iPads in my neighborhood

All the somewhat abstract discussion of ed tech have come home, to my own school district of St Paul, MN. I grew up in the Saint Paul schools and the superintendent, Valeria Silva, was one of my teachers at the spanish immersion school I attended for the first four years of my public education. Back then we shared a computer lab full of Apple IIe computers and we used Lego/Logo to build cool cars that we could program. Loved that stuff.

Now, iPads! Yes, Saint Paul Public Schools (SPPS) just approved a six-year deal with Apple. The 5-2 school board vote happened in late June, and they’re rushing to get iPads out as soon as they can. But two years ago, St. Paul taxpayers voted for a $9 million a year local levy increase for a Personalized Learning Through Technology plan that used Dell. This project has been described as “troubled” and is being abandoned. See the local reporting for some discussion of the Dell plan. According to the school district, the “personalized learning” program continues in updated form.

What, then, has been learned? What will be different this time?

Two thoughts: it sounds like the plan with Dell was truly innovative, and thus a mess to actually implement. Creating truly personalized learning technology is hard — so hard that just about no one has done it yet. Second, SPPS says that it’s planning to learn from the other districts in Minnesota that use iPads, and there are plenty. I hope that does happen!

Something that continues to bother me about using iPads in education, though, is that iPads facilitate consumption over creation, and all your exploration must be done within well-defined parameters. It’s hard to program on an iPad and you can’t change your own battery. I think kids ought to have some exposure to the parts of a computer, just as I think they ought to know that it’s a green-topped carrot that results in the little orange bullets in school lunches. There’s been a lot of discussion of iPads, consumption, and creation, but that’s for another post…

Privacy, education, e-texts

I found an interesting blog post recently that discusses briefly software that tracks how much and when you read your e-textbook. There’s so much nuance to this discussion. Compare the following:

This e-textbook integrates seamlessly with technology designed to analyze student reading habits, allowing teachers to understand where students are having trouble with readings and target classroom intervention. Data on when students read their textbooks and for how long will help teachers and students work together to create good study habits.”

I made that up to try to make this sound good. Now let’s see how it could sound bad:

“Student reading data can be used to evaluate their effort and commitment to a course; if reading quotas are used in grading, a student who already knows the material or uses other sources will not receive credit. In addition, student reading data could be used to profile students, selecting for those who seem to have long attention spans or discriminating against those who seem to jump around too much.”

What do you think? I’m really fascinated by this stuff, because I think data on student work habits and knowledge can be really useful. I’d love to know where students all gave up on a certain type of problem or reading. I would love to be able to show a student a graph that helps them understand that their pain point on probability problems wasn’t really probability, but full mastery of the algebra used in the solution. However, I’ve been victim of enough bad teaching or grading to be afraid that time spent reading might become a criteria for a certain grade, or that other proxies that don’t measure mastery of material might be pulled out for busywork grades.

I find the data in Moodle handy: it tells me when students are accessing different pieces of information, for instance. Using that I can conclude that nobody read my review sheet, or that everyone has accessed that video, or that only two people accessed the project grading guidelines earlier than the night before the project was due! This information allows me to adjust teaching or have a discussion on planning and pacing — whatever’s appropriate. I don’t know how much difference this makes. Is it an invasion of student privacy? Would it change my teaching if I couldn’t see it?

Perhaps one solution is that students have control of that data and whether or not to release it. This is something we might trust college students with, but it’s a decision that 8-year-olds might not be qualified to make without guidance. At some point, though, we do need to start having discussions with students and children about the data that is collected about them and who gets to have access to it. Schools are already discussing appropriate use of Facebook and cell phones. When do we start talking with kids about student data?

Finals awareness month

Ok, it’s not that. But many students across the US are aware of finals. So are many mathematicians, those in academia who are teaching….

One way that math and science and other fields have changed with the advent of the internet is the coalescence of the blogging community. There are academics from many fields blogging, some about more personal things, some about academic culture, some about their areas of research. An anonymous cross-cultural conversation is possible: you can read economists and ?? (social scientist!) talk about grading sanity strategies, you can amuse yourself with a physical scientist liveblogging her own exam, you can read about writing papers with grad students who don’t want to write papers from another physical scientist.

If you want to stick closer to math, you can read about the end-of semester crunch at PhD+epsilon. I think we all know what that’s like. I’d add my own lessons here except I’m at a conference and I need to do math! It surprises me a bit that there is not as much math culture discussion as there is, say, medical research discussion. One good place to find some mixed math and cultural insight and an extensive blogroll is at the Accidental Mathematician. I appreciate the recent cultural discussions. Another place to find a broad range of interesting links is the Blog on Math Blogs. Notice that two of the blogs in this paragraph are sponsored by the AMS: I am glad to see the AMS taking an active role in outreach via the internet.

What academic blogs do you read and what benefit do they bring to your life, if any?

One month — Math Awareness month

It’s math awareness month! It’s also a month of midterms, homeworks, projects, and articles for those in the academic milieu. And now we’re heading for the end of the semester… I have three more classes in which to cover the multivariable central limit theorem and Brownian motion. Ambitious.

Check out an NPR piece on Martin Gardner to start off your belated celebration of Math Awareness Month. Martin Gardner, of course, makes me think of the enormous world of recreational math communication, much of which now takes form on the internet. Can you claim to be a knowledgeable YouTuber or recreational mathematician if you’ve never seen one of Vi Hart’s videos, like the one on hexaflexagon safety  (Gardner connection there!) or pineapple accuracy on Nickelodeon? Or maybe you’ve encountered the blog of math poetry, or read a post by a math blogger like Evelyn Lamb. I am almost too young to remember how mathematics was popularized before the internet. How did people who like the stuff learn about it in “the old days” — did they read a book?!

Technology has really changed how we share fun stuff with friends. How often do you share math?

People love math (but they don’t know it)

The recent viral hit game 2048 is one reason I have not posted in a little while. (The other factors are midterm grading for two classes and a great week-long research binge with a collaborator.) 2048 is a simple and hauntingly addictive game — you just move pieces left, right, up, down, until two 2s combine to 4, two 4s combine to 8, eight and eight are sixteen, sixteen and sixteen are thirty-two… Alright. Nostalgia over.

2048 is not the only such game. It was inspired by the game 1024 and is conceptually similar to Threes, neither of which I have played as I have a dumb phone. Part of 2048’s success is its very clean interface. But look at what it has spawned:

I started out by wondering what mathematics the game really contains. It looks like the game 1024 is a bit more consciously “educational,” but 2048 has the same mathematical content and more. What’s the content?

Addition: You don’t really need to know that 32+32=64 to play the game — you’ll learn soon enough so I would not call it a prerequisite. It might be a good way for kids to impress knowledge of powers of two into a personal mental list.

Strategy: I have a feeling that there’s some math in the combinatorics of the strategy. It’s a bit weird because of the random generation of tiles containing 2 and 4 — randomness isn’t something I usually consider in combinatorial games.

Pattern formation from random processes: I want someone to enlighten me about this. If you press only “down” and “left” with a few “right” buttons when you get stuck, you’ll usually get something that looks like a lower-right-antidiagonal matrix with an antidiagonal of 2s, an antidiagonal of 4s, and an antidiagonal of 8s (try it and see what I’m talking about). It’s clear why this happens — since you get random 2s and 4s, this method pushes everything down and right until it can’t go any further (a 4 gets nestled between an 8 to the right and an 8 below). But this has got to have some connections to more formal mathematics. In what other systems does this phenomenon occur?

Where/how else does math appear in 2048? 

It is really cool that people have extended this to 3D and 4D versions: more mathematical layers start appearing and these are fun ways to get intuitive practice in spatial reasoning. The Fibonacci version also introduces people to some great number sequences!

How can we hijack the trend to do a little fun math ed?


Recent reading

  • We recently had a (small) in-person LIMIT institute meeting, and a big topic of discussion was Making Math. This is a company that came out of the work UIUC has been doing in online and distance math education, discussed briefly in a previous post. I owe you all a longer write-up about this.
  • If you’re interested in wider issues in education, consider putting Hack Education on your blogroll.
  • An interesting site aimed at teaching math outside the academy is Better Explained. The site has some very pretty and interesting explanations of math concepts like limits, Bayes’ theorem or Fourier transforms. One of the promises of technology that MOOCs are half-fulfilling is this access to non-book learning outside academia. Better Explained seems to be trying for a different niche and I’m interested to see how it’s going.
  • Another site with some cool articles about math is Math \cap Programming, which has longer-format articles on topics like martingales or computing homology.

As form changes, does function?

Today a few observations on journals and tech:

  • Scholastica is a company promising easy easy open-access journal publishing and management. Seems like a lot of law reviews use it currently. I like the pricing scheme, at $10 for each submission — this is something even a grad student can afford by planning ahead a week or two. It looks really interesting and has a nice slogan on the front page: putting scholarly publishing back in the hands of scholars. Of course, for mathematics, typesetting is a real issue. Could they handle that? Not yet, I think, but they’ve got a blog post on typesetting. They’re dealing with a totally different audience than mathematicians for the most part. Writing an article in Word?
  • In Scholastica’s blog posts they mention Editorially, a platform meant to make collaboration easy. That sounds nice. What about LaTeX? Yay — a collaborative web-based math typesetting platform exists at WriteLaTeX. Anyone used it? Is it better than the endless iterations of Dropbox files that I use with my collaborators?
  • Speaking of open access, I checked the Secret Blogging Seminar page after a long time and was interested to see a post on the Mathematics Literature Project, which looks at free availability of articles online by journal of publication. In a previous post I mentioned that a new federal law requires federally funded research to be made freely available (vast oversimplification here) and there were rumors that the arXiv is not enough. If mathematicians want to argue that the arXiv fills that role in mathematics, evidence like that at the Math Literature Project page will be very important to supporting the argument.

Interactive math exploration: RSK and other combinatorics

For a year and a half I have been musing about what kinds of technological experimentation with pure math concepts could be truly different on a smartphone or tablet, as opposed to ye old piece of paper, and combinatorial games that check for mistakes are one of the things I’ve come up with. I want to implement some. But I am not a stellar programmer or a UX professional.

But I keep an eye out for this kind of interactive math, and I found something! It is so cool! Check out Lauren K. Williams’ Javascript applets at her webpage at Mercyhurst College, and her RSK app for iPad. It’s along the lines of what I would love to do, and elegant and pretty. It is so cool.

That’s all.

Math online: links to textbooks and resources

I almost forgot to mention another set of conversations I had at the Joint Math Meetings, about open textbooks. Textbook prices are a real factor in the affordability of college; since in college I paid for textbooks through money I earned waiting tables I certainly paid attention to options cheaper than buying new. I still try to pay attention to textbook prices when I teach, and to balance them with quality. At St. Olaf College I asked my differential equations students to buy a >$200 textbook because I thought it was the best out there for the course I’d teach (Blanchard, Devaney, Hall if you’re interested), but I did not do so lightly.

Anyhow, at the Joint Meetings I was reminded of the American Institute of Mathematics’s (AIM) open textbooks initiative. They have links to many open textbooks. In my brief conversation with Jim Hefferon, author of Linear Algebra, he reminded me that we are all invited to contribute to the open textbook initiative by sharing exams from our courses, homework problems, and other teaching resources that might make it easier to teach from an open textbook.

It is now possible to share these textbooks almost for free, because of the internet and information technology. We are slowly starting to adopt electronic textbooks, and it’s a big market: Apple is in on the game, with iBooks textbooks, and Google has been renting electronic textbooks for a little while. I honestly haven’t seen any truly transformative electronic textbook experiences yet, instead simply seeing the same material on a screen with the ability to rotate a picture. Electronic textbooks are also lighter. There is some potential in what’s coming out of another AIM-supported effort, UTMOST, integrating SAGE and open textbooks. One of my dreams is to create a beautiful math text with interactive mathematical experiments and modeling, so if you see anything like that, comment or send me an email!

When I think about participating in such an effort, though, it comes back to economics. I am not a tenured professor. I’m an early-career mathematician in a non-tenure-track position. I do not see the benefit in creating content for a big publisher that will give me essentially no royalties. I see the idealistic benefit of contributing to open textbooks initiatives even in the absence of royalties, but I also need to prioritize activities that will lead to a remunerative job at some point. In software, people contribute to open software as a hobby or supported by a paying job. In mathematics, the number of jobs with decent pay for early-career people is somewhat restricted and many are temporary, and so much “free” work is required in order to get the tenured position that another “free” effort just doesn’t seem like a good idea. There is a lot of conversation about the public face of mathematics but I don’t see it honestly addressing the economics of supporting these contributions.

Also check out MIT’s Open Courseware textbooks page.

Last musings from JMM

To finish up on reporting from the Joint Mathematics Meetings, Eric Friedlander, former president of the American Mathematical Society (AMS), gave an address on changes in the profession. A few interesting points:

  • Among other things, he highlighted the changes that the “open access” movement brings. In particular, journals in math used to publish papers for free but charge for subscriptions. The open access movement wants to make access free, which is a great goal, but currently accomplishes this by charging to publish. There’s a lot of controversy about this and early-career scientists are often caught in a bind between wanting to make their research freely accessible and needing the prestige that comes with a non-open access journal (so they can get tenure) or being unable to pay the page fees for an open-access journal. In math, I thought we’d been able to bypass part of the ethical quandary by posting almost everything on the ArXiv, which allows anyone access for free. Friedlander pointed out a line in the new congressional omnibus bill that mandated open access and a machine readable version of the final peer-reviewed manuscript for much government-funded research. Is the ArXiv good enough, or is this going to add a layer of cost to mathematics research?
  • Friedlander mentioned that the PCAST report on higher ed and technology did not involve any mathematicians or the involvement of the AMS, even though it made some rather harsh recommendations on teaching of lower-level math courses in college. The AMS response is here.
  • He also discussed applications of math, the way math interacts with the other sciences, the public image of math, changes in who teaches and in who gets hired for what… His message in the end was that mathematicians must be involved or the change that happens will pass us by. There’s a theme in my last four posts!