Through Math for America, I am part of an ongoing collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here
Test Yourself Math — November 13, 2013
This question deals with the Common App, an online system that processes millions of college applications every year. What is the average number of applications processed per college?
We recently hosted artist and computer programmer Nathan Selikoff at our school, and he spoke to our students about art, mathematics, and technology.
Nathan Selikoff is an award-wining artist and an organizer of the Bridges Math and Art conference. In his talk, “Art, Chaos, and Computation”, Nathan provided an engaging overview of the history of computation in art while talking about his personal experiences conceiving and creating mathematical art.
The talk left quite an impression on our students, many of whom were not aware that mathematicians and computer scientists could also be artists. Students left the talk interested in experimenting with their own mathematical creations, and they were excited to play with the programs the artist generously provided.
A few student quotes nicely summarize the impact of the talk:
It made me want to learn more about the codes and the mathematical equations that make up the paradoxes of the chaotic art pieces.
This really makes me wonder about the extent of art that can be created. I’m curious to find out what I’ll be able to program.
The talk inspired me to create my own art with math equations.
Thanks to the artist for such a great visit! You can find out more about Nathan Selikoff here. And be sure to check out the Bridges Math and Art conference.
This is “As Above So Below” by Martin Levin. You can find out more about his work here.
This is another piece from the 2013 Bridges Mathematical Art Gallery.
A colleague and I had an interesting conversation about a quiz question of his. He asked students to put the four following quantities in order from least to greatest:
I don’t think I’ve ever written a problem like this for a test or quiz myself, which may explain why thinking about how to assess potential answers perplexed me so. How, exactly, would you grade this problem?
Suppose the correct order is A > B > C > D. A first attempt to grade this problem might be “One point for every item in the correct absolute position”. So
A > B > D > C
would earn two out of four points, as only A and B are in the correct absolute position, while
B > D > C > A
would earn one point, as only the C is in correct absolute position.
But there are some issues with this approach. This response:
B > C > D > A
earns zero points, since no item is in the correct absolute position. But in some sense this response is mostly correct: three of the items (B, C, and D) are correctly ordered relative to each other. Notice also that, in this scoring system, it is impossible to get 3 our of 4 points: the only possible scores are 0, 1, 2, or 4.
My suggestion was to consider all 
B > C > D > A
implies the following correct relationships: B > C, B > D, and C > D. The other three implied relationships are incorrect, thus this response would earn 3 out of 6 points.
The problem with this scoring system is that it is nearly impossible to get a zero! The only response that earns zero points under this scheme is
D > C > B > A
but this answer is compelling in its own way. The correct order is perfectly reversed, which strongly suggests the student knew something about the order of the items.
I like this problem, but I don’t think I”d put it on a test. It’s too hard to assess! But it was fun and mathematically interesting to think about, so maybe I’ll put the question “How would you grade this question?” on a test.
My latest effort for the New York Times Learning Network is a text-based lesson designed to get students thinking about the relationship between science and religion.
Using the NYT LN’s text-to-text format, we’ve put a 1930’s NYT editorial by Albert Einstein on “Religion and Science” together with a recent article about efforts between physicists and Tibetan monks to improve understanding between the two groups. Students read the two pieces with some guiding questions, looking for similarities and differences between what Einstein and the Dalai Lama are describing.
The Einstein piece is especially good. Here is a favorite excerpt.
It is therefore, quite natural that the churches have always fought against science, and have persecuted its supporters. But, on the other hand, I assert that the cosmic religious experience is the strongest and the noblest driving force behind scientific research … What a deep faith in the rationality of the structure of the world and what a longing to understand even a glimpse of the reason revealed in the world there must have been in Kepler and Newton to enable them to unravel the mechanism of the heavens in long years of lonely work!
In any event, I’m proud to have brought Albert Einstein, Richard Feynman, and the Dalai Lama together in one piece! You can read it here.
