(Originally posted at on February 28, 2011 7:29 AM)

A few days ago, I bought David Quantick’s Beck (Thunder’s Mouth Press, 2000) at a BOOKSALE for 45 pesos.  It is “an insightful biography, a comprehensive discography, and an evaluation of Beck’s position among the greats of rock music.”  It gave me some information I previously didn’t know, for example, that Beck was born Bek David Campbell (yes, without a “c”; he became Beck Hansen when his parents divorced) (p. 1) and that ‘Deadweight’ (one of my favorite Beck songs) was specially written for the movie A Life Less Ordinary (p. 89).

I first learned about Beck through his song ‘Loser’ when it first came out.  My sister bought his album Mellow Gold, but didn’t like it that much.  I saw the music video of ‘Where It’s At’ and decided to buy his album Odelay.  It was one of the best albums I had ever heard (even better than Edie Brickell & New Bohemians’ Shooting Rubberbands at the Stars and as good as the B-52’s Cosmic Thing).  It seems that I’m not the only one with this opinion.  Quantick writes “Critically, Odelay was liked by everybody in the world,” (p. 65) “There is not a bad track on Odelay,” and “Odelay is one of those albums where everything sounds like a great single, and several tracks in fact are great singles” (p. 66).

After Mutations and Midnite Vultures, I somewhat lost interest.  I bought Sea Change but didn’t even listen to it.

I’m currently in the process of letting go of most of my personal belongings and I’m looking for a good home for my Beck CD’s.  I have nine of them—the five mentioned above and the four shown below.  Contact me if you’re interested.


Duck Duck Go

(Originally posted at on February 18, 2011 7:43 PM)

If you have concerns about privacy, you might want to avoid using Google as your search engine.  I tried using AltaVista, but found it somewhat annoying.  (I couldn’t use it to search for exact phrases using quotation marks.)

I’m currently trying Duck Duck Go and it seems quite nice.  (Try using it to search for The Simpsons characters [without quotation marks].)  I searched for Combinatorics on words and my short presentation about it was listed as the sixth entry (at the time I wrote this blog entry).

IBM’s Watson on Jeopardy!

(Originally posted at on February 15, 2011 8:37 AM)

First it was IBM’s Deep Blue versus chess champion Garry Kasparov.  Now it’s IBM‘s Watson versus Jeopardy! champions Brad Rutter and Ken Jennings.  (For a short video showing Watson playing a mock Jeopardy! game, click here.)

Conceptual and Procedural Knowledge in Mathematics

(Originally posted at on February 9, 2011 8:40 AM)

Last night, I watched a nice talk by Eric Mazur about peer instruction.  (Click here for the video, which is around 1 hour and 20 minutes long.)  He focuses on the physics knowledge of undergraduates, but I believe that his statements also apply to undergraduates’ mathematics knowledge.  He makes some nice points, such as

The better you know something, the more difficult it becomes to teach because you’re no longer aware of the conceptual difficulties of a beginning learner. (at around 00:51:00)

My dissertation (which is still on-going) is about the relationship between conceptual knowledge and procedural knowledge in mathematics.  So I was very interested in what he was saying.  His statement that

Better understanding leads to better problem solving. (at around 01:02:00)

(gains in conceptual knowledge lead to gains in procedural knowledge) seems to be supported by many studies.

I do admire his honesty and humility.  While he says that

“Good” problem solving does not necessarily mean understanding. (at around 01:02:00)

note that he does not say that better problem solving does not lead to better understanding.  This is actually the main question that I want to answer:  do gains in procedural knowledge lead to gains in conceptual knowledge?  Many studies conclude that the answer is no.  But I think it’s because these studies use a narrow definition of procedural knowledge.

I believe that there is a way to teach mathematics that on the surface looks procedural but is actually procedural and conceptual at the same time.  I believe that the current dichotomy (conceptual vs. procedural) is producing more smoke than light.  Perhaps it’s time to see that focusing on both at the same time is better than focusing on one and not on the other.

Aquino signed notes

(Originally posted at on January 21, 2011 9:03 AM)

For the past few weeks I’ve been closely looking at the paper money I’ve been handling.  I’m not looking for the new designs released last December 2010.  I’m looking for the old designs that have the signature of President Benigno Aquino III (released on November 26, 2010 according to this article).  I expect bank notes using the old designs but with Aquino’s signature to be quite rare.  (So far I’ve found one of these “Aquino signed notes“—a 20-peso bill.)

Math teacher

(Originally posted at on January 20, 2011 8:13 PM)

Last night I became a registered user of MathOverflow.  I answered a question, and a few minutes later, my answer was voted up.  (Someone considered my answer helpful.)  And because my answer to the first question I answered was given at least one up vote, I got a bronze “teacher” badge.


(Originally posted at on January 15, 2011 9:12 AM)

My wife and I like to collect Hot Wheels. One of our prized possessions is a 1968 Silhouette, one of the first sixteen Hot Wheels models.  The body and the base are in Spectraflame gold.  It’s a U.S. casting; it has a clear dome and a white interior with a molded steering wheel.  (The Hong Kong casting has a blue-tinted dome and an inserted black steering wheel.)  The area surrounding the side exhaust pipes are part of the body.  (Other castings have them part of the base.)

I got my information from Edward Wershbale’s Hot Wheels Spectraflame: The Essential Guide (Krause Publications, 2008).