Hunger Games Sequence

I have a 45 minute drive to school each way. So, I've been picking up audiobooks to keep me company on the drive. Many of you have suggested reading The Hunger Games, so that was my latest acquisition. The whole thing is about 11 hours, I think, so I should finish it in about a week.

Anyways, getting through chapter one this morning, I listened to this bit:

The reaping system is unfair, with the poor getting the worst of it. You become eligible for the reaping the day you turn twelve. That year, your name is entered once. At thirteen, twice. And so on and so on until you reach the age of eighteen, the final year of eligibility, when your name goes into the pool seven times. That’s true for every citizen in all twelve districts in the entire country of Panem.

But here’s the catch. Say you are poor and starving as we were. You can opt to add your name more times in exchange for tesserae. Each tessera is worth a meager year’s supply of grain and oil for one person. You may do this for each of your family members as well. So, at the age of twelve, I had my name entered four times. Once, because I had to, and three times for tesserae for grain and oil for myself, Prim, and my mother. In fact, every year I have needed to do this. And the entries are cumulative. So now, at the age of sixteen, my name will be in the reaping twenty times. Gale, who is eighteen and has been either helping or single-handedly feeding a family of five for seven years, will have his name in forty-two times.

The Hunger Games by Suzanne Collins.
Chapter 1 as found here

Being a math teacher about to begin a unit on sequences and series in my Algebra II class (as well as a deeper study in Precalculus), I thought this would be an interesting problem to use. They are also all reading this book and seem to like it.

Teaching Resolution: Make More Mistakes

I have a problem with how I work in my classroom: I don't often make mistakes. I don't mean for that to sound conceited, but I generally like for people with authority to show few weaknesses and be both precise and accurate in their communication of concepts. It irks me when the principal (a former English teacher and currently moonlighting as a college professor for English education courses) writes an e-mail to the school that says something like, "We are starting this business that will be ran by..." or when our superintendent sends an e-mail to the entire district full of spelling and grammar mistakes.

I thought about it harder this past weekend, though and have come to a conclusion that this may not be the best strategy in the classroom. By limiting my own mistakes it sends a few false messages to students.

• It implies that it is bad to make mistakes.
• It implies that the concept or problem is (or should be) easy.
• It puts me on another plane than my students so that they think I am way above their level and they will never be able to attain that level of understanding of the subject.

So, I am resolving to make more mistakes in my classroom. Some will be intentional; some may not be. Just today in precalculus, for example, I was trying to number our examples as we went and I put up numbers 1, 2, 3, 6, and 7, then I asked them to work through those seven problems. Those students who were paying attention got confused and corrected me. Yay!

Vocabulary or Jargon?

While we're entering a new era or spelling in our culture, the debate reigns whether to join the revolution or fight for the original ways. It's a debate on which I can argue both sides and about one in which I have a hard time deciding my own position. While "kids these days" are writing things like "lol ur rong" does seem somewhat uneducated, it also gets the point across and isn't the point of language to communicate ideas?

While that example may fall more squarely into the English teachers' realm, I have an internal debate about it in my own classroom, too. How important is it really that I use the words "denominator" and "numerator," when it's so much quicker (and more easily understood) to say "bottom" and "top?" When a line with negative slope is changed to get more vertical, how wrong is it for me to say that the slope gets "more negative?"

I realize that there are some words that need to be defined and used correctly so as to avoid confusion. I just finished a section of Algebra 2 where we talked extensively about the difference between permutations and combinations. The words here are important to the understanding of the logic and the formulation of the mathematical expressions needed to solve these problems.

On the flip side, though, in precalculus we are discussing vectors. What is the real difference between calling two vectors orthogonal versus just the familiar "perpendicular" word they already know? Later we introduce the term "normal" for this same concept. Do we really need three words to express the same concept? (Or are they not the same concept and I'm thinking about it incorrectly?)

I realize that even the words "denominator" and "numerator" are important when we involve more complex expressions. But even they get confusing when we discuss things like "multiply both the numerator and denominator of the entire fraction by least common denominator of the terms in both the denominator and the numerator" to simplify an expression like

So, what say you? When teaching my students math, how important is it to indoctrinate them to the traditional language of mathematics and somewhat confusing vocabulary? Is it possible to communicate some concepts using more colloquial language?

iTextbook Thought

I have been intrigued by Euclid's Elements ever since I saw this website: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html. I'd always thought it would be a cool way to explore geometry. Begin with the basics and then see what you could do with those things.

So, my idea for an iTextbook is based around those ideas. You begin with some "simple" definitions and postulates as in Euclid's book. Maybe give some reasoning behind the postulates by asking questions like, "Why do we need 2 points to draw a line? Challenge: I am thinking of a line in this window. See if you can guess it with zero hints. (Student draws random line and it won't match what's in the computer.) Here. I'll give you one hint: This point is on the line (point appears, kid draws another line, it won't match). You missed because here are some example lines that it could have been (show a bunch of lines through the point). Here is a second hint: This point is also on the line (connect the dots = winner)."

Expand by asking students to create some tools needed. For example, show a picture of a pile of items that you might find in a junk drawer. These include, but are not limited to, some string, some push-pins, a pen, tape, scissors, a straightedge of some sort, etc. Ask students "How could you create a perfect circle (see definitions 15-16) from these items?" Once they arrive at a correct answer, they "level up." A screen appears with something like, "You have acquired the circle tool!" and the glittery circle button appears in their tool-bar at the top which works like it would in any drawing program (click for the center point, then click again for a point on the circle to fix the size).

Basically, you build geogebra tools by finding out how to construct each thing. You have the line-segment tool and circle tool, so Challenge 1 is available to you: construct an equilateral triangle using the tools you have.

Once you show you can bisect a given line segment, you get a new "midpoint" tool. This unlocks new challenges in which you need to use the midpoint for other constructions.

After you construct an object, you get follow-up questions like: In constructing the midpoint, do the two circles need to be the same size? Is the bisecting segment always perpendicular to the original segment? Does the original segment bisect the segment you created? etc.

It'd be dynamic as with geogebra or sketchpad or anything like that, but you can only use the tools when you "level up" by figuring out how to get build them from more basic tools.

There's a "sandbox mode" where you can play around with tools you have or preview what will become available later. Challenges available are based on the tools you have acquired so far, so they are somewhat ordered, but not necessarily linear. They could be labeled with a difficulty level. Unlocking new tools unlocks new challenges. Hints can be available for the tougher constructions/proofs, like in most games, too.

Anyways, what do you think? The idea just struck me this afternoon, so I haven't thought through all the angles (pun intended), but it seemed like an interesting way to introduce parts of geometry.

Differentiating the Holidays

I am shamelessly stealing this from a coworker. It is a horrible way to come back after a long hiatus of no blog posts. I apologize. I have blog posts in my head, but am not motivated enough to write.

I also hate the idea of FWD FWD FWD e-mails, but I did think this one was fun enough to share beyond our school:

The Top Ten Ways to Differentiate Thanksgiving Dinner

10. Serve all of your guests on different-sized plates
9. Make each of your guests focus on just one or two foods instead of the whole buffet
8. Eat in shifts in different rooms
7. Let your visual guests just enjoy looking at the food while your kinesthetic guests get to eat it
6. Allow the turkey to have a say as to whether he should be oven-roasted or deep-fried
5. Serve dessert first, then the hot dogs
4. Pair everyone up with an eating buddy
3. Serve the simpler foods first like mashed potatoes and work your way into the more complex foods after your guests have showed mastery of eating
2. Allow your quick eaters to put their food in a blender for faster consumption
And the number one way to differentiate Thanksgiving Dinner…
1. Serve Thanksgiving, but call it a Fourth of July celebration

"Real World" Problem Solving: I Give Up!

I have a SMART board in my room. One of maybe 3 in our school. I also share my room for one period a day with a teacher who doesn't like to use it. So, the board is on a wheeled mount so I can move it out of the way for the 45 mins a day he is in my same classroom. This means I have to orient it at least twice a day and don't really get to ever lock it into place.

We take attendance online in our gradebook program and it is the expectation that attendance be done in the first 10 minutes of class (to catch skipping students). Since doing this on my own daily leaves the first 5 minutes of class where the students goof around instead of working, I decided to use the SMART board to my advantage.

This is what our attendance looks like (names cropped to protect the young):

I set everyone to the far right column (absent) and when students arrive, they are to hit the leftmost bubble next to their name to mark themselves present (the middle option is for tardies). Generally, they like being able to come up to the SMART board and having it work for them. Win-win.

Here's the issue: Since it's never perfectly calibrated (especially with students going to the board and slightly moving the mount to one side or the other), hitting the board in the right spot is often difficult. When you hit the board, a time diamond-shaped cursor shows up and blinks where it thought you touched, but even moments after I orient/calibrate it, some sections of the board will be off by a centimeter or two.

Many of my students have the hardest time getting it to work. I understand that it's somewhat unpredictable on your first touch, but they will continue to hit the same spot (usually harder and harder) and continue to get more and more frustrated.

Part of me wants to laugh and part wants to cry. Is it really that hard to compensate for the issue? You hit it on the button exactly the first time and you see the cursor a bit below your name so it doesn't work. Try hitting it a centimeter higher, right? They will try four or five times and then either try to get a friend to do it or give up and walk away mad and throw their hands up in the air saying, "I can't do it. You just do it for me."

Then I try to teach them how to problem solve math problems and they react the same way. Is it surprising?

I'm all for trying to tap into student intuition and their own internal motivation (a la Shawn Cornally, but what can I do with students like this? Am I being overly dramatic in this observation of student behavior?

(NB: Not all are like this. About half of them figure it out and there are no problems, but about half have the issue as described.)

Pretests (2011-12)

Presented without real comments, here are my pretests for Algebra 2 and Precalculus this year:

Alg2Pretest

Pre Cal Pretest