It is a question that comes up regularly in my upper division math courses. Most of our upper division math students at Peru State College are aspiring high school or junior high math teachers. At some point in vector spaces, non-Euclidean geometry, or two variable linear systems of differential equations, someone will say something like, "All I wanna do is teach algebra in high school. Why do I need to know this stuff?" For the answer, enter Adam from Satan and Adam.
Realistically, you won't get much out of the video if you don't have any knowledge of playing the harp or at least some basic knowledge of music theory. Kind of like an algebra lecture, I suppose. So, I will summarize for you, my gentle readers. Though I sometimes think it's more like gentle reader. As in singular. Thanks, Mom!
What is a blue third?
Scales are easily one of the most important building blocks in music. In nearly all music that isn't based on power chords, much of the character in a harmony or a chord comes from the third note in the scale. As an aside, I've read that Pete Townshend was greatly influenced by Henry Purcell's use of fifth chords.
Arguably the most common scale is the major scale. In the key of A, the major scale is A-B-C#-D-E-F#-G#-A or do-re-mi-fa-so-la-ti-do. Major scales tend to be used in happier songs. A natural minor key (different from the harmonica minor) has the 3rd, 6th, and 7th notes lowered one-half step. So, the natural minor scale in A is A-B-C-D-E-F-G-A.
The punch-line to all of this is that the third note in both scales is either C# or C natural. But in the blues scale, the third note is neither C# nor C natural. The so-called blue third is a note in between these two notes. This makes instruments like harmonica and guitar particularly suited to the blues since a piano (for example) is not designed to play a blue third. To sound a blue third on a harmonica in second position (cross harp), a player must bend the three-hole draw down about a quarter step.
Power in reserve
Here's the rub. Between four and five minutes into this video, Adam provides the answer I now have for anyone who asks, "Why do I need to learn all this?" Because you need to have what Adam calls power in reserve.
Have you ever wondered why a family station wagon has a speedometer that goes all the way up to 160 mph? Does anyone need to go that fast in a country where most states have a speed limit of 70 or 75 mph? Of course not. But what would happen if the engine in your family wagon were designed for a top speed of 80 mph? The engine would fall apart after a few weeks, because you can't run an engine near top speed all the time.
Let's get back to the harmonica. If I can bend the three-hole draw down one-quarter step, then I can play the blue third. So, I'm done. Why learn how to bend it any farther? Well, if I want to apply vibrato, I need to pull it down a little more and shake. To take advantage of the vocal qualities of the harp, I can play the minor third and release the note up to the blue third. Not my point-- Adam mentions this in his videos.
My point is that the quarter step bend on three-hole draw is not the end of learning the blue third. It's the beginning. Just like second semester calculus is not the end of content knowledge for 7-12 mathematics education.
Learning requires growth - Yoda knows it
In math, as well as music, history, or rhetoric for that matter, one mark of a well-trained person is that he or she knows more than he or she will generally need. For an aspiring high school math teacher, teaching constantly at the upper limit of one's knowledge is a recipe for frustration at best, disaster at worst.
As Maslow might have said, you can choose between safety and growth. Stepping out of our comfort level at least on occasion is necessary for us to become the type of people we aspire to be.
You might not be surprised to hear that one of my all-time favorite movies is The Empire Strikes Back. My two favorite scenes from all of Star Wars happen in the middle of The Empire Strikes Back when our hero, Luke Skywalker, meets the inimitable man among muppets, Yoda.
In the first of these scenes, Yoda tests young Skywalker's patience by acting the impish prankster. "Awww. Cannot get your ship out," has long been one of my favorite catch-phrases. The second of those scenes is where Luke discovers that the imp is, indeed, the great Jedi master, Yoda. In the ensuing conversation, Luke and the disembodied spirit of Obi-Wan Kenobi attempt to convince Yoda to train Luke in the ways of the Jedi.
No one questions that young Luke has the aptitude to succeed. He is, after all, the son of Anakin Skywalker. However, Yoda is uncertain that Luke will finish what he begins. When he voices this concern, Luke responds, "I won't fail you. I'm not afraid." To which Yoda plainly states, "You will be. You will be."
Yoda realizes, as all good teachers, trainers, and coaches realize, that the true mettle of a student is not evident until the learning becomes difficult. And learning is always difficult at times. At those times, the single worst thing you can tell your students is that they don't really need to learn that anyway. I'll be blogging in more detail on this subject in a later entry. For now, I'll note that a student dropping out of school is not as dramatic as losing an apprentice to the dark side of the force, but it is a tragedy nonetheless.
The simple point is this. If you want to be a teacher, you need to enable your students to grow. As a matter of teaching philosophy, mathematics to me is like faith to religious people. You can't know too much about it. Our nation will not come out of recession, develop sustainable energy technologies, and lead the world in the 21st century with a gaggle of math teachers who don't need to know more than second semester calculus.
No comments:
Post a Comment