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)


  1. Some of the more innovative work is done by people who rethought the idea of a career. The choices of fighting or complying are both poor. Why not build your own systems?

  2. Pat is concerned about eliminating math classes for teachers as unnecessary and the Dean mentioned above stresses this opinion indirectly saying - why do need to know mathematics. Teaching mathematics in school is not about memorizing facts (unfortunately - this is a part stressed on standardized tests) - but learning the way of thinking. If prospective teachers are denied a possibility to acquire mathematical way of thinking they are made poorer teachers.

  3. Teachers should never stop learning.

    “The kids come first, teachers are a close second, because if anything happens in education it happens in a classroom between a teacher and the kid.” Duanne Kelly