#### Foyofame

YouTube has become a routine attention grabbing tactic in many high school classrooms. Do the growing number of online math rappers simply pander to the youth-of-today's unhealthy need to be entertained while robbing them of the pleasure and beauty of mathematics found inherently in the subject?
For the sake of conversation, i provide an example rap tackling the quadratic formula. Where would you use this in a lesson/unit? At the intro to peak interest? As a teaching tool in itself? As a reinforcement of more rote instruction? Purely as a memory device? As a fun unit-end summary? Basically, is there educational value or just entertainment value? Are teachers engaging students creatively or catering to the lowest common denominator in a cheap bid for attention?

http://youtu.be/emJk5_qxEFs

#### Joeyjojo

Foyofame said:
...the youth-of-today's unhealthy need to be entertained...
Are you a robot? Everyone has always wanted to be entertained. I don't see what's unhealthy about a desire to be entertained. How could any of the great mathematicians have achieved what they did without enjoying their field?

...the pleasure and beauty of mathematics found inherently in the subject
$$\displaystyle Beauty is subjective, not inherent; If we have students who enjoy math, one student might not have the same reason for liking math as the next student does. (Why do you like math, Foyo? ) Where would you use this in a lesson/unit? At the intro to peak interest? As a teaching tool in itself? As a reinforcement of more rote instruction? Purely as a memory device? As a fun unit-end summary? Basically, is there educational value or just entertainment value? I don't see how a lot of these questions relate to what you're asking. In any case, it seems obvious to me that the value of the video is twofold: - It connotes the quadratic formula with something many students find enjoyable (i.e. music) and; - Parts of the song can be used as a mnemonic device. So it follows that the song you've linked is educational and entertaining -- just like this one http://www.youtube.com/watch?v=5rzaEqKWhIk Are teachers engaging students creatively or catering to the lowest common denominator in a cheap bid for attention? I'm not sure I understand what you mean by this. Are you asserting a dichotomy? Are you suggesting that songs like the one you linked bid cheaply for students' attention? To me the song just seems like a creative way of engaging students who're musically inclined. You're reading into it too much, Foyofame.$$

#### CRGreathouse

Forum Staff
Foyofame said:
Ythe pleasure and beauty of mathematics found inherently in the subject
I'm actually very curious about this -- what is it that makes a piece of math beautiful? I think I'll start a thread on it; if you or Joey have anything to say I'd love to hear it.

As for the video, I thought it was... fine. The key parts in my view were (1) the idea that the quadratic formula is a good thing, because you can use it to solve any quadratic rather than learn special methods for different cases, (2) the way to use the formula itself, and (3) the proof of the quadratic formula, showing that it's not magic. I think the first two succeed, but I don't think the last did. Basically the proof has lots of easy steps and one mysterious one: adding the constant (b/2a)^2. If a bit more time had been spent there perhaps it would come clear, but without that it seems like a way to know that the formula is right without actually showing students how to derive it on their own. IMO.

#### Foyofame

Hi GreatHouse!
-- what is it that makes a piece of math beautiful?
Math is like a lens by which we can view and describe the patterns and relationships that exist in our world. The fact that the largest square built against a right angled triangle is equal in area to the two smaller squares is... beautiful! While the Pythagorean relationship is quite well known, there are countless other relationships to discover.
I find beauty also in the way that these relationships can be expressed and arrived at in multiply ways... Take Pascal's triangle for example. The n'th row adds to 2^n. This could be viewed as the number of all possible subsets formed from n objects. This connects to the fact that any number can be expressed as a distinct sum of powers of 2, which is essentially binary code.... Everything is so interconnected! That is beauty in math to me. Showing equivalence and connections. I love how the same concept can be expressed algebraically, logically/allegorically, geometrically... that's what makes teaching math fun. Showing students that they are not 'dumb' just because they did not click with the one way the material was presented to them.

one mysterious one: adding the constant (b/2a)^2
.
I agree that this step seems to be pulled out of thin air.. Here is were a graphical illustration (or algebra tiles!) help in understanding/motivating this step. I never understood why we even call it "completing the square" until I was in teachers' college! I'll try to attach a power point I created to motivate this step...You can youtube "completing the square with algebra tiles" and I"m sure there are good step by step examples too.
I think (b/2a)^2 still seems like magic to students because they are not accustomed to working with a purely algebraic equation.. usually it's nice and pretty like x^2 + 6x +____

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