Niels Bohr, the 1922 Nobel Laureate in Physics once said:
The opposite of a correct statement is an incorrect statement. The opposite of a profound truth is another profound truth.
I was reminded of this when I saw this TED video. Check it out…
(h/t Andrew Sullivan)
TPACK involves understanding the capabilities of technology – understanding how we make meaning with it, how we can manipulate it to communicate, engage and teach. I include below an extraordinarily powerful use of media, created with the simplest of tools, one camera, a couple of people and some music. No 3-d aliens, no fancy digital effects – but (and this is important) the designers clearly have a deep understanding of the nuances of meaning that can be generated through subtle yet powerful use of the tools at hand. Zooms and pans, dissolves and wipes, memories and meanings.
Think about this video when people ask of what value are these new digital tools? Tell them we don’t know – but maybe a few years from now someone will surprise us by creating something this touching and breathtaking.
Russ Goerend over at Learning is Life has initiated a fascinating discussion on the TPACK framework on his blog. It all revolves around a blog post he titled The force is strong with the shiny one. I shall not seek to summarize the discussion here (please go read it for yourself) but there are a couple of things he wrote that connected with me and that I would like to comment on. He wrote:
When I think of the TPACK diagram, I picture horseshoe magnets on the outside of each circle, pointed into the middle. Those magnets are what keep the quality teacher balanced in the center, each magnet pulling and building a feeling of equilibrium. This is obviously best-case scenario.
He describes the evolving knowledge of the teacher as (and I love this phrase) Journey to the Center of the Venn. As Matt Koehler and I have written earlier, we see all good teachers as sitting right in the middle of the three intersecting circles. Elsewhere we had written:
Clearly, separating the three components (content, pedagogy and technology) in our model is an analytic act and one that is difficult to tease out in practice. In actuality these components exist in a state of dynamic equilibrium, or as the philosopher Kuhn (1977) said in a different context, in a state of “essential tension.” (This is in our original TC Record article that introduced the TPACK construct, though it was then called TPCK. I am sure we have written about this elsewhere as well, but I am being a bit lazy here.)
From the Saline Schools, right here in Michigan, comes a video about how teachers and students are using cellphone in the classroom to enhance teaching and learning. Check it out
The video below has been getting a lot of attention on the blogs lately, and despite that it is pretty good. No kittens riding skateboards or mentos and Coke here. Just a beautifully constructed take down of TV News. A must see for all media literacy courses.
Check it out.
Our very own Leigh Wolf is quoted in a story in today’s State News. Check out, Education unlocked: MSU professors use open courseware to provide class materials for students
Leigh manages to bring in the MAET program in to the picture (why am I not surprised?) and how we have been using some of these technologies for recruitment and community building. Here is a quote (though you should go read the entire article, right?)
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.
The Rethink Scholarship is an scholarship for aspiring art directors and designers to Langara College’s Communication and Ideation Design program. This video is to publicize the program.
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.
Hot off the press:
Schmidt, D. A., Baran, E., Thompson, A. D., Mishra, P., Koehler, M.J. & Shin, T. S. (2010). Technological Pedagogical Content Knowledge (TPACK): The development and validation of an assessment instrument for preservice teachers. Journal of Research on Technology in Education, 42(2), 123 – 149.
Abstract: Based in Shulman’s idea of Pedagogical Content Knowledge, Technological Pedagogical Content Knowledge (TPACK) has emerged as a useful frame for describing and understanding the goals for technology use in preservice teacher education. This paper addresses the need for a survey instrument designed to assess TPACK for preservice teachers. The paper describes the survey development process and results from a pilot study on 124 preservice teachers. Data analysis procedures included Cronbach’s alpha statistics on the TPACK knowledge domains and factor analysis for each domain. Results suggest that, with the modification and/or deletion of 18 of the survey items, the survey is a reliable and valid instrument that will help educators design longitudinal studies to assess perservice teachers’ development of TPACK. (Keywords: TPACK, instrument development, preservice teachers)
I stumbled across this little machine that shuts itself off once it has been switched on! How cool is that. I don’t have an clue whom to credit it to and would appreciate a heads up on that. I was reminded of the myth of Sisyphus which led to a great piece of hand-drawn animation on YouTube. So here they are… somewhat apt images for a dull, dreary day in mid-Michigan.
You can watch the Sisyphus youtube video here. And here is a link to another small animated gif about Sisyphus.
I received an email from Michael Porter of the Littleton Public Schools in Colorado about a version of the TPACK game Michael and his colleagues recently conducted with their K-12 Leadership team (building principals and district administrators). I know that Matt Koehler and I had discussed a TPACK mashup game in our SITE 2008 Keynote but what Michael and his colleagues have done is something different. Essentially they gave their participants a set of scenarios that they then had to evaluate using a TPACK lens. They ended up what a set of “scatter plots” that reveal the manner in which each of the scenarios integrated technology, pedagogy and content. Read the post (The TPACK game) to see just how this plays out.
Photograph of “scatter plot” generated by the TPACK game,
Image credit Littleton Public Schools & Michael Porter
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:
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
The other day, for one reason or another, I did a Google search for the word “recursion.” According to Wikipedia, recursion
… in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition; specifically it is defining an infinite statement using finite components.
This is a screen shot of what Google gave me as a result of my search: (Click on the image for a larger version).
Look carefully at what Google suggests. It says.
Did you mean: recursion
The exact same word that I had searched for… For a moment or two I thought I had found a glitch in Google’s suggestion mechanism… but it suddenly hit me, that this was exactly what recursion meant! If I clicked on that link I would be taking the first step into an endless cycle, an infinite loop, which would end only when I “got it.”
This has been an inside joke amongst programmers for a while. Wikipeda provides one example from a hypothetical dictionary that goes as follows:
So in some sense Google provides a “working definition” of the word – that explains it better than just reading a definition in a dictionary. How cool is that. I think it is little games like this one that make Google so much fun to use.
(I must add that this is not a new discovery. The Wikipedia page about recursion does mention this Google trick – but it was new to me!)
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…
TPACK Newsletter, Issue #6, January/February 2010
Welcome to the sixth edition of the TPACK Newsletter, with 642 subscribers (representing a 13% increase during the past 2.5 months), now appearing twice each fall and spring semester. If you are not sure what TPACK is, please surf over to www.tpack.org to learn more.
Gratuitous Quote about Technology
“Technology presumes there’s just one right way to do things and there never is.” ~Robert M. Pirsig
0. In this Issue:
-2. Introductory Blurb
-1. Gratuitous Quote about Technology
0. In This Issue (You are here.)
1. Recent Journal Articles and Conference Papers about TPACK
2. Recent TPACK-Related Dissertations
3. Join a Fireside Chat about TPACK
4. TPACK @ SITE 2010 Conference
5. TPACK Handbook Reviews
6. The Future is Now … So Now What?
7. Learning and Doing More with TPACK
–. Un-numbered miscellaneous stuff at the end
Martin Luther King, Jr.
January 15, 1929 – April 4, 1968
Human salvation lies in the hands of the creatively maladjusted
—in Strength to Love, 1964
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…
I guess once the bug bites, it never really lets go. So here’s another poem (to follow this and this and this). As it turns out this is my second poem on the Goldbach Conjecture. I realized after I had written the first one that I had actually messed up the history a little bit. As it turns out the conjecture that Goldbach had written in his letter to Euler was different from the one connected with his name today. In fact, the one we know today as Goldbach’s conjecture was actually developed by Euler. As this article [pdf] on the American Mathematical Association website states,
I was intrigued by the fact that even though the the final form of the conjecture was developed by Euler, the more famous mathematician, it is known as Goldbach’s conjecture. This poem below is my attempt to have some fun with this. Read the rest of this entry »
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…
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:
I had written about the EduPunk movement earlier, in fact had even designed a logo for it.
A brief description of Edupunk can be found on Wikipedia (a google search will reveal many more). Wikipedia describes it as follows:
Edupunk is an approach to teaching and learning practices that result from a do it yourself (DIY) attitude. The New York Times defines it as “an approach to teaching that avoids mainstream tools like Powerpoint and Blackboard and instead aims to bring the rebellious attitude and D.I.Y. ethos of ’70s bands like The Clash to the classroom.”
Well, I am no expert on 70’s bands but the EduPunk title does appeal to me. It appeals to me because for the longest tie the main attraction of digital technology, to me, has been this DIY attitude, the fact that I can, over an evening or two, create a stop-motion movie with my kids (here or here), or mashup a commercial, or, in this case, create my own course website. The final product may not have the finish or sheen of a commercial product but it is in some key way “authentic.” It is mine. It embodies me, my sensibility, my approach, my vision in ways that other products can not.
For my entire tenure here at MSU I have constructed my own course-websites, cobbling them together with what I have often jokingly called “duct-tape and magic.” I have even written about this, long before the EduPunk moniker came along (see links at end of post). What I want to describe in this post are my current experiments (for my CEP817 Learning Technology by Design course) using using Wordpress as a learning management system, and boy am I impressed!!
[My partner in crime in this is Kristen Kereluik, a graduate student in our program.]
I had written previously about a blog started by students in our Educational Psychology and Educational Technology Ph.D. program (ideaplay.org) and had designed a couple of ambigrammatic logos for them. You can see the original post here. Here is one of the original designs I had provided:
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.
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.
I have had a lot of fun this year playing with video. Most of these experiments were done with my kids (nothing like combining work with pleasure). One of the things we had done last year was a stop motion new year’s card. So we just HAD to create one this year as well. Enjoy!
[FYI: Links to last year's creations can be found below]
Best Wishes for 2010!
from Shreya, Soham, Smita & Punya!
Here is a list of other explorations in video made in the past year or so with family. As you may notice some of these movies (particularly the series Explore, Create, Share) are ones that I use in my teaching – nothing like getting your kids to do your work for you 
Have a wonderful new year!
