January 7, 2014 § Leave a Comment
The new year begins with the publication of 2 key articles in our series Rethinking Technology and Creativity in the 21st Century. Co-authored with Danah Henriksen and the Deep-Play Research Group these two articles seek to develop a better understanding of where creative ideas come from.
Henriksen, D., Mishra, P., & the Deep-Play research group (2014). Twisting knobs and connecting things: Rethinking Technology & Creativity in the 21st Century. Tech Trends, (58)1, P. 15-19
Mishra, P., Henriksen, D., & the Deep-Play research group (2014). Revisited and Remixed: Creative Variations and Twisting Knobs.Tech Trends, (58)1, P. 20-23
In these two articles we question the “myth of the genius” and argue that creativity is not a “magical” process, but rather creative ideas emerge from combining pre-existing ideas and concepts in unique and new ways. Though this may appear to be a simplistic formulation, we suggest that it is far from that. Creating these novel, effective and whole combinations is unpredictable and requires people to bring together a wide range of background knowledge and experience. It is this breadth of knowledge and experience that allows creative individuals to see novel connections and act on them. The second article extends and grounds these ideas by offering specific examples taken from the world of puzzle and game design.
December 31, 2013 § 10 Comments
It is that time of the year… the time for the Mishra/Sawai family new year’s video. As tradition has it the video needs to be some kind of a typographical animation, typically a play with words that is synchronized to music, and attempts to incorporate a visually interesting “aha!” moment. The video never includes people (except for may be a still-shot of the entire family somewhere towards the end).
The videos have become more complex over the years and the challenge, of course, is to create something that exceeds what we did the year before. Our budgets have also risen – going from zero when we first started to around $10 this time around. What has not changed is the fun we have in creating these videos and sharing them with all of you. Below is our latest video, titled Point of View: Happy 2014. Enjoy.
Wish you a great 2014!
From Shreya, Soham, Smita & Punya
Here are links to the videos from the previous years (along with some other videos made as a family):
- Dimensions, Happy 2013: Anamorphic card for 2013
- Did you catch that?: Stop motion card for 2012
- The Power of the Shadow: Stop motion card for 2011
- Happy 2010: Stop motion card for 2010
- Happy 2009: Stop motion card for 2009
- Explore | Create | Share: 3 short videos with typographical twists
- Finding Nemo, the sea-quel: A stop motion sequel to Finding Nemo
- or, view my video channel on Vimeo (including the Hari Puttar Trailer and the Socha Hai music vide0
December 10, 2013 § Leave a Comment
Mathematicians love puzzles—they love to play with numbers and shapes but often their love can turn to words and other areas that, at least on the surface, have little to do with mathematics. One form of visual wordplay with some deep connections to mathematics, and one that I have played with over they years, are called ambigrams. (Click here for examples of ambigrams I have published on this blog in the past.) Ambigrams exploit how words are written and bring together the mathematics of symmetry, the elegance of typography and the psychology of visual perception to create surprising, artistic designs. For instance see the rotational ambigram for the word-pair “create-math” at the top and a design for “theorem” below. In both cases the words read the same even when rotated 180 degrees.
Till recently ambigrams were something I created for fun. I knew of their mathematical underpinings, explored them once in a while, but never really took that part seriously. This despite my interest in creativity and the value of making connections across disciplines. Well that has changed…
July 19, 2013 § Leave a Comment
You are cordially invited to our current MAET Summer 2013 students’ final project showcase, on July 26th, at 10am, in room 252 Erickson Hall. As you may know from your own past experiences with the summer program, our students spend several intensive weeks of work, study, and play during the summer — where they are involved with a range of creative educational technology projects. These projects involved technology and new media of all kinds, and showcase the innovation, research, and technology leadership that we take pride in amongst our graduates.
As a proud MAET graduate, current student or friend of the program, you are invited both to the technology showcase session that morning, as well as the potluck lunch that follows at 11:30. It would be wonderful to share with you some of the current work in our program, and to hear more about your own continued successes as a technology teacher/leader/innovator.
Please complete this short Web-form to let us know if you will be able to make it to the 2013 project showcase: https://docs.google.com/forms/
We hope to see you there!
May 31, 2013 § Leave a Comment
The latest in our series Rethinking Technology and Creativity in the 21st Century is now available. The article was co-authored with William Cain, Sandra Sawaya and Danah Henriksen (and the Deep-Play Research Group) and deals with the issue of how expertise may actually hinder creative solutions and that novices may be the source of creative solutions—only if the experts learn to listen to them and to “try to understand the deeper patterns of human interaction, to learn from scholars and history, and to listen to what users are saying. But most importantly, to closely observe what they do.” We ground this broader issue in issues related to the design of hybrid or blended learning spaces, specifically referring to some fascinating work being done by William, Sandra and John Bell on developing a typology of models of interaction in face to face, online and hybrid courses.
May 2, 2013 § Leave a Comment
AERA 2013 – San Francisco, a set on Flickr.
Photographs from the annual meeting of the American Educational Research Association (AERA) 2013 at San Francisco. It was great meeting up with friends and colleagues, present two talks and take in some of the sights. Enjoy.
February 13, 2013 § 1 Comment
I am am member of the PhD-Design listserv, “a list for discussion of PhD studies and related research in Design.” I am not very active on the list but have found it an invaluable resource that helps me think. The dialogue is often of pretty high quality and I have learned a lot just by lurking. Recently the discussion focused on the “craft, guidelines, and traditions of research.” Dr. Ken Friedman posted a note which he adapted from a summary statement prepared for a 2006 conference on research (Summary Statements from the UK AHRC Practice-Led Review). I recommend reviewing the entire document since it provides an intelligent and thoughtful summary of the discussions that occurred at the conference. This post however, focuses on what Ken calls “a small library of nine valuable books that will help Ph.D. students do serious work—as well as helping supervisors do a solid job in supervising… These books can help to teach and develop good research habits, habits of mind and habits of behavior.” I thought that this would be of great help to our graduate students and got his permission to include his list here. « Read the rest of this entry »
November 26, 2012 § Leave a Comment
I am pleased and proud to announce that Mike DeSchryver recently defended his dissertation, titled:
Toward a Theory of Web-Mediated Knowledge Synthesis: How Advanced Learners Used the Web to Construct Knowledge about Climate Change Behavior
This is an excellent piece of research pushing new boundaries in our developing understanding of the process of learning from the Web.
October 10, 2012 § Leave a Comment
Welcome to the (long-awaited!) twelfth edition of the TPACK Newsletter! TPACK work is continuing worldwide, appearing in multiple publications, conferences, and professional development efforts. This document contains updates to that work that we hope will be interesting and useful to you, our subscribers.
If you are not sure what TPACK is, please surf over to http://www.tpack.org/ to find out more.
Gratuitous Quote About Technology
“You affect the world by what you browse.”
In This Issue
October 2, 2012 § Leave a Comment
I do not want my house to be walled in on all sides and my windows to be stuffed. I want the cultures of all the lands to be blown about my house as freely as possible. But I refuse to be blown off my feet by any—Mohandas Karamchand Gandhi (10/2/1869 – 1/30/1948)
[Side note: A few years ago I discovered an interesting personal connection to Gandhi. The full story, that speaks to creativity, the nature of the web and can be read here: Gandhi, ambigrams, creativity & the power of small pieces loosely joined. Enjoy.]
August 5, 2012 § Leave a Comment
My friend, Hartosh (I had written previously about his mathematical novel here ) and his wife Pam, recently had their second child, a baby boy. Since I had created an ambigram for the first guy (click here to see the ambigram for Nihal), I felt it was required of me me to create one for the new guy as well. Here is the ambigram for Nirvaan. Enjoy!
February 4, 2012 § 1 Comment
Polish poet Wislawa Szymborska passed away a couple of days ago. I first heard of her on an NPR show a few years back (and had included a couple of her poems on the blog – see here and here). If you have never read her work, I entreat you to do so. She is an absolutely brilliant poet, simple, straightforward, yet deep, with a wonderful touch of whimsy and humor. Here are a couple of her poems: « Read the rest of this entry »
February 2, 2012 § 3 Comments
Readers of this blog know that I am always looking for examples of good / bad design (actually I am usually not looking for bad design – it just sort of comes and slaps me on the side of the head!). I thought I might share one with you today, that I found in my hotel room in Barcelona. First off here is what it looks like. « Read the rest of this entry »
October 30, 2011 § 2 Comments
Much has been written about Steve Jobs in the past few weeks since his passing but the best piece I have come across is the eulogy by his sister Mona Simpson. Mona Simpson is an author and professor of writing and delivered this eulogy on Oct. 16 at his memorial service at the Memorial Church of Stanford University. It must be read in it entirety (NYTimes: A sister’s eulogy for Steve Jobs) but the thing that stands out in this eulogy was just how Jobs was truly a person who understood the here-now-ness and enchantment of every moment. The feeling of wonder that is at the heart of creativity, of living life to its fullest.
Read the entire article for your self… (as one of my friends said, it is a “lump-in-throat kinda moving”) but what I want to highlight is how it ends. Mona describes his last battle against ugliness, his final battle with cancer and says:
But with that will, that work ethic, that strength, there was also sweet Steve’s capacity for wonderment, the artist’s belief in the ideal, the still more beautiful later.
Steve’s final words, hours earlier, were monosyllables, repeated three times.
… Steve’s final words were: OH WOW. OH WOW. OH WOW.
Oh Wow! What a way to live. What a way to go.
September 11, 2011 § 1 Comment
For Whom the Bell Tolls
— John Donne
May 30, 2011 § 16 Comments
I just found out that I made “The Big 10: The Most Influential People in EdTech for 2011.” This list is created by the Tech & Learning journal—a magazine for Ed Tech leaders. This news came as a total surprise to me since I did not know that I was even in the running for something like this. The June issue, which has this as a cover story, will be out in a few days though you can access it on the web (link below). Here’s the cover, and that’s me on the first row (second from the left). « Read the rest of this entry »
March 15, 2011 § 6 Comments
I had a bunch of presentations at the recently concluded SITE2011 conference at Nashville TN. There is a lot to post about the conference, particularly the presentations I made at the beginning of the day… but that will have to wait until later. This posting is about the various presentations I was involved with. The topics ranged from a study of adolescent’s activities online to TPACK to developing a better understanding of what we mean when we say 21st Century Learning. I am including below, the title and abstract of the presentation along with a pdf of the final presentation. If you have any questions, or need more details on these studies, please feel free to email me…
Adolescents’ activities online and how their notions of learning shape strategies and expectation
Kristen Kereluik & Punya Mishra, Michigan State University
Abstract: This paper reports on a case study of adolescents’ experiences online. Specifically this study sought to explore adolescents’ typical Internet use and understand how adolescents’ notions of learning impacted their use of self-regulated learning strategies online. Interview data was collected from 13 adolescent participants and their parents and was coded using grounded theory analysis (Glaser and Strauss, 1967) and the constant comparative method. Analysis indicates that participants’ Internet use is highly dynamic and not easily categorized. Additionally, results suggested that adolescents’ notions and understanding of learning influenced their computer and Internet use. Participants reported differential computer use based on the specific task (academic or informal) and held differing expectations for possible and intended outcomes. Implications for findings are discussed as well as necessary next steps and future directions.
Teachers’ assessment of TPACK: Where are we and what is needed?
Joke Voogt, Ghaida Alayyar, Petra Fisser, Douglas Agyei, Bart Ormel, Chantal Velthuis, Jo Tondeur: University of Twente, Netherlands; Tae Shin: University of Central MissouriPunya Mishra & Matt Koehler: Michigan State University, Denise Schmidt, Evrim Baran, Ann Thompson, Wei Wang: Iowa State University; , Edith Stein: University of Applied Sciences, Netherlands; University of Ghent, Belgium; David Gibson (discussant), Global Challenge.
Abstract: Technological Pedagogical Content Knowledge (TPACK) has emerged as a useful conceptual framework for understanding the teachers’ knowledge base needed for effectively teaching with technology. The symposium aims to further our thinking about TPACK as a conceptual framework and to relate TPACK as the teachers’ knowledge base for teaching with technology to factors affecting teachers’ adoption of technology. Various ways (self-report data, observations, tests) to assess teachers’ TPACK and adoption of technology will be presented.
We had a lot of fun creating this presentation. As you will see we developed a “film theme” with actual movie posters introducing each of the speakers. We also created a poster for the session (see below and click for a larger version).
What 21st Century Learning? A review and a synthesis
Punya Mishra & Kristen Kereluik, Michigan State University
Abstract: The discussion of 21st century skills has become increasingly prevalent in educational discourse and several organizations have developed 21st century frameworks. This papers seeks to compare prominent 21st century frameworks to both provide clarity on what it actually means to teach and learn in the 21st century and to find common themes across frameworks.
Developing Trans-disciplinary creativity, rethinking the C in TPACK
Kristen Kereluik & Punya Mishra, Michigan State University, USA
Abstract: This brief paper discusses the 21st century skills movement, and transformative learning theory as a framework for fostering these skills in both teachers and students. TPACK is discussed as a bridge between theory and practice and as a route towards preparing educators for teaching in the 21st century and to natives of the 21st century. A masters level course in educational technology is presented as an example of bringing together 21st century skills, trans-disciplinary teaching and learning, and the TPACK framework. The course is briefly discussed and examples of student products are presented. Finally, conclusions and possible future directions are discussed.
December 19, 2010 § 3 Comments
Christine Greenhow from the University of Maryland visited the College of Education this past week. She gave a talk and met with various faculty members and graduate students. I had met Christine a couple of years ago when we had both been invited to the National Technology Leadership Summit and had kept in touch off and on (more off than on) on Facebook.
It was great to host her visit and I am including below
This talk was also streamed live and was recorded as well - though I don’t have the link to the archived talk. I will post it here when I get it.
I also had fun creating an ambigram of her name, which I didn’t get a chance to share with her. So here it is.
July 23, 2010 § 15 Comments
A few weeks ago I posted a note about an assignment I gave my students in the on-campus version of the MAET program. They had completed an unit on motivation and had watched the RSA / Daniel Pink video and their task was was to create demotivational posters, (along the lines of those on despair.com) using ideas either from their readings/discussions or from the Pink video.
The posters were a huge success. In fact Daniel Pink tweeted them (Thanks Daniel) and lots of his followers ended up on my website to see the work done by the students, which is all very cool.
Well, I am now in Rouen, France, meeting with the students in the off-campus MAET program. I got a chance to work with each of the groups (representing year 1, 2 & 3) and had them create similar posters as well. So now we have a total of 17(!) posters. It is interesting to see just how different they are, even the ones that tackle the same concept do it differently.
I have included all of the posters below — the one’s from East Lansing as well as the one’s created here at Rouen. Click on the words to see the posters (the names of the students who created them is provided below each of the posters).
Rawad Bon Hamadan
June 24, 2010 § 6 Comments
In my summer teaching I often start the day with some examples of interesting things that happened that day in history. It is a fun way to start the day, and I seek to find examples that connect with things/issues we are covering in class, often related to technology, psychology and so on. A few years ago, when researching historical events that occurred on the 25th of June I came across an interesting problem. There was an event that some sources reported as having occurred on the 25th of June 1178 and other sources that reported it as occurring on the 18th of June of the same year. Clearly both of these dates could not be right… so what was going on?
Particularly beguiling to me was that this event was something that I had learned about many years ago, when in high school in New Delhi, from Carl Sagan’s TV series Cosmos. I was a huge fan of this series and had seen it more than once and had read the book cover to cover many times. So this mystery of the two conflicting dates was doubly interesting. As it turns out my attempts to figure out this inconsistency led to some wonderful insights about history, calendars and the very nature of science itself.
First to provide some context about the event itself. In one of the episodes of Cosmos, Sagan describes an even that took place in 1178. You can watch it for yourself in the clip below (start around 2 minutes in)
Here is a transcript (archived here)
On the evening of June 25, 1178, five British monks reported something extraordinary, which was later recorded in the chronicle of Gervase of Canterbury, generally considered a reliable reporter on the political and cultural events of his time, after he had interviewed the eyewitnesses who asserted, under oath, the truth of their story.The chronicle reads: There was a bright New Moon, and as usual in that phase its horns were tilted towards the east. Suddenly, the upper horn split in two. From the midpoint of the division, a flaming torch sprang up, spewing out fire, hot coals, and sparks.
The astronomers Derral Mulholland and Odile Calame have calculated that a lunar impact would produce a dust cloud rising off the surface of the Moon with an appearance corresponding rather closely to the report of the Canterbury monks. If such an impact were made only 800 years ago, the crater should still be visible. Erosion on the Moon is so inefficient, because of the absence of air and water, that even small craters a few billion years old are still comparatively well preserved. From the description recorded by Gervase, it is possible to pinpoint the sector of the Moon to which the observations refer. Impacts produce rays, linear trails of fine powder spewed out during the explosion. Such rays are associated with the very youngest craters on the Moon-for example, those named after Aristarchus and Copernicus and Kepler. But while the craters may withstand erosion on the Moon, the rays, being exceptionally thin, do not. As time goes on, even the arrival of micrometeorites-fine dust from space-stirs up and covers over the rays, and they gradually disappear. Thus rays are a signature of a recent impact.
As it turns out the records of the monks are now available online and this is what the Chronicle of Gervaise a 12 century manuscript says (from here):
“In this year, on the Sunday before the feast of St. John the Baptist, after sunset when the moon has first become visible, a marvellous phenomenon was witnessed by some five or more men who were sitting there facing the moon. Now there was a bright new moon, and as usual in that phase, its horns were tilted towards the east and suddenly the upper horn split in two. From the midpoint of this division a flaming torch sprang up, spewing out, over a considerable distance, fire, hot coals and sparks. Meanwhile the body of the moon, which was below, writhed, as it were, in anxiety, and, to put it in the words of those who reported it to me and saw it with their own eyes, the moon throbbed like a wounded snake… Then after these transformations the moon from horn to horn, that is along its whole length, took on a blackish appearance.”
As Sagan says, the generally accepted interpretation of this narrative, first suggested by Dr Jack B Hartung some 800 years later, is that it is a description of a crater impact. The “upper horn split in two” is the apparent effect of a plume of dark dust or vapour, the “flaming torch [of] hot coals and sparks” describes the molten ejecta, and the way in which the rest of the Moon “writhed”, “throbbed” and eventually “took on a blackish appearance” could be the effects of a temporary lunar atmosphere of gas and vapour created by the impact. As Sagan says in his documentary:
The meteoriticist Jack Hartung has pointed out that a very recent, very fresh-looking small crater with a prominent ray system lies exactly in the region of the Moon referred to by the Canterbury monks. It is called Giordano Bruno after the sixteenth century Roman Catholic scholar who held that there are an infinity of worlds and that many are inhabited. For this and other crimes he was burned at the stake in the year 1600. Another line of evidence consistent with this interpretation has been provided by Calame and Mulholland. When an object impacts the Moon at high speed, it sets the Moon slightly wobbling. Eventually the vibrations die down but not in so short a period as eight hundred years. Such a quivering can be studied by laser reflection techniques. The Apollo astronauts scattered in several locales on the Moon special mirrors called laser retro reflectors. When a laser beam from Earth strikes the mirror and bounces back, the round-trip travel time can be measured with remarkable precision. This time multiplied by the speed of light gives us the distance to the Moon at that moment to equally remarkable precision. Such measurements, performed over a period of years, reveal the Moon to be quivering with a period (about three years) and amplitude (about three meters), consistent with the idea that the crater Giordano Bruno was gouged out less than a thousand years ago.
How very cool is that. I remember this episode well because it is a powerful one, connecting an event that took place in the 12th century with today’s science. It appealed to the rationalist, nascent scientist in me in a powerful way.
So imagine my surprise to find these two different dates being referenced for the event. Notice the date that Sagan references in Cosmos is the 25th of June. Here are two others that cite June 25.
… and here are two that reference the June 18 date.
So what is going on here? Why two different dates?
It turns out that this problem was not all that hard to figure out. A bit of research showed that this dual-date conundrum was really a function of the kind of calendar system being used to set the date, i.e. the specific date depended on whether one used the Gregorian or the Julian calendar. You can test this out yourself by visiting Tarek’s Hijri/Gregorian/Julian Converter (http://bennyhills.fortunecity.com/elfman/454/calindex.html) which contains a Gregorian to Julian (and vice versa) converter. 18th June 1178 in the Julian Calendar turns out to be 25th June, 1178 on the Gregorian calendar. So in some sense, both dates are right (or wrong, for that matter). As date-problems go this one of the less complicated ones. For instance, consider the following:
… an article appeared in the Edinburgh Courant of February 19, 1706. The article was an abridgment of one published in the London Gazette of February 13, 1705, which, in turn, was a translation from the Amsterdam Gazette of February 22, 1706. All three were published in the same week. The discrepancy in year was caused by the fact that Scotland and the Low Countries began the year on January 1, while England, until 1752, began it on March 25. The discrepancy in days was caused by the use of the Gregorian calendar in the Low Countries, at a time when England and Scotland still adhered to the Julian calendar. (http://bennyhills.fortunecity.com/elfman/454/calindex.html)
Anyway, coming back to the story of the Canterbury Monks, the successful resolution one paradox (of the dueling dates) led to another one, more interesting by far. As a fallout of my web searches I came across some recent evidence that questions the existence of the very event itself – and all the scientific conjecture regarding collisions and wobbling moons that it engendered. Here’s what I found out:
In 2001, Paul Withers, then a graduate student in astronomy at the University of Arizona (here is his current website) in an article published in the journal “Meteoritics & Planetary Science” debunked the moon collision theory. He argued that the consequences of such a collision would have been quite significant and the fact that no astronomers (anywhere in the world) reported anything like this happening seems to indicate that this was a more local phenomena – one that could be observed just at Canterbury. Withers suggests that the monks just happened to be at
… the right place at the right time to look up in the sky and see a meteor that was directly in front of the moon, coming straight towards them…. And it was a pretty spectacular meteor that burst into flames in the Earth’s atmosphere — fizzling, bubbling, and spluttering. If you were in the right one-to-two kilometer patch on Earth’s surface, you’d get the perfect geometry,… That would explain why only five people are recorded to have seen it.
I won’t claim that I wasn’t a bit disappointed at reading this. This story has been such a part of me, for so long, to find it debunked was slightly bothersome. That said, this entire episode, represents for me the self-correcting nature of science, where truths are determined by data (not by opinion). Also important to highlight here in the role that Internet based technologies play revealing this aspect of science to us. This makes science more accessible and more true to itself. This is a great lesson to learn.
The complete reference to the Wither’s article is as follows:
Withers, P. (2001). Meteor storm evidence against the recent formation of lunar crater Giordano Bruno. Meteoritics & Planetary Science Volume 36, Issue 4. p. 525-530. (Table of contents available at http://www.uark.edu/~meteor/36-4toc.html)
This was also reported in the scientific press. For instance check out these two news stories.
March 3, 2010 § 2 Comments
A few weeks ago I had posted about the hybrid Ph.D. program that we recently announced. There has been terrific interest in this program (but we are still looking for more people – so keep the emails and questions coming).
As we were reviewing the various emails we are receiving, it struck me that we (here at MSU) have not really done a good job of capturing all the different options we offer to practicing educators (teachers and administrators in K-12, community college and higher education settings).
The goal in each of these programs is to work collaboratively with practitioners to creatively integrate technology in their practice. Built around the TPACK framework these programs run the gamut from a 10 credit certificate in Ed Tech, to a 30 credit master’s degree, from an Edupunk orientated refresher that can be taken for credit or no-credit (for those who already have a master’s), to two versions of a doctoral program (on-campus and the new substantially online hybrid program).
This led to our designing a graphic that attempts to capture all of our different initiatives. (Thanks also to Leigh Wolf and Robin Dickson for their input. Any errors are of course mine, and mine alone.) The blue arrows indicate “points of entry” i.e. spots that you can enter the program.
These “blocks” build on each other but there is no obligation to do the whole thing. Each block is self-contained i.e. there are multiple “off-ramps” from the program. Also, classes are customized to the needs and requirements of practitioners and can be taken in a variety of formats: online, face to face (on campus, off campus and abroad) as well as hybrid combinations thereof. For instance, we have students who have taken some certificate courses over weekends, at sites near their schools, followed that with some coursework on campus and online (over summer and regular semester) and received their master’s by completing their courses with one final summer, abroad.
February 15, 2010 § Leave a Comment
Theresa Hamilton & Amy Gracik are two of our Technology Interns in Education. They are now part of a pilot project to offer software technology support to students in our MAET program. This help-desk available online at http://groups.google.com/group/maetsupport. Please follow the link for more information. (Thanks to Terri Gustafson & Leigh Wolf for making this happen – and of course to Theresa and Amy for their time).
January 15, 2010 § 1 Comment
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 »
January 12, 2010 § 3 Comments
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…
January 12, 2010 § 3 Comments
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, 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.
January 2, 2010 § Leave a Comment
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.
December 22, 2009 § 1 Comment
Mark Ambinder at the Politics blog at the Atlantic
President Obama plans to name Howard A. Schmidt, a veteran cyber security warrior with experience at senior levels of government and industry, to fill a long-anticipated cyber coordinator position at the National Security Council, administration officials and outside consultants confirmed.
As far as one can see Mr. Schmidt is well qualified for this position, having served both in industry and in the government in the past. However, one fact about his background caught my attention and prompted this note. In describing his qualifications Ambinder wrote
Schmidt has credentials unique to the job: he received his masters in organizational management from the University of Phoenix, a (fully accredited and esteem) mostly online university.
Apart from the typo on esteem, what struck me was this positive mention of the University of Phoenix, something I often do not see or hear. Over where I live and breathe, the good old-fashioned bricks-and-mortar university, the University of Phoenix is not regarded as having much esteem. I have argued here and elsewhere that this will soon change. That most of us at the “traditional” university have underestimated just how powerful the forces of change are. Online learning (and for profit universities) are here to stay and maybe even take over universities as we know them.
Reading about Mr. Schmidt’s credentials just reminded me just how quickly this change is happening.
December 16, 2009 § 11 Comments
There is an article in today’s Chronicle titled Matching Teaching Style to Learning Style May Not Help Students.
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)?
October 16, 2009 § 2 Comments
For an interactive card click here … .
Remember to turn your volume way up, and click anywhere in the sky
above the Taj Mahal for some environmentally friendly, fireworks.
September 22, 2009 § 2 Comments
I had written recently about TPACK being the top story on eSchoolNews (see TPACK is top story on eSchoolNews or go directly to the article: TPACK explores effective ed-tech integration). What I didn’t realize at that time is that there were actually three stories about TPACK, one in August that I had blogged about and two in Septmber. The two that I had missed were actually more interesting to me personally since they dealt with the manner in which the TPACK framework was actually being used in schools. Both these stories deal with the manner in which the San Diego Unified School District is embracing the idea of TPACK as a key piece of their strategy to transform how their students are taught.
These two other articles (also written by Senior Editor Laura Devaney) are titled (a) San Diego explores effective ed-tech integration through TPACK: New professional development model focuses on the intersection of technology, pedagogy, and content knowledge; and (b) Reinventing education: As schools nationwide examine new federal priorities, San Diego unveils a five-year plan to transform the way students are taught
This news makes me extremely happy, for the simple reason that this means that our ideas have moved beyond graduate school curricula, beyond research articles, beyond doctoral dissertations into actual practice. This is every educational researcher’s dream. Here are some key quotes from these articles.
The San Diego Unified School District (SDUSD) has embraced a concept called Technological Pedagogical Content Knowledge (TPACK) in its professional development model, to ensure that the smart use of technology drives every aspect of classroom teaching and learning.
As technology becomes an increasingly important tool for teaching and learning, this relatively new concept, which focuses on how educators can integrate technology effectively into their instructional practices, is making its way into pre-service and in-service teacher education programs.
TPACK is based on the work of Punya Mishra and Matthew Koehler, both associate professors of educational technology in the College of Education at Michigan State University.
“We worked closely with the [district] Educational Technology department to design a professional development program that is all-encompassing,” LaGace said. “When you look at the TPACK model, it gets around to improving the whole classroom experience. … It puts the focus not on teaching teachers how to turn on a Promethean Activboard, but why to turn it on.”
Why turn it on? What a profound question, and one that hopefully will be asked by every teacher in San Diego.
Can you guess why I love my job?