see the sun slow and actually backtrack a short distance before continuing its slow march across the sky. Then the very long night would follow.
We take one more look around this world. No, Mercury is not an enticing place for humans to visit. Maybe one day we will have reason to be here, either for the rich deposits of iron and other metals or for observational purposes, but this is not the day.
Studies of Mercury Through History
Mercury has been know and observed at least since the times of the Sumerians in the 3rd millennium BC. Following the Sumerians there is better documentation from the Babylonian Empire. Records from the 7th century BC refer back to much earlier records which described observations of the planet. The Babylonians called the planet Nebu, after the messenger of the gods in their mythology. This is an interesting parallel to the later Greek mythology and reference to the innermost planet. The ancient Greeks had two names for the planet, Apollo visible in the morning and Hermes visible in the evening. They eventually came to understand that these were the same object, and it was even proposed this early in history that Mercury and Venus orbited the sun.
Early modern astronomy began making observations of Mercury in the early 17th century when Galileo turned an early telescope to the inner world. A sketchy vision of the planet developed from that point, but its proximity to the sun has always made this one of the most difficult members of our solar system to study. It has only been recently with the advent of new imaging techniques that ground-based observation has drastically improved.
And what of research with space probes? This is also laced with technical difficulties. An application of Newton's Laws of Motion shows that it takes more rocket fuel to achieve an orbit around Mercury than it takes to escape the solar system. Because of this only one spacecraft has visited the planet to date, the Mariner 10.
The Mariner 10 was launched on November 3, 1973 to study both Venus and Mercury. After its study of Venus, the probe made three flybys of Mercury in 1974 and 1975 when it mapped about 45% of the planet's surface. Its closest approach was 203 miles on March 16,1975. The Mariner 10 circles the sun in its own lone orbit around the sun to this day, although its electronic instruments have long since been destroyed by the sun's intense radiation.
Our most ambitious Mercury research project to date was begun August 3,2004 with the launch of the Messenger by NASA from Cape Canaveral. After two quick flybys of Venus in 2006 and 2007 the Messenger will finally work its way inward and make three flybys of Mercury in 2008 and 2009. Then in March of 2011, if all goes well, it will finally become the first orbiting spacecraft around Mercury. It is carrying high resolution imaging devices, spectrometers to determine the composition of the crust, and magnetometers to study charged particles around the planet.
There is an astronomical event which is of interest to amateurs and professionals alike, but not necessarily for any scientific value. Once every couple of centuries there is an occultation of Mercury and Venus. This occurs when Venus actually passes directly in front of Mercury for a few minutes. The last one occurred on May 28,1737 and the next will occur in 2133.
Structure of Mercury
Much of Mercury's mass is composed of an iron rich core. Current theories suggest that this core comprises most of the 4879 mile diameter of the planet. This is surrounded by a 350-400 mile thick mantle and finally by a crust some 100 miles thick. Because of Mercury's slow rotation period, there is very little tectonic or volcanic activity.
There have been several theories presented to explain why Mercury is so metal rich, and why its core comprises such a huge part of the planet's structure. One popular theory is that the planet was struck by a large body early in its history and lost most of its outer, "lighter", mantle. Another theory is that the extreme heat of the early sun vaporized the outer part of the planet, giving the young Mercury a dense atmosphere of gaseous rock, which was carried away by the huge solar winds of a much more volatile sun. The competing theories to explain the unusually heavy composition of Mercury will be tested by the upcoming Messenger mission.
The Future of Mercury and Its Possible Role in Our Own Future
Mercury's most dominant feature makes it an attractive part of our future: its huge stores of heavy metals, especially iron. Although its proximity to the sun makes it hard to imagine humans working and living there, I can envision automated factories mining its surface and freighters picking up the ore to bring it back for our use.
Mercury will remain pretty much as it is for billions of years to come. As the sun slowly gains in intensity over the next 4 to 5 billion years, the planet's surface temperature will slowly rise with it. Then a singular moment will arrive as the entire solar system changes with the beginning of the sun's passage into its next phase. When the sun consumes a critical amount of its hydrogen fuel it will, within a matter of just a few days, enter its red giant phase.
At that time Mercury will be the first of the inner planets to be entirely consumed.
(Look for more articles soon in the Planetary Series.)
Planetary Statistics of Mercury
closest distance to the sun (perihelion)..............46,001,272km (28,583,865 miles)
farthest distance from the sun (aphelion)...........69,817,079km (43,382,322 miles)
density..............................................................5.427 g/cubic cm
diameter...........................................................4879.4km (3031.9 miles)
orbital period (year)..........................................87.96934 days
rotation period (day).........................................58.6462 days
max surface temperature...................................700K (800F)
satellites............................................................None
atmospheric pressure.........................................trace
surface gravity.................................................. 38% Earth's
Future-Seek.com is a Futurist/science website featuring more articles like this.
American Patriotism
The Random House dictionary defines a patriot as one who "defends his or her country and its interests," but it also regards a patriot as a "defender, esp. of individual rights, against presumed interference by the federal government."
Our country today is troubled not only with another war abroad, but with a war of words at home. On one side are those who defend the present government without question. They are angered by those on the other side, who speak out against policies and decisions made by those in power today. Both sides claim patriotism, but to what? Could it be that our differing definitions of 'patriotism' could be undermining the stability of the very country we are all claim to be defending? Lao Tzu wrote in his Tao Te Ching, "When the country falls into chaos, patriotism is born." Has it gotten that bad already?
The Revolutionary War was fought by so-called 'patriots' – those who sought freedom from a government they didn't agree with. Did Britain consider them to be patriots? In a sense these 'patriots' were actually rebels, engaged in what they considered to be a righteous rebellion against tyranny. Adlai Stevenson said, "Do not... regard the critics as questionable patriots. What were Washington and Jefferson and Adams but profound critics of the colonial status quo?"
And what issues did our founding fathers have with this 'tyrannical' rule of the time? Our forefathers sought freedom from taxation without representation; they sought religious freedom; they sought freedom of speech and expression; they sought self-rule. The resulting Declaration of Independence and Constitution attempted to provide a satisfactory alternative to rule by monarchy.
Especially since 9/11, many argue that some of these freedoms have been curtailed, ironically by the USA Patriot Act, and other acts of government in which the general population had no say. Was it done, as they say, to protect our freedom? I suppose, as I believe Donald Rumsfeld once said, that we can have freedom or security, but not both. Of course now we are at war as well, and many cry out in against those who choose not to support our government in this effort, claiming such people are un-patriotic.
I support our troops without question. Those men and women didn't start the war, they are just doing their duty, which happens to be following orders - many times to the death. I applaud these people for their fortitude and stamina in this seemingly unending war against terrorism. Regardless of the arguments some make about Iraq not having WMDs, or that Iraq didn't destroy the WTC, or that war is a means to profit for the elite – these men and women in uniform aren't to blame and should have our gratitude and respect.
But to call someone un-patriotic for questioning their government? Of course the government itself feels slighted, so as Henry Steele Commager said, "Men in authority will always think that criticism of their policies is dangerous. They will always equate their policies with patriotism, and find criticism subversive." But going back again to the days of Thomas Jefferson and George Washington, certainly these men would support the right to speak out. They hoped the republic they created would provide a balance between the rulers and the ruled. They provided the right to free speech and to bear arms – not so people could run around yelling and killing each other, but so they could defend themselves from a dishonest government if need be. Certainly the citizenry will not always agree on whether this is the case - but don't we have the right to disagree? Shouldn't we at the very least respect each other's opinion, and take the time to listen to each other? Isn't that really what it means to be an American?
If you research famous quotes on patriotism the result is surprising. Those who refuse to question the policies of our government might be advised to reread a little history. It's our job as patriots! I saw a bumper sticker once which said, "Sometimes a patriot needs to defend his country against its government." And along those lines many famous people have spoken out over the years.
From Teddy Roosevelt, "To announce that there must be no criticism of the president, or that we are to stand by the president, right or wrong, is not only unpatriotic and servile, but is morally treasonable to the American public." (1918)
From Mark Twain: "The government is merely a servant -- merely a temporary servant; it cannot be its prerogative to determine what is right and what is wrong, and decide who is a patriot and who isn't. Its function is to obey orders, not originate them."
From James Baldwin: "I love America more than any other country in this world, and, exactly for this reason, I insist on the right to criticize her perpetually."
From Edward R. Murrow: "We must not confuse dissent with disloyalty. When the loyal opposition dies, I think the soul of America dies with it."
To be loyal to America doesn't mean to sit back and allow one administration or another the power to make decisions without debate or dissent. To be a loyal American is to stand up for our original freedoms, to stand up as our forefathers did, as 'rebellious patriots', and fight for the rights that made our country great - particularly the right to disagree, without repercussion. This is the heart and soul of America, and when that is gone, then we become Americans in name only. Some argue, this has already happened, but as long as this article remains posted we still have a chance.
Someday soon, I fear, being an "American" could become a thing of the past, in name as well. As Ronald Reagan famously said in 1985, "I couldn't help but say to [Mr. Gorbachev], just think how easy his task and mine might be in these meetings that we held if suddenly there was a threat to this world from another planet. [We'd] find out once and for all that we really are all human beings here on this earth together." If we are truly on the road to world government, as many believe, we as Americans will have a lot more to fight for someday. If our sovereignty is ever threatened, I can only hope that all Americans – those on both sides of the 'patriot' argument today – will come together to defend her from those who seek ultimate power. As Daniel Webster said in 1850, "I was born an American; I will live an American; I shall die an American!"
