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.
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!
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.
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.
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:
Recursion
If you still don’t get it, see: “Recursion”.
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!)
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
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…
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 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:
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.
I have been somewhat skeptical of the learning styles literature for a while, not the least for hearing the phrase being bandied about without much thought. I have heard people claim without much evidence, that today’s kids are visual learners. I have heard a teacher say that as a consequence, that visual learners prefer reading text from a Powerpoint slide, rather than read it on a blackboard! (Those who know me that I am rarely at a loss for words, but that statement truly struck me dumb! In Wolfgang Pauli’s words, that statement was not even wrong.) I have also had students claim that they did not do well in a certain course because it did not match their learning style!
Anyway, the study reported in the article
… does not dispute the existence of learning styles. But it asserts that no one has ever proved that any particular style of instruction simultaneously helps students who have one learning style while also harming students who have a different learning style.
What does this non-finding mean for practitioners (teachers and professors)?
Numbers are seen as being critical to developing our understanding of a subject. As Lord Kelvin, (1824-1907) said:
… when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
More succintly he said, “To measure is to know.” Numbers provide us (particularly academics) with credibility.
Of course this dependence on mathematics and numbers can often be misplaced. I am always impressed how we use numbers mindlessly – sometimes to levels of accuracy that don’t really convey much. I was reminded of this while reading a recent NYTimes article A Deluge of Data Shapes a New Era in Computing.
Students in my CEP 818 (Creativity in Teaching and Learning) have been using digital photography to explore a variety of topics related to trans-disciplinary creativity. I hope to showcase some of their work on this blog once the semester gets over. In the meanwhile, I received an email from Michael Hughes, a former alumnus of this course, and a teacher in Jakarta, Indonesia. In his email he provided some links to some really cool work his students have been doing.
Ambigram.com is a website about ambigrams and the people who make them. Lots of cool stuff for enthusiasts and novices alike. They often conduct competitions and other fun challenges for readers. One recent one was related to palindromes. In brief, they challenged people to create palindromic ambigrams. This is something I had tried a few time a long time ago – but their challenge pushed me to go back and come up with some solutions.
Well, I ended up with more than I had anticipated. I now have a technique, using which, anybody can create a palindromic ambigram of any length! How cool is that.
How does technology change what we do? Often when a new technology appears we tend to see it in terms of existing practices and structures. So an e-book is the same as a book, except in digital format. E-books still have “pages” which we “turn” (with a flick or our finger or if you are stuck with the Kindle, by pressing a button), though digitality does not require pages or turning them. Similarly the design of most early online courses attempted to replicate face-to-face modes of teaching (capturing lectures through video, for instance), instead of pushing for exploring the possibilities of this new medium. This is often most obvious in the kinds of iconography that new technologies generate. So the icon for Microsoft Word document looks like a piece of printed paper, an email-box looks like a regular mailbox (think AOL and its “You’ve got mail” message) and so on.
However, new technologies do not just replicate what we could do before – they insidiously and fundamentally change the nature of the tasks we perform. Think of the idea of hyperlinks! Regular texts go hypertextual through developments like the table of contents, indices etc. however, these are weak attempts at best. True hypertext emerges only through digitality.
I was reminded of this when reading a recent NYTimes article on video bingo and the controversies it is causing in Alabama. The article begins by describing traditional bingo:
Everybody knows what this is: dozens of people, mostly retirees, hunched over paper grids in a smoke-filled American Legion hall on a Sunday evening listening eagerly to a woman recite numbers.
Now we have a new player on the block, video bingo! which is described as follows:
But what about this: a dim warehouse of flashing, jingling video terminals with names like Boomtown Bonanza where, early on a weekday morning, people sit on stools pushing buttons and watching cherries and 7s reel by.
A new ambigram created in memory of Jere Brophy, world renowned scholar on psychology of motivation. The ambigram reads, “motivation” one direction and “Jere Brophy” when rotated by 180 degrees. Click on the image to see a larger version, hosted on Flickr.
Well, it is the top half of a lake-reflection ambigram. What this means is that if you reflect what you see along a horizontal line at the bottom of the image, the picture you will then get will spell a word. Can you figure out what it says?
While you think about that, let me tell you about this new group-blog set up by graduate students in our Educational Psychology and Educational Technology Program. The blog is called IdeaPlay and is available at ideaplay.org. So sitting here in India I had a few moments to sketch out some ambigrams for their blog. Here are two…
The first is a rotational ambigram that reads the word “Idea” if you go clockwise and the word “Play” if you go anti-clockwise.
And as for the lake reflection ambigram (half of which you saw up there)… well (no great surprise) it reads IdeaPlay as well, like so..
I hope you liked these new ambigrams, and I hope you will check out the the ideaplay.org blog.
Robin Revette Fowler sent me a message on Facebook regarding my recent posting(s) about moving from incompetence to mastery (see the two previous posts here and here). She took issue with my idea that mastery requires some kind of meta-level, self-awareness. She said
It seems like the issue is with either the meaning of “mastery” or perhaps with the types of skills you’re talking about.
Conscious/unconscious knowledge is especially interesting to me re: linguistics. Most native speakers have only unconscious competence of their language– I used to hear Writing Center tutors telling ESL students, “you need an ‘a’ here; I don’t know why” all the time. Many NNSs, on the other hand, have much stronger conscious competence– they often know “rules” about how to use determiners much better than Native English speakers, for example. At the same time, I’m not sure they would be said to have “mastery.”
And I don’t know that the conscious competence is the important thing here. Would you argue that only linguists who can describe their determiner choices have “mastery” of English grammar?
At first blush Robin seems to be making a good point. Do writers need to know how and why they do what they do they do as long as they get it right? There is a surface plausibility to the argument but I am not sure that it stands muster if we dig deeper. Read the rest of this entry »
In a couple of previous posts I had talked about the idea of postdiction (see the posts here and here). The argument being that good teaching (among a long list of other good things) is postdictable, i.e. it walks the line between predictability and chaos, and most importantly makes sense post hoc. To make my point I had posted a couple of videos that were good examples of being postdictable.
Closely connected to the idea of postdictable is the idea of creating anticipation and suspense. Once again other artists (particularly those working in temporal media such as film, and advertising) seem to have grasped the importance of this earlier than educators. Good film-makers can create suspense out of pretty much the flimsiest of materials. Think of the first scenes from Tarantino’s Reservoir Dogs. The way the scene builds tension out of a disagreement over whether or not to tip is pitch perfect. There is more tension in that scene than in dozens of other “suspense” thrillers.
However making suspense work is difficult. Navigating this line between predictability and tension over the unknown is a fine art. (This is where, of course, the connection with postdictability becomes most clear.)
Check out the two videos below, which highlight just how fine the line is between succeeding at creating suspense and anticipation and failing to do so. Both of these videos are interesting and well made – both have pace and rhythm but one of them builds anticipation while the other just happens. One tells a story, the other doesn’t. Read the rest of this entry »
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. Read the rest of this entry »
As readers of this blog know I love examples of seeing things in new ways. That to me if often the crux of creativity. Anyway here are two examples. The first curtesey of Leigh Wolf is a new advertisement from some credit card company. The ad is actually pretty average but what is really cool are the visuals. Read the rest of this entry »
The Institute of Education, University of London is organizing a series of seminars on New forms of doctorate i.e. the manner in which multimodality and e-learning are influencing the nature and format of doctoral theses in Education and the social sciences.
This is a topic of great interest to me and I spent a bit of time browsing through some of these presentations. There is a lot to learn here. One thing that stood out for me is just how influenced by technology and cultural/historical context the Ph.D. thesis / dissertation really is. Several of the presentations, make this point. In fact, the entire symposium series is predicated on some version of this idea.
One presentation that really stood out for me, particularly given some of the discussions that are going on in my department is by Prof. Carol Costley Institute for Work Based Learning, Middlesex University.. Below is a brief description of her presentation followed by a copy of her slides (sadly there is no audio track).
On the distinction (if any) between doctorates which are research qualifications and those which are qualifications in advanced practice.
Since the early 1990’s work based learning (WBL) has been developing in UK universities within subject disciplines and also outside disciplinary frameworks as a field of study in it own right. Both forms of WBL (as a mode of study and as a field of study), have developed pedagogies that have moved away from more traditional approaches. In some part this can be attributed to the mature adult community who are attracted to part-time courses that incorporate study into their work rather than a learning experience unrelated to working life. However, the developing pedagogies also relate to a wider, more transdisciplinary reflection of a knowledge-based society.
Following the successful institution of WBL ‘taught’ degrees at Bachelor and Master levels the natural progression was to introduce work-based doctorates. Professional doctorates had already started to increase in the UK and in the late 1990’s the Doctorate in Professional Studies sometimes called Professional Practice (DProf. sometimes called Prof D.) was introduced. The DProf is aimed at the actual work activities and circumstances of people engaged in high-level professional practice. Candidates already have considerable expertise in their work and their work-based research and development projects are likely to draw upon knowledge from a range of fields and also on tacit and professional knowledge. The Candidates’ situatedness outside the academic sphere brings about a balance of activity, focus and control between the academic and the professional environments.
Drawing mainly on the DProf., the presentation explores how postgraduate WBL works in higher education and there is some consideration of its academic underpinning (Costley and Stephenson 2008). There is discussion concerning generic assessment criteria; the structure of the doctoral programme; the kinds of research and development projects undertaken by the candidates; and the learning and teaching processes which are ‘essentially concerned with the individual and their own practice’ (Scott et al 2004).
Leigh Wolf, my partner in crime as far as the MAET program goes, recently presented at Ignite Lansing. She talked about her two passions, teaching and food (not sure which order to place these). Specifically she talked about food photography and the connections she sees between what she does there and her other life as an educator. It is a lovely presentation, and the video is now available on YouTube. Take a look.
I am always looking for examples of looking at the world differently – of making the familiar strange and the strange familiar. This is of course connected with the veja du assignments I give my students.
I just came across a couple of very interesting video examples of this on the site LikeCOOL. This site has everything from after-office neckties, to inflatable boxing gloves… but in between these crazy things are some cool videos. Here are three (in increasing order of coolness):
Two robots made entirely using Lego Mindstorms NXT Retail-kit that can solve Sudoku problems and the Rubik’s Cube! How totally cool is that. LEGO Mindstorms is a line of Lego sets combining programmable bricks with electric motors, sensors, Lego bricks, and Lego Technic pieces (such as gears, axles, and beams). See Wikipedia article on Lego Mindstorms
See the videos below, and check out the website for the project: Tilted Twister
Sudoku Solver
Rubik’s Cube Solver
This is truly amazing… What is also great is that the designer also include directions for making these robots. I gotta get myself one of these
One often hears the criticism that students today don’t know how to write… the part of the blame is placed on technology, on the limitations of texting and twittering! For instance, here are two quotes from a book review TXTNG: THE GR8 DB8 by Marcus Merkmann in the New York Post.
[Texters are] vandals doing to our language what Genghis Khan did to his neighbors 800 years ago – John Humphrys, British TV presenter.
Texting is bleak, bald, sad shorthand which masks dyslexia, poor spelling and mental laziness – John Sutherland, author
technology isn’t killing our ability to write. It’s reviving it—and pushing our literacy in bold new directions…. young people today write far more than any generation before them. That’s because so much socializing takes place online, and it almost always involves text. Of all the writing that the Stanford students did, a stunning 38 percent of it took place out of the classroom—life writing, as Lunsford calls it. Those Twitter updates and lists of 25 things about yourself add up.
It’s almost hard to remember how big a paradigm shift this is. Before the Internet came along, most Americans never wrote anything, ever, that wasn’t a school assignment. Unless they got a job that required producing text (like in law, advertising, or media), they’d leave school and virtually never construct a paragraph again.
Well, maybe youth today are writing more, but is it any good? Turns out that college students today are not just producing a greater number of words, but these words are of better quality as well.
Lunsford’s team found that the students were remarkably adept at what rhetoricians call kairos—assessing their audience and adapting their tone and technique to best get their point across. The modern world of online writing, particularly in chat and on discussion threads, is conversational and public, which makes it closer to the Greek tradition of argument than the asynchronous letter and essay writing of 50 years ago.
There is actually one concern that this research has pointed out, however the accusing finger points not at the students but rather at us, the professors. For today’s students:
… writing is about persuading and organizing and debating, even if it’s over something as quotidian as what movie to go see. The Stanford students were almost always less enthusiastic about their in-class writing because it had no audience but the professor: It didn’t serve any purpose other than to get them a grade.
Now this is something to think about…
And finally, what about the pernicious influence of texting on student writing… sadly, no evidence of that could be found!
Glad to put that myth to rest!
Finally, just in case something thinks that this “adult” condemnation of what young people do is something recent… well, turns out there are historical antecedents for that as well. The quotes below are not directly related to the issue of technology and writing, but are revealing about our attitudes all the same.
We live in a decaying age. Young people no longer respect their parents. They are rude and impatient. They frequently inhabit taverns and have no self-control — Words inscribed on a 6,000-year-old Egyptian tomb.
What is happening to our young people? They disrespect their elders, they disobey their parents. They ignore the law. They riot in the streets, inflamed with wild notions. Their morals are decaying. What is to become of them? — Plato, 4th Century BC
The young people of today think of nothing but themselves. They have no reverence for parents or old age. They are impatient of all restraint … As for the girls, they are forward, immodest and unladylike in speech, behaviour and dress — Peter the Hermit, 1274 AD
As they say, Plus ça change, plus c’est la même chose…. The more things change the more they stay the same
Note: I am not sure the Stanford project looked at the different kinds of media use that students engage in today (photos, video, mashups etc.), because that is a huge part of how the very idea of literacy is being redefined today. I don’t necessarily want to get into that issue here in this post, but is clearly a huge part of the kinds of literacy activities students today are engaged in.
Just discovered a podcast on TPACK (titled Understanding TPCK) at the msad75mltinews website. It appears to be based on the article (Too cool for school) that was recently published in Learning & Leading with Technology.
A while ago I had written about how we use language to capture intangible ideas – and the risks associated with not paying attention to these intangibles. I had said (though you can read the complete post A different language):
For instance wine connoisseurs have developed a specialized language (which sadly is quite opaque to me) to explain to each other characteristics of wine. So the words “fruity” and “dry” have specific gustatory connections… What we need to do is develop a language that allow us to somewhat consistently express and represent the intangibles of teaching, somewhat like what Bird does in explaining his music (or wine connoisseurs do when describing wine). The lack of such a language essentially prevents us from recognizing that classrooms are far more than 4 walls, a teacher and a bunch of students… and that aesthetics play a great role in the act of teaching and learning.
When we read prose—whether technical or literary—our mind parses sentences to recover their meaning. Yet, the flow of the words themselves can invoke surprising or unexpected sensory responses, even for the writer. Even a very rational and technical text can typically affect the reader on multiple cognitive levels, in addition to its basic task of transmitting the author-intended meaning.
This led them to wonder about the kinds of words used in scientific texts, specifically biomedical texts. Being good scientists, the decided to test this out:
In this study, we therefore analysed the frequencies of use of sensory words and time-related terms in a large collection of biomedical texts, and compared the results with similar analyses of a collection of news articles, a large encyclopaedia, and a body of literary prose and poetry.
And what did they find? No real surprises here:
We found that, unlike literary compositions and newswire articles, biomedical texts are extremely sensory poor, yet rich in overall vocabulary. It is likely that the sensory-deprived writing style that dominates the biomedical literature impedes text comprehension and numbs the reader’s senses and mind.
In conclusion they say:
In short, we believe that scientific prose should be enriched with sensory words, provided that they clarify the meaning rather than obscure it, in much the same way as a good statistical data visualization involves the mapping of abstract data into colours and three-dimensional shapes, to help the reader or viewer discover meaningful patterns.
I think the analogy to visual representation is right on… and I could not agree more with their conclusion.
