… although teaching students involves imparting knowledge, it is also a calling with other dimensions beyond the cognitive … It is about the formation of minds, the molding of destinies, the creation of an enduring desire in students not only to know, but also to care for others, appreciate beauty, and much more. In some sense of the word, teaching is a spiritual, although not necessarily religious, activity. When done well, it cultivates human intimacy and allows teachers to find creative self-expression in classroom community.

The authors define reverence as follows:

Reverence is comprehension of human limitation, imperfection, and our appropriate place in the cosmos as a consequence of the humility that arises from feelings of awe, wonder and admiration before something or someone that meets at least one of the following conditions: (1) Something or someone that cannot be changed or controlled by human means; something we are powerless to alter. (2) Something or someone we cannot create. (3) Something we cannot completely understand. (4) Something or someone transcendent; something supernatural.

Though I have not used the word “reverence” in my own writing / thinking I have often said the same thing about the role of the aesthetic in teaching in learning and the need for us to develop a language that allows us to include these dimensions of the human experience in our work. I have some reservations about the word “reverence” – mainly because of the religious connotations which can sometimes lead conversations into directions one may not necessarily want to go. (Though, I must add, that Garrison and Rud, take pains to write that “teaching is a spiritual, although not necessarily religious, activity.”)

Some examples from my previous writing on this blog that allude to similar ideas are provided below.

• A different language
• The one rule of teaching
• Bringing sensory richness to scientific texts
• Teacher as Filmaker
• Translations & Technology: Reflections on French Lieutenant’s Woman
• 2001, 4o years after

I want to end with something I wrote about the movie 2001 A Space Odessey:

2001 is a movie of big ideas: about what it means to be human, what is our relationship to technology, about our place in the cosmos, and our inability to answer some of these questions. 2001, thus, is a profound, deep and thoughtful attempt to use the medium of film to explore these ideas. And the style Kubrick chooses is intensely visual, deliberately paced, with minimal dialog. The first section of the movie has no dialog because there are no thoughts to express and no words to express them with. This is mirrored in the third and final section which has no dialogs because thoughts have far outstripped the ability of words to convey meaning. The section in between, set somewhere in the near future (as the 1960?s would imagine 2001 to be) has words, but even here it is amazing just how few, and ineffectual they are. Humans for the most part seem remote and disconnected from each other and, strangely enough, the most engaging character is the computer HAL!.

As is clear, 2001 is a ambitious movie (some would even say too ambitious). But it does do one thing right – it asks the right questions and tries to come up with an answer. And it does so in an ambiguous manner, allowing for multiple interpretations and readings. And that is its strength. It seeks, through the medium of film, to penetrate a “fundamental disparity between the way we perceive the world, including our own experience in it, and the way things actually are” (Dalai Lama quoted by Eberhart). That this is an effort doomed to failure is neither here nor there. In fact, the last line of dialog in the film speaks to this very possibility of failure: “Its origins and purpose [are] still a total mystery.” In the movie this dialog is about a black monolith – but works as aptly for the universe we live in.

In fact, as I think about it, 2001 is a deeply reverent movie. The question I have is whether we have created similar spaces for reverence in our classrooms? Have we even considered it? Or have we killed the idea with our focus on No Child Left Behind and Race to the Top?

Punya,
Here is the palindromic poem that I wrote recently, but I made it so that the words are reversed instead of just the lines. It adds another layer of difficulty to creating it, and I recommend trying it if you get the chance.

Falling Snow

snow falling gently
on stomping feet
cold stinging
the teasing and laughing children
sculpted beautifully – crystals form
flakes dancing gracefully
tumble and spin
spin and tumble
gracefully dancing flakes
form crystals – beautifully sculpted
children laughing and teasing the
stinging cold
feet stomping on
gently falling snow

How awesomely cool is that! I wrote back to him right away saying

Jake. This is awesome!!!! I just shared it with my family and we were unanimous in our appreciation and praise for your achievement. Not only is it a doubly palindromic poem, an achievement in and of itself, it is a wonderful poem in it’s own right….

Thank you so much for sharing this with me. It completely made my day.

Don’t you just love the open-architecture of the web (and why I resist the closed worlds of Facebook).

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.

Now I don’t consider myself a poet in any serious sense of the word (my dabbling in mathematical poetry or palindromic poetry notwithstanding). But it is great feeling when something you create and put out there in the world connects with someone else, someone who you would never otherwise have met or gotten to know. Here is what I wrote back to Jake:

Dear Jake –
Thank you so much for writing to me. I am honored to make it to your list of poets and glad that you are interested in palindromic poetry.

As for my history: I am professor at Michigan State University in East Lansing MI. I am originally from India where I studied engineering and design before coming to the US and getting my PhD. My wife is a graphic designer and I have two kids: my son who is a freshman in high school and my daughter who is in 6th grade.

Ever since I was a kid I have always been interested in puzzles and mathematics and poetry and visual design. That I think led to a habit of playing with words and images… so I do a lot of doodling and sketching (specially when I in meetings). I am fond of asking questions and looking at things around me in new ways. For instance, I love photography, on my Flickr site you will find photos of silly things like finding alphabets in cracks, and faces in everyday things. See this link and this one…

• Alphabets in cracks
• Faces we see

Then there are the videos I make with my kids. For instance see the new year’s card we made recently.

This also led to my creating ambigrams, which are words that are written in a special ways so that they can be read multiple ways. You can find a bunch of such designs on my website.

So I guess, palindromic poetry emerged out this desire or propensity to see the world in weird ways. And the challenge of writing poems that read the same backward and forward was inherently interesting. I particularly enjoyed writing ones that flipped in their meaning when you cross the half-way point. For instance in the poem “Me as I sit” the poem switches from me watching you to you watching me!

Finally, as must have noticed, from the dates, most of these were written a bunch of years ago when I was a graduate student at the University of Illinois. I haven’t written too many recently but the fact that they are on my website leads people to them – and I form all kinds of cool connections – such as the email I just received from you. A year or so ago I heard from someone who uses my poetry to teach poetry to inmates in prison (how cool is that!). You can read about that here.

That’s all for now.. I would love to read any palindromic poetry you may have written, if you are comfortable sharing them with me. Thank you again for your interest in my work. I look forward to hearing from you and let me know if there is anything else you need to know.

take care ~ punya

Note: I got Jake’s (and his parent’s) permission to post our correspondence on this blog under the condition that I not include his email address or other contact information.

Many moons ago I had written about the idea of the web as small pieces loosely connected (read Gandhi, ambigrams, creativity & the power of small pieces loosely joined) that allow people to pursue their passions and share it with the world at large. This is what gives the web its power, and this is also why I am not as comfortable with the barricaded worlds created by Facebook, which would not have allowed someone like Jake to easily find me, (but that is a rant for another day).

A wordle of some of the ideas that we touched upon can be found below (thanks Nick Sauers)

You can find a PDF document of my slides as well as a PDF of the demotivational posters created by the participants. (Even if you don’t see my slides, you MUST see the posters… they are funny and worth a moment of your time).

A couple of participant took notes during the day and have kindly made them available:

• Nick Sauer’s Notes | Blog posting
• Matt Townsley’s Notes (Incidentally Matt and I have known each other for a while now but had never met. It was great to finally meet up with one of my online buddies. Matt blogs at MetaMusing)

The participants also created (as a part of the workshop) some poems. I am including them below:

Creativity Haiku
by Karry, Michelle, Kathleen, Beth, Todd, Kathy
technology is
creative innovation
tpack makes us think

Limerick
by Deanne, Ruth, Jason
Administrators, librarians and teachers
Came to learn about “teachnology” features
TPACK is the focus
Dr. Punya is the “mostest”
They came out of there much wiser creatures

Untitled
by Joe, Kay, and Jessica
While spoon feeding our students in class
We focus on the Total PACKage
As we use, integrate, and innovate
To help them Know-Act-Value
We find-Everything is NEW

Deja Who?
by Amy, Christopher, & Mike
There once was a man from MSU.
He Déjà Vu’ed and Veja du’ed.
TPACK was his shared view
of all that was NEW!

Poem
by Melva, Cathy, Jan, Kim, Dianna
Acronyms, acronyms, here’s what we found
TPACK is where teaching hits the ground.
Technology, Pedagogy, Content and Knowledge
Will take teaching beyond the cutting edge.

NEW stands for Novel, Effective and Whole
And if something is meant to roll, it should roll.
We’re learning how in our classrooms to apply
All of this information which is in great supply.

Team TPACK
by Tony, Mary, Kelly, Jodi
There once was a teacher from Marimac
Who wanted to teach with his Mac
His friend said now Jo
Just take it slow.
Remember to think about TPACK

Poem
by Mary, Brad and Jan
Teaching 3 knowledge bases
Providing framework for technology integration
And
Creativity
Keeping learning déjà vu and veja du

Creativity
by Brian, Lisa, Seth, Julie, Stacy
There was a smart man from MSU,
who defined creativity as N-E-W.
He effectively did present
technology, pedagogy and content
and it all started with veja du.

Thanks to Andy and his team for this wonderful opportunity.

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.

Educational Technology had quite stringent word-limits and length requirements, so the final published article is much shorter than what we had originally submitted. And since I had already felt that the original article was shorter than it needed to be… the final version seems more than a bit truncated. For this reason I am providing links below to both the published piece and a longer unpublished version. If I had to choose, I would read the longer version but that need not be your choice.

Mishra, P., Koehler, M.J., & Henriksen, D. (2011). The Seven Trans-Disciplinary Habits of Mind: Extending the TPACK Framework Towards 21 st Century learning. Educational Technology, 51(2) 22-28.

Abstract: In this article we examine the need for fostering transformative learning, emphasizing the roles that trans-disciplinary thinking and recent technologies can play in creating the transformative teaching and learning of the 21st century. We introduce the Technological, Pedagogical Content Knowledge (TPACK) framework as a starting point for discussing the special kinds of knowledge, skills, and understanding that teachers require in order to become effective classroom mediators of transformative learning experiences. Within this framework, we propose seven cognitive tools needed for success in the new millennium, and describe examples of how teachers can repurpose digital technologies to use these cognitive tools. We explore the implications for research and practice.

Here is a link to the longer (draft) version.

Mishra, P., Koehler, M.J., & Henriksen, D. (draft). The Seven Trans-Disciplinary Habits of Mind: Extending the TPACK Framework Towards 21 st Century learning (full version).

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!

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.

Click here to view the embedded video.

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!

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.

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. 

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!!

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.

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 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!

(1)

Once upon a time there was an idea
But now we need new creativity
TPACK came around suddenly
This idea is new, whole and effectively
The righ knows were found, finally!

(by Mirjam van den Biggelaar, Eline Roelofs, & Leonie van Eeten)

(2) This poem is in a form called Elfje. Essentially it consists of 11 words in total, where each line has 1, 2, 3, 4, 3, 2, 1 words in it.

Conative
TPACK model
task-oriented coaching
learning output and process
creativity

(by Juo-Lan Li, Judith van Kesteren, Larissa Odendaal)

(3) The third poem has a unique structure. I needs to be read twice, first as it and then second time after “tweaking some knobs” i.e. the words have to be shuffled around.

TURN the knobs right
blue violets are
Red roses are
Know what do to and you.

And now the shuffled version

Roses are red
Violets are blue
Turn the right knobs
And you know what to do

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.

Sean Nash (of Nashworld and speaking in rhymes in biology class fame) in his post speaks of a step by step process that one follows when writing such poems. He writes of science but I think the same argument works for mathematics as well. One of the key things he writes is the value of summarizing, which I take to mean truly understanding something before you can translate it (in this case from prose to poetry). I am doing something similar here, where I take something written in mathematical language and translate it into rhyming verse.

The poem below was my attempt at writing a poetry version of Euclid’s proof that there are an infinite number of primes (see the actual mathematical proof). What was interesting was that I started writing the poem based on my recollection of the proof. Once I had a draft I went off and found some actual proofs to link to – and then while reading them, I realized that I had made some subtle but critical mistakes in my poem. [For instance here is a page that gets it right, and here is another that doesn't.] Which meant that I had to go back to the editing table, and a few surgical strikes later, I had a poem that (at least to my eyes) is mathematically sound (its value as poetry is another matter altogether).

Prime Circle by modern_country

As I was doing this, it struck me that this act of writing poetry actually helped me learn and understand this proof. I can’t wait to get back home and share this understanding with my kids. So this poetry has a educative component, not necessarily for the ones reading it (they may as well read the proof in its mathematical form, it isn’t that hard, it is shorter, and they don’t have to deal with my forced rhymes). But it did help me learn.

So this is a good example of how the process of constructing something (the act of design) can be as important, maybe more so, than the actual product that emerges. So the proof of the pudding is not necessarily in the eating but rather may lie in the cooking. But here the proof of the proof lies in the creating not in the reading, but I include the pudding (er… I mean poem) here anyway, for the record.

The infinity of primes

Over numbers and their combinations if you sit and mull
You will find that not one of them is uninteresting and dull.
But it is a certain class of figures that most attention stirs
Yes, I am speaking of those special ones, the prime numbers.

Prime numbers are interesting, the mathematician posits,
‘Cos they make up all the others, the so-called composites.
Here’s an imperfect analogy, a simple little working rule,
Consider the prime to be an atom, then a composite’s a molecule.

Prime numbers by chrisinplymouth

To carry the chemical analogy completely out of bound,
Consider these atoms (primes) as randomly strewn around
Some here, others there, their patterns concealed
Few sequences stand out, no deep design is revealed.

As the ladder of digits you will climb
Hoping to predict the appearance of a prime
One fact stands out, above all else, as you stare
Prime numbers become more and more rare.

The solitude of primes
from View from Here Magazine

In other words, there are fewer primes the higher you go
Does this heightened rarity mean something, or no?
Is there a prime that is the biggest one?
If there is, finding it could be fun.

Of course, there’s another option, it is clear
Is it that primes get rarer but never disappear.
They get fewer and fewer the further we see
But they never really get done, on to infinity.

Which of these two options is the one that’s true
And how much arithmetic do you have to do
To show whether the primes are finite or not?
Ideally via a nice elegant proof, in one clean shot.

Euclid by waxesstatic on Flickr

Euclid, the geometry guy, comes to the rescue
And produced a cool little proof, whew!
So here’s my attempt to show in rhyme
There’s no such thing as the largest prime.
But don’t take my word for this information
Let us take a moment to look at Euclid’s creation.

Now here’s a critical (and smart) mathematical move
Euclid said, that in order the converse to prove,
Let’s start by assuming there is one (whatever it may be)
Let’s give it a name, this biggest prime, let’s call it p.
This largest prime, (p) when all is said and done
Is divisible just by itself and the number 1.

Now lets multiply together all these primes we have, then
We get a humungous number, we shall, for now, call N.
(This number we shall capitalize
To represent its rather large numerical size.)
Because N is the product of every prime we know,
It is divisible by every one of them, that’s easy to show.

Now take this N and to it, just add 1 (that’s all)
A difference that you may consider as insignificant and small.
But think about it for a moment and you may see
What a difference this addition makes to divisibility.

Divisibility, Image from Math is fun

This new number N + 1 you will soon realize
In the case of divisibility can really surprise.
Take any number on our list including p, our largest prime.
N+1 is not divisible by any of these atoms of the number line.
Whichever way you put N+1 through the division blender
You will always be left behind with one solitary remainder!

Stay with us for a moment, we are almost done
In fact, this is where it gets to be kinda fun.
Notice, there are just two possibilities at this juncture
Let us, in turn, consider each conjecture.

Fork on the road by Jessi Joy

Either N+1 is a prime, or it is not.
If it is a prime, our assumption is shot!
For N+1 is clearly
Much bigger than p!
Something that contradicts what we started with
The idea that p is the largest prime must be a myth

Or, it could be that N+1 is a number composite
Implying there are some primes that can cleanly divide it.
One thing for sure, this divisor cannot be
A prime in our original list we see.
‘cos we just showed that dividing N+1
By primes in the first list just cannot be done!

This just means, there are some primes we missed
When we were building our initial complete list.
And if we missed one, you can sure
There are just an infinity more.
Isn’t it time you said to me
Those magical words, QED.

To sum up, the finite prime set idea is pure fiction
Since assuming it leads to a contradiction.
Primes may be rarer and rarer the higher we go
But they do go on forever, and this Euclid did show.

Infinity by Sven Geier

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