Friday, January 3, 2014

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

January 2004 – July 2011

August 2011 – present

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?

June 2008, It Ain't No Repeated Addition

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

September 2008, Multiplication and Those Pesky British Spellings

December 2008, How Do We Learn Math?

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

January 2010, Repeated Addition - One More Spin

January 2011, What Exactly is Multiplication?

November 2011, How multiplication is really defined in Peano arithmetic

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?

October 1996, Wanted: A New Mix

September 1999, What Can Mathematics Do For The Businessperson?

January 2008, American Mathematics in a Flat World

February 2008, Mathematics for the President and Congress

October 2009, Soft Mathematics

July 2010, Wanted: Innovative Mathematical Thinking

September 2012, What is mathematical thinking?


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

November 2012, MOOC Lessons

December 2012, The Darwinization of Higher Education

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

February 2013, The Problem with Instructional Videos

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

September 2013, Two Startups in One Week

More about MOOCs

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


An irregular series of posts starting on May 5, 2012


December 2013, MOQR, Anyone? Learning by Evaluating

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

March 27, 2013, Can Massive Open Online Courses Make Up for an Outdated K-12 Education System?

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

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

No comments: