More Vindication

The main policy of the district where I work: Close the achievement gap.

I have done this before with a forward thinking Principal. Double the time that students take math and the achievement gap narrows.

From an article in the New York Times:

‘No Child’ Law Is Not Closing a Racial Gap

'Where we see the gap narrowing, that’s because there’s been an emphasis on supplemental education, on after-school programs that encourage students to read more and do more math problems,” Dr. Hrabowski said. “Where there are programs that encourage that additional work, students of color do the work and their performance improves and the gap narrows.”'

But then there is the problem that most math teachers are familiar with:

'But Dr. Hrabowski said said that educators and parents pushing children to higher achievement often find themselves swimming against a tide of popular culture.

“Even middle-class students are unfortunately influenced by the culture that says it’s simply not cool for students to be smart,” he said. “And that is a factor here in these math and reading scores.”'

I love it when what I read confirms what I know.

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URL Change

Hello Readers,
Please note that the url to my blog has changed.
It is now:
http://www.mathmethinks.com/

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A Personal Odyssey

I felt vindicated when I read Thomas Sowell's autobiography.

Any teacher who considers rigor to be important, who has been tormented by students who want the good grade but are too lazy to work for it, who has felt pressured to compromise his or her standards by 'politically correct' but misguided administrators, who has been bullied by parents who think their children are little gods and goddesses, will appreciate Sowell's perspective on education.

The mediocre and poor teachers in the system, who are soft on rigor and give easy 'As', are the educators that no one complains about. It is a pity that so many people, probably the majority, would rather get a meaningless 'A' than really learn something but have to work for it. It is delightful to read about an educator who had the courage to stand by his principals instead of bend to the pressure of just about everyone.

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Daniel Tammet Can Recite 22,514 Digits of pi From Memory

From Scientific American: Daniel Tammet can recite 22,514 digits of pi. He holds the European record for such a feat. So, I guess there is a competition? The article covers an interview with Mr. Tammet in which he discusses memory and I.Q. tests.


As I peruse the internet I am fascinated with the many different ways people spend their time. How long did it take Daniel Tammet to memorize that many digits of pi?

Typing pi to 22,514 digits in a continuous (no spaces) stream, in a Word document with smaller than average margins, using Times New Roman, size 12 font, single-spaced, would take 5 or 6 pages of paper.

An interesting relation: Suppose Mr. Tammet can recite 2 digits per second (a reasonable estimate). Then it would take approximately 3.13 hours to recite 22,514 digits. In other words, it would take close to pi number of hours to recite pi to 22,514 digits.

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Arabic Tiling or Tessellation

This was created in Geometer's Sketchpad, put could just as well be created with a compass and straight-edge.

1. Start with a circle. Draw lightly if using a pencil, because the circle will be erased later. Make certain the center point is marked.


2. Using the same diameter, draw circles around the original one, using the intersections as the center points. Each outer circle intersects the center of the original circle.



3. Continue until six circles are drawn around the original.

There are a couple of interesting asides:

Six circles, with a constant diameter, fit perfectly, overlapping at the center points, around a center circle with that same diameter.

Also, six circles of the same diameter, fit perfectly around a center circle with that diameter.




4. Draw sets of parallel lines through the intersection points. Again, if using a pencil, draw lightly because the lines will have to be erased.



5. Continue, drawing the parallel lines in the 3 possible directions.



6. Erase the original circle design. Continue drawing parallel lines in the three different possible directions. Use the intersection points as guides.



7. More of the same.



8. For my design, I continued until I could draw a hexagon, whose sides were the width of 6 rhombuses.



9. Using the lines, starting from the center, draw a pattern of stars and hexagons. I chose to put a star at the center, but it could easily have been a hexagon.



10. Erase (delete) the lines and start coloring the stars...



11. ... and hexagons.

12. Finished (points were also deleted).

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