The math-po (and sci-po) stream keeps flowing. Math Mama Writes, who started the whole math-poetry movement has some more on her blog, and here is Erin Nash with some really beautiful biological poetry. And of course, here’s her husband Sean Nash having his students writing poetry too. Of course let’s not forget my daughter Shreya (who sort of started this whole thing) and her sci-po’s at her blog Uniquely Mine.

Below are some thoughts about math-poetry – but you can ignore all that and scroll right down to the poem: The infinity of primes!

Math art by durentu

Through all this I have been plugging away at my math poetry. I know the original challenge was to write something to motivate students to learn math (and I did write one along those lines). But more interesting to me has been this theme I have picked up, which is of writing proofs as poetry. I know many people have described mathematics in poetic terms but I am trying something slightly different here. I am trying to explain theorems (as in these couple of instances, see here, here, here and here) and speficially in the poem included below, I am actually trying to construct a mathematical proof in rhyming verse.

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Image credit: eoliene_pe_campii

Mathematical Beauty: A limerick
Punya Mishra, Jan 27, 2010

Doesn’t it just gladden your heart to see

These games we can play with infinity?

How can one stay aloof

From the elegance of a proof

And remain immune to mathematics’ subtle beauty?

Image Credit Leeks

As readers of the blog know, Matt Koehler and I work together quite a lot. In fact we just rotate author-order in our papers since it is hard to keep track of individual contributions. (I would like to claim that the cool ideas are mine – but again he is bigger and stronger than me so I don’t often do that, at least not any more.) We are also huge fans of Douglas Adams and his Hitchhiker’s Guide to the Galaxy trilogy (which consists of 4 books, something that makes perfect sense if you have ever read Adams). Anyway, a bunch of years ago we decided that we needed to act on our love for this man, and his writings, by citing him in an academic paper. To our great pride, we did it! In fact we started the article with a citation to Adams.

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I recently received an email from a teacher in Poland, seeking advice for a curriculum outline for their Design Technology Section. They said, and I quote:

Unfortunately, I have minimal experience with the subject as a teacher or as a student in my younger years, consequently, I have little background as to what a DT class should look like.

As you might guess I’m struggling trying to put together some sort of DT curriculum for our Middle School.

Our small school does not not have any kind of fabrication equipment so our DT class is currently heavy on IT design aspects….(web design, research on a topic and devise a solution, book creation,etc… )

The specific request was for”some useful and practical information that I can implement fairly easily.”

Is this what design is? by StephenMitchell on Flickr

As I crafted the response I realized that (given my lazy self) that it would make a good blog post. So here is what I wrote back:

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Sean had this wonderful post on his blog (Is this a sluggish strategy?) about this whole scientific and mathematical poetry that is going around. He links to some excellent sci-po’s written by his students (see Pushing Scientific Thought Into Art) and also provides a nice protocol for those who want to apply it in their own classrooms.

It is amazing to me just how this idea has spread. It has en-livened my life, I can say that much. Anyway, I wanted to say thanks to Sean (and his students) – and what better way to say it than in verse. So here is: For Sean & his students

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Those who follow this blog know that I love visual wordplay. This is most commonly seen in my ambigram work but another area where I have spent some time is in writing palindromic poetry. I wrote a whole series of poems when I was in graduate school at Illinois and they have been online, moving from server to server, for over 15 years now. I had written about my interest in palindromic poetry a couple of time before (see this and this). Now these were pieces created for fun and I had no real intention or interest in doing anything with them. I wasn’t even sure if anybody ever read them. That is, till a couple of days ago…

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Steve Wagenseller, a student in my 817 Learning Technology by Design seminar wrote something so cool in the class forum that I felt that it was worth recording on my blog…

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A tangent, a line and a circle
A math poem

Image credit: chrstphre (on Flickr)

A point outside a circle,
shoots out two lines
one heading for the center
the other more feline
smoothly kisses the curve
That delicate swerve
of the ball and then, abruptly
turns to the center,
making an angle
and meets the first
which went on straight
To thus form a triangle.

The angle formed by the tangent
And the other line, the radius
the mathematical mind sees
is exactly 90 degrees!

And funnily enough, it doesn’t matter
where the initial point is, the starter
Where ever it may be
(as long as it is outside the circumference)
The angle will always be 90!
Did that make sense?

A poem on the fact that a tangent to a circle is perpendicular to the radius drawn to the point of tangency. See image below

Image from ETC, an online service of Florida’s Educational Technology Clearinghouse

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…

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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.

A 5th grade science assignment, transformed. A rant about Mother Goose. A math poetry challenge!  How did that come to be? And what does that have to do with loving the Interwebs? Read on…

I had written earlier about how my 10 year-old daughter had been writing poems on science (Scientific Poems or Sci-Po’s for short). It all started with an extra-credit assignment she needed to do for her science class, and a need, I perceived, to keep her blog (Uniquely Mine) up-to-date. She has quite a few written now. For instance here is one about a news item about scientists finding dinosaur eggs (and other dino-stuff) in India (Cluster of dinosaur eggs found in southern India), and here’s the poem:

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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.

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Jordy Whitmer over at the Birmingham School district forwarded me this link to this really cool video by George Kembel on Awakening Creativity. There is a lot in the video to ponder and discuss but I want to focus on something he said about music learning that really hit home with me. Citing some research on music learning he describes a strong link between speaking a tone language, such as Mandarin, and having perfect pitch. A search on Google led to the following article: Tone Language Translates To Perfect Pitch: Mandarin Speakers More Likely To Acquire Rare Musical Ability. As this article says:

Perfect, or absolute, pitch is the ability to name or produce a musical note of particular pitch without the benefit of a reference note. The visual equivalent is calling a red apple “red.” While most people do this effortlessly, without, for example, having to compare a red to a green apple, perfect pitch is extremely rare in the U.S. and Europe, with an estimated prevalence in the general population of less than one in 10,000.

Image credit: Tom Carmony

So think about this for a second. Here is an ability that was once thought to be extremely rare, within the capability of just extremely talented musicians. People born with this talent, as it were. This research, however, shows just how mistaken this view is.

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Our family’s stop-motion animation festival continues with our latest offering: Finding Nemo, the sea-quel!!  This movie was conceptualized by Shreya and filmed by all of us over a couple of days. What was interesting about this movie was just how many technologies got utilized in creating it (a complete list comes at the end of the movie) – and just how seamlessly these different tools could be integrated together. As we have been making these movies I have seen a greater level of sophistication and thinking from both my kids about the possibilities of stop-motion animation in particular and the visual aspects of telling a story through film. I can pretty much step back and let them do it. That has been fun to watch.

Anyway, before the movie, I need to give a shout out to our family friend, Amol Pavangadkar, who made all this possible by helping us create a really cool animation stand. We were inspired by this design and here it is, in use, by Shreya’s friends, as they made their animation movie.

So using this set up we have already created three movies. You can see the first one here, the new year’s card here and the third one below. Enjoy, Finding Nemo, the sea-quel!

My daughter, Shreya, had some friends over yesterday and they created a short stop-motion animation film with the new setup in our basement. Enjoy

More videos made with my kids can be seen by clicking here.

Ambigram.com is a website about ambigrams and the people who make them. Lots of cool stuff for enthusiasts and novices alike. They often conduct competitions and other fun challenges for readers. One recent one was related to palindromes. In brief, they challenged people to create palindromic ambigrams. This is something I had tried a few time a long time ago – but their challenge pushed me to go back and come up with some solutions.

Well, I ended up with more than I had anticipated. I now have a technique, using which, anybody can create a palindromic ambigram of any length! How cool is that.

What is a palindromic ambigram you ask? A palindrogram? An Ambidrome? Read the rest of this entry »

For Halloween, my daughter, Shreya’s fifth grade class entertained a bunch of first-graders with a spooky music and dance show. A news reporter was there and her photo (Shreya’s not the news reporter’s) ended up on the cover of The Towne Courier, the local community newspaper. Here is a link to the story and since it may not remain online forever, I have kept a screenshot here. Here she is, dressed up as a Spider Queen(?), spinning “a musical web on her xylophone.”

I came across this sign when I was in India recently and I just HAD to take a picture of it.

Click on the picture for a larger version

Of course, much of the effect comes from the inadvertent yet appropriate peeling of the paint from the letter “R.” But fun nonetheless.

A new ambigram created in memory of Jere Brophy, world renowned scholar on psychology of motivation. The ambigram reads, “motivation” one direction and “Jere Brophy” when rotated by 180 degrees. Click on the image to see a larger version, hosted on Flickr.

Enjoy.

Robin Revette Fowler sent me a message on Facebook regarding my recent posting(s) about moving from incompetence to mastery (see the two previous posts here and here). She took issue with my idea that mastery requires some kind of meta-level, self-awareness. She said

It seems like the issue is with either the meaning of “mastery” or perhaps with the types of skills you’re talking about.

Conscious/unconscious knowledge is especially interesting to me re: linguistics. Most native speakers have only unconscious competence of their language– I used to hear Writing Center tutors telling ESL students, “you need an ‘a’ here; I don’t know why” all the time. Many NNSs, on the other hand, have much stronger conscious competence– they often know “rules” about how to use determiners much better than Native English speakers, for example. At the same time, I’m not sure they would be said to have “mastery.”

And I don’t know that the conscious competence is the important thing here. Would you argue that only linguists who can describe their determiner choices have “mastery” of English grammar?

At first blush Robin seems to be making a good point. Do writers need to know how and why they do what they do they do as long as they get it right? There is a surface plausibility to the argument but I am not sure that it stands muster if we dig deeper.
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Ken Friedman, whose article I had used as the basis of my previous posting, From incompetence to mastery, the stages dropped me an email in response to my critique. To provide some context, (you can read my full post here) I had suggested in my posting that it may be inappropriate to label the the highest level of mastery as being unconscious competence. My concern, of course, was with the “unconscious” part – since I felt that true mastery requires a level of reflection, something denied by the word “unconscious.”

Ken wrote that he actually sees examples of unconscious competence everywhere. He went on to say (quoted with permission) Read the rest of this entry »

One who knows and knows he knows is a wise man, Follow Him
One who knows and knows not he knows is asleep, Awaken him
One who knows not and knows he knows not is a child, Teach him
One who knows not and knows not he knows not is a Fool, Avoid him.
– Attributed variously to Confucius, Socrates and others

I was reminded of this quote while reading an article by Ken Friedman titled, Design Science and Design Education and came across a section that described a view of learning. Friedman describes a framework on going from incompetence in a domain to mastery in the same domain. More specifically, Skoe talks of this process as having four key stages. These four stages are: unconscious incompetence, conscious incompetence, conscious competence, unconscious competence. Here is Friedman:
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There is a nice article in the State News about Jere Brophy including quotes from his daughter Cheri Spier, my department chair Dick Prawat, and my former advisee (now faculty member at Drexel) Aroutis Foster.

Read MSU professor dies, honored by colleagues as field pioneer

In a couple of previous posts I had talked about the idea of postdiction (see the posts here and here). The argument being that good teaching (among a long list of other good things) is postdictable, i.e. it walks the line between predictability and chaos, and most importantly makes sense post hoc. To make my point I had posted a couple of videos that were good examples of being postdictable.

Closely connected to the idea of postdictable is the idea of creating anticipation and suspense. Once again other artists (particularly those working in temporal media such as film, and advertising) seem to have grasped the importance of this earlier than educators. Good film-makers can create suspense out of pretty much the flimsiest of materials. Think of the first scenes from Tarantino’s Reservoir Dogs. The way the scene builds tension out of a disagreement over whether or not to tip is pitch perfect. There is more tension in that scene than in dozens of other “suspense” thrillers.

However making suspense work is difficult. Navigating this line between predictability and tension over the unknown is a fine art. (This is where, of course, the connection with postdictability becomes most clear.)

Check out the two videos below, which highlight just how fine the line is between succeeding at creating suspense and anticipation and failing to do so. Both of these videos are interesting and well made – both have pace and rhythm but one of them builds anticipation while the other just happens. One tells a story, the other doesn’t.
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The Lansing temple recently organized a special Diwali program. My daughter Shreya participated in a dance and I, as always, took photographs of the event. Click here or the image below to see all 161 of the photographs I took.

Enjoy.

You can also read a poem written by Shreya on Diwali on her blog Uniquely Mine.

Carole Ames, Dean of the College just sent out this note regarding the sad news of Jere Brophy’s passing. She has asked for it to be shared with our broader networks, so I do so.

Note: The memorial service for Jere Brophy has been scheduled for Monday, October 19th 2009, from 10 – 12 at the MSU Alumni Memorial Chapel

It is with great sadness that I write with the news that our dear colleague, Jere Brophy, died last night from an apparent heart attack. There are no words to express the loss of this intellectual giant to the field of education, but more importantly, we have lost an esteemed colleague, a cherished friend, and generous mentor. Jere’s warmth of character was apparent in all his interactions. He always had an inviting smile, was known for his laid-back manner, and greatly enjoyed a good chuckle. He had a genuine interest in other people, their families, lives, work and ideas. To the world, Jere was an internationally-renown scholar whose writing informed researchers, policy-makers, and practitioners alike. To us, he was all that, but, in addition, we had the privilege of having him as our beloved colleague.
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As readers of this blog know I love examples of seeing things in new ways. That to me if often the crux of creativity. Anyway here are two examples. The first curtesey of Leigh Wolf is a new advertisement from some credit card company. The ad is actually pretty average but what is really cool are the visuals.
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Shreya, my daughter has a blog, Uniquely Mine. An RSS feed from her blog can be found right here (just scroll down and see the right column). Anyway, over the past few weeks she has been doing something for extra credit for the science class. Her fifth-grade teacher has asked all students to find stories related to science in the newspaper, create a short writeup about it to share with the other children. I asked her to add another layer of challenge to that. Once she has her report all typed up, she needs to write a short poem about it and post it to her blog.

I asked her to do this partly because I was concerned that she would not be able to keep up her blog once school started. As most people she was very excited to have a blog and wrote a bunch of stuff for it in the beginning. Then life began to take over and her postings grew few and far in between. What was needed, I figured, was a way to keep her writing regularly. So this idea of piggybacking on something she was already doing. The poems she writes are often short and it didn’t seem like much of an imposition to ask her to write little poems based on the science articles she has been finding for her school report.

Well, so far so good. She has a quite a bit of writing (mostly poems) in a genre we have decided to call Sci-Po a.k.a. Scientific Poems! (It’s a obvious ripp-off on the term Sci-Fi). It has also been a lot of fun.

When we first set up the blog, I advised her to not allow commenting. I was not sure what kinds of comments she would generate and it just seemed as if we were asking for trouble (especially exposing a 10 year old to the kind of junk that is prevalent on the Internet). However, after much consideration we finally decided to open up her site and allow people to comment. So if you read this blog, click over to her site and drop her a note. Please, remember this is a 10 year old so be polite Of course all comments are moderated so I still hope to protect her from some of the nastier aspects of the world (not that I can do that forever but at least I can try).

Anyway, check out her writing. I think you will like it. Here is my favorite. It is a non-sense poem (not a Sci-Po but fun none-the-less) titled, Salt’n Pepa in Santa Fe. Here is is:

Salt’n Pepa in Santa Fe
by Shreya Mishra

Squigles-squagles, pinchley pooh
Slip’n sliding on my shoe
Dimpo-doby dorkly dake
Gently eat the slice of cake
Shickly-bumbly rabbity-red
Back at home, tucked in bed