9/13/13 Wants

I want more time. Someone needs to invent a personal time machine that somehow doesn’t age you, so if I use it several times a day I won’t die at thirty. Maybe a normal time machine should be prototyped first.

A machine like that would give me time to do homework, practice piano, read the many books in my queue, get ahead of my classes by reading the textbook, keep up with my Edx and Courseera courses, peruse Khan Academy, examine the various languages that interest me, try composing some music, learn more about Java and C++ as well as the web suite of tools (HTML, CSS, Javascript, etc.), examine Haskell, find out what discrete math is, work on my merit badges needed to get to Eagle, learn more about nanotechnology and try to penetrate quantum physics, learn more about circuitry and basic electronics (and build a Tesla coil!), get my ham radio license, find an examiner for my NAP exam, finish Deus Ex and start the other games in my queue, and possibly hang out with some friends once or twice.

I’m sure I’ve forgotten something; I might edit the post later.

EDIT: 10/2/13: I have completed Deus Ex. It was magnificent.

Diagonal of a Square

So I was reading “A Mathematician’s Lament” by Paul Lockheart (http://www.maa.org/devlin/lockhartslament.pdf). The document laments the teaching of math in public schools, and has all sorts of dignified grumbling within. It’s an interesting read.

Later in the essay, he gives several sample problems to replace the less interesting ones, and the suggestion to calculate the diagonal of a cube caught my eye. I had never done anything like that before. I didn’t take a traditional geometry class, it was an online thing. Maybe that’s why I hadn’t calculated it before. Regardless, I set to work.

Well, I suppose I should draw a cube first, and draw the diagonal.

Now… Huh. How do I solve for that line? Well, maybe if I draw a line like this…

Okay, this is promising. Before I go any further, I should give the sides a length. Let’s call them x.

If I solve for that bottom dotted line, I’ll be able to solve the diagonal! So I’ll call that thing f.

Let’s do a little more algebra…

Alright, now let’s solve for the diagonal. Well, after labeling it d.

I bet we can condense that, though.

Hold on a second. What if instead of putting a square root on both sides, I combined the xs?

So I can find the diagonal of a cube by multiplying the side length by the square root of 3? That’s pretty awesome.

My math teacher, Ms. Ogden, gave me the idea for the last step. I had already compared the diagonal to the side of several squares, and found the whole square root of three relationship. I just had trouble algebraically proving it. So, credit to her for fixing my math.

Busy busy bees

Last semester, Algebra II was fun. For homework, all we had were a couple interesting problems, maybe ten or so. Now? We get more like twenty or thirty problems- and these are in-depth, five-minute problems. If I can do these things five or ten times, I can do them twenty times (assuming skills are not introduced within the homework, which would be another problem within itself). This is why I rarely enjoyed classes in elementary school and why I used to read under my desk all the time.
I understand the teacher is trying to figure out how to help the kids who did poorly on the midterm by making them practice more, but this is not a solution. If they failed to understand the material before, what makes you think they will understand better once they copy even more of their friend’s answer, or follow the same set of instructions more times, but still come out with the wrong answer, thus teaching the kid the wrong solution, confusing him and undermining his confidence, and wasting everyone’s time? This just makes them hate the class more than they may have before. Busywork is (almost) never ever ever the answer.

A better solution would be to list problems in addition to a few for homework that are, say, extra credit, or even completely optional. If you fail a test, you must do more homework/worksheets than before the last test (not for extra credit, for a grade- probably just a completion grade). If you pass the next test, the worksheets are optional again.
This teaches kids responsibility- if they need to do extra work to pass the class, and they know it, it becomes their responsibility to work harder until they actually do fail a test, at which point the teacher intervenes. It gives the kid a fair chance to be mature and grow up (several chances, actually) while not leaving their success entirely up to them.

Naturally, special exceptions must apply, such as a kid who misunderstood one critical skill but otherwise excels, and once taught the missing skill demonstrates a good understanding of the material. That was just a summary of what I believe would work better.Богородица

About Me

I am (at the time of this writing) 15 years old, and a sophomore at the Knox County STEM Academy (soon to have a real name, I hope). I have many varied interests, from Boy Scouts to programming, reading to video games, and music to writing. I enjoy pretty much every subject- that leads me to believe that I just like learning. I’m more interested in some courses than others of course, but for the most part I’m happy in every class I take (if I have a competent teacher). As a conversationalist, I am sadly lacking. I think (not positive) that I might be a little introverted (not antisocial, introverted- this means I don’t seek out social contact; antisocial means I avoid it). I can talk for a while if it’s about a subject I enjoy, but few are they who I can talk to for any real length of time. Luckily, my family is included in that number.
I joined Cub Scouts in 1st grade, which started my Scouting career. Believe me when I say that Boy Scouts are much better. I went on trips to only four different places over several years- Ripley’s Aquarium of the Smokies (in Gatlinburg), the Knoxville Zoo, Camp Buck Toms, and an unnamed camping area… Somewhere. I don’t know where.