Teaching And Learning Problems

This is one of the best articles I have read so far. http://socrates.berkeley.edu/~kihlstrm/GSI_2011.htm

Another nice article: http://www2.math.umd.edu/~jnd/Fractions.html

I keep wondering. Some children understand stuff fast and some don't. The best for the latter category, it seems to me, that one can do is to make sure they practice a lot and with rote learning these students can get higher grades. Unfortunately, these students prepare primarily for an exam and once the exam is over, they forget what they learned because it goes into short term memory. Unless one maps a new knowledge to something else that one already knows, the newly learnt stuff remains an "orphan" and has no roots to remain (in the memory) and soon it goes away. 

What then is the point of teaching or learning stuff that remains only in the short term memory? What is the benefit of conducting exams and evaluating students when what is being evaluated has a short validity? Few weeks after the evaluation, the results of evaluations are mostly null and void?

Then why teach or learn which won't go into the long term memory? What should those average and below average students (of a subject) do while learning that subject?

The two links on top should be read with this question in mind.

Comments welcome.

Maths Puzzle: Geometry

An equilateral triangle is drawn with each side = 10. With the base of the triangle as one side, a square is drawn (with each side = 10) below the triangle. What is the radius of the circle on which the top tip of the triangle and the bottom two vertices of the square lie?

Height of triangle = sqrt (100-25)=sqrt(75)

Take the origin to be the bottom left point on square (1) = 0,0

Bottom right point on square (2) = 10,0

Top tip of triangle (3) = 5, 10+ sqrt(75)  

Assume 5,b is the center (meaning the height of the center is "b" from the bottom side of square).

Square of Distance from center to points on square (=radius squared) = 25+b²

Square of Distance from center to top point on triangle = ((10-b) + sqrt(75)) ²  

Now solve for b.

Puzzle - Killer's Love

http://www.albinoblacksheep.com/text/funeral

Speed At Work

A friend of mine (LEH) is a teacher. While at school, she is usually busy teaching or correcting papers. One day she was correcting papers. Generally, she hardly looks up to see what is happening around her. It was late afternoon and teachers started to leave for home one after another. LEH continued her corrections unaware of what was happening around her. 

Around 6PM she looked up to see that she was alone in the room and saw there were birds chirping outside. She smiled to herself and went back to her work thinking she will finish her work in a few minutes and then leave. 

She finished and then turned to look outside the window. Her jaw dropped, she started shaking. It was pitch dark outside and eerie. No noise.

There was no one within 100 ft of her. She desperately wanted to run down from the staff room and away from the school to civilization where there was light and where there would be people.

She knew the principal would be working late. But she was too embarrassed to call and request the principal on the phone to come up to the staff room and escort her down. LEH was too proud. No, she would manage on her own.

But she had to close the windows and lock the room before leaving. The school where she works is rather strict in these matters. She tiptoed to the window and in 10 minutes bolted the windows (her hands were shaking terribly by now, she was imagining faces outside the window) and walked fast back to the door. She closed the door and in the dark found the right key and with a snap (of her teeth which were chattering rather loudly) locked the door and swiftly flew down the stairs to light and safety.

After a couple of days she recounted this incident to me. As per her request I am letting others know of this incident. Correcting homework is quite harmful to health.

What Qualities Make A Good Teacher

http://jan.ucc.nau.edu/~slm/AdjCI/Teaching/Teacher.html

This article contains the opinions of two award winning teachers. What each one says is different. I relate to what Peter Beidler says but I don't understand much what Sally Phillips says.

Beidler says that a teacher who models his teaching style on the characteristics valued by students will be a successful teacher. Here I wonder. Can someone "model" his style? Is the style not largely, if not fully, innate to a teacher? Perhaps if he rephrased what he said as "a teacher, whose teaching style is in sync with what students value, will be a successful teacher" I would be more comfortable.

Birds Of Like Feathers Attract

I had earlier asked "Is there a rule that will determine when "Opposites attract" and when "Birds of the same feather flock together"?

A friend and I were trying to answer this question. There are two kinds of love that a person has. 

1. A love for something, an attribute (I call this a strong attribute; say, honesty), that a person themselves espouses. The person may not tolerate any person who does not have that strong attribute. In cases of such attributes, the person will flock  together with people who share the same attributes. There are other attributes, weak ones, which a person likes (rock music, traveling) which may be personal preferences and in such cases the person may still like other people who do not share these attributes.
2. A love for something, an attribute (say, tolerance, kindness) that a person needs and themselves don't have. Such a person will repel other people who are similar to themselves.

What does this tell us about ourselves? 

When we find that we cannot spend a lot of time with another person, either the other person:

• doesn't share an attribute that we have or 
• the other person doesn't complement us; they don't have that thing that we also lack.

This list of things that the other person, whom we dislike, lacks tells us about what we have (and need in the other person) and what we don't have (but expect the other person to have / provide it). The list has many attributes not all of which are equally important to us.

We do not give the same weight to all the attribute that we seek in another person. For example, in the movie Six days and Seven Nights, the man lived in a remote island and the woman was based in New York. The thought of being together was very difficult to digest initially. Subsequently they each figure that the other person had many other things which made their conflicting location preferences seem like a much smaller issue. (We do know what happened after they were together for 3 years. That is a very different story!)

Additional Reading:

• https://www.diigo.com/list/jazmynledford/annotated-bibliography-wp2
• http://www.examiner.com/article/do-opposites-attract-or-do-birds-of-feather-flock-together

Logical Puzzle

http://interviewkiller.com/question/1045-statements-all-rats-are-cows-no.html

Is there anything wrong with the options a, b, c, d?

Maths Puzzle

https://m.facebook.com/photo.php?fbid=635822939765412&id=489817594365948&set=a.490144640999910.130029.489817594365948&from_feed=1&refid=7&_ft_=qid.5870085079935915066%3Amf_story_key.-3908465476357452283