Eye Teasers

1. Read out loud the text inside the triangle below.

More than likely you said, "A bird in the bush," and........
if this IS what YOU said, then you failed to see
that the word THE is repeated twice!
Sorry, look again.
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2. What do you see?
In black you can read the word GOOD, in white the word EVIL (inside each black letter is a white letter). It's all very physiological too, because it visualize the concept that good can't exist without evil (or the absence of good is evil ).
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3. Now, what do you see?


You may not see it at first, but the white spaces read the word optical, the blue landscape reads the word illusion. Look again! Can you see why this painting is called an optical illusion?
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4. What do you see here?


This one is quite tricky!
The word TEACH reflects as LEARN.
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5. What do you see?

You probably read the word ME in brown, but.......
when you look through ME
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ALZHEIMERS' EYE TEST

Count every "F" in the following text:

FINISHED FILES ARE THE RE
SULT OF YEARS OF SCIENTI
FIC STUDY COMBINED WITH
THE EXPERIENCE OF YEARS...

(SEE BELOW)

HOW MANY ?
WRONG, THERE ARE 6 -- no joke.
READ IT AGAIN !
Really, go Back and Try to find the 6 F's before you scroll down.


The reasoning behind is further down.

The brain cannot process "OF".
Incredible or what? Go back and look again!!
Anyone who counts all 6 "F's" on the first go is a genius.
Three is normal, four is quite rare.
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More Brain Stuff . . . From Cambridge University.

O lny srmat poelpe can raed tihs.

cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg. The
phaonmneal pweor of the hmuan mnid, aoccdrnig to a rscheearch at Cmabrigde Uinervtisy,

it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm.

Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh? yaeh and I awlyas tghuhot slpeling was ipmorantt! if
you can raed tihs psas it on !!


(Shared by Hwee Peng, 2006 July)

That's Mathematics

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(Shared by Paul, 2006 July)

8 Gifts that Do Not Cost a Thing

1) THE GIFT OF LISTENING...
But you must really listen
No interrupting, no daydreaming,
no planning your response.
Just listening.

2.) THE GIFT OF AFFECTION...
Be generous with appropriate hugs,
Kisses, pats on the back and hand holds.
Let these small actions demonstrate
the love you have for family
and friends.

3.) THE GIFT OF LAUGHTER...
Clip cartoons.
Share articles and funny stories.
Your gift will say, "I love to laugh with you"

4.) THE GIFT OF A WRITTEN NOTE...
It can be simple
"Thanks for the help" note or a full sonnet.
A brief handwritten note may be
remembered for a lifetime.
and may even change a life.

5.) THE GIFT OF A COMPLIMENT...
A simple and sincere,
"You look great in red," "You did a super job."
or "That was a wonderful meal"
can make someone's day.

6.) THE GIFT OF A FAVOR...
Every day, go out of your way
to do something kind.

7.) THE GIFT OF SOLITUDE...
There are times when we want
nothing better than to be left alone.
Be sensitive to those times and give
the gift of solitude to others.

8.) THE GIFT OF A CHEERFUL DISPOSITION....
The easiest way to feel good is to
extend a kind word to someone,
really, it's not that hard to say,
Hello or Thank You.

One more from somewhere else...

*THE GIFT OF ACCEPTANCE.. .
Everyone does the best they can
with what they have to work with
be it their head or their heart.*

(Shared by Hwee Peng, 2006 December)

Classification of Paradigms

(by Kemmis and Atkin – How Do Students Learn)

Instructional Paradigm

• To teach a given piece of subject matter, or to impart a specific skill. Involves a breaking down of tasks into sub-tasks, each with its own stated objectives and pre-requisites. Separate tasks are then structured and sequenced to form a coherent whole.
• Examples are drill and practice, skill and drill
  

Revelatory paradigm

• This involves guiding a student through a process of learning by discovery. The subject matter and its underlying model or theory are gradually “revealed” to the student.
• ICT tool acts as a mediator between the student and a hidden model of some situations. Exemplified in educational programmes by simulations of various types.
  

Conjectural paradigm

• Students are allowed to manipulate and test their own ideas and hypotheses, e.g., by modelling whereby the user creates a model of a situation and may go on to test it. Modelling is different from simulation as in a simulation, the model is pre-created by the programmer.

Emancipatory paradigm

• ICT is used as a labour saving device, tool that relieves mental drudgery. For example, ICT tools are used fro tabulating data, calculating, statistical analysis, or drawing graphs.
• ICT is used purely as a tool for learner’s convenience, to be used when and where as needed. ICT is only partly involved in the learning process, i.e. to take over the “inauthentic” learning part of the learning task.

In comparison with ICT in Education - Claims, Issues and Perennial Questions

(a) Claims

• Motivate and excite learners
• Increase achievement
• Allow differentiation and individualisation of learning
• Increase learner autonomy and independence
• Provide an enriched, stimulating teaching and learning environment
• Allow learners to learn at their own pace
• Have a positive impact on standards and achievement
• Focus student attention
• Teach important facts and skills
• Enhance the learning of difficult, abstract concepts
  

(b) Issues

• Lack of training
• Lack of time to learn
• Lack of access and availability
• Attitude to and fear of using ICT
• Scepticism about its actual benefits in the classroom
• Lack of collegial support, e.g. Principal, HOD
• Lack of technical support
• Danger of unrestricted access to the Internet

(c) Perennial Questions

• Why should ICT be used in Education?
• When should it be used?
• When should it be not used?
• How can ICT use be successfully integrated into the curriculum?
• What do teachers and learners actually gain from using ICT?

(Shared by Mr Ang, 2007 June)

Being a Mother

After 21 years of marriage, my wife wanted me to take another woman out to dinner and a movie.
She said, 'I love you, but I know this other woman loves you and would Love to spend some time with you.'
The other woman that my wife wanted me to visit was my Mother, who has been a widow for 19 years, but the demands of my work and my three children had made it possible to visit her only occasionally.

That night I called to invite her to go out for dinner and a movie. 'What's wrong, are you well?' she asked. My mother is the type of woman who suspects that a late night call or a surprise invitation is a sign of bad news.

'I thought that it would be pleasant to spend some time with you,' I responded 'just the two of us.' She thought about it for a moment, and then said, 'I would like that very much.'

That Friday after work, as I drove over to pick her up I was a bit nervous. When I arrived at her house, I noticed that she, too, seemed to be nervous about our date. She waited at the door with her coat on. She had curled her hair and was wearing the dress that she had worn to celebrate her last wedding anniversary. She smiled from a face that was as radiant as an angel's.
'I told my friends that I was going to go out with my son, and they were impressed,' she said, as she got into the car. 'They can't wait to hear about our meeting.'

We went to a restaurant that, although not elegant, was very nice and cozy. My mother took my arm as if she were the First Lady.

After we sat down, I had to read the menu. Her eyes could only read large print. Half-way through the entrees, I lifted my eyes and saw Mother sitting there staring at me. A nostalgic smile was on her lips.

'It was I who used to have to read the menu when you were small,' she said. 'Then it's time that you relax and let me return the favor,' I responded. During the dinner , we had an agreeable conversation nothing extraordinary but catching up on recent events of each other's life. We talked so much that we missed the movie. As we arrived at her house later, she said, 'I'll go out with you again, but only if you let me invite you.' I agreed.

'How was your dinner date?' asked my wife when I got home. 'Very nice, much more so than I could have imagined,' I answered.

A few days later, my mother died of a massive heart attack. It happened so suddenly that I didn't have a chance to do anything for her. Sometime later, I received an envelope with a copy of a restaurant receipt from the same place Mother and I had dined. An attached note said: 'I paid this bill in advance. I wasn't sure that I could be there; but, nevertheless, I paid for two plates - one for you and the other for your wife. You will never know what that night meant for me.'

'I love you, son'

At that moment, I understood the importance of saying in time: 'I love YOU' and to give our loved ones the time that they deserve. Nothing in life is more important than your family. Give them the time they deserve, because these things cannot be put off till some 'other' time.

Somebody said it takes about six weeks to get back to normal after you've had a baby... somebody doesn't know that once you're a mother, 'normal' is history.

Somebody said you can't love the second child as much as you love the first... somebody doesn't have two or more children.

Somebody said the hardest part of being a mother is labour and delivery....somebody never watched her 'baby' get on the bus for the first day of kindergarten... or on a plane headed for military 'boot camp.'

Somebody said a Mother can stop worrying after her child gets married... somebody doesn't know that marriage adds a new son or daughter-in-law to a mother's heartstrings.

Somebody said a mother's job is done when her last child leaves home... somebody never had grandchildren.

Somebody said your mother knows you love her, so you don't need to tell her... somebody isn't a mother.

Pass this along to all the GREAT 'mothers' in your life and to everyone who ever had a mother.

This isn't just about being a mother; it's about appreciating the people in your lives while you have them... no matter who that person is!

Watch your thoughts, they become words.
Watch your words, they become actions.
Watch your actions, they become habits.
Watch your habits, they become character.
Watch your character, for it becomes...your destiny.

'Be kinder than necessary, for everyone you meet is fighting some kind of battle'.

(Shared by Adeline, 2008 May)

Wonderful Creations

(Shared by Poh Heng, 2008 April)

4 Squares

(forwarded by Adeline, 2008 July)

Maths Fallacies & Parodoxes

1. The Barber's Paradox
Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men who do not shave themselves.
Under this scenario, we can ask the following question: Does the barber shave himself?
Asking this, however, we discover that the situation presented is in fact impossible:
If the barber does not shave himself, he must abide by the rule and shave himself.
If he does shave himself, according to the rule he will not shave himself.

2. The liar's Paradox
A man says that he is lying. Is what he says true or false?
Known to the ancients as the pseudomenon, the liar paradox encompasses paradoxical statements such as "This sentence is false." or "The next sentence is false. The previous sentence is true." These statements are paradoxical because there is no way to assign them a consistent truth value.

3. The Birthday Paradox (Not exactly a paradox, but answer is quite counter-intuitive) (http://www.efgh.com/math/birthday.htm)
A favorite problem in elementary probability and statistics courses is the Birthday Problem:
How large must N be so that there is > 50% chance that at least two of N randomly selected people have the same birthday (Same month and day, but not necessarily the same year)?

The answer is 23, which strikes most people as unreasonably small. For this reason, the problem is often called the Birthday Paradox. Some sharpies recommend betting, at even money, that there are duplicate birthdays among any group of 23 or more people. Presumably, there are some ill-informed who will accept the bet.


4. The Monty Hall Problem (Not exactly a paradox, but answer is counter-intuitive) Try it: http://math.ucsd.edu/~crypto/Monty/monty.html
The problem is also called the Monty Hall paradox, as it is a veridical paradox in that the solution is counterintuitive.

Here's the problem:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Answer: Yes, switch your choice!
Because there is no way for the player to know which of the two unopened doors is the winning door, most people assume that each door has an equal probability and conclude that switching does not matter. In fact, in the usual interpretation of the problem the player should switch—doing so doubles the probability of winning the car, from 1/3 to 2/3.

A good info source on the problem: http://en.wikipedia.org/wiki/Monty_Hall_problem
Monte Hall problem - logical fallacy made by researcher in psychology experiment: http://www.nytimes.com/2008/04/08/science/08tier.html?em&
An excellent discussion forum with active & constructive discussions on the problem: https://nrich.maths.org/discus/messages/8577/7628.html?1077045704

An equivalant version using cards:
Suppose you have three cards:
a black card that is black on both sides,
a white card that is white on both sides, and
a mixed card that is black on one side and white on the other.
You put all of the cards in a hat, pull one out at random, and place it on a table. The side facing up is black. What are the odds that the other side is also black?

The answer is that the other side is black with probability 2/3. However, common intuition suggests a probability of 1/2.
In a survey of 53 Psychology freshmen taking an introductory probability course, 35 incorrectly responded 1/2; only 3 students correctly responded 2/3.
(Received from Hong Pin, 2008 July)

Optical Illusions (I)

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(Received from Adeline, 2008 July)

Video clips on Mathematics

Learning Math



Abbott and Costello - Math