Making connections between the movie The Prestige, and the design of 2 activities to build trust and a shared vision in teams…
What does a teacher need to know to intelligently integrate technology in their teaching? Or better still, what is it that teachers need to know to become effective teachers?
So this morning I was playing around with a wordcloud generator. Throwing in words from our notes from the Scottsdale Design day… and I got to thinking about how it could be used as an educational tool, specifically to teach mathematics.
Now, I know what you are thinking, Wordle’s are so passe´, so yesterday. Everybody (and their uncle) uses them and it’s not clear (at least to me) most of the time what value it is bringing into teaching. So bear with me and let me see if I can explain (a) how it can be used to teach mathematics, or at least some content in mathematics; and (b) what implications it has for teacher education and teacher professional development.
For the past 17 years (with just two exceptions) my summers have been spent teaching in the MAET program. 2016 was the last time I did that, teaching in Chicago the third cohort of the MSUrbanSTEM project. The MAET program runs somewhat concurrently in three locations—two cohorts in East Lansing MI; two in Chicago, IL and three in Galway, Ireland. For the past two years we have tried to collectively create an artifact that speaks to our sense of community, and creativity. You can see previous examples here (MAET Words) and here (MSU Fight Song MAET style). This year we asked the everybody involved in the summer programs at these three sites to reflect on what the word “connection” means to them, except that they had to do it in either 5 or 7 syllable words or phrases. And viola… here you have it, the MAET random haiku generator! You will need to reload the page to see a new haiku! Enjoy.
I have always been intrigued by the manner in which everyday ideas get “mathematicized” (if that’s a word). For instance, the other day, on a bus-stop by my office I noticed an equation written on the wall. I have no idea why it was there, but there it was.
Happiness equals reality minus expectations – Tom Magliozz
As I have written elsewhere, mathematization is actually quite common. For instance, we sometimes “thoughtlessly assign specific numbers where such specificity is not warranted” and the results may actually be fictional in their relationship to reality. You can read that blog post here: Number (non)sense & flatulence. It is a post where I bring together petabytes, Moby Dick, Indian elevators, Samuel Beckett and flatulence into one sweet(?) package! How often do you see that? It’s worth a read (if I say so myself) so here’s the link again.
A somewhat related issue is how we often take ideas that are extremely subjective and try to express them mathematically, often in the form of an equation. Of course, once we express something as an equation, it is easy to conceive of some interesting variations, generated through simple algebraic manipulation. For instance, here is the equation I saw at the bus-stand:
Turns out that they got the name of the person wrong (thanks Google). It should be Tom Magliozzi (with an i at the end), the late, much beloved, co-host of NPR’s Car Talk, the one who never drives like his brother.
A simple algebraic manipulation leads to this deep insight:
Reality = Happiness + Expectations
Did you know that Reality is nothing but happiness combined with expectations? Frankly I did not know that, but thanks to mathematics, I now have a deeper understanding of reality (or at least of alternate reality, an idea that goes well with alternate facts)!
The next image, and example, comes from Dean Basile:
Hmm… lets shift a few of these variables around and we get the following:
You = Impact – Generosity
Reflect on that for a minute (or two). You are whatever is left behind when you subtract your generosity from your impact! Like I said… hmmm…
The question that remains, of course, is what is your relationship to this new reality?
Just some visual wordplay that I have indulged in, just for the heck of it. Nothing really special, though I am partial to the “Explore, Create, Share” design. That was the motto of the MAET program at MSU that I directed for years.
2 on Creativity
Explore Create Share
I was interviewed recently by Mark Brodie of KJZZ.org for a story titled: STEM Vs. STEAM: Educators Urge Adding The Arts To Classrooms. You can listen to the interview on their page by clicking on the link above, or the MP3 below. My piece comes in at around the 3:14 (yay pi!!) mark but listen to the whole story.
Since 2009, our family has made short videos to welcome the new year. These videos are great fun to create, often requiring days of discussion, planning, construction, shooting and editing. They are always typographical in nature, often with a visual twist or illusion. We have no budget to speak of—$10 is around as much as we have ever spent. Below is our latest effort, titled Perspective, shot on our dining table with a budget of around 7 dollars. Enjoy, and yes have a great 2017.
Perspective: Goodbye 2016, Welcome 2017
From Shreya, Soham, Smita & Punya
Those interested can see videos from the years past by going to
Illusory New Year Videos.
How was this done?
In keeping with the holiday theme (see Christmas ambigram below) it seemed appropriate to create a design for Hanukkah. That task actually turned out easier than I had expected – with some natural symmetries that I could take advantage of. The “U” at the center, and the “HA” start paralleled with the “AH” end – just asked to be ambigrammed! If only all words were this easy. A few tweaks later, here is a mirror symmetric design for Hanukkah. Enjoy.
What better way to wish everybody Merry Christmas than with a custom ambigram. The design above, reads Christmas when reflected in a mirror (a wall-reflection) or from either side of the page. For instance imagine printing it on a glass door – it would read the same from either side of the door! Jon Good, my former doctoral student at MSU, created a 3D printed version (shown in the photos below). I think it would make an awesome Christmas Tree ornament – since it would read the same even as it rotated freely when hanging from the tree.
Note: Full disclosure, this technically is NOT a new design. I actually created this a couple of years ago – but since I hadn’t posted it on to the blog, I consider it as being a “new” design.
In this article, in our ongoing series on Rethinking technology & creativity in the 21st century, we interview Dr. Keith Sawyer, Morgan Distinguished Professor in Educational Innovations at the University of North Carolina in Chapel Hill, and one of the most prominent scholars of creativity. In this interview, Dr. Sawyer speaks to the social and collaborative nature of creative work as a form of structured improvisation. Read the complete article below:
Henriksen, D., & Mishra, P., (2016). Between Structure and Improvisation: A Conversation on Creativity as a Social and Collaborative Behavior with Dr. Keith Sawyer. Tech Trends (61)1.
Note: As anyone who follows my blog knows that I love to play with visuals and typography. The “Improv(e)” visual at the top of the page was one I came up with while writing this blog post. Below the jump are a couple of ideas that didn’t make the cut – but I wanted to preserve none-the-less. In each of these the idea is to convey something about the ideas in the Sawer interview – specifically around structured improvisation. Enjoy.
The US department of Education recently released a policy brief, titled: Advancing Educational Technology in Teacher Preparation. As they describe it
This policy brief identifies key challenges and solutions to the effective integration of technology in teacher preparation, provides guiding principles on how to move the field toward effective integration of technology in teacher preparation programs, and identifies areas of opportunity and collaboration for stakeholders across the field.
Speaking selfishly, as a researcher and as a member of the leadership team at Arizona State, I have to point out two key references made in the report.
The first, speaks to my research (a collaborative effort with Matthew Koehler at MSU), namely the TPACK framework. Within the context of one of the key principles described in the report, that of “building sustainable, program-wide systems of professional learning” the report says:
To create expert teachers, preparation programs may find it helpful to incorporate a combination of skills and knowledge often referred to as TPACK: Technological Pedagogical Content Knowledge. Graduates should be able to incorporate a solid knowledge of content matter, a deep understanding of how students learn, and a practical facility with technology.
Second, is the reference in the report to some exemplary work being done under the leadership of one my colleagues, Teresa Foulger, here at ASU. As the report states:
Teresa Foulger, an associate professor at the Mary Lou Fulton Teachers College at Arizona State University, is leading a working group of educational technology faculty-researchers to develop a set of competencies for use by teacher educators in teacher preparation. The goal of the Teacher Education Technology Competencies (TETC) project is to define the knowledge, skills, and behaviors of higher education faculty who support pre-service teachers in learning to teach with technology. The competencies are being created using crowdsourced scholarly literature as a base, then a collaborative Delphi methodology where input is attained from an international base of teacher educators and content experts. The research team plans to release the competencies in Spring 2017.
Teresa recently presented her work in this area at a meeting at the White House!
The latest version of the TPACK newsletter (#31) can be found here December 2016 (pdf). All previous issues are archived here. A shout-out to Judi Harris for all the work that goes into this. As I had said in a previous post, based on Judi’s numbers, the work on TPACK continues to grow. As per Judi, there are 665 articles, 199 book chapters, 23 books, 182 dissertations around TPACK.
* Image: TPACK ambigram created for a t-shirt
I had recently posted a video of my talk fall Doctoral Research Forum for the Mary Lou Fulton Teachers College on the ASU West campus. As I had written in my post, “I thought it best to speak about the role of theory in research. This is something that troubles graduate students a lot as they move through the program (and I have posted about it earlier here and here). I contextualized the discussion within the history of the work that Matt Koehler and I did in developing the TPACK framework.”
Following the post, I received a lovely email from Judi Harris complimenting me on the talk, but also pointing out few gaps in the story that I had told. With her permission, for the sake of getting the story right, I am including relevant excerpts from her email (with some comments/responses from me embedded in between. This would also be the right moment to thank Judi for her service to the broader scholarly community – through her work with the TPACK newsletter (issues archived here) and the TPACK sig. TPACK would not have been as influential without her unstinting efforts. Her email and my responses below:
My college (The Mary Lou Fulton Teachers College) was one of the sponsors of the Arizona School Board Association Annual Conference. As a part of this, we got the privilege to introduce and have lunch with the keynote speaker. As it turns out the keynote speaker this year was David Pogue – and it fell to me to introduce him to the attendees. I have been a huge fan of his for a long time, and in fact still miss his presence at the New York Times, so I put in some effort to create something that would be fun (for both the people in the audience and for David as well). I, of course, created a new ambigram for the occasion… anyway you can see the short introductory video (that I edited to my recorded comments), the ambigram and a picture with the speaker himself with the ambigram! Enjoy.
Back in 2013 we proposed a framework for 21st century learning based on a synthesis of a range of reports, books, and articles (Kereluik, Mishra, Fahnoe & Terry, 2013 & diagram above). That article however was relatively abstract and what was unclear was whether this framework was consistent with what educator really think. This article provides the results of a survey on what educators think about 21st century learning. The results are thought-provoking—and we argue in some senses deeply misguided. We identify are three key myths about 21st century learning and suggest that these emerge as a consequence of an unreflective emphasis on the power of technology to access information as well as a fundamental misunderstanding of the very nature of learning and the broader goals and purposes of education. Complete reference, pdf of article and abstract below.
Note: There is an update / correction to this post which
can be found here: Update on “The TPACK story” or “Oops!“
I was recently invited to speak at the fall Doctoral Research Forum for the Mary Lou Fulton Teachers College on the ASU West campus. (A bit more context about the event, from a couple of years ago, can be found in a blog post by my colleague Sherman Dorn titled “Observations from a Doctoral Research Forum“). In speaking with Craig Mertler, who directs the EdD program here, I thought it best to speak about the role of theory in research. This is something that troubles graduate students a lot as they move through the program (and I have posted about it earlier here and here). I contextualized the discussion within the history of the work that Matt Koehler and I did in developing the TPACK framework. This was a fun talk to create and share. I created a narrated video of the slides of the talk, embedded below:
Note: There is an update / correction to this post which
can be found here: Update on “The TPACK story” or “Oops!“
On October 21, the Office of Scholarship partnered with the Research Advancement Office and the Teachers College Development Team to host the first MLFTC Grant Hackathon at ASU SkySong. Over 30 faculty and staff members attended the event. More information about the event (photos, slides etc.) can be found here …
You have wakened not out of sleep, but into a prior dream, and that dream lies within another, and so on, to infinity… The path that you are to take is endless, and you will die before you have truly awakened — Jorge Luis Borges
Borges’ quote of reality being a dream within a dream within a dream for ever and ever brings to mind the idea of infinite regress. This is the same as the hall of mirrors effect—the infinite reflections one generates when one places two mirrors parallel to each other—the same object repeated over and over and over. A similar idea can be seen in the design by “Whirlpools” design by M. C. Escher (above) where he combines one of his signature tessellations into two infinite spirals – spiraling inward forever.
These ideas led to my coming up with a new design for the idea of “infinite regress.” I have created many ambigrams to represent the idea of infinity (click here for examples) but this one is different in that it is a visual pun: The design itself is a 180-degree rotational-chain ambigram of the word “regress” mapped onto the universal symbol for infinity — hence “infinite regress.”
Over the past two-and-a-half years we have worked with STEM educators in Chicago Public Schools as part of the MSUrbanSTEM project. We have presented about this project at a few conferences over the past few years, and now we have our first publication. I am particularly happy with the title of the paper, an homage to one of my favorite poems, In broken images by Robert Graves. Complete reference, abstract given below:
Seals, C., Horton, A., Berzina-Pitcher, I., & Mishra, P. (2016). A New Understanding of our Confusion: Insights from a Year-Long STEM Fellowship Program. In C. Martin & D. Polly, (Eds). Handbook of Research on Teacher Education and Professional Development. Hershey, PA. IGI Global. 582-604.Continue reading →
The word “math” written such that it has rotational symmetry
i.e. it reads the same even when rotated by 180-degrees.
The relationship between mathematics and visual wordplay is one I have played with and writing about for a while (More here). I just discovered a YouTube video of a talk given by my partner-in-crime Gaurav Bhatnagar at a Math Ed conference (TIME 2015) in India, titled: On Punya Mishra’s mathematical ambigrams. Continue reading →
In this article, in our ongoing series on Rethinking technology & creativity in the 21st century, we interview Dr. Jung. Dr. Jung is a neuro-psychologist, brain imaging researcher, and a clinical professor of neurosurgery at the University of New Mexico. He started his graduate career interested in issues of intelligence… With time, however, Dr. Jung increasingly came to realize that intelligence was not enough to explain the vast array of human capabilities—particularly to issues such as creativity and innovation. For this reason, he has devoted the second decade of his career to better understanding creative cognition from a neuroscientific perspective. He speaks to three key ideas that (a) creativity can be cultivated; (b) it is (in)disciplined in nature – in that it requires both deep knowledge of a field as well as a willingness to step of the the discipline; and finally that (c) creativity needs downtime. Read the complete article below:
Mehta, R., Mishra, P., & the Deep-Play Research Group (2016). Downtime as a key to novelty generation: Understanding the neuroscience of creativity with Dr. Rex Jung. Tech Trends (60)6.
For the past 4 years, the Deep-Play group has written a series of articles for the journal Tech Trends under the broad rubric of Rethinking Technology & Creativity in the 21st Century. The first article was published in 2014 and we are still going strong. Over that time we have written 23 articles with 4 more in various stages of preparation. Writing these articles has been a wonderful experience, allowing all of us to play with ideas and, most importantly, to keep writing. There is a lot to be said for the discipline required to meet a deadline every two months.
The interesting thing is that in all these years, I have never held any of these 20+ issues of the journal in my hand. Not once. That changed this morning when I got into my office – and there was a packet with the past 4 issues – each with an article in the series. I must say it felt good to hold those volumes and skim through them. So I guess despite my digital dependence, there still is something special in seeing your name in print, or actually touching a “real” journal
For those interested the entire series is here: Rethinking Technology and Creativity
In the rush of summer and the move to Arizona I missed posting #28 and #29 of the TPACK newsletter, and before I knew it, #30 was here as well. Well here are links to the PDFs of all three newsletters
Once again thanks to Judi Harris for all the work that goes into curating these resources and putting them together on a regular basis. All previous issues of the newsletter can be found here
As I dig through my Research Gate requests I realize that I have missed out on putting some of my articles onto my website. Here is another one (and on a side note, it never hurts to make a Led Zeppelin reference in your paper – actually the paper starts with a quote from the band!):
Mishra, P., Koehler, M. J., & Kereluik, K. (2009). The song remains the same: Looking Back to the Future of Educational Technology. TechTrends, 53, 5. p. 48-53.
I recently received a request (via ResearchGate) for something I had written back in 2004. In looking for it I realized that it had not been updated on my website. So below is the complete reference, abstract and link to a pdf.Continue reading →
I have been a huge fan of Bill Atkinson, creator of MacPaint, one of the key players in developing the GUI for the original Macintosh including coming up with things as the double-click, the menu bar, marquee selection and lots of interface ideas we take for granted today. His most impressive achievement, personally speaking, was Hypercard, which more than anything is responsible for my getting into the field of educational technology. So when I came across this quote below, about the design process, I felt the need to create a visual design to better represent it. Here is the quote, and the design below (you can click on it to get a larger version).
The process of [software] design really is one where you start with a vague notion of what you’re trying to make, and that vague notion slowly congeals and gets better defined. As you work with it more, it gets to the point where it is something, but as you try it you realize, “You know, I’ve kind of missed the mark here. This is sort of what I want to do, but what I really want is more like that! — Bill Atkinson
One of the highlights of my career at MSU was the partnership we built between the College of Education and the Azim Premji University / Azim Premji Foundation. This partnership now nearing 6 years has transformed my life in many ways and has led to some powerful and deeply meaningful friendships. It has been a wonderful journey and, as in life, some of what happened was planned and some of it sort of just happened. So, it is no surprise that when we wrote a book chapter about this partnership we titled it By Design and by Chance: The Story of One International Partnership (reference, abstract and link below):