Tuesday, August 16, 2016

Points in Networks (Day 1)

So, what was my first day of school like, you ask? Well, let's first look at today's Blaugust prompt:

16. A  mentor/colleague who impacted your classroom/teaching…

Well, as a first-year math and science teacher, I ought to say that the other math and science teachers at my school are my mentors. But unfortunately, I'm the only math and science teacher here. But at least the other middle school teachers -- one history, the other English -- were somewhat like my mentors, especially on the first day of school.

The history teacher taught at my school last year, so he already knows the school -- and he also knew the names of many of the returning students. The English teacher is also new, but she at least has some teaching experience at another school. Pay attention to the impact my fellow middle school teachers had on my first day of school. I'll post just the basics of what my day was like except for the point where I met my eighth grade class, since this is where I want to focus.

7:45 -- I arrive at my school.

8:00 -- I report to the playground, where many students are beginning to arrive. The students are told to gather in a circle for the flag salute.

8:25 -- My first class, a sixth grade class, begins. There are 18 students in this class. Most of the students behave well. One student is a Spanish speaker who knows very little English, but fortunately another student volunteered to translate for him. As a teacher, I know how important it is to provide alternate material for English learners.

9:45 -- My sixth graders leave and my seventh graders arrive. To our surprise, there are a whopping 25 students in this class. I know -- this is still quite small by the standards of public schools, where there are often 30, 35, or even 40 students in one class. But by our charter school standards, this is large, considering that there are only 24 seats in the classroom. This is the class with which I struggle the most with classroom management -- the history teacher warned me that every 7th grader is either one he remembers as a troublemaker last year, or a newly enrolled student!

11:05 -- My seventh graders leave for nutrition.

11:25 -- My eighth grade class arrives. This is my smallest class, with only 12 students -- but there are only eight students present at the start of class. I begin the class the same way I start all my classes, with a Warm-Up question:

What is 2 * 2 * 2 * 2? (That is, 2 times 2 times 2 times 2.)

Most students answer correctly, although a few tried to add. A student or two is upset that the very first thing we do on the first day of school is multiply. I point out that the answer is 16 -- and that today is the 16th. I always go around to stamp correct papers -- many teachers point out that students enjoy getting stamps, and my students are no exception.

11:35 -- My student support aide arrives -- the English teacher and I are each assigned one. Actually, she arrives with the four missing students, all girls.

We move on to an Opening Activity -- the Konigsberg Bridge Problem. I've written about this problem previously on the blog and even suggested it as a first day of school activity -- well, now I'm finally giving the activity on an actual first day of school. This is a little of what I said about this problem here on the blog:

The Königsberg Bridge Problem is a famous math problem from nearly 300 years ago. Fawn Nguyen, a well-known math blogger and fellow Southern Californian -- she lives in Ventura County -- used this as an activity in her geometry class:


As we all know, the Königsberg Bridge Problem is impossible to solve -- it has no solution. But I don't want to start the class with a problem that the students can't solve -- they're already frustrated enough with problems that do have solutions when they just can't find them.

The whole point of this lesson is to point out that students should look for patterns, and that sometimes it's just as important to know why something is impossible as it is to know why something is possible.

Let me complete this with a note on pronunciation. The U of Chicago text points out that the name Euler ends up sounding like "Oiler." But how does one go about pronouncing the name Königsberg? I once read that the o-umlaut ends up sounding like "uh," almost like "ur." A Google search reveals a ten-second video in which this name is pronounced:

By the way. some students believe that they have a solution to the Konigsberg problem, but actually they are crossing one of the bridges twice (they start on island D, cross the bridge towards C, but then head back to D). I start to explain about Euler and why the problem is impossible -- and as I do so, the student who earlier complained about 2 * 2 * 2 * 2 figures out that the impossibility has to do with there being an odd number of bridges from each land! I'm impressed!

12:05 -- Because I know how tough the 80-minute block schedule can be on middle school students, I provide a music break. I get out my guitar and I play the following inspirational song:

The Dren Song -- by Mr. Walker

I don't know why I take math.
I'm all caught up in its wrath.
I'd rather just be a dren.
I would be so happy then.
Tell me what would happen when,
I'm no longer just a dren.
What if I were great at math?
What would be my future path?
Customers won't think it's strange,
When I figure out their change.
Algebra and calculus,
Get me in a cool college.
Once I finish my degree,
Future employers will see,
Of my strong background in STEM.
I know that will impress them.
Reach the moon, be a hero!
I won't just be a zero!
I'll be great, or it may seem,
That this all is just a dream,
'Cause my math skills are so bad.
I can't subtract! I can't add!
I can't multiply by ten.
I will always be a dren.
Now I know why I take math.
Help me find a better path!
I would be so happy then.
But I'm just a dren.

Along the way, I explain that a "dren" is a reverse-nerd -- a nerd is someone who's good at math, and a "dren" is someone who doesn't understand the basics of arithmetic. As it turns out, the student who complained about 2 * 2 * 2 * 2 enjoys this song and looks forward to my next song.

I show my students the September 2015 Boys' Life article about the mathematicians and scientists who work for NASA and the possible future of people traveling to and living on the moon. But as it turns out, eight of the 12 students in my class are girls, so I don't expect Boys' Life to motivate them.

Instead, I tell them about the movie trailer that was released just yesterday -- Hidden Figures, about the scientist Katherine Johnson who worked for NASA and the Apollo projects in the 1960's. For those of you who have read my blog before, it goes without saying that I plan on watching this movie, and I highly recommend that my students watch it in January as well.

12:15 -- I proceed with my next Opening Day activity -- Personality Coordinates. This activity comes from the King of the MTBoS, Dan Meyer:


Each person in a group picks a dot and writes her name next to it.
Now the group’s job is to label the axes. Physical attributes don’t require all that much thought and don’t reveal all that much, so don’t allow them.
That’s it. It requires a surprising amount of creativity and conversation. Happy first day of school, teachers.

12:30 -- My support aide leaves, and this is a good time to end the period with an Exit Pass:
If you don't know the answer, ..
The answer is "at least know where to find it," which is posted in a corner of the room. (I mentioned this in an earlier blog post.) Some wrong answers are "ask the teacher" and "you're a dren."
12:45 -- My eighth grade class goes out to lunch.

1:35 -- My sixth grade class returns for a special "Math Intervention" class. There is special software for this class, but I spend the entire period acquainting the students with the laptops, including making sure that the students all have the correct password.

2:35 -- My sixth graders go out to P.E. class. The history teacher, English teacher, and I watch as we discuss our plans for the next day. The English teacher comes up with the idea of having the students come up with rules on the posters.

4:00 -- I go home for the day and head for my computer to type up this blog entry.

If there's anything I could change about the way I ran the class today, it would be to teach the entire class in reverse order. That way, the Exit Pass becomes a Warm-Up, a scavenger hunt to find the rest of the quote, Personality Quotes occur earlier in the class, and the 2 * 2 * 2 * 2 question doesn't turn off students right at the start of the period.

I would also rewrite the Konigsberg worksheet. I'd already changed the worksheet to add more bridge problems, including some trivial ones. But now I'd number those trivial problems #1 and #2 (rather than #3 and #4, as they were numbered today).

Another problem I have has to do with explaining my directions clearly. I was hoping to create a seating chart directly from the Personality Coordinates worksheet (since the students are already seated in groups of four), but I couldn't because some groups randomly labeled the dots rather than place the student sitting northwest in the upper-left corner of the page. Also, some students wrote the Exit Pass on a separate sheet of paper rather than the back of the Warm-Up.

I remember explaining my directions to the students -- but I could be remembering my explanations to the 6th and 7th grade classes, not the 8th grade class. Anyway, I know that I don't always explain instructions clearly to my students from my days as a sub, so I must give the students the benefit of the doubt whenever I see them misinterpreting instructions.

Here is a copy of the Konigsberg worksheet as I actually gave it in class today. Again, I point out that there are still ways that I can improve this worksheet.

And thus ends my first day of school. Today I am a teacher.

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