The Mathematics of Redistricting

Dr. Moon Duchin is an associate professor of mathematics at Tufts University and the founder of the Metric Geometry and Gerrymandering Group.

AGENDA
3:00 – 4:00 p.m.   First Lecture: Gerrymandering and the Mathematics of Voting Rights
4:00 – 4:30 p.m.   Refreshments
4:30 – 5:30 p.m.   Second Lecture: Discrete Curvature in Redistricting and Group Theory

Seating is limited.
For more information, contact Ronald Perline at [email protected].

Getting Sets Quickly in Columbus

Available at the special price of $21 through 9/15/2016 with discount code EX097

Available at the special price of $21 through 9/15/2016 with discount code EX097

Hannah Gordon won the championship for the game Set in 2006 the one time it was held. She returned to Columbus, Ohio, this week with her parents Liz McMahon and Gary Gordon, for the Mathematical Association of America MathFest 2016. She challenged conference attendees to the game. In the unlikely event she were to be defeated, attendees would get a free copy of their book The Joy of Set.
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Early Math is as Important as Early Literacy

— by Connie Orman

How can we help our children become academically accomplished? Parents want to do what is best for their children, but don’t always know how they can help. According to a Northwestern University 2007 study of 35,000 preschoolers in the United States, Canada and England, when controlling for IQ, family income, gender, temperament, type of previous educational experience, and whether children came from single or two parent families, the study found that the mastery of early math concepts on school entry was the very strongest predictor of future academic success. “Mastery of early math skills predicts not only future math achievement, it also predicts future reading achievement,” Greg Duncan, author of the study, said. “And it does so just as reliably as early literacy mastery of vocabulary, letters and phonetics predicts later reading success. The opposite, reading skills predicting math success, does not hold up.” However, in early learning environments, most of the time and attention are focused upon early language and literacy skills.

More after the jump.
According to Jennifer McCray of the Erikson Institute, for every 100 early childhood classrooms in session on a day, 96% would engage in language and literacy activities that day, 30% would engage in some form of art or music, but only 21% would engage in any math activities. Early childhood settings are not engaging in mathematics in even the most cursory manner.These are the findings for formal child care settings and preschools. Children that stay at home, stay with relatives or are in home child care settings, are most likely receiving even fewer opportunities to explore mathematical concepts.

Parents and educators are encouraged to provide early literacy and language activities such as reading to children, teaching the left to right convention, singing the alphabet song, pointing out letters and words, sounding out letter phonics and words, correcting misconceptions and errors. Yet when similar mathematical concept activities are provided, it is often looked at as not developmentally appropriate or necessary.

Mathematical literacy is not just as important as reading literacy, it has been proven to be even more so. Just as reading literacy should be introduced from birth with reading and language activities, mathematical concepts should be introduced early and often as well.

The reality is that we do math every day at every age in multiple ways. We graph, sort, compare and contrast, group, measure, count in context, do 1-1 correspondence, quantify, pattern, study geometry, and the list goes on. It is all done through hands-on, playful activities.

So if you have the care of a young child and are not currently doing activities that enhance math concepts, I strongly urge you to do so. All it takes is looking for fun, preferably hands-on or movement-based opportunities.

  • Count blocks, toys, the number of flowers on a page in a book, using the child’s finger, or toe, or elbow to touch each one as the number is said.
  • Pattern cars, blocks, rocks, Fruit Loops.
  • Line up the teddy bears or dollies from smallest to biggest and the other direction.
  • Measure how long some things are in the number of your hand prints and the child’s and compare the two.
  • Discuss amount concepts such as more/less, greater/fewer, a little/a lot, taller/shorter, bigger/smaller.
  • Discuss time concepts such as morning, night, later, after, before, when.
  • Discuss ordinal count concepts such as the third dolly in line is wearing a pink dress, you go first and I’ll go second.
  • Point out numbers in the environment such as price signs and license plate numbers.
  • Count stair steps and anything else that can be felt through movement or touch.
  • Introduce a ruler, tape measure, pound scale, balance scale, yardstick, measuring cups, etc. as tools to measure.
  • Discuss the weather temperature.
  • Discuss prices and money. Don’t just say it costs too much, say it costs $5.46 and I don’t have enough money for that.
  • Discuss shapes in the environment, and not just circles and squares. A sliver of moon is a crescent, an oat container is a cylinder, a ball is a sphere.
  • Deconstruct quantities into various equations, “You have 6 cars. Three red cars and three blue cars. That makes 6 cars in all. Three and three is six, two threes is six.”
  • “Do you want 1 or 2 cookies?” Hold up both quantities so the child can grasp the significance.  Believe me. An 18 month old can figure out which is better. One plus two!
  • Mathematics has its own language, whenever available use the opportunity to describe mathematical thinking. “If we divide this candy bar into four equal pieces, then each of us will get the same amount, one-fourth of the candy bar.”

Just as a child will not immediately be able to read from being read to, a child will not immediately be able to do math from being introduced to math concepts. But similarly, it sets the stage for scaffolding knowledge. It builds a repository of information for them to access as they encounter relevant situations and opportunities to test and manipulate that information.

Since so little attention has been paid to mathematics as an early introduction subject, it will be interesting to see what children can accomplish if it is given the same time and attention as early literacy. I know my students far exceed my expectations of what they should be capable of understanding.

With earlier attention to this important aspect of children’s education, maybe the science, technology, engineering and mathematics initiatives will begin to have even greater success in luring students into these fascinating and needed fields.

Connie Orman is the creator of Little Stars Learning.

A Film Informs My Sh’ma: Powers Of Echad

— by Rabbi Avi Shafran

As a single young man in 1977, I once found myself in a science museum where I viewed a just released short film that — there’s really no other way to put it — expanded my consciousness.  It apparently did the same for many others and remains to this day, despite powerful advances in special effects, an impressive work.

More after the jump.
Produced the year I encountered it by husband and wife team Charles and Ray Eames, Powers of Ten begins with a simple scene, a picnic in a Chicago park.  As predicted by the voice-over, though, the camera pulls away from the picnic, at a rate of one power of ten per 10 seconds.  The zoom-out continues straight up, so that, in a few seconds, the picnic blanket is but a dot of color against the green expanse of the park, which soon enough, with the camera continuing to soar heavenward, itself shrinks to a speck.  Then the viewer sees the outline of Lake Michigan, then North America; the earth’s cloud cover next fills the screen, and then earth itself, which itself quickly recedes into the distance.  Eventually we see an image of our solar system and then the galaxy to which it belongs, before it, too, becomes but one of many galaxies.  The camera seems to fly ever backward, until it reaches the farthest reaches of space.


The effect is visceral, or at least it was for me.  It recalled to me how, as a child, I would sometimes lie flat on my back on our lawn on a clear dark night and concentrate my vision on the starry sky until I felt an inexplicable and sudden shock.  It was as if the sheer vastness of the stars, of the universe itself, had somehow reached out and seized me; it was a frightening experience, yet one that, when feeling brave, I would occasionally seek out.  Although Powers of Ten on a screen could not quite evoke that childhood shudder, it visually captured, maybe even more compellingly, the vastness of the cosmos.

The film, which proceeds from outer space to inner space, zooming back in to the picnic and then further, into the skin of a picnicker, into one of his cells and its DNA, then into an atom and an electron, has been recently celebrated on the 35-year anniversary of its release.  (Charles Eames passed away the following year, in 1978, and his wife Ray, in an arresting irony, died precisely — to the Gregorian calendar day — ten years later.)

The short film actually plays a role in my life as an observant Jew, thrice daily when reciting the fundamental Jewish credo, the Sh’ma (at morning and evening prayers and before retiring). The Sh’ma declares G-d’s transcendence of time and space, and, as we pronounce the word echad (“one”) halacha prescribes that we try to conceptualize, to the degree we can, the immensity of the universe – “above and below and in all four directions” (Brachos 13b) — and the fact that the Creator of it all is not of it at all but “beyond” it and in control of it.

One of the ancient Hebrew euphemisms for G-d is “Makom,” which literally means “place.”  The Talmud explains that the word describes the Divine because “the universe is not His place, but rather He is the ‘Place’ of the universe.”  

Leaving — even in our imaginations — the dimensions of time and space isn’t an option for us mortals.  We are like the two-dimensional residents of Flatland, Edwin Abbott’s 1884 satirical fantasy world, trying to comprehend three-dimensional existence.  There is a reason the Hebrew word for both time and space is “olam,” rooted in “ne’elam,” which means “hidden.”

And yet, we are required all the same to concentrate, as we recite the first verse of the Sh’ma, on G-d’s transcendence of time and space.  That can be done in an entirely intellectual manner, without any sort of visualization.  I find it helpful, though, when I recite the Sh’ma, to try to capture something of the feeling I felt as a child lying on the lawn on those starry nights. Images from Powers of Ten, as they did 35 years ago, provide me a “visual” to accompany the intellectual recognition of the scope of the olam.

I doubt that the Eamses ever thought of their film as something that would come to invigorate a Jewish religious devotion.  But that’s what it did, at least for this Jew.

© 2012 Rabbi Avi Shafran

It’s All in the Angle (Torah Temimah Publications), a collection of selected essays by Rabbi Shafran, is now available from Judaica Press.