23 and Me. Play it again, Sam

It’s one of the most famous lines from one of the most famous movies of all time, Casablanca. Except it’s not what Ilsa, played by Ingrid Bergman, actually said, which was “Play it once, Sam, for old times' sake . . . [NO RESPONSE] . . . Play it, Sam. Play 'As Time Goes By.'”

This month’s column is in response to the emails I receive from time to time asking for a reference to articles I have written for the MAA since I began on that mathemaliterary journey back in 1991. (Yes, I just made that word up. Google returns nothing. But it soon will.)

I first started writing monthly articles for the MAA back in September 1991 when I took over as editor of the Association’s monthly print magazine FOCUS. When I stepped down as FOCUS editor in January 1996, the MAA launched its website, and along with it Devlin’s Angle.

During that time, in addition to moving from print to online, the MAA website went through two overhauls, leaving the archives spread over three volumes:

January 1996 – December 2003

http://www.maa.org/external_archive/devlin/devlin_archives.html

January 2004 – July 2011

http://www.maa.org/external_archive/devlin/devangle.html

August 2011 – present

http://devlinsangle.blogspot.com

Throughout those 23 years, I’ve wandered far and wide across the mathematical and mathematics education landscape. But three ongoing themes emerged. None of them was planned. In each case, I simply wrote something that generated interest – and for one theme considerable controversy – and as a result I kept coming back to it.

I continue to receive emails asking about articles I wrote on the first two of those three themes, and the third is still very active. So I am devoting this month’s column to providing an index to those three themes.

I’ll start with the most controversial: what is multiplication? This began innocently enough, with a throw-away final remark to a piece I wrote back in 2007. I little knew the firestorm I was about to unleash.

What is Multiplication?

September 2007, What is conceptual understanding?

http://www.maa.org/external_archive/devlin/devlin_09_07.html

June 2008, It Ain't No Repeated Addition

http://www.maa.org/external_archive/devlin/devlin_06_08.html

July-August 2008, It's Still Not Repeated Addition

http://www.maa.org/external_archive/devlin/devlin_0708_08.html

September 2008, Multiplication and Those Pesky British Spellings

http://www.maa.org/external_archive/devlin/devlin_09_08.html

December 2008, How Do We Learn Math?

http://www.maa.org/external_archive/devlin/devlin_12_08.html

January 2009, Should Children Learn Math by Starting with Counting?

http://www.maa.org/external_archive/devlin/devlin_01_09.html

January 2010, Repeated Addition - One More Spin

http://www.maa.org/external_archive/devlin/devlin_01_10.html

January 2011, What Exactly is Multiplication?

http://www.maa.org/external_archive/devlin/devlin_01_11.html

November 2011, How multiplication is really defined in Peano arithmetic

http://devlinsangle.blogspot.com/2011_11_01_archive.html

Mathematical Thinking

I first started making the distinction between mathematics and mathematical thinking in the early 1990s, when an extended foray into mathematical linguistics and then sociolinguistics led to an interest in mathematical cognition that continues to this day.

April 1996, Are Mathematicians Turning Soft?

http://www.maa.org/external_archive/devlin/devlinangle_april.html

October 1996, Wanted: A New Mix

http://www.maa.org/external_archive/devlin/october.html

September 1999, What Can Mathematics Do For The Businessperson?

http://www.maa.org/external_archive/devlin/devlin_9_99.html

January 2008, American Mathematics in a Flat World

http://www.maa.org/external_archive/devlin/devlin_01_08.html

February 2008, Mathematics for the President and Congress

http://www.maa.org/external_archive/devlin/devlin_02_08.html

October 2009, Soft Mathematics

http://www.maa.org/external_archive/devlin/devlin_10_09.html

July 2010, Wanted: Innovative Mathematical Thinking

http://www.maa.org/external_archive/devlin/devlin_07_10.html

September 2012, What is mathematical thinking?

http://devlinsangle.blogspot.com/2012/08/what-is-mathematical-thinking.html

MOOCS

No introduction necessary. MOOCs are constantly in the news. Though I was one of the early pioneers in developing the Stanford MOOCs that generated all the media interest in 2012, and I believe the first person to offer a mathematics MOOC (Introduction to Mathematical Thinking), the idea goes back to a course given at Athabasca University in Canada, back in 2008.

May 2012, Math MOOC – Coming this fall. Let’s Teach the World

http://devlinsangle.blogspot.com/2012_05_01_archive.html

November 2012, MOOC Lessons

http://devlinsangle.blogspot.com/2012_11_01_archive.html

December 2012, The Darwinization of Higher Education

http://devlinsangle.blogspot.com/2012/12/the-darwinization-of-higher-education.html

January 2013, R.I.P. Mathematics? Maybe.

http://devlinsangle.blogspot.com/2013_01_01_archive.html

February 2013, The Problem with Instructional Videos

http://devlinsangle.blogspot.com/2013_02_01_archive.html

March 2013, Can we make constructive use of machine-graded, multiple-choice questions in university mathematics education?

http://devlinsangle.blogspot.com/2013_03_01_archive.html

September 2013, Two Startups in One Week

http://devlinsangle.blogspot.com/2013_09_01_archive.html

More about MOOCs

In addition to the MOOC articles listed above, I have also written articles about the topic in my own blog MOOCtalk.org and for the Huffington Post. Here are the references:

MOOCTALK

An irregular series of posts starting on May 5, 2012

http://mooctalk.org

HUFFINGTON POST

December 2013, MOQR, Anyone? Learning by Evaluating

http://devlinsangle.blogspot.com/2013_12_01_archive.html

March 2, 2013, MOOCs and the Myths of Dropout Rates and Certification

http://www.huffingtonpost.com/dr-keith-devlin/moocs-and-the-myths-of-dr_b_2785808.html

March 27, 2013, Can Massive Open Online Courses Make Up for an Outdated K-12 Education System?

http://www.huffingtonpost.com/dr-keith-devlin/massive-open-online-courses_b_2946591.html

August 19, 2013, MOOC Mania Meets the Sober Reality of Education

http://www.huffingtonpost.com/dr-keith-devlin/mooc_b_3741625.html

November 18, 2013, Why MOOCs May Still Be Silicon Valley's Next Grand Challenge

http://www.huffingtonpost.com/dr-keith-devlin/why-moocs-remain-silicon-_b_4289739.html

Math Ed? Sometimes It Takes a Team

In last month’s column, I reflected on how modern technology enables one person—in my case an academic—to launch enterprises with (potential) global reach without (i) money and (ii) giving up his day job. That is true, but technology does not replace expertise and its feeder, experience.

In the case of my MOOC, now well into its third offering, I’ve been teaching transition courses on mathematical thinking since the late 1970s, and am able to draw on a lot of experience as to the difficulties most students have with what for most of them is a completely new side to mathematics.

Right now, as we get into elementary, discrete number theory, the class (the 9,000 of 53,000 registrants still active) is struggling to distinguish between division—a binary operation on rationals that yields a rational number for a given pair of integers or rationals—and divisibility—a relation between pairs of integers that is either true or false for any given pair of integers. Unused to distinguishing between different number systems, they suddenly find themselves lost with what they felt they knew well, namely elementary arithmetic.

Anyone who has taught a transition course will be familiar with this problematic rite of passage. I suspect I am not alone in having vivid memories of when I myself went through it, even though it was many decades ago!

As a result of all those years teaching this kind of material, I pretty well know what to expect in terms of student difficulties and responses, so can focus my attention on figuring out how to make it work in a MOOC. I know how to filter and interpret the comments on the discussion forum, having watched up close many generations of students go through it. As a result, doing it in a MOOC format with a class spread across the globe is a fascinating experiment, when it could so easily have been a disaster.

My one fear is that, because the course pedagogy is based on Inquiry-Based Learning, it may be more successful with experienced professionals (of whom I have many in the class), rather than the course’s original target audience of recent high school graduates. In particular, I suspect it is the latter who constantly request that I show them how to solve a problem before expecting them to do so. If all students have been exposed to is instructional teaching, and they have never experienced having to solve a novel problem—to figure it out for themselves—it is probably unrealistic to expect them to make that leap in a Web-based course. But maybe it can be made to work. Time will tell.

The other startup I wrote about was my video game company. That is a very different experience, since almost everything about this is new to me. Sure, I’ve been studying and writing about video game learning for many years, and have been playing video games for the same length of time. But designing and producing a video game, and founding a company to do it, are all new. Although we describe InnerTube Games as “Dr. Keith Devlin’s video game company,” and most of the reviews of our first release referred to Wuzzit Trouble as “Keith Devlin’s mathematics video game,” that was like referring to The Rolling Stones as “Mick Jagger’s rock group.” Sure he was out in front, but it was the entire band that gave us all those great performances.

In reality, I brought just three new things to our video game design. The first is our strong focus on mathematical thinking (the topic of my MOOC) rather than the mastery of symbolic skills (which is what 99% of current math ed video games provide). The second is that the game should embed at least one piece of deep, conceptual mathematics. (Not because I wanted the players to learn that particular piece of mathematics. Rather that its presence would ensure a genuine mathematical experience.) The third is the design principle that the video game should be thought of as an instrument on which you “play math,” analogous to the piano, an instrument on which you play music.

In fact, I was not alone among the company co-founders in favoring the mathematical thinking approach. One of us, Pamela, is a former middle-school mathematics teacher and an award winning producer of educational television shows, and she too was not interested in producing the 500^th animated-flash-card, skills-mastery app. (Nothing wrong with that approach, by the way. It’s just that the skills-mastery sector is already well served, and we wanted to go instead for something that is woefully under-served.) I may know a fair amount about mathematics and education, and I use technology, but that does not mean I'm an expert in the use of various media in education. But Pamela is.

And this is what this month’s column is really about: the need for an experienced and talented team to undertake anything as challenging as designing and creating a good educational learning app. Though I use my own case as an example, the message I want to get across is that if, like me, you think it is worthwhile adding learning apps and video games to the arsenal of media that can be used to provide good mathematics learning, then you need to realize that one smart person with a good idea is not going to be anything like enough. We need to work in teams with people who bring different expertise.

I’ve written extensively in my blog profkeithdevlin.org about the problems that must be overcome to build good learning apps. In fact, because of the history behind my company, we set our bar even higher. We decided to create video games that had all the features of good commercial games developed for entertainment. Games like Angry Birds or Cut the Rope, to name two of my favorites. Okay, we knew that, with a mathematics-based game, we are unlikely to achieve the dizzying download figures of those industry-leading titles. But they provided excellent exemplars in game structure, game mechanics, graphics, sounds, game characters, etc. In the end, it all comes down to engagement, whether the goal is entertainment and making money or providing good learning.

In other words, we saw (and see) ourselves not as an “educational video game company” but as a “video game company.” But one that creates video games  built around important mathematical concepts. (In the case of Wuzzit Trouble, those concepts are integer arithmetic, integer partitions, and Diophantine equations.)

Going after that goal requires many different talents. I’ve already mentioned Pamela, our Chief Learning Officer. I met her, together with my other two co-founders, when I worked with them for several years on an educational video game project at a large commercial studio. That project never led to a released product, but it provided all four of us with the opportunity to learn a great deal about the various crucial components of good video game design that embeds good learning. Enough to realize, first, that we all needed one another, and second that we could work well together. (Don’t underestimate that last condition.)

By working alongside video game legend John Romero, I learned a lot about what it takes to create a game that players will want to play. Not enough to do so myself. But enough to be able to work with a good game developer to inject good mathematics into such a game. That’s Anthony, the guy on our team who takes a mathematical concept and turns it into a compelling game activity. (The guy who can give me three good reasons why my “really cool idea” really won’t work in a game!) Pamela, Anthony, and I work closely together to produce fun game activities that embed solid mathematical learning, each bringing different perspectives. Take any one of us out of the picture, and the resulting game would not come close to getting those great release reviews we did.

And without Randy, there would not even be a game to get reviewed! Video games are, after all, a business. (At some point, we will have to bring in revenue to continue!) The only way to create and distribute quality games is to create a company. And yes, that company has to create and market a product—something that’s notoriously difficult. (Google “why video game companies fail.”) Randy (also a former teacher) was the overall production manager of the project we all worked on together, having already spent many years in the educational technology world. He’s the one who keeps everything moving.

Like it or not, the world around us is changing rapidly, and with so many things pulling on our students’ time, it’s no longer adequate to sit back on our institutional reputations and expect students to come to us and switch off the other things in their lives while they take our courses.

One case: I cannot see MOOCs replacing physical classes with real professors, but they sure are already changing the balance. And you don’t have to spend long in a MOOC to see the similarities with MMOs (massively multiplayer online games).

We math professoriate long ago recognized we needed to acquire the skills to prepare documents using word processing packages and LaTeX, and to prepare Keynote or PowerPoint slides. Now we are having to learn the rudiments of learning management systems (LMSs), video editing, the creation of applets, and the use of online learning platforms.

Creating video games is perhaps more unusual, since it requires so many different kinds of expertise, and I am only doing that because a particular professional history brought me into contact with the gaming industry. But plenty of mathematical types have created engaging math learning apps, and some of them are really very good.

Technology not only makes all of these developments possible, it makes it imperative that, as a community, we get involved. But in the end, it’s people, not the technology, that make it happen. And to be successful, those people may have to work in collaborative teams. 

Two Startups in One Week

Last week turned out to be far more hectic than most, with the simultaneous launch of two startups I have been involved in for the past few years.

When I went into the life of academic mathematics some 42 years ago, I could never have imagined ever writing such a sentence. Nor, for that matter, would I have had the faintest idea what a “startup” was. It’s a measure of how much society has changed since 1971, when I transitioned from being a “graduate student” to a “postdoc,” that today everyone knows what a startup is, and many of my doctorate-bearing academic colleagues have, as a sideline to their academic work, started up labs, centers, or companies. What was once exceptional is now commonplace.

Massive changes in technology have made it, while not exactly easy, at least possible for anyone in academia to become an “edupreneur,” to use (just once, I promise) one of the more egregious recent manufactured words. This means that, when our academic work leads to a good idea or a product we think could be useful to many of our fellow humans, we don’t have to sit back and hope that one day someone will come along and turn it into something people can access or use. We can make it available to them ourselves.

MOOCs are one of the most recent examples. If any of us in the teaching business finds we have developed a course that students seemed to have benefited from and we are proud of, we can (at least to some extent) bottle it and make it available to a much wider audience.

Of course, we have had versions of that ability since the invention of the printing press. Today, millions of people, academics and non-academics alike, use those printing press descendants, websites and blogs, to achieve a much wider audience for their written word.

A somewhat smaller (but growing) number have used platforms such as YouTube and Vimeo to make video-recordings of their lectures widely available.

To some extent, MOOCs can be viewed as an extension of both of those Internet media developments. A MOOC sets out to achieve the very ambitious goal of bottling an entire college course and making it available to the entire world—or at least, that part of the world with broadband access.

The launch this past weekend of the third iteration of my constantly-evolving MOOC on Mathematical Thinking was one of the two startups that gobbled up massive amounts of my time over the past few weeks. Even though, having given essentially the same course twice before, the bulk of the preparatory work was done, implementing the changes I wanted to make and re-setting all the item release dates/times and the various student submission deadlines was still a huge undertaking. For with a MOOC, pretty well everything for the entire course needs to be safely deposited on (in my case, with my MOOC on Coursera) Amazon’s servers before the first of my 41,000 registered students logged on over the weekend.

When you think about it, the very fact that a single academic can do something like this, is pretty remarkable. What makes it possible is that all the components are readily available. To go into the MOOC business, all you need is a laptop, a word processor (and LaTeX, if you are giving a math course), possibly a slide package such as PowerPoint, some kind of video recording device (I use a standard, $900 consumer camcorder, others use a digital writing tablet), a small microphone (possibly the one already built in to your laptop), and a cheap consumer video editing package (I use Premiere Elements, which comes in at around $90). Assuming you already have the laptop and a standard office software package, you can set up in the MOOC business for about $1500.

Sure, it helps if your college or university gives you access to the open source MOOC platform edX, or is willing to enter an agreement with, say, the MOOC platform provider Coursera. But if not, there are options such as YouTube, websites, Wikis, and blogs, all freely available.

My second startup was supposed to launch at least a month before my MOOC, but a major hacking event at Apple’s Developer Site delayed their release of the first (free) mathematical thinking mobile game designed by my small educational software company, InnerTube Games. Both launches falling in the same week is not something I’d want to do again!

Why form a company to create and distribute mathematics education video games that incorporate some of the findings and insights I’d developed over several years of research? The brutal answer is, I had no other viable option. Though several years of research had convinced me that it was possible to design and build “instruments” on which you can “play” parts of mathematics, in the same way a musical instrument such as a piano can be used to play music (in both cases by passing the need for static symbolic representations on a page, which are known to be a huge barrier to learning for many people), I simply was not successful in convincing funders it was a viable approach.

Clearly then, I had to build at least one such instrument. More precisely, I had to team up with a small number of friends who brought the necessary expertise I did not have. Again, a few years ago, it would have been impossible for an academic to found and build a small company and create and launch a product in my spare time. But today, anyone can.

Sure, even more so than with MOOCs, to form and operate an educational software company, you need to work with other people—three in my case. (That, at least, has been my experience.) But the key point is, the technology and the resources infrastructure make it possible. You don’t have to give up your day job as an academic to do it! And just as a MOOC provider (or a YouTube, website, blogging platform combo) takes care of the distribution of your course, so too the Web (in my case, in the form of Apple’s App Store) can make your creation available to the world. At no cost.

We are not talking about enterprises designed with the purpose of making money here—I am essentially in the same game as the writing of academic works or textbooks, and in my case less so, since my books cost money but my MOOC and my game are free. Rather we are making use of a global infrastructure to make our work widely accessible. If that infrastructure involves for-profit MOOC platforms or software companies, so be it.

The fact is, it has never been as easy as it is today for each one of us to take an idea or something we have created and make it available to a wide audience. Sure, for both my examples, I have left a lot unsaid, focusing on one particular aspect. (Take a glance at my video game website to see who else was involved in that particular enterprise and the experience they brought to the project. That was a team effort if ever there was!) But the key fact is, it is now possible!

For more about my MOOC, and MOOCs in general, see my blog MOOCtalk.org. For my findings and thoughts on mathematics education, see many of the posts on my other blog profkeithdevlin.org together with some of the articles and videos linked to on the InnerTube Games website.

And for another (dramatic) example of how one person with a good idea can quickly reach a global audience, see Derek Muller’s superb STEM education resource Veritasium.