I have left Harvard as of July 1, 2008 to take a position at
NYU.
This website has been cached and left static. Feel free to browse
my
new website,
aka "What the heck is a Clinical Associate Professor?"
02.18.08
Posted in News, Education at 2:29 pm by leingang
Today I saw in one of the University of Michigan student papers an article about a WSJ blog post about a Chronicle of Higher Education column about a new book about college freshmen and their first experiences away from home. The Chronicle story is called “The Myth of First-Year Enlightenment” and the book tries to burst the bubble of those who picture a monumental eye-opening and metamorphosis during the first year. Instead of undergoing then sudden realization that the world is much bigger than they originally thought and what they had come to value was now clearly so…philistine (this was the word used at my freshman orientation), Tim Clydesdale writes,
Most of the mainstream American teens I spoke with neither liberated themselves intellectually nor broadened themselves socially during their first year out…What teens actually focus on during the first year out is this: daily life management.
Most American teens keep core identities in an ‘identity lockbox’ during their first year out and actively resist efforts to examine their self-understandings through classes or to engage their humanity through institutional efforts such as public lectures, the arts, or social activism. Contemporary teens are practical men and women. They . . . manage their daily lives fairly well. But they are not, by and large, thinking men and women.
Practical rather than paradigmatic shifts, I suppose. Clydesdale writes that some students do undergo big philosophical changes, but those are the exception. They end up becoming college teachers and perpetuate the metamorphosis myth.
How does that affect current college teachers? I think the older I get the more I appreciate the college experience, but I have to remember what I was actually like as a college freshmen. And even then I have to acknowledge that my experiences of learning the discipline I teach aren’t shared by the general population of students taking introductory courses in that discipline. Although Math 160’s at the University of Chicago changed the way I think about mathematics, that doesn’t mean that everyone should take it. But understanding where students do come from helps me reach them.
Getting this away from me: James Lang writes in the Chronicle story that we can do better at motivating our courses with what our students are seeking. No, not grades. 
But practical-minded students need the tools to communicate, to analyze, to formulate, to critique, to defend, to think, to solve problems, and so on. He says he’s stopped advertising that he plans to change the way students think, leaving it as a covert mission. Now he focuses on teaching them to think in the first place.
Blogged with Flock
Tags: teaching, freshmen
Permalink
Comments off
11.16.07
Posted in Education, Web at 3:02 pm by leingang
I was at the monthly web pegagogies free lunch sponsored by the Bok Center today and we talked a little about using social bookmarking sites like del.icio.us to collect bookmarks as a group. (There was also a nice demonstration of Facebook by two students, but I’ve already blogged about a similar presentation they made last Spring). I like the idea, but I’m wondering about the methodology.
In the examples of this that I’ve seen, a delicious account is created and the password is given to all the students in the group. The account is given a course-specific username like “history1667″ Then students use that account to save tagged bookmarks relevant to the course. Then to view all the bookmarks tagged by the group you go to the group’s user page.
I think this unnecessarily confuses the distinction between a user and a tag. It seems to me that people in the group should use their own delicious accounts to add a “history1667″ tag to their bookmarks. Then you can view the collection of pages tagged for the course by looking at that tag’s page.
That would certainly result in more links as students who already use delicious regularly wouldn’t have to log out/log in to do their research (delicious integrates well with browsers and can be hard to extricate). And it means that people could add links to that collection even after they left the course, and new students would have at their fingertips all the old links, without having to worry about passwords. And the entity “History 1667″ seems more to me like an attribute of the link than an agent in and of itself.
I’ve started doing this for my courses. If I’m looking at a page that might be useful for my Math 20 or Math 21b course, I can just tag it. I don’t have to re-login. I can tag the same page for as many of my courses as I want. And if my students want to do the same, the bank becomes richer.
There are, I suppose, reasons for having a controlled account. There might be another course numbered History 1667 at another university. Well, make the tag less common (I almost said “more unique” there) by calling it “HUHist1667″ or “HUHist1667Fall2007″ (then, if you want a fresh batch every semester you just change the tag). Most delicious interfaces feature tag-completion so you don’t even have to worry about it being easy to remember. Or, you can just apply the philsophy of folksonomy: don’t worry about it. Tag clouds make sure that the most important (as defined by user activity) links bubble up. It’s only going to become a problem if the tag is used by two groups equally frequently, which is unlikely and can by choice of tag name be made even less likely.
Another worry might be that outsiders might start using the tag to randomly bookmark irrelevant things like, as someone suggested, a picture of a cat. Again, I think the response is don’t worry about it. A basic tenet of semantic web philosophy is that anybody should be able to declare anything about anything, and it’s up to another layer to endow the trust. In this case, the user him/herself is the trust layer by visually weeding out the irrelevant links, and the tag cloud by making pages more users have marked with the same tag more connected to that tag.
A third objection might be that we don’t want to force students to create accounts on third-party services if they don’t want to, or to open up their use of a third-party service to a class. I can kind of see that, although delicious is for sharing bookmarks, so if you don’t want to share them with the world, why are you using it? But I can see wanting to share different things with different groups (and under different identities). So then maybe you have a group account for those who don’t want one, or encourage users have don’t want to use their “private” delicious accounts to create another one specifically for coursework.
So there’s a tradeoff between openness and quality, but I say, the more the merrier.
Blogged with Flock
Tags: tag, folksonomy, web, pedagogy, bookmarking, del.icio.us, delicious
Permalink
Comments off
10.04.07
Posted in Math, Education, Pop Culture at 10:04 am by leingang
Today marks the 50th anniversary of the launch of Sputnik 1, a mostly harmless satellite but only the first man-made object to orbit the earth. It had a profound effect not only on world politics but on education in the United States. As written in Air Force Magazine this month:
In beating Washington to the punch in space, the Kremlin really hit us where it hurt—in our technological ego. Sputnik instantly catapulted the Soviet Union onto the world’s scientific top shelf, raising doubts about America’s own standing…After initial soul-searching, the US embarked on a massive and determined space effort. The Pentagon formulated a huge program. On the civilian side, newly created NASA did the same. The aerospace industry exploded. Colleges were flooded with new engineering students eager to take up the Russian challenge. Public education turned hard toward math and science curricula. Sputnik may have started the Space Age, but America created the Space Race. Soon, the US was to leave Moscow in the dust.
Thanks, comrades! But that was 50 years ago—I’m looking forward to the next big push in science and math education. Or, results of it.
Blogged with Flock
Tags: sputnik, education
Permalink
Comments off
05.21.07
Posted in Math, Math 1b, Math 1a, Education at 7:50 am by leingang
Last week an Ontario-based programmer named Antonio Cangiano started writing his Math Blog - Mathematics is wonderful! (I agree, BTW). Only two articles so far, but one of them rose up the digg ranks pretty quickly and crashed his server. So maybe he’s doing something right.
Refresh your High School Math skills is a post containing precalculus math problems. I’d agree with him that these are the kinds of faculties we’d like our students to have going into calculus–algebra, trigonometry, inequalities, familiarity with exponentials and logarithms, etc. I wish we could assume more of the conic sections material was taught but it doesn’t seem that way anymore.
His other post is called “The most enlightening Calculus books” and is about his favorite books. There is massive debate among college math teachers about how best to teach calculus: reform, IBL, “Harvard Calculus” (which I do not teach), the list goes on. And as someone who has perused dozens of free calculus books from publishing companies, I can say that I still haven’t found the perfect book for wide university appeal.
What I want in a freshman calculus book is:
Tell no lies
I don’t insist on epsilons and deltas in a book, but I think we can get within epsilon of it (sorry). The concept that f(x) can be made arbitrarily close to L by taking x sufficiently close to a is precisely the definition without the greek letters, absolute value bars, and the dreaded less-than sign.
I think the derviative should be defined as a limit of difference quotients, and the integral should be defined as a limit of Riemann sums. I don’t think we need to prove that all continuous functions are integrable (that requires uniform continuity, which requires compactness of closed intervals, which I think is a little much), but the Fundamental Theorem of Calculus needs to be proved.
There is a tightrope to walk here. If you get too technical, students’ eyes will glaze over. I just don’t think everyone needs to know about epsilons and deltas. But if you get too hand-wavy, you lose the faculty to speak in any rigorous fashion about any limit, and suddenly every theorem becomes an article of faith.
Relevance
I think today’s students are interested in putting everything together rather than following many subjects down their separate paths. So I’d like a book that includes as many applications as possible. Calculus is the universal language of science, and I want my students to think of it as something that continues to be relevant. Of course there are the myriad physics applications that mathematicians are most familiar with, but the majority of our students are concentrating in (a) economics or (b) some sort of life sciences or pre-med. So give me problems in comparative statics, theory of the firm, population systems, rates of absorbing medicine, etc.
Problems
Many of our students get discouraged about the difference between homework and test problems. I really believe that for a student to demonstrate mastery of calculus, they need to be able to solve “new” problems. I don’t think the students are well served if each exam problem is similar to a homework problem. Again, calculus is not something that has been solved and put in books to be memorized; it is a tool which can be used ad infinitum.
So I also want conceptual problems that are unique, and enough of them to give the impression that this is what calculus “is.” I like drill-type problems for practicing the techniques (after all, the word “calculus” means a set of rules for deriving something), but limiting calculus to that is like saying all you need to know to be a carpenter is how to saw a board in half.
Antonio’s a big fan of Calculus by Michael Spivak. Indeed, it is a beautiful book; it changed my life in my first year of college at the University of Chicago. It has excellent prose, wonderful, challenging problems, and the kind of snarkiness that appeals to smart math students and their teachers. I still pick it up about once a month. Yet, as someone in charge of teaching calculus to hundreds of college students, I can’t imagine using it. I don’t think every single student is going to be receptive to that kind of book.
So the quest continues.
technorati tags:math, books, calculus, spivak
Blogged with Flock
Permalink
05.11.07
Posted in Teacher Training, Education, Math E-304 at 8:13 am by leingang
I’m really looking forward to the Critical Issues in Education: Teaching Teachers Mathematics 
conference at the Mathematical Sciences Research Institute coming up at the end of the month.
This workshop will focus concretely on courses, programs and materials that aim to increase teachers’ mathematical knowledge for teaching. Both courses and programs that lead to initial certification and professional development of current teachers will be examined at the workshop. In addition, the workshop will examine efforts by colleges, universities, school districts, professional organizations and funding agencies to support people who teach these courses or lead these workshops.
I work with the Harvard Extension School’s Master of Liberal Arts in Mathematics for Teaching program, which aims to acquaint schoolteachers with higher mathematics. The goal is not so much to give them material that will be directly applicable to the classroom, but to stretch their minds mathematically so they will be able to stretch their students’ minds.
This past semester I’ve taught a probability course in this program using the Moore method. It’s been a real challenge for my students and me because I’ve never done that before. But I found it enjoyable and the students seem to have received it well, too. My colleague Bret Benesh and I will be presenting at this conference on our experiences with Inquiry-based courses in the ALM program.
technorati tags:msri, teaching, conference, harvard, extension, school
Blogged with Flock
Permalink
Comments off
05.02.07
Posted in Math, Education at 9:24 pm by leingang
A colleague of mine once tried assigning a lot of writing in his introductory calculus class. He got results that might be expected by somebody who has tried this before: resistance from many of the students. He told me a student complained on his evaluations:
This is a MATH class. I shouldn’t have to write anything.
Why do some students perceive math and writing as opposites? Here’s a sample scan from one of my favorite mathematics papers: “The moment map and equivariant cohomology,” by Sir Michael Atiyah and the late Raoul Bott, published in the journal Topology (Vol. 23, No. 1, pp. 1-28, 1984).
I would guess there are about 800 words and 11 equations on this pair of pages. These two mathematicians are absolute titans of the 20th century, and are considered brilliant lecturers as well as excellent writers (I took a number of classes from Bott as a graduate student. I eulogized him on this blog last year.) I think the case that can be made that they are good at conveying the mathematics because they are able to say so much without resorting to notation. And being able to talk about mathematics probably was a part of their being able to create such beautiful mathematics.
Blogged with Flock
Permalink
Comments off
Posted in Education, Web at 5:38 am by leingang
Anne Davis at Georgia State University has a nice little post about the Rationale for educational blogging. What I get out of it is that blogging allows writing skills to be coached and practiced in a web environment, which is what they will be writing in eventually anyway. I would love to teach those same skills in mathematics classes.
This semester I started a blog for each of my courses and recommitted myself to blogging on my home page about more general topics. I put in an item every day summarizing the class, and I thought I could use the comments for answering questions. But I got very few comments and no questions so far.
I think that’s something that can be addressed at the beginning of the course. If a tone can be set that this blog is there for the class to use, then maybe more can be gotten out of it.
But still, I like the practice and will continue it. Maybe there’s no “cool” factor left in blogging, but I do enjoy demonstrating that I exist outside of class. And it’s fun to put up non-course, but math-related stuff that they might find interesting, or at least notice that I find interesting.
Blogged with Flock
Permalink
05.01.07
Posted in LaTeX, Education at 6:39 am by leingang
I found The TeX showcase
a while back and thought it was pretty neat. People use TeX and LaTeX for lots more than beautifully typeset documents. At this site you can find beer bottle labels, maps, and book covers all done with this powerful language.
But what I’m really interested in these days in the integration of TeX with PDF. In the olden days the workflow was to run (la)tex on a source file to make a DVI file, then convert the DVI file to PostScript and print it, and then (once the web came about) convert PostScript to PDF and publish it on the web. More often now people use the pdftex and pdflatex tools which go straight from source to PDF. Mac’s OS X has native support for PDF so the TeX tools for the Mac are centered around a final PDF product.
PDF is almost bloated with features, including embeddable media, fill-in forms, hyperlinks, and even JavaScript support. This means you can conceivably use TeX to make all sorts of full-featured PDFs. Plus–and this is the big boon to mathematicians and mathematics teachers–you get the full flexibility of the TeX language to typeset complicated mathematical expressions easily.
The LaTeX Beamer Class implements a lot of these, and I’ve used beamer to make some pretty cool slide shows for classes, if I do say so myself. But I was really impressed with what they do at MacQuarie University in Sydney. They write interactive quizzes in LaTeX that are dynamic PDFs. You can have multiple-choice, check-the-box, or even short-answer questions (I guess this is where the JavaScript comes in). Once the quiz is over students can see the solutions worked out in the same document. Very, very cool.
Apparently you need to be a student to take the “real” quizzes, but they have a demo at the TeX Showcase. Now if they would only get rid of that tired Computer Modern font!
technorati tags:latex
Blogged with Flock
Permalink
Comments off
04.28.07
Posted in Education, Web at 12:30 pm by leingang
At the last web pedagogies lunch Michael Hemment told us about Edtags, a social-bookmarking service for educational resources. He’s also blogged about it here. it seems like a fun tool, and I think like to play with it, but I’m wondering if they’d be upset by the intrusion of an undergraduate educator.
But my main question is this: Why use this instead of del.icio.us? To me it seems like creating a search engine that focuses on pages about fishing. You can just add “fishing” to your search query in a real engine like Google and probably get better results. So why not use the same tags on del.icio.us and benefit from the larger community?
Update: Apparently TeachingHacks recommends just that.
Blogged with Flock
Permalink
04.26.07
Posted in Education at 9:09 am by leingang
Oliver forwarded me this article from the BBC in which two mathematics problems are compared.
These pictures say a thousand words apiece…
Blogged with Flock
Permalink
Comments off
« Previous entries ·
