"So there are Oliphaunts. But no one at home will ever believe me."
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Caveman Grammar

I just taught what was quite likely the best 25 minute introduction to grammar, ever, and I made it all up on the fly.

I did it by describing language as developing first from the caveman’s desire to name things, and from that came the first NOUNS. So any word that names a thing—objects, people, ideas—is a NOUN. Next cavemen wanted to describe those things by size, shape, or color, so the ADJECTIVE was invented. Eventually it wasn’t enough to talk about things, and people needed to talk about what things-with-names were doing, so VERBS were created. Just like the ADJECTIVE was needed to NOUN, the ADVERB was needed to describe the VERB’S activity.

It may sound simple, but those guys learned more about the parts of speech in 25 minutes that they had in four years of high school. They were able to identify word roles easily where 30 minute earlier they couldn’t even say with confidence what the parts of speech were.

Of course language almost certainly did not develop that way at all, but that’s some effective pedagogy.

May 19, 2010   Comments Off

Like Ripkin

I haven’t been sleeping well so I was almost relieved when I got back to my CHU after teaching math for two hours at the end of the day to find that the Internet had gone down and I wouldn’t have to make a post. Then of course nature kicked in and I had to fiddle with it until it started working again.

The math class had an interesting problem on some of the homework I had assigned. I knew how to figure it out using a brute force-like approach but I stumbled for a good ten or fifteen minutes trying to figure out an elegant way to explain the problem: something simple enough to be understood while providing a good foundation for future reasoning, rather than a simple trick based on memorization or a pseudo-formula magic incantation. The problem was “If it takes 5 men working 4 days to load 5000 tons, how long does it take 8 men to load 10,000 tons?”

Well, the elegant way is to figure it takes one man four days to load 1000 tons, or “1000 tons per man per 4 days” which is trivially rewritten as “250 tons per man per day.” Now, you multiply the whole thing by 8 men: 2000 tons per day. Then 10,000 tons divided by 2000 tons/day is (10,000 tons/2000 tons) * 1 day, or 5 days. It looks a lot better written out because you can see the units build up and then cancel out, which is how you know you have the right answer. The units in this case are: tons, days, and men.

May 10, 2010   Comments Off

Triangle Man, Triangle Man

In case you were wondering, here is the answer to the pop quiz.

I made this presentation completely on the iPad—more as a proof of concept or trial run than by way of doing serious work. I learned several of the kinks and quirks of Keynote on the iPad this way. Of course I went over the top with animations just to see what it could really do, making it highly questionable from an aesthetic perspective. The mixture of typefaces is also rather… eclectic.

It’s just for fun.

Update: Yeah, I made an error in the presentation. Well, at least one. I found it myself though so it’s cool. Fixed now.

April 28, 2010   Comments Off

Three corners, three sides, infinite possibilities

Kids, even grown up ones, ask the darnedest things. During class yesterday we talked a little bit about geometry, and one asked, “How many kinds of triangles are there?” We had been discussing the concept of congruency, and I drew some examples of right triangles, equilateral triangles, and isosceles triangles.

I was actually stumped by this question. I vaguely remembered that triangles were sometimes called obtuse and acute, but I wasn’t sure if that was a common use, or if it was more typical to describe them as having “an obtuse angle” or “all acute angles.” Somebody said, “I think one is type is scalene.” Right, there is that. I was able to do a simple proof in class that a triangle could only have one obtuse angle. That is, since the inside angles of a triangle come to 180º, and since an obtuse angle is one that is greater than 90º, it follows that the other two angles must be acute (less than 90º). I still wasn’t sure if I could enumerate all types of triangles, or if it was even possible to do so. I promised them I would give them an answer. Here it is—or at least, close enough.

Triangles can be classified according to the size of their interior angles. Based on the fact that the interior angles must add up to 180º, it follows that there are three kinds:

  • All of the angles are less than 90º (acute). For example, 80º—60º—40º. This is known as an acute triangle.
  • One of the angles is obtuse, that is, greater than 90º. The other two angles must be acute. This kind of triangle is an obtuse triangle.
  • One of the angles is exactly 90º. As expected, the other two must add up to 90º (for example, 1º and 89º), so they are acute. This is a right triangle.

It turns out you can also classify triangles according to the relative lengths of their sides.

  • Suppose your triangle’s three sides are the same length. This is an equilateral triangle. It turns out that there is only one way to make such a triangle to work out, and that is by having all of the interior angles the same. Since they must sum to 180º, each angle is 60º.
  • Perhaps only two sides are the same length. It works out here that the angles of the “odd” side are identical to each other. This shape is an isosceles triangle.
  • Finally (since there are only three sides to consider!), there is the possibility of having a triangle where all three sides are different. This rogue is the scalene triangle.

So, pop quiz. How many types of triangles are there?

April 27, 2010   Comments Off

Staying the Course

Just now finished teaching the first session of our second math improvement class. This class will go much better. One reason is that I learned a lot in the previous course about how to teach the subject matter effectively, but the biggest reason is that in this course we had a large enough population to cut the applicants who were below a 10th grade math level. I had no problem teaching individuals at any level, but in the previous class the population, based on our initial test results, consisted of students performing as low as third grade math to beyond high school level. Since we are all doing our full time job in addition to the class, it was virtually impossible to manage.

I just did an introductory overview today, quickly covering many topics that we’ll later cover in depth, but in many ways it felt like we already went further in this class than we did in two weeks in the previous class.

In other news, I received the news today that I am cleared to spend at least one, and probably two more years in my current assignment and location. Now, we just need to figure out the lodging and commuting puzzle and we’ll be settled.

I’ve started a transition into a completely new job, in charge of computers, radios and communications. I miss my old job dealing with logistics. If I were looking for a different job I would strongly considering making the leap into a new field in some sort of logistical support role. I cannot complain, however, that this new job offers me a lot more free time, and obviously plays to my strengths.

April 26, 2010   1 Comment