Tuesday, January 25, 2011

Playful Math: Doodling to Aleph_null

I believe most people who really get mathematics are the ones who see the frivolity in much mathematical construction not as a flaw, but as a strength ( I am teasing my profession here). And sometimes presenting mathematics in playful ways is precisely the best way to expose deep meaning.

With a hat-tip to Engineering Innovation (@JHU_EI), a high school summer program in the Whiting School of Engineering here at Hopkins, I am reposting a video from one of their recent tweets.
Doodling in Math Class: Infinite Elephants
Have fun!

Oh, and BTW, we mathematicians tend to associate letters from other alphabets to important constants and concepts in our work. Aleph (the first Hebrew letter) is commonly used for measures of infinity. Aleph_null, or Aleph with the subscript zero, is used to denote a kind of infinity called countable infinity, and denotes the size of a set of objects that can be placed in a one-to-one correspondence with the natural numbers 1,2,3,... Jus'sayin'....

Thursday, January 20, 2011

Math (not quite) in the Media... College not producing?

A new study has come out which seems to conclude that a college education may not be worth the many hundreds of thousands of dollars it is costing these days. Here is an article from the Huffington Post detailing some of the points coming from the data. I have not read the study. The article, I have, and am less than impressed.

My take: While there may be quite an important trend uncovered by this survey, I believe (from my position) that some of the assumptions may not be fully vetted.
45% of Students Don't Learn Much in College
The article starts off well enough (emphasis mine):

A new study provides disturbing answers to questions about how much students actually learn in college – for many, not much – and has inflamed a debate about the value of an American higher education.

The research of more than 2,300 undergraduates found 45 percent of students show no significant improvement in the key measures of critical thinking, complex reasoning and writing by the end of their sophomore years.

However, this part bothers me:

One problem is that students just aren't asked to do much, according to findings in a new book, "Academically Adrift: Limited Learning on College Campuses." Half of students did not take a single course requiring 20 pages of writing during their prior semester, and one-third did not take a single course requiring even 40 pages of reading per week.

Where is the metric measuring critical thinking and complex reasoning OUTSIDE of a writing class? Mathematics and physical science-based courses are prime venues for the development of rational and analytic reasoning, no? How come no mention of non-writing-based courses in the ENTIRE article? Perhaps no data from these courses is in the study?

More from the article:

Three of the five classes [Julia Rheinecker, a freshman at the University of Missouri,] took... were in massive lecture halls with several hundred students. And Rheinecker said she was required to complete at least 20 pages of writing in only one of those classes.

I am very dubious about any direct link between college class size and either the difficulty of a course or its perceived lack of rigor. Large-lecture courses can be quite challenging and yet every bit as personal and interactive as small seminar-type classes. I doubt this study had any focus on class size at all. So this part is not relevant, IMHO.

And finally, some additional conclusions in the study:

_Students who studied alone, read and wrote more, attended more selective schools and majored in traditional arts and sciences majors posted greater learning gains.

_Social engagement generally does not help student performance. Students who spent more time studying with peers showed diminishing growth and students who spent more time in the Greek system had decreased rates of learning, while activities such as working off campus, participating in campus clubs and volunteering did not impact learning.

Knowing something about how math is taught and learned at the university level, I am hard-pressed to believe any data showing that studying alone is better than studying with peers. On this point, I can write volumes! And there are data and programs (Think PLTL, for example) to support the opposite conclusion. In fact, we have a local PLTL program here at Hopkins, and our data do not support this study's conclusion in this point.

Overall, I see this study as being a bit alarmist. Critical studies on the effectiveness of college education are absolutely necessary. I will read this study. But I am already biased due to this article. Oh well....

Tuesday, January 11, 2011

Undergraduate Research Opportunity!

I just got a solicitation for a great summer program in research for undergraduates. Click on the flier to see the details. It is the Research in Industrial Projects for Students (RIPS) program at the Institute for Pure and Applied Mathematics (IPAM) at UCLA. Top-notch, IPAM is, and I am sure the opportunity is quite competitive. But the program is a good one, and will make for a great credential (not to mention the experience!). Check it out and let me know if you plan to apply: The deadline is February 10. Plenty of time to get your act together, no?