Tuesday, September 27, 2016

Test #2 and What's the Best Advantage? (Days 29-30)

Today the students take a test. This is for all three grade levels, now that I've changed my original assessment schedule. The eighth grade test is on rational approximations. So far, many students fare well on the test, since much of it involves approximating a square root on the calculator and rounding it off from zero to three decimal places.

Day 30 marks the midpoint of the trimester. In the past I've referred to half of a trimester by a special name -- the "hexter." This is what I wrote in the past about the name "hexter":

The name hexter is interesting indeed. But to discover the origin of this name, we must first consider the origins of the words semester and trimester.

Where does the word semester come from? Some people might recognize a prefix semi- meaning "half" -- for example, in geometry a semicircle is half of a circle. Since a semester is half of an academic year, this seems logical -- but it's wrong. As it turns out, the word semester actually means "six months" -- it comes from Latin sex-, "six," plus mes- or mens-, "month." (Notice that in Spanish, the word mes still means "month.") But a semester can't possibly last six months, since then two semesters would be twelve months, the entire year, with no time for summer vacation. As it turns out, the word semester doesn't come directly from Latin, but passed through German. In German universities, the two semesters actually are six months long -- the winter semester lasting from October to March, and the summer semester lasting from April to September. There actually are breaks corresponding to our summer break, but they're actually included as part of the semesters! So semester means "six months," sex- plus mes-, but Latin speakers often drop the letter x when it appears right before the letter m, just as emigrate is really ex- (out of) plus migrate.

Therefore, a trimester actually means "three months" -- since it comes from tri-, "three," plus mes-, which we already identified as "month." It does not mean "one-third of a year." But since the school year is approximately nine, or three-squared, months long, one-third of the year just happens to be around three months. The term of a woman's pregnancy is also around three-squared months, and so some might believe that trimester means one-third of a pregnancy, but it still means "three months."

And so what about hexter? Now hex- is Greek for six (think hexagon), but is a hexter six of something, or one-sixth of something else? This word doesn't contain mes-, so it has nothing to do with six months or one-sixth of a month. On one hand, there are six hexters in a year, so this word,hexter, appears to be one-sixth of an academic year. But a hexter is also six of something -- it is close to six weeks in length, since there are approximately 36 or six-squared weeks in a school year! The answer is that we can't be sure, since the academic term hexter, while used at some schools, doesn't appear in a dictionary where we can discover its etymology.

Finally, notice that hex- is Greek while all the other numerical prefixes for academic terms are derived from Latin. Recall what I wrote about this lack of linguistic purity in geometry, where we have both hexagons (hex-, Greek) and nonagons (non-, Latin). To be linguistically consistent, we ought to use the Latin prefix sex- and call it a "sexter." The problem is that most schools using hexters are middle schools, and students at that age will assume that this has something to do with sexuality, even though the Latin sex, "six," has nothing to do with the Latin sexus, "sex." In order to avoid trying to explain to middle schoolers how "sexter" and "sexual" come from two completely unrelated Latin roots, the schools just throw linguistic purity out the window and use Greek-based "hexter" instead.

Notice that trimesters, and therefore hexters, appear mainly at the middle school level. High schools almost always use semesters instead, as this is what the colleges expect on the transcripts. But I have seen a few high schools give report cards three times per semester -- in other words, the progress report occurs at the end of every hexter.

By the way, since I wrote the above, I found a link to an actual high school using the term "hexter":


In 10th grade, beginning at the end of the first hexter (six week period), students who have demonstrated mastery of Habits of [...]

This is at a high school in New York. I've never seen any California school use the term "hexter" -- and that includes my own middle school. But still, I will use the term "hexter" both in the classroom and on the blog as a convenient word to refer to the progress reporting period.

I've written about my plans to give four tests this trimester. Therefore, I ought to have two tests during each hexter. But as it turns out, I ended up giving only one test the first hexter, since I printed up the progress reports before grading the tests. Furthermore, the last major grade before printing the first hexter progress reports was a Dren Quiz, which was easy.

As it turns out, all of my eighth graders are earning a C or better. But there are a few students who were failing until the Dren Quiz raised their grades to a C. This might make the progress reports misleading, since the grades were artificially inflated by a Dren Quiz -- oops! As it turns out, most of my failing students are seventh graders. The first test was difficult, and no Dren Quiz can erase all the 10% and 20% scores received on the test.

Here is the song for today:


If you want to find unit rates,
There's one thing you must know.
To find a unit rate,
All you do is divide!
To see if it's proportional,
All you do is divide!
Write it as a fraction,
Reduce it then you're fine.
Graph it at (0, 0),
Then just draw a line.

If you want to find square roots,
There's one thing you must know.
To find an estimate,
4 and below, round down!
To find an estimate,
5 and above, round up!
1 place for tenths, 2 for hundredths,
3 for thousandths, you're fine.
Graph it between two values,
Right on the number line.

Tomorrow is also the beginning of a new module. Learning Module 3 of the Illinois State text is called "What's the Best Advantage?" In this module, students will finish the mousetrap cars that they started back in Module 1.

For my eighth graders, this will be an excellent opportunity to integrate science in the lesson. As I wrote earlier, the next NGSS science lesson on the computer is on motion and force. I've been delaying it until the students can learn about force and Newton's Laws. Well, as it just so happens, the students are supposed to measure the force used to launch the mousetrap cars -- in Newtons! So the idea is to have the eighth graders use the first hour to use the mousetrap cars and then the second hour to complete the online assignment.

But the problem is that our mixed-up Wednesday schedule might finally be changing. Here's how the old schedule worked: first period I would have sixth grade, then second period I'd have the eighth graders for "science" (the online assignment), and then third period I'd keep the eighth graders for STEM (which I'd use for either math or an Illinois State project). The problem with the old schedule is trying to fit music into the schedule. According to the music teacher's schedule, eighth grade music started near the end of first period and was intended to last into second period. So the eighth graders began the day in the history classroom and switched to music when the music teacher arrived -- only to have it end 15 minutes later when the sixth graders arrived to the history classroom.

The new, more logical schedule has eighth grade music line up with second period. This means, among other things, that the eighth graders won't be in my room for both an online science lesson and a STEM project, since they'll still be in music. I assume that I will begin the day with the sixth graders in my room -- but I can't send them to the history classroom after first period, since the eighth graders will still be in there for the music lesson. So I'd either keep the sixth graders an extra period or have them go to English and have the seventh graders come to my room.

Under the old schedule, the seventh graders came to my room for fourth period -- but then their music lesson took place in my room, and I didn't see them for math or science at all! Frankly, I wouldn't mind seeing the seventh graders tomorrow, and I bet they'll enjoy beginning the project. If they're in my room only for music as usual, then I'll just have them do the project on Thursday -- indeed, I suspect the project will bleed into Thursday for all the grades no matter what.

And if I do lose an hour with my eighth graders, then I'll just do the project today and have them do the online science assignment tomorrow after lunch -- that time on Thursday is usually for online math assignments, but I'll just have them do science instead.

But this is a two-day post, and I won't know what happens until tomorrow. That's right -- we received an email informing us of the new music schedule, but we were never told what to do with the students outside of music time! The English teacher has given up trying to figure out the schedule and says that she'll just give an online English assignment to whatever kids show up in her classroom! So this is what Wednesdays are like at our middle school, even one hexter into the year!

My next post will be Thursday.

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