Monday, November 22, 2010 Physics Tutor in Brooklyn Physics Tutor in Brooklyn

Physics Tutor in Brooklyn

Physics Tutor in Brooklyn

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Phone: 718-223-0228

Teaching by Asking Instead of by Telling

Teaching by Asking Instead of by Telling

The Socratic Method:
Teaching by Asking Instead of by Telling
by Rick Garlikov

       The following is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. I present my perspective and views on the session, and on the Socratic method as a teaching tool, following the transcript. The class was conducted on a Friday afternoon beginning at 1:30, late in May, with about two weeks left in the school year. This time was purposely chosen as one of the most difficult times to entice and hold these children's concentration about a somewhat complex intellectual matter. The point was to demonstrate the power of the Socratic method for both teaching and also for getting students involved and excited about the material being taught. There were 22 students in the class. I was told ahead of time by two different teachers (not the classroom teacher) that only a couple of students would be able to understand and follow what I would be presenting. When the class period ended, I and the classroom teacher believed that at least 19 of the 22 students had fully and excitedly participated and absorbed the entire material. The three other students' eyes were glazed over from the very beginning, and they did not seem to be involved in the class at all. The students' answers below are in capital letters.

         The experiment was to see whether I could teach these students binary arithmetic (arithmetic using only two numbers, 0 and 1) only by asking them questions. None of them had been introduced to binary arithmetic before. Though the ostensible subject matter was binary arithmetic, my primary interest was to give a demonstration to the teacher of the power and benefit of the Socratic method where it is applicable. That is my interest here as well. I chose binary arithmetic as the vehicle for that because it is something very difficult for children, or anyone, to understand when it is taught normally; and I believe that a demonstration of a method that can teach such a difficult subject easily to children and also capture their enthusiasm about that subject is a very convincing demonstration of the value of the method. (As you will see below, understanding binary arithmetic is also about understanding "place-value" in general. For those who seek a much more detailed explanation about place-value, visit the long paper on The Concept and Teaching of Place-Value.) This was to be the Socratic method in what I consider its purest form, where questions (and only questions) are used to arouse curiosity and at the same time serve as a logical, incremental, step-wise guide that enables students to figure out about a complex topic or issue with their own thinking and insights. In a less pure form, which is normally the way it occurs, students tend to get stuck at some point and need a teacher's explanation of some aspect, or the teacher gets stuck and cannot figure out a question that will get the kind of answer or point desired, or it just becomes more efficient to "tell" what you want to get across. If "telling" does occur, hopefully by that time, the students have been aroused by the questions to a state of curious receptivity to absorb an explanation that might otherwise have been meaningless to them. Many of the questions are decided before the class; but depending on what answers are given, some questions have to be thought up extemporaneously. Sometimes this is very difficult to do, depending on how far from what is anticipated or expected some of the students' answers are. This particular attempt went better than my best possible expectation, and I had much higher expectations than any of the teachers I discussed it with prior to doing it.

        I had one prior relationship with this class. About two weeks earlier I had shown three of the third grade classes together how to throw a boomerang and had let each student try it once. They had really enjoyed that. One girl and one boy from the 65 to 70 students had each actually caught their returning boomerang on their throws. That seemed to add to everyone's enjoyment. I had therefore already established a certain rapport with the students, rapport being something that I feel is important for getting them to comfortably and enthusiastically participate in an intellectually uninhibited manner in class and without being psychologically paralyzed by fear of "messing up".

        When I got to the classroom for the binary math experiment, students were giving reports on famous people and were dressed up like the people they were describing. The student I came in on was reporting on John Glenn, but he had not mentioned the dramatic and scary problem of that first American trip in orbit. I asked whether anyone knew what really scary thing had happened on John Glenn's flight, and whether they knew what the flight was. Many said a trip to the moon, one thought Mars. I told them it was the first full earth orbit in space for an American. Then someone remembered hearing about something wrong with the heat shield, but didn't remember what. By now they were listening intently. I explained about how a light had come on that indicated the heat shield was loose or defective and that if so, Glenn would be incinerated coming back to earth. But he could not stay up there alive forever and they had nothing to send up to get him with. The engineers finally determined, or hoped, the problem was not with the heat shield, but with the warning light. They thought it was what was defective. Glenn came down. The shield was ok; it had been just the light. They thought that was neat.

        "But what I am really here for today is to try an experiment with you. I am the subject of the experiment, not you. I want to see whether I can teach you a whole new kind of arithmetic only by asking you questions. I won't be allowed to tell you anything about it, just ask you things. When you think you know an answer, just call it out. You won't need to raise your hands and wait for me to call on you; that takes too long." [This took them a while to adapt to. They kept raising their hands; though after a while they simply called out the answers while raising their hands.] Here we go.

1) "How many is this?" [I held up ten fingers.]


2) "Who can write that on the board?" [virtually all hands up; I toss the chalk to one kid and indicate for her to come up and do it]. She writes


3) Who can write ten another way? [They hesitate than some hands go up. I toss the chalk to another kid.]

4) Another way?

5) Another way?

                        2 x 5 [inspired by the last idea]

6) That's very good, but there are lots of things that equal ten, right? [student nods agreement], so I'd rather not get into combinations that equal ten, but just things that represent or sort of mean ten. That will keep us from having a whole bunch of the same kind of thing. Anybody else?


7) One more?

                        X       [Roman numeral]

8) [I point to the word "ten"]. What is this?

                     THE WORD TEN

9) What are written words made up of?


10) How many letters are there in the English alphabet?


11) How many words can you make out of them?


12) [Pointing to the number "10"] What is this way of writing numbers made up of?


13) How many numerals are there?

                             NINE / TEN

14) Which, nine or ten?


15) Starting with zero, what are they? [They call out, I write them in the following way.]

9 - Electricity Quiz - Electricity Quiz


What is the equivalent capacitance (in µF) between points A and B as shown if x is 2.91 µF, y is 2.02 µF, and z is 3.96 µF?


How much charge (in µC) can be stored by a parallel-plate capacitor with a plate area of 0.00131 square meters having air (8.85 X 10^-12 C^2/(Nm^2) between the plates where the magnitude of the electric field is 3.18 MN/C? 

A wire with a resistance of 3.19 ohm connected across a 111 V source carries current for 23.7 minutes. How much charge (in C) passes through the wire?

An appliance draws 7.1 amps of current when connected to 120 V. What is the cost (in $) of operating it for 15.8 hours at $ 0.137 per kWh?

An appliance delivers 496 J of energy when its capacitors discharge. If the device has a capacitance of 4.18 mF, how much charge (in C) is delivered?

A resistance thermometer has a resistaqnce of 40 ohm at a temperature of 16.2 ºC. At what temperature (in ºC) will it have a resistance of 46.4 ohm (linear coefficient of expansion = .00392 /ºC). 

Sunday, November 14, 2010

Do You Have a Tutor?

Do You Have a Tutor?

Questions about issues in the news for students 13 and older.

Many students use after-school tutors, tutoring centers and private tutors, as well as “homework helpers” or “homework coaches.” Why do you think many students and parents seek the support of tutors? Do you have a tutor or homework helper?
In the article “Like a Monitor More Than a Tutor,” Sarah Maslin Nir examines the trend of students’ receiving help with organization and homework:

If a student finds French grammar or algebra incomprehensible, a tutor in those subjects can help. But if the problem is a child who will not budge from the Xbox, or pens doodles instead of topic sentences, some harried parents with cash to spare have been turning to homework helpers who teach organizational skills and time management, or who sometimes just sit there until the work is finished.

As schools have piled on expectations and as career paths have sucked in both mothers and fathers, this niche industry is catering to “students who are capable of doing the work” but “need someone there who can just be there with them to consistently do the work in a regular manner,” said Mike Wallach, who along with Ms. Kraglievich runs the service Central Park Tutors.

But it has also led some educators to question whether this trend might simply be a subcontracted form of “helicopter parenting,” depriving children of the self-reliance they will need later in life.

Students: Tell us what you think about tutors and homework helpers. Have you had one to help you with schoolwork, time management or organization? Why or why not? If so, do you think it helped you? If not, how do you stay organized and on top of your work?


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Wednesday, November 10, 2010

Kremlin PR - "Допустимо прикольно!..."

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Сайт, угрожавший расправой зверски избитому журналисту Кашину, в настоящее время недоступен. "Допустимо прикольно!..."

Monday, November 8, 2010

Free Classifieds бесплатные объявления - Popular ads

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Tuesday, November 2, 2010

Giant Waves Solve Saturn Ring Mystery

Giant Waves Solve Saturn Ring Mystery


Saturn’s largest ring appears to behave like a mini spiral galaxy. NASA’s Cassini spacecraft caught enormous waves sloshing back and forth across Saturn’s B ring, similar to waves believed to give galaxies their spiral shapes.

“This is a major result,” said Cassini imaging team leader Carolyn Porco of the Space Science Institute. “Saturn’s rings are tiny tiny tiny compared to a galaxy, but we see the same physics.”

The new observations also show two warped regions, including a tall arc of spiky peaks that rise almost two miles above the ring plane. These perturbations may have been sculpted by small moons that migrated across the ring disk, a process believed to be important in shaping planetary systems.

Saturn’s most massive ring, the B ring, has baffled astronomers since the Voyager spacecraft flew by in 1980 and 1981. Those observations showed the B ring was sculpted into a flattened football shape with a sharp outer edge by the moon Mimas. But even in the Voyager images, it was clear the B ring was too complex and chaotic to be shaped by Mimas alone.

Now, in a new analysis published in the Astronomical Journal, thousands of Cassini images gathered over the course of four years have revealed three separate wave patterns that are not driven by any moons, but spring up spontaneously by drawing energy from the small, random motions of ring particles. The waves, which can be hundreds of miles long, keep themselves going by reflecting off the ring’s edges.


“Think of it like waves in a pool,” Porco said. If two kids are hopping up and down at either end of a pool, she says, the waves they send sloshing across the water will pass through each other and reflect off the edge of the pool.

In Saturn’s rings, the waves are more like compressions in a Slinky than water waves, but the physics is similar. “These waves just go back and forth, and keep reflecting until they finally grow large enough so that we can actually see them,” Porco said.

“Normally viscosity, or resistance to flow, damps waves — the way sound waves traveling through the air would die out,” said planetary ring expert Peter Goldreich of Caltech and the Institute for Advanced Study in Princeton, who was not involved in the new study, in a press release. “But the new findings show that, in the densest parts of Saturn’s rings, viscosity actually amplifies waves, explaining mysterious grooves first seen in images taken by the Voyager spacecraft.”

Cassini has also observed similar waves on smaller scales, with wavelengths around 300 feet. Computer models of galaxies and protoplanetary disks around other stars have shown similar randomly generated waves with proportionally larger wavelengths. But because those waves would take hundreds of millions of years to complete one slosh, astronomers can’t observe them directly.

“This is the first time we’ve seen these things in nature,” Porco said. “It underscores the deep, physical connection between what we’re studying at Saturn’s rings, and disk systems across the universe at a very large range of spatial scales.”

Cassini has also snapped pictures of sharp, stalagmite-like peaks at the edge of the B ring that made themselves known by throwing long spiky shadows (below).

The new study suggests this region of the rings contains small moons that compress the ring material like a soda can and force it upward. This idea is supported by the presence of at least one moonlet, caught during Saturn’s summer equinox when it cast a shadow across the rings.

These moonlets may have migrated across Saturn’s rings, and become trapped in a gravitational resonance with the larger moon Mimas. This process of migration and trapping is exactly how scientists believe the solar system achieved its current architecture.

In this way, Saturn serves as a nearby laboratory to study celestial structures on all scales, from planets to solar systems to galaxies.

“There are basically two shapes in the universe, there’s disks and there’s spheres,” Porco said. “Saturn’s rings allow us to understand one of the two main structures in the universe: a celestial disk system.”

“This is not just a slight addition, it’s something significantly new,” Goldreich told Goldreich and colleagues predicted the presence of these waves in 1985, but the Cassini observations provide the first proof.

“A lot of times, you don’t expect to be around to see whether you made a prediction that worked,” Goldreich said. “I was quite pleased to see it.”

Video and Image: NASA/JPL/Space Science Institute

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