Tuesday, December 17, 2013

But Seriously... Is Algebra Necessary?

A friend tagged me in a FB post with a link to a New York Times article by Andrew Hacker Is Algebra Necessary? I need to process this, so here goes....

I saw the article as having two distinct parts. Here are my reactions to each part.

Part The First: Math Is a Useless Pain

The first half or so of the article indicates that math causes high dropout rates and is basically useless to everyone not bound for MIT or Caltech. Well, if math causes high dropout rates, then I think there is a reasonable discussion to be had about how we address the issue. What should we do?
  1. Prepare students more effectively from the beginning. That is, should we fix our elementary and middle school math programs so that students can have more success later in their math careers.
  2. Fix the high school math curriculum so more students can find success and gain the math skills they need for life and for later mathematical study.
  3. Give up. Stop requiring so much math.
The eye-grabbing headline and some of the arguments in this first part seem to imply that Hacker is suggesting a focus on option 3, but after reading the second half of the article, I think he is making more of an argument for option 2. I believe that we need to focus on options 1 and 2.

By the way, the Common Core standards should  help with option 1. A coherent curriculum that focuses on important mathematical practices and covering fewer topics, but with more depth is a great place to start. It isn't a panacea, but spending more time on fewer topics can help everyone out. I think the Common Core standards do a pretty good job of mapping out a coherent mathematical progression from elementary school through the end of grade 8. Then, we come to...

Part the Second: The Traditional Algebra 1-Geometry-Algebra 2 High School Math Sequence Is Mostly Useless and Should Be Improved

OK. This is where Hacker and I agree. In an earlier post, I said that we drive too many kids (like cattle) on the pathway that leads to Calculus. As I said in Math Illiteracy, everyone needs to master some math skills and understand some math concepts, but these don't necessarily map well to the cattle drive to calculus that I think is over-enrolled. By pushing just about every kid through the same cattle drive, we are driving kids away from math and putting up barriers to later pursuits that should not be dependent upon relatively esoteric skills such as learning how to factor cubic polynomials.

Maybe most kids should take a (perhaps more applications-oriented) course in Algebra, but maybe fewer kids need to take geometry and Algebra 2. Maybe a course in Practical Math (the actual title of a course on which I am working) could help. This sort of course can help students see how math can be a tool for solving problems. It can still be a pretty rigorous course, though it certainly wouldn't prepare anyone for calculus. But then again, not everyone needs to take calculus.

From my perspective, the tricky part centers around mobility. If we have a math pathway that prepares potential engineers, scientists, and mathematicians with the math skills they need, and we create a separate pathway that helps the general non-mathy population acquire the skills they need, then how do we ensure that a student who starts on a less rigorous pathway can change his or her mind and switch to the mathy pathway? How do we make sure that the less rigorous pathway doesn't become a dumping ground for students who are ill-prepared for the more rigorous pathway? These are very real concerns. Perhaps I'm being a paranoid Black man, but I know that this sort of dumping ground mentality has been wide-spread in the past, and I'd hate to create a two-tiered curriculum that institutionalizes it.

The Bottom Line

As Hacker says:
Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
Here, he is talking about how medical schools (and other post-graduate programs) use calculus as a way to identify students who have the right academic stuff. Honestly, I can't see that changing any time soon. Also, I'd be interested in a study about this. Maybe being able to learn calculus has a high correlation with the ability to survive and thrive in medical school. Maybe this extends to undergraduate studies as well. As the author of the A Mind for Madness blog says in Thoughts on Nicholson Baker’s Case Against Algebra II:
... if a high school diploma is meant to indicate some level of readiness for college, then algebra is probably a good indicator. This does not mean that you will use it, but will just point out that you have some ability to do some abstract things. I’m not saying it is the only way to test this, but it is probably a pretty good one.
Regardless, I think we need to:
  • Prepare more students for success in mathematics more effectively. We shouldn't focus solely on the cattle drive to calculus, but then again, we shouldn't ignore it either.
  • Do a better job of creating math courses that engage all students. We need to have students wrestle with more authentic real-world applications and see how math can help solve real problems.
  • Help students see the beauty in math in addition to the utility it affords in problem-solving contexts.

Wednesday, January 2, 2013

Kennedy Center Honors: Led Zeppelin

A friend at work sent me a link to a video from Heart's tribute to Led Zeppelin at the Kennedy Center Honors:

Heart Performs Stairway to Heaven

The Washington Post's Chris Richards' Led Zeppelin: Rock-and-roll’s most magical formula, struck me as remarkable. The best music critics can put into words that which you or I can only feel, but not articulate. Chris Richards has done just that in this article. Richards also has an interview with the surviving members: Kennedy Center Honors recipients Jimmy Page, Robert Plant and John Paul Jones on Led Zeppelin’s fabled chemistry and unwritten future.

I'm not Chris Richards, so I will keep this short: From the first time I heard Led Zeppelin, it seemed like an echo of some tribal rhythm that had always been there. What's remarkable to me is that it still feels the same way. So many of their songs seem to plug directly into my soul.

Thursday, December 27, 2012

Grey Explains

C.G.P. Grey is really kinda awesome. He has a series of videos called Grey Explains. Each video is short, but crams a ton of information (and more than a little humor) into its 3-6 minutes. Here are some of my favorites:

The United Kingdom Explained
The Difference Between Holland and the Netherlands (and a whole lot more)
Coffee: The Greatest Addiction Ever
Death to Pennies

Just awesome. I really need to watch each of these several times.

Monday, December 10, 2012

Music Monday: Buddy Freakin' Rich

I have a ton of holes in my musical knowledge. I have started filling one of them: Buddy Rich. I remember his appearances on The Tonight Show with Johnny Carson, but I never really listened to him since then.

Live in The Hague in 1976
This concert is a good intro to what he and his big band were all about. Skip the first 5 minutes unless you want to practice your Russian, but once the music starts, it's a great concert. My favorite part starts at about 37:20. Birdland is a wonderful song, then at around 45:00, Channel One Suite includes one of the most amazing drum solos you will ever hear and see. Just wow.

One O'Clock Jump
This is a Count Basie standard on which Buddy's band does a nice job.

Seinfeld and the Buddy Rich Tapes
OK. This isn't his music. This is more about how much "fun" he must have been to work with.

Friday, December 7, 2012

Web Stuff Friday: WeatherSpark and Nand2Tetris

WeatherSpark -- Such a great way to visualize the weather. Their tagline is "Beautiful Weather Graphs and Maps," and I agree. It looks good.

From NAND to Tetris is an interesting idea: It is a course that endeavors to have students build and program a working computer from first principals. Both Boy Kid and Girl Kid will have to do this at some point, but it will take some time for them to develop the necessary background. One of the founders of the effort has a YouTube video: Nand2Tetris in a Nutshell as well as a TED Talk: The Self-Organizing Computer Course (more on those ideas will come in a separate post).

Wednesday, December 5, 2012

On Nostalgia and Repetition

Chuck Klosterman's article Nostalgia on Repeat at Grantland struck a chord with me.

Like Klosterman, I had a limited set of albums and cassettes when I was a kid. When I lived in Sierra Leone between the ages of 4 and 6, we had no television, and radio was pretty useless. All I did was listen to a short list of albums:
  • Easy Rider (motion picture soundtrack)
  • Sgt. Pepper's Lonely Hearts Club Band, by The Beatles
  • ABC, by The Jackson 5
  • The Sound of Music (motion picture soundtrack)
  • 1812 Overture, by Tchaikovsky
  • Carnival of the Animals, by Saint Saens
That's it. I listened to those albums pretty much every day for easily a year and a half. I put a lot of time in listening to these albums, and thus listening to anything from them brings back feelings that are out of proportion to the quality of the music (though you gotta admit that it isn't a bad list of albums. It could have been a whole lot worse, right?).

The great mathematician John von Neumann said "Young man, in mathematics you don't understand things. You just get used to them." As a math educator, I interpret this as a call to practice, practice, practice. I wonder if this idea can apply to music as well? Perhaps the key to really appreciating music is to listen, listen, listen.

I still sometimes get into a mood where I listen to the same album (or short list of albums) pretty often in a short time. The good new is that I'm pretty sure that Boy Kid does the repetition thing, too. The bad news is that his list of albums isn't nearly as good as mine was. One step at a time.

Monday, December 3, 2012

Music Monday: Tiny Desk Concerts

NPR's All Songs Considered has a series of Tiny Desk concerts. In a sense, this is sort of a polar opposite of the Concerts a Emporter, which are recorded in various open air locations around France. The tight space makes for an interesting setting, and a diverse set of artists have tried it out.

Booker T. Jones: Green Onions, [conversation], Born Under a Bad Sign, Down in Memphis
Holy cow! This is THE Booker T with a Hammond B3 right there at the tiny desk. Green Onions is such an iconic song, but he breathes new life into the classic he wrote 5 decades ago. He then describes how he first encountered the B3 and the story is delightful. If you only watch one of these videos, let this be the one.

tUne-yArDs: You Yes You, Doorstep, My Country
OK, so Merrill Garbus is insanely cool and she rocks that sample pedal. Watching her spin her magic on the fly is great.

Adele: Someone Like You, Chasing Pavements, Rolling In The Deep
Everyone seems to love her, but I've never really sat down to listen to Adele. I can see why she is so well loved. She has tremendous talent.

Foster the People: Houdini, Helena Beat, Pumped Up Kicks
The contrast between this and the beautiful energy they exude in full concerts is remarkable. Honestly, I am rather sick of Pumped Up Kicks, but this version is nice.

More that caught my ear:
  • Givers: Meantime, Up Up Up, Atlantic
  • Basia Bulat: The Shore, W Zielonym Zoo, Heart of My Own, In the Night
  • They Might Be Giants: Can't Keep Johnny Down, Cloisonne, Fingertips
  • The Cranberries: Linger, Tomorrow, Ode To My Family, Zombie, Raining In My Heart
  • Bill Frissell: Nowhere Man, In My Life, Strawberry Fields Forever
  • Beirut: East Harlem, Santa Fe, Serbian Cocek
Check out some of the other concerts: Tom Jones, Yo Yo Ma, Noah and the Whale, Gogol Bordello, YACHT, Esperanza Spalding, Fanfarlo, and many more.