## The Constant Dilemma

Today I was a 6th grade math teacher at Edison Middle School in Champaign. If I had been the reading teacher, we would have been in the library, which would have amused me to no end. Alas, no library for me today! In fact, I actually had to teach math. Or, at least, attempt to do so. I don’t know if I actually succeeded.

The students in the regular math classes were practicing dividing fractions by fractions, and learning the strategy of multiplying the first fraction by the inverse of the second. I don’t know how many really understand how or why this method works, nor did they really understand the strategy in the first place. Heck, I’m still not sure *I* fully understand how or why it works. Many times, though, I am content to know that it *does *work until I finally understand *why*. Even without fully understanding, though, I am confident in my ability to teach the strategy and to illustrate what is being done in the division process. Unfortunately, most of the students with whom I was working were not interested in learning this. Rather, they seemed interested in doing what many middle schoolers in Champaign do: ignore their substitute.

Sigh.

But at the end of the day, I had two classes who had the honors students. They were completely different. They were reviewing different math topics, and many were challenging. Rather than complain that it was too hard and just play around all period, though, they worked at it. They tried it. And they asked me to help them when they were thoroughly stumped. They were respectful but they were also fun. I was able to joke with them and they were able to joke with me, all while learning and understanding difficult math problems.

Here’s a question that I need answered from someone who knows math better than me: is it possible to determine the surface area of sphere? I don’t know. And yes, I realise that I can just Google this. I’d like to know if it can be explained to me, though. The reason I ask is because the teacher for whom I was subbing has a poster that shows the formulas for finding volume and surface area, but for spheres, the surface area was listed as “n/a” (also for a cone). Just curious if there is a reason why.

Anyway, at the end of the day, I found myself debating the dilemma I’ve been debating for years: do I want to invest the time and money required to get the endorsements to teach middle grades? The endorsements would allow me to teach middle school or junior high social studies, science, and possibly English/Language Arts. On the one hand, I love working with older students. They are interesting, interested, and full of a desire to understand. On the other hand, it seems like I encounter many who are belligerent and unresponsive. Is that because they are adolescents, or is it because I am a substitute teacher and that is just how adolescents treat substitute teachers? I can’t believe that the men and women I know who teach at the middle schools have days filled with trials like mine. Also, if I can add a third hand, I would point out that I have long said that I would love to teach fourth or fifth grade. This is still true. But I am wondering if it would be worthwhile to get the endorsements to teach older students. Would it make me more marketable? Would it increase my chances at finding full-time employment? The classes required for the endorsements can be taken online, and will cost between $2000-3000. It is possible that I would qualify for student aid, though. I really would be interested in knowing what others would suggest. Help me out, friends and strangers!

Jenny LinsenmeyerIt’s both- they’re adolescents, you’re a substitute teacher. They assume that’s the way the relationship should be.

The middle school endorsements would make you more marketable. If you take them online, they can be relatively inexpensive, and not too time-intensive.

However, don’t waste your money if you really don’t want to teach middle school.

Have you considered a gifted education endorsement?

January 18, 2011 at 8:44 pm

LarsTo answer your question about the sphere and cone, you have to go into calculus to understand

why. Rest assured that there is awhythough. Wikipedia even goes into thewhy: http://en.wikipedia.org/wiki/Sphere (to give away the ending, volume = (4/3)*pi*r^3, surface area = 4*pi*r^2). The cone is at http://en.wikipedia.org/wiki/Cone_%28geometry%29, volume = (1/3)*pi*r^2*h, and the surface area is pi*r^2 (for the circular bottom) + pi*r*sqrt(r^2 + h^2).At the risk of boring you and/or your readers– that ugly formula for the area on the side of a cone comes from pretending that the bottom isn’t a circle, it’s some kind of polygon. Then it’s easy to measure the sides, because they’re all triangles. Then you calculate it again, using a polygon with more sides. The more sides you add, the closer it becomes to a circle on the base, and the closer the area gets to that pi*r*sqrt(r^2 + h^2).

Grade school math teachers have a tough balancing act. Feeding kids formulas to memorize is hardly teaching them how to understand math, but on the other hand explaining the

why‘s requires some tricky math.January 30, 2011 at 2:35 pm

Alex T. ValencicThanks, Lars, for the explanation of sorts. I took calculus in high school, barely managed to slog my way through enough to get a 4 on the AP exam, and then promptly forgot just about all of it. Even now, the thought of doing calculus again sends shivers down my spine (even though I LOVE “Stand and Deliver”).

So if the topic arises, I’ll tell the students that there is indeed a formula, but it requires advanced calculus to really understand how it works, and I don’t want to just give them a formula without them being able to understand why the formula works.

January 30, 2011 at 5:18 pm