I guess once the bug bites, it never really lets go. So here’s another poem (to follow this and this and this). As it turns out this is my second poem on the Goldbach Conjecture. I realized after I had written the first one that I had actually messed up the history a little bit. As it turns out the conjecture that Goldbach had written in his letter to Euler was different from the one connected with his name today. In fact, the one we know today as Goldbach’s conjecture was actually developed by Euler. As this article [pdf] on the American Mathematical Association website states,

I was intrigued by the fact that even though the the final form of the conjecture was developed by Euler, the more famous mathematician, it is known as Goldbach’s conjecture. This poem below is my attempt to have some fun with this. Read the rest of this entry »

I guess ’tis the season of Math-Po’s! Sue VanHattum, whose challenge started all this, commented on my recent Math-Po (Math-Po (Mathematical Poetry): Goldbach’s Conjecture) by providing an example of her own writing, a poem titled Imaginary Numbers Do the Trick. That piece so inspired me that I spent the next hour (and a good part of a faculty meeting), writing one on the same idea. A close read of both these poems (hers and mine) will reveal that I was more than inspired… some phrases and words from Sue’s work insinuated themselves into my pre-frontal cortex and ended up in my poems. As they say, plagiarism is the sincerest form of flattery. Read, The Mathematical i, after the cartoon…

Read the rest of this entry »

My previous post (Poetry, Science & Math, OR why I love the web) mentioned a challenge by Sue VanHattum of “Math Mama Writes” to “write a little kids’ poem … and that tells of the beauty of math, or, that mentions math and challenge, both in a positive way.” Well, I got inspired and took a part of my lunch break today to write something up. I am not sure it technically fits Sue’s challenge but here it is none the less. [If you are interested in learning more about the history and mathematics behind Goldbach's Conjecture, one of the oldest unsolved problems in mathematics, check Goldbach's Conjecture on Wikipedia.]

Goldbach’s Conjecture
Goldbach, a mathematician, serious and stern
Many years ago noticed a pattern
He wrote, to Euler, the math genius
Here is something, he said, to excite us!

I have seen, he scribbled, with my imagination
That every even digit
(except two, which doesn’t fit)
Can be broken into a partition
Of two primes which add
To the original even digit
(Now, Euler, don’t fidget!)
But isn’t that totally rad!

Now since that day this simple thesis
Remains just that, a hypothesis
Forcing number lovers to lose their slumber
As they try to prove, primes in pairs can add up to any even number.

(Two is the exception, as we said before
Which is, come to think of it, a bit of a bore).

You can see an original of the letter that Goldbach wrote to Euler at mathisgoodforyou.com.

I recently received the following email:

Sir, I was reading the article in Wikipedia on ‘Samarangana Sutradhara’ (King Bhoja’s treatise on Architecture). I was of the impression that there is no translation of the work in English. Though the article says that there is a translation by you of the work, the list of your works and publications on your webpage does not include any such work. Kindly let me know if you have indeed translated the treatise. If so kindly let me know how I can access a copy.

The fact that I had translated this ancient Sanskrit treatise came as a surprise to me.

Read the rest of this entry »

Mark Ambinder at the Politics blog at the Atlantic

President Obama plans to name Howard A. Schmidt, a veteran cyber security warrior with experience at senior levels of government and industry, to fill a long-anticipated cyber coordinator position at the National Security Council, administration officials and outside consultants confirmed.

As far as one can see Mr. Schmidt is well qualified for this position, having served both in industry and in the government in the past. However, one fact about his background caught my attention and prompted this note. In describing his qualifications Ambinder wrote

Schmidt has credentials unique to the job: he received his masters in organizational management from the University of Phoenix, a (fully accredited and esteem) mostly online university.

Apart from the typo on esteem, what struck me was this positive mention of the University of Phoenix, something I often do not see or hear. Over where I live and breathe, the good old-fashioned bricks-and-mortar university, the University of Phoenix is not regarded as having much esteem. I have argued here and elsewhere that this will soon change. That most of us at the “traditional” university have underestimated just how powerful the forces of change are. Online learning (and for profit universities) are here to stay and maybe even take over universities as we know them.

Reading about Mr. Schmidt’s credentials just reminded me just how quickly this change is happening.

There is an article in today’s Chronicle titled Matching Teaching Style to Learning Style May Not Help Students.

I have been somewhat skeptical of the learning styles literature for a while, not the least for hearing the phrase being bandied about without much thought. I have heard people claim without much evidence, that today’s kids are visual learners. I have heard a teacher say that as a consequence, that visual learners prefer reading text from a Powerpoint slide, rather than read it on a blackboard! (Those who know me that I am rarely at a loss for words, but that statement truly struck me dumb! In Wolfgang Pauli’s words, that statement was not even wrong.) I have also had students claim that they did not do well in a certain course because it did not match their learning style!

Anyway, the study reported in the article

… does not dispute the existence of learning styles. But it asserts that no one has ever proved that any particular style of instruction simultaneously helps students who have one learning style while also harming students who have a different learning style.

What does this non-finding mean for practitioners (teachers and professors)?

Read the rest of this entry »

I had written recently about TPACK being the top story on eSchoolNews (see TPACK is top story on eSchoolNews or go directly to the article: TPACK explores effective ed-tech integration). What I didn’t realize at that time is that there were actually three stories about TPACK, one in August that I had blogged about and two in Septmber. The two that I had missed were actually more interesting to me personally since they dealt with the manner in which the TPACK framework was actually being used in schools. Both these stories deal with the manner in which the San Diego Unified School District is embracing the idea of TPACK as a key piece of their strategy to transform how their students are taught.

These two other articles (also written by Senior Editor Laura Devaney) are titled (a) San Diego explores effective ed-tech integration through TPACK: New professional development model focuses on the intersection of technology, pedagogy, and content knowledge; and (b) Reinventing education: As schools nationwide examine new federal priorities, San Diego unveils a five-year plan to transform the way students are taught

This news makes me extremely happy, for the simple reason that this means that our ideas have moved beyond graduate school curricula, beyond research articles, beyond doctoral dissertations into actual practice. This is every educational researcher’s dream. Here are some key quotes from these articles.

The San Diego Unified School District (SDUSD) has embraced a concept called Technological Pedagogical Content Knowledge (TPACK) in its professional development model, to ensure that the smart use of technology drives every aspect of classroom teaching and learning.

As technology becomes an increasingly important tool for teaching and learning, this relatively new concept, which focuses on how educators can integrate technology effectively into their instructional practices, is making its way into pre-service and in-service teacher education programs.

TPACK is based on the work of Punya Mishra and Matthew Koehler, both associate professors of educational technology in the College of Education at Michigan State University.

Here’s another:

“We worked closely with the [district] Educational Technology department to design a professional development program that is all-encompassing,” LaGace said. “When you look at the TPACK model, it gets around to improving the whole classroom experience. … It puts the focus not on teaching teachers how to turn on a Promethean Activboard, but why to turn it on.”

Why turn it on? What a profound question, and one that hopefully will be asked by every teacher in San Diego.

Can you guess why I love my job?

Leigh Wolf and Ken Dirkin, instructors in the year III of the MAET program in Plymouth have been assigning, what they call, Quick Design assignments. These are quickfire challenges for students to showcase their talents under pretty severe constraints (of time, software to be used, final result desired and so on). Over the past four weeks students in the program have been forced to complete a range of such assignments.

Well, yesterday the tables were turned. The students gave the instructors a quick design assignment. I am not exactly sure how I got caught in this since Leigh and Ken were the two people most responsible for putting the students through these “create under pressure” scenarios … but be that as it may, we were given on hour to create an original video (less than 2 minutes in length) around the theme of Convincing faculty of the use of technology.

All I can say is that an hour goes by fast!! But we did finish our video in time (and it is included below).

As important as the video is just what went into making it. The overall idea comes from a commercial from monster.com (see that here). The images are all from photographs taken by the three of us (which we picked off from our respective Flickr sites), the music is original, composed right then and there by Ken using HobNox (an online music synthesizer) and edited using iMovie on Leigh’s Mac. In fact that the only stumbling block was the new version of iMovie, which has some non-conventional interface issues (to put it mildly). Anyway it was done in time.. so here it is, enjoy:

Those of you who have been following this blog know, over the past few months I have made a few short videos with my kids. The ones I am most proud of are a set of three made around the words Explore, Create, Share (you can see them all here). There were great fun to make, and have turned out pretty nicely, if I say so myself

These videos have a few things in common. First, they are short (the longest is a minute long) and involve minimal post production, if any. Second, they always focus on a specific word and attempt to express the meaning of the word through video. Third, each video ends with that word represented in some creative, interesting way.

The other day, while talking with Leigh Wolf, I realized that there was no reason why we could not share the joy of making something like this with others. Why not solicit similar videos from other people? One thought led to another and this competition is the result. The rules of the competition are simple – building on the similarities described above.

1. Each video MUST have a core theme that can be captured in a word (or two). We recommend choosing evocative words related to learning and technology (like design, innovation, invent and so on).
2. The video MUST be original i.e. don’t just copy someone else’s idea, or footage. This is NOT a mashup of existing video.
3. The video should be short (30 seconds to a minute, no more) with minimal editing or post-production.
4. Each video should end with the thematic word represented in some fashion (see the original videos Explore, Create, Share to see how this works).
5. The video MUST use one of the music clips available for download below. These clips were composed specifically for this competition by Sonny Mishra, a freelance musician from Seattle. [Music Clip 1 | Music Clip 2]
6. Once you have created a video, upload it to the web (say YouTube) and send me the link. Please DO NOT send me actual movie files.
7. All links to movies have to be turned in by Wednesday the 22nd of July, 2009.

A jury consisting of myself, Leigh Wolf, Soham & Shreya (the two people who helped make the first three) and Sonny (the music composer) will judge these movies and nominate the winner. The winner will receive a copy of Robert and Michele Root-Bernstein’s book Sparks Of Genius: The Thirteen Thinking Tools Of The World’s Most Creative People, autographed by the authors. How cool is that!!

Do let me know if you have any questions about this competition. Enjoy!

LET THE GAMES BEGIN!!!

Just came up with this in response to something Leigh had said on Facebook… thought it ought to be saved for the future:

Great fools think that birds of a feather seldom differ together!

I wonder what it means? Can you identify the three nuggets of wisdom that went into this concoction?

I am working on changing the layout of my blog… so be prepared for sudden and abrupt changes (as well as possible downtimes). Apologies to all but it has been a while since I played with the layout and its been getting kinda boring around here…

Note: When Sean of Nashworld asked me to guest blog while he was gone I had a couple of different things I wanted to write about. Something I had been wanting to write about for a long time was the idea of how different media engender different ways of meaning making. So I spent a good part of a day writing that up but finally, when I was done, choose not to post it to Nashworld, mainly because it was too long. So I ended up writing about something else altogether (read A TPACK video mashup!), but I was now left with a freebie blog post… Enjoy.

When we think about different media for communication we tend to think of them as being somewhat interchangeable. For instance, we often compare teaching online with teaching face to face. This, to me, is a fundamental misconception of what media can do. At the heart of this mis-characterization is the idea that media is a neutral pipe or conduit for information. But just as McLuhan said many years ago, the medium is the message. In another context I had written the following:

… technology is not neutral with regard to its effects on cognition… different technologies (or media) engender different mind-sets or ways of thinking. Relatedly, many of the characteristics that promote these ways of thinking are inherent in the nature of the media and, thus, invisible to the users of these media.

Since this may seem somewhat abstract I would like to make this concrete through an example taken from the cinematic adaptation of books. Two different media, two different ways of communicating. There are a few examples I can speak about but I will restrict myself to one, the book The French Lieutenant’s Woman by John Fowles and its movie version. (A related essay about 2001 A Space Odyssey can be found here).

I do not understand David Brooks. Brooks is an op-ed columnist for the NYTimes. For the most part his columns are right-of-the-political wing nuttiness, garbed in some erudite clothing. I am not linking to them here but his past few op-eds suggesting that McCain would make a great president despite the shallow, erratic and negative campaign he has run have become somewhat repetitive and tiresome.

And then, once in a while, when I have just about decided not to read his columns any more, he throws out some really cool and interesting stuff. Read the rest of this entry »

typing on this keyboard is still kind of painful, though I am getting better every word I type.

I love visual proofs of mathematical theorems. One visual proof I use quite often in my design courses (CEP817 or CEP917) is a visual proof of the fact that the sum of consecutive odd numbers is a square number.
Read the rest of this entry »

Did you know that any email sent to barackobama@Gmail.com goes to an Indian software developer! Strange but true!

I have been teaching summer course in our master’s program for years now and for the most part have found them to be the most enriching teaching experiences I have had. These are intense 8 hours a day, 5 days a week programs that typically go on for a month. [We are currently experimenting with a hybrid version but that's a story for another day.] I haven’t written much about these programs, despite having taught them multiple times, but for one book chapter that was written many years ago (but for one reason or other was published just last year, in 2007). Read the rest of this entry »

In a previous post I mentioned a new study on children and the internet recently completed by Warren Buckleitner for Consumer Reports Web Watch. Anyway, towards the end of the post I mentioned how the final report includes links to YouTube videos of the actual data and how that shifts the interpretive balance of power from researcher to reader. This is not to say that the researcher has no role at all, clearly it is their agenda, interests, style that is driving the project, but rather that by allowing readers to see the raw data (once again, within limits, since there is editorial control of this by the researcher) it changes the control the researcher has over the conclusions and the meanings one can draw from the research. What I didn’t realize just how deeply YouTube was used in this research… Read the rest of this entry »

Ira Socol has a great post on his blog (SpEdChange) titled Humiliation and the modern professor, in which he speaks to the issue of students bringing laptops to the classroom. Some professors have banned laptops from their classes (I personally know a couple who would like to, and at least one who has). It seems to me, that Ira makes a great case for why students should be allowed to bring laptops into the classroom. Read his post to find out why… On a more personal note, Read the rest of this entry »

Musings on local newspaper headlines, 2001 A Space Odyssey, media and creativity, and ending with some thoughts on the meaning of life… a lot to fit into one blog post but again I had the weekend to work on this. Read the rest of this entry »

Matt and I will be at New Orleans next week for the AACTE Annual Conference. The last time I went to New Orleans must have been in 2000 or 2001… so I am looking forward to going there. There are three specific things we will be involved with.

• Meeting of the AACTE’s Innovation and Technology Committee, Thursday, February 7 from 4:15-6:15 p.m. Norwich Room on the 3rd floor of the Hilton New Orleans Riverside
• Book signing for Handbook of TPCK, Friday, February 8, 2:00 – 3:30. We are expecting the following authors/editors: Matt Koehler, Punya Mishra, Mario Kelly, Nancy DePlachett, Marcela van Olphen, Raven McCrory, Joel Colbert…Having never participated in a book signing before… I am kind of excited, even though this is an edited book, and I have just one chapter in it, co-authored with Matt. That said, it is a book on TPCK, which is cool.
• AACTE Major Forum, Saturday, Feb. 9, 2008 at 10:30 a.m. in the Versaille Ballroom
  I have blogged about this event before… more details, and copy presentation coming soon.