Thursday, December 30, 2010

Happy New Year!

This is that time of the year when you suddenly realize that only one last day is left for all the things you wanted to accomplish this year.
 May be that is even better - to have still things to do on a list. It means that instead of making a new list there will be already "to do" list to keep going!
Thank you for visiting my blog and hope you will come back here next year!

Wednesday, December 22, 2010

No need to know the area of the rectangle?

Last time I was in New York I saw an exhibition at New York University's Institute for the Study of the Ancient World about  Babylonian mathematics. It is not particularly large but it was very special for me. The first book on the history of mathematics I ever read was a book on mathematics in Ancient Egypt and Babylon by Vygotsky M. Ya. Арифметика и алгебра в древнем мире, 1967
This book was given to me as a present from my beloved math teacher. Since then I was dreaming one day to see these mathematical cuneiform tablets and now finally my dream came true.
These tablets are showing that in Ancient Babylon people knew equivalent of Pythagorean Theorem which nowadays children in US schools first learn in grade 8 according to new Common Core Standards.
Pictorially this theorem is known as:
or we can say that the area of the green square equals the sum of the areas of the blue and red squares.
Too often when I talk about hyperbolic planes people say "oh, I am not good at math". Usually that is said with some regret that they did not have good math teachers at school or were discouraged to be more serious about learning math.  I have often wondered - what is wrong with school math? Why it leaves in so many people so bad memories?
There is a saying in Latvian - ' Fish begins to rot at its head." meaning that the source of the problem is at the top not bottom - e.g. we should not blame teachers without first looking how they have been prepared.
Today I heard a shocking quote:
"I got to be a full professor without knowing how to find the area of a rectangle.  Why should you expect third graders to learn that?" I think that ANY person should know that but this was not an ordinary person who said that - it was  the Dean of Education School of one of NJ colleges.
This story really struck me, so I decided to post it on my blog:

 Pat Kenschaft wrote to my husband : "... my spouse was fired last Thursday, allegedly because of an email that I wrote to my list of people who want New Jersey to require preservice elementary school teachers to
take at least one course in mathematics relevant to their teaching. (I'm told on good authority that a dozen NJ deans of education oppose this.Montclair State's said to me, "I got to be a full professor without knowing how to find the area of a rectangle. Why should you expect third graders to learn that?" I have taught areas of rectangles to hundreds of third graders without failure in the sense that they knew it when I left the room.) ".

Here follows the e-mail that had such dramatic consequences:

---------- Forwarded message ----------
Date: Tue, 14 Dec 2010 20:43:48 -0500 (EST)
From: Pat Kenschaft <>
To: undisclosed-recipients:  ;
Subject: letter to editor re math for elementary school teachers

I had the letter below about the need for elementary school teachers to be taught more mathematics in the "Montclair Times" this past Thursday It is not copyrighted and you are free to use or forward it however you like.
The importance of this issue was emphasized to me recently when a friend reported a conversation with a Monclair second grade teacher. She said she knew plenty of math for her job because the teacher's manual of "Everyday Mathematics" tells her just what she should say each day. She said the children should learn only one way, so there is no need for her to answer probing question or explore their ideas of other methods for solving problems. This, I know, is not in the spirit of those who wrote "Everyday Math," nor is Montclair an impoverished school district. It is exactly the kind of approach that keeps children from growing mathematically. Alas, I fear it is all too typical of American elementary school teachers.
What can be done? I fear that our current governor might use this issue as another reason to undermine teachers, which would mean we would continue to lose our good and experienced teachers. Teaching has always been a challenging career, and now it is losing its advantages with alarming rapidity.
On the other hand, if the state and municipalities really want to improve mathematics education, I believe this is the most crucial step.

To the Editor:

Improving Math Education

After New Jersey's first high school proficiency test was instituted, I noticed a remarkable DROP in the math preparation of my non-majors in college. Test-prep is not education, despite the pressure for AYP.
What to do? Teach the mathematics to elementary school teachers that they are supposed to teach the children! They are capable and eager to learn. They are angry when they realize how much they have been deprived the needed knowledge. Once the children are damaged, it is VERY difficult
to undo when they reach middle or high school. Many again take remedial courses in college.
A national coalition of fifteen mathematics organizations recommends four APPROPRIATE mathematics courses for future elementary school teachers. I know of only two states requiring four, but quite a few require three. New Jersey requires NONE. A reliable source I dare not reveal assures me there are a dozen deans of education in New Jersey adamantly opposing a certification requirement that future elementary school teachers be taught appropriate mathematics.
Concerned citizens can let state officials know of their concern and email me at kenschaft @pegsasus. They can read about my seven years of helping elementary school teacher mathematically in my paper "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" .
At the beginning of this program I worked with two fine Montclair teachers. Montclair stiffed its teachers, so we didn't contract with Montclair again. Both teachers worked hard anyway. Their students improved greatly, but then one was switched to full-time social studies. We have a new administration now, so Montclair might want to help its elementary school teachers mathematically.
I repeat: the teachers are plenty smart and eager enough! Like the children, they have been let down by our system."

Pat Kenschaft  added in today's e-mail:
"This stuff is politically dangerous, but we who do not have a lifetime career to lose any more need to work at it. "(bold/underlining mine -DT)

Tuesday, December 14, 2010

Art Break in NYC

yes, indeed, this is that time of the year when people go to New York to see Christmas lights and all what goes with it. I had two days full of art there. First, to the DUMBO in Brooklyn - I went to see Maddy Rosenberg in Central Booking where we chose 9 of my works which will be in the upcoming show. Then my dear friend Gail took me to the Park Avenue Armory to see Peter Greenaway's vision "Leonardo's Last Supper".   Peter Greenaway was trained as a painter, so it was really interesting to see what he saw in this painting. The first experience walking in and having a first glimpse of the painting reminded me of the time last year when David and I saw the original in Milan, except there you come in through the door on the right side of the painting. In this performance there is a time in the beginning to take it in as it is. I had another opportunity to check the lines of perspective in this painting, this time avoiding security guards jumping at me and checking what I have in my hand as it happen in Milan - there they thought I am taking forbidden pictures.  the look on their faces after I explained that I am mathematician and looking for geometric constructions in the painting was worth the entrance fee...
There is a special border, the border between art and life that often shifts deceptively. Yet, without this border, there is no art. In the process of being produced, art borrows material from life, and the traces of life still shine through the completed work of art. But, at the same time, the distance from life is the essence, the substance of art. And, yet, life has still left its traces. The more scarred the work of art is by the battles waged on the borders between art and life, the more interesting it becomes.
--Anselm Kiefer
Then Gail took me to the two openings - both near Chinatown - it was already dark and I was happy that Gail was leading the way. 

When we walked in the first one I saw a guy offering some wine to the guests, he had only one glass left on his try and I thought I should take it. When I took it, I could read in his eyes that he thought I did not deserve it because I am certainly not the one from this crowd. He was right. I found a huge gap in my art appreciation palette. I noticed a tiny sketch of nude, like the ones my classmates in 6th grade where drawing when they first discovered that girls are different from the boys. I thought it was a joke to frame it and put it on a show. I was wrong - these were all donated works and this one had a price....$17,500.....
At that point it was clear that I do not understand this show and it is time to move to the next, several blocks away.
Sorry for forgetting the author's name but he was a handsome man, originally trained as a painter. This place was small but tightly packed with a younger and more democratic crowd than the first place.
Then we returned to Brooklyn to see Gail's own painting.
More of Gail's work is on her webpage. I got to know Gail through her interest in my work, and I am so happy we found each other. I am really thrilled about the unexpected side effect of "hyperbolic crochet" - hundreds of people who did not know each other, get together and connect. One day I will write more about my own experiences, but my friendship with Gail is certainly one of them. Some times I never meet people but we have only e-mail contact. Like it was with Cat Bordhi - she has wonderful knitting books with a mathematical twist. Marie-Christine Bevington came to my talk in Kitchen (February 5, 2005). She told me that she was surprised to find out then that she was making hats with some hyperbolic crochet in them. That talk inspired her to further explore the possibilities and she came up with many more interesting hats. On Friday I had a chance to see all these hats.
This hat is Christine's original design - made of hexagons, pentagons, squares, and triangles. This hat snugs any head really nicely due to positive curvature formed.
All these different hats were fiber art objects on their own right. Thanks, Christine, for inviting me!
I visited also Cooper-Hewitt museum to see the National Design Triennale, and of course, The Bleached Reef in it.
How about the Christmas lights? Well, did catch some just before the bus back to Ithaca.

Saturday, December 4, 2010


First - this is a reason for not posting:
It is not all new - this is the same large pink hyperbolic plane made of 88 skeins of yarn seen in my book with a cat. Now it is 20 skeins larger (I found some leftover stock of discontinued yarn on eBay). It actually is just two more rows added but with more defined outer edge and some support and now it measures 30 x 30 x 22 in and weighs about 6 kg.

Hyperbolic Crochet Coral Reef is featured in today's National Geographic News blog - look for a video and nice pictures from the exhibit in Museum of Natural History in Washington, DC.