Saturday, February 9, 2013

Via Being Liberal / FB:

"This. Is. Excellent. Image from Mike Luckovich AJC, that guy is an incredibly bright artist."

Reposted from the Being Liberal fan page.
(M) This. Is. Excellent. Image from @[200178736879:274:Mike Luckovich AJC], that guy is an incredibly bright artist.

Posted on the @[177486166274:274:Being Liberal] fan page.


Friday, February 8, 2013


JMG Photo Of The Day:

I've blogged quite a bit about the construction of the Second Avenue Subway here on the Upper East Side, but haven't said much about the project to connect Long Island Railroad to Grand Central Terminal.
Buried 16 stories beneath Grand Central Terminal a new commuter rail is being blasted and tunneled out of solid bedrock as part of an audacious $15 billion development that will span 14 miles throughout the city. The grand concourse, seen at a massive eight stories high surrounded by dripping stone walls and lapping puddles, will provide more floor space than New Orleans' Superdome stadium when finished. It is just one of three monumental projects underway beneath New York City's streets to expand what's already the nation's biggest mass transit system transporting 5 million riders a day.
But even with blasting and machinery grinding through the rock day and night, most New Yorkers are blithely unaware of the construction or the eerie underworld that includes a 160-foot cavern, miles of tunnels and watery, gravel-filled pits. Down below them, engineer Michael Horodniceanu says it's an astonishing sight that gets him every time. 'I look at it and I'm in wonder, I'm in awe,' said Horodniceanu, president of capital construction for the state Metropolitan Transportation Authority. 'I feel like when I went to Rome and entered St. Peter's Basilica for the first time. ... I looked at it and said, "Wow, how did they do that?"' 
Hit the link for many more very cool photos. So far the digging under Grand Central has removed enough material to cover all of Central Park under a foot of rock.

Reposted from Joe

Wednesday, February 6, 2013

Via The Peoples Boycott / FB:

From Mathematics for Teaching website. See
George Polya's Ten Commandments for Teachers
[Posted by Erlina Ronda]       
This is George Polya's 10 commandments for teachers:

1. Be interested in your subject.
2. Know your subject.B
3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.
4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.
5. Give them not only information, but "know-how", attitudes of mind, the habit of methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand as may be useful in solving the problems to come - try to disclose the general pattern that lies behind the present concrete situation.
9. Do not give away your whole secret at once-let the students guess before you tell it-let them find out by themselves as much as feasible.
10. Suggest it, do not force it down your throats.

I got this from the plenary talk of Bernard Hodgson titled Whither the mathematics/didactics interconnection? at ICME 12, Korea, where he highlighted the important contribution of George Polya in making stronger the interconnection between mathematics and didactics and between mathematicians and mathematics educators.
If it's too hard to commit the 10 commandments to memory then just remember the two rules below which is also from Polya. Combine it with Four Freedoms in the Classroom and you are all set.

The first rule of teaching is to know what you are supposed to teach.

The second rule of teaching is to know a little more than you are supposed to teach.


The Four Freedoms in the Classroom  []
[Posted by Erlina Ronda]       
You will find that by providing the following freedoms in your classroom an improved learning environment will be created.

The Freedom to Make Mistakes
Help your students to approach the acquisition of knowledge with confidence. We all learn through our mistakes. Listen to and observe your students and encourage them to explain or demonstrate why they THINK what they do. Support them whenever they genuinely participate in the learning process. If your class is afraid to make mistakes they will never reach their potential.

The Freedom to Ask Questions
Remember that the questions students ask not only help us to assess where they are, but assist us to evaluate our own ability to foster learning. A student, having made an honest effort, must be encouraged to seek help. (There is no value in each of us re-inventing the wheel!). The strategy we adopt then should depend upon the student and the question but should never make the child feel that the question should never have been asked.

The Freedom to Think for Oneself
Encourage your class to reach their own solutions. Do not stifle thought by providing polished algorithms before allowing each student the opportunity of experiencing the rewarding satisfaction of achieving a solution, unaided. Once, we know that we can achieve, we may also appreciate seeing how others reached the same goal. SET THE CHILDREN FREE TO THINK.

The Freedom to Choose their Own Method of Solution
Allow each student to select his own path and you will be helping her to realize the importance of thinking about the subject rather than trying to remember.

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