Punya Mishra's Web

I wanted to bring attention to two articles that came across my desk today. The first was in the Chronicle of Higher Education titled Creativity: a Cure for the Common Curriculum on efforts at range of universities seeking “to train students in how innovative thinkers …[and] use the tools of creativity to solve problems.”

The second article in yesterday’s Washington Post was titled Engineering students learn how to swing dance during class to help with problem-solving skills.

I have been thinking and writing about this for a while now – and it is good to see some of these initiatives taking root. These are difficult issues to deal with mainly because the return on investment, as it were, for teaching creativity is hard to measure. But that just makes the task all the more interesting.

I am now, officially, a published poet!

My poem on imaginary numbers (The Mathematical “i”) was published in the March 2013 issue of At Right Angles, a school mathematics journal.   You can download the entire issue here (it is a large download) or view the magazine in sections here with a link to the poem as a googledoc.

We just completed our symposium at SITE titled: Breaking Disciplinary Boundaries in 21st Century Learning: Creative Teaching with Digital Technologies. The symposium consisted of 7 presentations followed a summary by Teresa Foulger (of Arizona State University). In brief, we argued the following:

The past few decades have seen a tremendous burst of creativity and innovation fueled by digital technologies.  From Google to YouTube, from cloud computing to mobile devices, new technologies have had an immense impact on how we live, work, play, and thereby how we teach and learn (Florida, 2002).  Given the relationship between creativity and technology, it is not surprising that educators have argued that teaching and learning in the 21^st century must emphasize both the issues of technology and creativity (Mishra & The Deep-Play Research Group, 2012).  This symposium suggests that a new framework for creativity – trans-disciplinary thinking – provides an invaluable set of meta-level cognitive skills for flexible use in creatively teaching with technology (Mishra, Koehler & Henriksen).  Presentations will describe the framework, present a broader context for 21^st century skills such as technology and creative thinking, and discuss a range of examples of ways this framework has been used by skillful, creative K-12 teachers.  The symposium will conclude by describing new directions for research relating to trans-disciplinary thinking among teachers learning to use the framework.

The complete set of slides that went with the presentations can be found below, as well as brief descriptions of each of the presentations.   Read the rest of this entry »

Jim Garrison and A. G. Rud have a wonderful article on TCRecord on Reverence in Classroom Teaching. Though, reverence may be “too exalted a word to associate with the practical and often mundane activities of teaching,” it appears to me that ignoring these deeper impulses impoverishes us as individuals and as a society. Framing teaching as being just about imparting skills, and knowledge, aimed at achieving instrumental goals (jobs, career and the like) misses something crucial. As they write: Read the rest of this entry »

A few weeks ago I had written about an email that I received from an eighth grader in Colorado. Jake, a budding poet, was interested in learning more about me in the context of some palindromic poetry I had written many years ago. I wrote back to Jake (you can see the correspondence here) and a couple of days ago I received another email from him, this time containing a palindromic poem written by him. With his permission, I am including his email and poem below:

Read the rest of this entry »

I recently received this email:

Dear Mr. Mishra,

I am currently working on a poetry research project for school, and one of the requirements is researching five different poets. While looking for people who wrote palindromic poetry, I found your website and decided to use you in my project. The only problem is that I can’t find much information about you for my research. If you could, please respond to this e-mail with a little information about your history (i.e.-date and place of birth, family relations, etc.) as well as your inspiration for writing your palindromic poems. Thank you for your support!!!!!
Sincerely, Jake

P.S.- I am an eighth grader from Colorado and an aspiring poet.

Read the rest of this entry »

I had a wonderful day at the Grant Woods Area Education Agency at Cedar Rapids, Iowa. I was invited there by Andy Crozier and his team as a part of their 21st Century Learning Institute. I spent the day with 50+ teachers, library media specialists, and administrators talking about TPACK, creativity, technology integration and other fun stuff. This was a great group of people and I had a great time (and I hoped that they did too).

Read the rest of this entry »

Over the past few years my scholarly focus has shifted into areas related to teacher creativity and transdisciplinary learning. I see this as being the next step in my research work. Though I have been thinking quite a bit about this, have applied to to my teaching (particularly my course on Creativity in Teaching and Learning), and there have been occasional blog posts about this as well, it has not had much of an impact on my academic writing. A large part of it has to do with the fact that academic writing (writing for journals and edited books) has, by necessity, a longer time-frame than teaching or blogging. Writing and submitting, taking care of changes suggested by editors and reviewers, and then waiting for the actual publication to emerge, all take time.

To cut a long story short, the first article about this new line of work has finally been published. It is a special issue of the journal Educational Technology devoted to Emerging Technologies and Transformative Learning. This special issue was edited by George Veletsianos and Brendan Calandra (thanks for giving us the opportunity) and was co-authored with Matt Koehler (no surprise there) and Danah Henriksen.

Read the rest of this entry »

I spent a two days a couple of weeks ago with the faculty and leadership of Bloomfield Hills School District. The first day was a workshop on teaching, technology and creativity with the faculty of Model High School and Bowers Academy. Leigh and I had been invited there by Bill Boyle, the principal (read his blog). We spent the day exploring ideas of TPACK and creativity and it was great fun (see poems and images below).

Two days later I was back again, this time invited by the district Superintendent, Rob Glass, working with the entire school leadership on issues related to social media and what it means for schools and school districts. The morning was led of by Social Media guru, Shel Holtz, who talked about how social media was transforming the world of work and learning. [You can download his presentation here, though I must say that it is a 175MB download.] Building on Shel’s presentation I facilitated a series of brainstorming activities with all the administrators about specific things they could do in their schools and classrooms to meet these challenges. At the end of the day we had a series of key action items (short term and long term) for a range of different contexts.

All in all it was an extremely productive and fun day.

I am including below some of the stuff that emerged out of that meeting. The first is a slideshow of photographs from these two days.

Created with Admarket’s flickrSLiDR.

And of course whenever I do a workshop on creativity can bad poetry be far behind? So here are some of the poems (and a rap song!) that emerged from the first workshop on creativity.Enjoy.

1.
There once was a professor whose goal

Was to teach that creativity is whole
Effective and new
We’re making a stew
Of technology, content, pedagogy and soul

2
Some teachers on PD
Learned about creativity
They found creative products are new
From our pasts came only a few
for their own students they hope this won’t be

Deanna Vetrnone, Geoffery Parkinson

3.
Whole, roll, jellyroll
Effect, Defect, and reflect
Novel Pavel Datsyuk

Peg Pasternak, Bruce Kezlarian, Cullen Murphy

4.
There once was a girl from Nantucket
Who was so bored she said *@%& it
She developed something N.E.W.
To away her blues
And forever vowed to think outside the bucket

Matt Autha, Rosalie Burnett, Bill Boyle

5. PD Rap

I can’t believe the of change
It makes my brain feel deranged
It has my whole body freakin’
But now I’ll start my creativity tweakin’

Rapping to you in rhyming couplets
Rain my words like drops in a bucket
Like the girl on Nantucket
Who looked around and just said f%$# it

Suffering from deep amnesia
Out of lots of inertia, a little fantasia
While waiting for lunch from La Marsa.
Thinking about the old days
With nostalgia.

When we had pencils and chalk
Things moved slow
Now we start to balk
But it’s go go go
But no we know technology’s just a tool
We’ll keep up, won’t be no fool
And our whole school will rule!

I was recently invited to present a keynote address at the 21st Century Instructional Technology Conference (titled Elements of Technology) at the Clark County School District in Las Vegas, Nevada. Clark County is the 5th largest school district in the country with over 300,000 students and it was a great privilege to be invited to present there. I was invited there by the Instructional Technology Department (led by Loretta Asay) and my contact person was Project Facilitator, Sherwood Jones. They are a great group of people and I truly had a wonderful time there.

Apart from the Keynote I also conducted a workshop on Creativity and Teaching with Technology. I had anticipated having around 25 people for the workshop but the room was overflowing (at least 15 more than I had anticipated). That did throw a few kinks into my routine but nothing that was unsurmountable. I am sharing below some of the things that people created during this two hour workshop.

I explained my idea of a creative idea or product as being Novel, Effective and Whole (the so called New NEW)! This led Terra Graves, Thomasina Rose and Kristina Ernest to create this acrostic poem.

New
Organic
Visual
Engaging
Longevity

Educational
Fun
Freedom
Everyone
Creativity
Teachers
Innovative
Variety
Enthusiasm

Winning
Holistic
Outside the Box
Learning
Exciting

Here are a few more from Lisa Widmer, Katie Jones, Brent Mesenburg and Robert Jackson

The first two are limericks that summarize some of the things we had talked about in the first half of the workshop.

Creativity is our goal
Make it Novel Effective and Whole
When in doubt
Turn it about
And satisfy your soul

A second, funnier, version is as follows:

Creativity is our goal
Make it Novel Effective and Whole
When in doubt
Don’t Freak out
It’s quite alright if you stole

The same team wrote another poem, synthesizing some of the ideas we played with in the second half of the workshop.

Being creative is like heaven
Mimic the great Magellan
And fear not missteps
Just use the five steps
And crank that knob to eleven

The “crank the knob to eleven” of course being a response to the (in)famous scene from This is Final Tap.

A couple of other pieces that emerged from this team (can you tell this was a prolific group) was the quote:

“Tweak it to Teach it”

Somewhat along the same lines was Patrick Whitehead who suggested the following two:

Thinking is tweaking your mind

Think better… TWEAK your mind!

Apart from this display of verbal dexterity, the participants also completed a “letter search” task where they looked for letter that spell out the word “Relax, Repose, Reteach.” I had done a similar activity with students in our MAET program a year ago in Plymouth. Essentially what I did was create a somewhat awkward problem scenario the solution to which were the words Relax, Repose, Reteach. So these were the letters students searched for… and this is what they came up with.

Now for the twist! As it turns out one of the themes of the keynote (and the workshop) were the three words “Explore, Create, Share.” Students watched each of the three videos that we had created (see them here) as well as the mashup that had inspired us to begin with (see the original and the mashup here).

What the students didn’t know was that the three words (Relax, Repose, Reteach) could be rearranged to read… (surprise, surprise) the words Create, Explore, Share!! Here is what that looks like…

I must give a shout-out to High School Freshman Bryan Jones who I “volunteered” to help me out. He had a tough job, collecting all the pictures since there were multiple cameras (from regular digital cameras to iPhones), missing cables, a mac that was running Windows (which mean iPhoto wouldn’t cooperate)… and he had to pull everything together in around 25 minutes while the workshop was still going on… And he managed it without fuss and stress. Thanks!

Finally, we all watched the new Steven Johnson video “Where good ideas come from” and created demotivational posters based on what they heard and saw. Below is the video (just in case you haven’t seen it already) and below that the posters the students created.

Choose Wisely Patrick Whitehead Tim Hart	Innovation Karen Decker Terry Ector	Don’t Worry Michael C. Gregory
This is a hunch Thomasina Rose Kristina Ernest Terra Graves	Ideas Brandi Mizner Beth Pearson Holly Marich Laurie Koelliker Gary Eisnor	Creativity? Roger Mayo Matt Keener

As you can imagine this was a hectic workshop for all of us. We covered a lot of ground and the participants also created some interesting artifacts that can have a life beyond the immediate workshop. What fun!

I have always been interested in what lies at the intersection of science and art. There are of course many different ways of looking at this. There is the idea of scientific creativity being both similar to and different from artistic creativity. And then there is the idea of artistically representing scientific ideas. I have written about this elsewhere in the context of poetry (both scientific poetry / sci-po or mathematical poetry / math-po). I have also argued that this process of “translation” from one medium to another is a very powerful way of both understanding the issues at hand but could also be an interesting teaching tool. For instance see these sci-po’s written by Sean Nash’s students. As I had said before, echoing Sean, in the context of writing a mathematical proof in verse (click here if you are interested), this act of writing a poem about mathematics forces you to truly and deeply understand the idea before you can start playing with it.

Such artistic representations of science can also be a powerful tool for outreach – to communicate often abstruse and complex ideas to a wider audience. One of the best approaches that has received some attention in the past years is Dance your Ph.D. As the Science Mag website says

The dreaded question. “So, what’s your Ph.D. research about?” You could bore them with an explanation. Or you could dance.

That’s the idea behind “Dance Your Ph.D.” Over the past 3 years, scientists from around the world have teamed up to create dance videos based on their graduate research. This year’s contest, launched in June by Science, received 45 brave submissions.

Today, judges—including scientists, choreographers, and past winners—announced the finalists in four categories: physics, chemistry, biology, and social sciences. Each receives $500.

Click here to see and vote for the finalists.

Greg Casperson is a graduate student in our Ed Psy & Ed Tech program. He has been engaged, over the past few months, in the most interesting experiment. He carefully selects and posts to his website one poem every day! Greg’s RSS feed has become one of the first things I check out every morning. He has impeccable taste, since, for one reason or another, he seems to select poems and poets that I love.

I had been wanting to blog about his “poem a day” website for a while now but then he did something that caused me to question his taste! He posted a poem written by me! I must admit I loved the attention but, truth be told, I am not sure I deserve being in such exalted company. What he posted this Friday was a poem I had written and posted on my blog, a few months ago. I wrote this poem in response to a poem by Grace Paley. I had come across Paley’s poem in a book I had picked up at a sale. Though I loved the original poem, something about it bothered me. I even read it to my kids and discussed my concern with them. Then, later that evening, I felt the urge to write a  response. And an hour or so later, there it was, Poem or Pie. Greg, for reasons known only to himself, decided to do a double-poem day and chose to link to my post.

Whether or not you like my poem, I strongly recommend adding Greg’s website to your RSS feed. Trust me, there is no better way to start the day than by reading a thoughtfully selected poem. And did I mention that Greg has impeccable taste (his occasional forays into pleasing his program faculty aside).

Anyway enjoy Greg’s “A poem a day” or surf over to my post that includes both the original poem my Paley, and my response. Do take a moment to read the first comment on my post. Turns out Grace Paley’s daughter read my poem and chose to drop by my website and write a comment! How cool is that. 

My daughter on her blog has a new poem / haiku called Sweat, a haiku with one glich. She is in India right now where the temperatures are easily in the 90′s – which I guess explains the genesis of the poem. What was more interesting, to me however, was the manner in which she, quite instinctively, breaks up a word in the poem. Interestingly, she regards that as a “glich!”

Here is the poem.

Sweat

Sticky, icky, ew!
I wipe it off, and it trick-
les, right back again!

“trick-”

“-les”

down the page. Reminds me of one of my favorite poets, e.e.cummings and how he plays with words. For instance here is a poem by him

l(a
le
af
fa
ll
s)
one
l
iness

It takes a bit of effort to read but it is worth it. With some thought you will see that in the parenthesis is the phrase “a leaf falls,” broken up so that it runs down the page, rather than across it. So instead of “a leaf falls” you read

(a
le
af
fa
ll
s)

Of course breaking it all up forces you (the reader) to read the lines in slow-motion, with pauses as it were. Also the shape of the letters comes through now as do the alliterative / symmetric “le” “ll” and “af” “fa” sounds. There is a visual and audio pattern here… a verbo-visual pun maybe. Sort of what Shreya did with the word “trickles.”

But there is more…

Outside the parenthesis is the word “loneliness” broken up so that you can see the words “one” sandwiched between two “L’s.” The “L” is written in lower-case, which again makes it look like the number “1″ or capital “I.”

l
one
l
iness

So the repetition of the idea of “one” or “I” (once as “one” and twice as the number or the “I”) emphasizes the solitary nature of this experience. It could be 1 leaf falling, or one person watching one leaf fall… And all the pieces come together to set up a sad mood of one lonely person watching one leaf fall

How clever of mr. cummings. And how cool that Shreya, discovered something similar in breaking up “trickles” into two parts, showing how the sweat actually

“trick -

- les”

down.

To me it is an indication of her increasing comfort with language. It is only when we are comfortable with the rules that we start to break them, and it is there that true creativity and one’s one “writerly” voice emerges. So I would argue, despite Shreya’s thinking that it is a glitch, that it is not. It actually her noticing a pattern, imposed on her by the syllable count required by the Haiku structure itself, and then using that constraint for a creative purpose.

As for the mis-spelling of “glich” – I hope she doesn’t correct it. Because the poem now does have one glitch, the mis-spelling of the word “glitch.” How self-referential!!

All in all, what a wonderful way to begin a Sunday, reflecting on creativity and writing, inspired by a poem written by 11 year old Shreya. How very cool!!

My friend and colleague Leigh Wolf forwarded me this article on Edward Tufte: The Many Faces (And Sculptures) Of Edward Tufte. I have been a fan of information design guru Edward Tufte’s work for years (decades?). I love his emphasis on clarity and simplicity in presenting information. I love the fact that he designs and publishes his own books (so that he can have full control over each and every aspect of the presentation). What I didn’t know of was his playful artistic side. It turns out that ET (as he is known) is also an artist, crafting giant metal sculptures in his “back yard” (if you can call the hundreds of acres that stretch behind his house a “back yard!”).

Over the past few years I have been thinking quite hard about the idea that creative people are not creative in just one area but rather tend to play within and across multiple disciplines or areas. Robert and Michele Root-Bernstein have in their book Sparks of Genius often talked about how the most creative scientists are polymaths, often having artistic and other interests that go beyond their immediate professional interests. In fact they argue, and I would tend to agree with them, that creativity cannot be forced into one box or domain. Creative individuals are curious about everything and often engage in creative activities in multiple areas, though they may specialize in just one area (usually the domain they are most known for).

This is true for the most creative people I know. For instance, consider Douglas Hofstadter (best known for his book Godel, Escher & Back and is work in Artificial Intelligence) dabbles in everything from mathematics to music, wordplay to art. Similarly Scott Kim (best know as a puzzle game designer) creates ambigrams and composes music, plays the drums and teaches mathematics using dance!

In my own way I have tried to do the same. Everything I do, from creating ambigrams to teaching, from photography to developing keynote presentations, from being a parent to advising students on their research, seems to me to be connected and inter-woven. I think my success as a researcher and scholar (to whatever extent I have been successful) derives from this “dabbling” across disciplines.

What is sad, however, is how much such “dabbling” is frowned upon. Through high-school and college, through graduate school and even as a faculty member, I have been advised, always by by well-meaning people, to focus, to find my niche, to become an expert on one thing. I have resisted it, mainly because knowing just one thing, seems, at least to me, such an impoverished way of being.

And I understand why I have received the advice I have. We live in a specialized world. A world where expertise is valued.  And an expert, after all, is someone who knows more and more about less and less. There is no space for dabbling in this world of.

But I wonder about that. I have a friend who is a successful professor of civil engineering. Turns out, that as he was growing up, what he really wanted to be, was a chef! I haven’t had a chance to talk to him about this but I wonder how his vision of being a chef influences what he does as a researcher and a teacher? Does it contribute (in some subconscious manner) to his work? Or has he suppressed it completely?

Either way I see it as a tragedy, in the first case because we haven’t developed a way of speaking of these influences, and in the second case because a possible, fruitful career was nipped in the bud.

The sad thing is that I am seeing school do the same thing to my kids, in fact to most kids I know. NCLB has not helped either. Don’t get me wrong. This is not an argument for some form of dilletantism (dabbling for the sake of dabbling). Not at all. What I am recommending (thanks to the Roob-Bernstein’s for this term) is polymathy. One of my students, Danah Henriksen, is currently working on a dissertation on looking for polymathy in teachers. As she says:

“Polymathy” may be thought of as an informed enthusiasm for more than one field of knowledge or expertise, or excellence in several realms that might seem distant from each other.  It has been suggested that what makes polymaths so successful and fluidly creative is an ability to cross-pollinate ideas and information.  People who open their minds to, and who learn from, multiple knowledge areas can apply new information and unique ways of thinking from one discipline into another.

This for me is the biggest reason for supporting such playing around in multiple areas. These experiences at the fringes (so to speak) of our professional lives, provide us with newer ways of being in the world. They allow us to see the world in new ways. They allow us to question things the field may have taken for granted. Just as Tufte says at the end of the piece, my goal, is to “make people see a little differently.” Turns out one of the best and easiest ways of doing so is by seeing through different disciplinary eyes.

We need to provide better opportunities for our students to do the same.

How can anybody resist this flowchart / visual representation of Hey Jude! Check it out. Don’t you just hear the song as you move through the boxes and arrows.

I recently read the following poem by Grace Paley and just had to write a response. Anyway, here’s the original poem:

The Poet’s Occasional Alternative
by Grace Paley

I was going to write a poem
I made a pie instead     it took
about the same amount of time
of course the pie was a final
draft     a poem would have had some
distance to go     days and weeks and
much crumpled paper

the pie already had a talking
tumbling audience among small
trucks and a fire engine on
the kitchen floor

everybody will like this pie
it will have apples and cranberries
dried apricots in it     many friends
will say     why in the world did you
make only one

this does not happen with poems

because of unreportable
sadness I decided to
settle this morning for a re-
sponsive eatership     I do not
want to wait a week     a year     a
generation for the right
consumer to come along

And here’s my response (this has been edited after it was first posted)

Poem or Pie
by Punya Mishra

I just read this poem
about a poet who chose to
bake a pie,
than write a poem!

It was weird, since in my hands
was a poem, not a slice of pie!

Was this the poem
That was not written?

And where was the pie?
Its existence, of course, had to be inferred,
assumed, taken at face value…

which made me question
whether that pie ever really
existed

having caught one
possible contradiction
I doubted everything.

I read this poem to my daughter
Who was more forgiving
maybe, she said, they baked
a pie AND wrote a poem

I wasn’t buying that!
Because in my heart I knew
that poets will do anything
lie, steal, stab and kill
to get the right slant on an idea

To get the right hook
that will make the reader smile
and pull them in to

Wallow in the here-nowness
Of baking a pie, and poking fun
At airy-fairyness of poetry
(in a poem no less). Who could resist
that?

But the truth is
I know it, and you do too,
that some days, a poem beats a pie

Though it is cute, in a self-deprecating
humble kind of way,
to claim the reverse.

I just finished a marathon session of presentations and discussions with the master’s students in Curriculum Development and Educational Innovation at Twente University. It was wonderful to meet with them and discuss creativity, teaching, design, TPACK, among other things. Here are the slides I used in pdf format. Photos from the past few days can be found on my Flickr site or on the Picasa site maintained by Petra Fisser (one of the organizers of the symposium).

I had them (as one of the mini-activities around half-way through the day) write a poem capturing their understanding. Here are the poems they came up with (with the names of participants at the end). Sadly no one took me up on writing a poem in Dutch!

Read the rest of this entry »

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?

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:

Read the rest of this entry »

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

Read the rest of this entry »

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 had written earlier about the idea of “postdictable” which was defined as something that is “surprising initially, but then understandable with a bit of thought.” It lies at the spot between predictability and total chaos. The movie Sixth Sense is postdictable in the best sense of the world. Good teaching I believe needs to be postdictable. That is what keeps us engaged, keeps us waiting for more, the payoff as it were. And best of all, once all the pieces are in, we can’t wait to go back and review everything again, to see just how beautifully the whole thing holds together. There is a strong aesthetic component to this – a sense of wholeness, closure, elegance, and inevitability. Good poems have this quality, as do mathematical theorems. A well crafted lecture or a lesson plan has this quality as well. In my mind these ideas are closely tied to the Dewey’s idea of experience and to the idea of design. Hopefully I will have a chance to explore these connections in a later post but for now, here are a couple of commercials that I think were postdictable in a really cool kind of way.
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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

My daughter, whose creative exploits have been featured here before (for instance see her design for a math-music game), now has a blog, titled Uniquely Mine. It features original writing (poems, stories) by her. Do check it out. You can find regular updates on this blog via the beauty of RSS feeds on the right column (just scroll down).

The one piece by Shreya I would like to draw attention to is a story titled Obtuse can be right. She wrote this as a part of a fourth grade assignment, and it is pretty cool, with interesting geometry-related wordplay. Enjoy.

My friend Gaurav Bhatnagar (whose doggerel on ambigrams is featured on my blog as well) gave it high praise in his facebook update, saying, “This is a masterpiece. Highly recommender (sic!). As good as Asimov’s short shorts.” I haven’t had a chance to see Asimov’s short shorts but I guess they are cool!

Yesterday I had blogged about poems written by the year I students at the Plymouth MAET program. Today I spent time with the 2nd year cohort and this is what they came up with. Enjoy.

There once was a hidden tiger in all,
at times it will make you think you’ll fall.
Many ideas, down to one,
novel, effective, whole, fun.
With Punya’s help we’ll answer the call
- Michelle, Johnny, Eliza, Lauren

There once was an idea called TPACK
but it wasn’t just about looking back
move forward and create
your teaching will be great
Relax, Repose, Reteach lessons do not lack
include NEW ideas, add a sixth line, LIMERACK!
- Sean Sweeney, Rawad Bou Hamdan, Alfred McDonnell

I started the class with amnesia,
Became totally engrossed in fantasia,
Found myself steeped in inertia,
Sighed…oh, for the world of nostalgia.
- Camilla

There was a group of creative boys,
Who loved to play with their toys,
“The effect”, one boy said
Is completely dead
A novel idea lets employ
- Jason Shulha

Creativity cannot be taught
Nor is it something that can be bought
Listen to Punya
He’ll tell this to ya,
If you don’t practice, have it, you’ll not!
-Kristin Bergeron

Seeing the world differently
I what we call creativity
No more amnesia,
Inertia or fantasia
Explore, create, and share effectively
- Ashley Priem

I think I must understand how
To become the one purple cow
No inertia, amnesia,
Nostalgia or fantasia
So NEW is my cool buzzword now
- Jacquie Courtney

As yesterday the students engaged in searching for alphabet-shapes in the world around us, but this time with a twist. I created a problem scenario (a rather awkward one, truth be told involving Shulman, videos about amnesia, fantasia, and inertia) the solution to which were the words, Relax, Repose, Reteach. So these were the letters students searched for… and this is what they came up with.

Now for the twist! As it turns out one of the themes of today’s presentation were the three words “Explore, Create, Share.” Students watched each of the three videos that we had created (see them here) as well as the mashup that had inspired us to begin with (see the original and the mashup here).

What the students didn’t know was that the three words (Relax, Repose, Reteach) could be rearranged to read… (surprise, surprise) the words Create, Explore, Share!! Here is what that looks like…

I am in Plymouth, England, for a week, as a part of our off-campus MAET program. I spent time today with the first year cohort, talking with them about creativity in teaching (with our without technology). One of the short (5-10 minutes) activities they completed around an hour into the session was writing short poems about the creative process. Here is what they came up with:

Step by step (to be creative!)
By Miguel Herrera

Step by step… Uh baby… have some tips to be creative in this world
Step by step… uh baby…if they work, would you please let me know….

Step 1: to be NOVEL is fun!
Setp 2: if it’s not EFFECTIVE they will boo!
Step 3: Sir, would you like some tea?
Step 4: it has to be WHOLE… That’s it… I’m done….

…Would you please let me know!!!!

The New NEW
Alyssia and Katie

There once was a teacher with technology,
Who tried some creative pedagogy,
She tried something new,
And it went askew,
So she used the NEW methodology!

There was once a man from msu
From Drew, Tara, and Larissa

There was once a man from msu
Who came to us with something NEW
It wasn’t a novel effective or whole
But learning from him was quite brilliant and droll

Be creative
Cathy Emery

Be creative, quick! go! now!
You don’t need HTML know-how
How can you make a purple cow?
Weird teapots make us go wow!
Change comes quickly now..
Ciao

Knowledge
Consuelo Salazar

Jumpin’ Jesus is upon us
He started slowly
But, as we meet in the present,
His face is blurred by
The flying debris of technology
soaring between us.

They also took a moment, or two, to search for letterforms in the world around us…. here is what they spent their time discovering.