Naught Much

Here’s my latest addiction. It’s a game called Planarity. Rearrange the blue vertices so that none of the edges overlap.

So far, I’ve made it to the 16th level with a score of 6611. Take a screenshot of your best score and post it in the comments.

This past Friday, my school had an inservice day for the teachers. I was responsible for a small portion of the day. It was my task to provide a demonstration of the Four Corners differentiated instruction strategy to the rest of the faculty. I decided the best way to accomplish that was to actually go through the activity instead of just telling my colleagues about it. So of course, I based the activity on a mathematical statement. Usually, any discussion of mathematics with the faculty in general is met by moans, groans, and eye-rolling. This time, I was surprised. But I’ll get to that in a minute.Four Corners works like this:

1. Teacher writes a debateable or controversial statement on the board.
2. Students move to the corner of the room where the sign is posted that most closely represents their opinion on the statement.
3. Discussion, questions, and debate are then allowed between the four groups.
4. Next, students are allowed to switch to another corner if they changed their opinion.
5. Students are invited to explain what caused any change of opinion.

The statement I posed to the faculty was this:

There are more integers total (… -3, -2, -1, 0, 1, 2, 3, …) than there are decimal numbers just between 0 and 1.

The four statements that I posted in the four corners were:

I was quite surprised by the amount of discussion that my statement generated. It was very interesting to see how “non-math” people think about mathematics in a purely theoretical setting. The faculty really “dug” the discussion and many of them switched corners as thoughts and arguements were shared.

Ultimately, they ended up fairly evenly divided amongst the four corners. By the end of the activity, they were begging me to tell them which response was actually the correct one (I had told them that one and only one of the responses was indeed correct). I eventually did tell them. But in this post, I’ll leave it to one (or more) of my readers to leave a comment as to which response should be chosen to the above statement.

As the first quarter grading period will end this Friday, students are suddenly very interested in their grades. It’s so curious how they will wait until the last week of the grading period to ask forgiveness for the previous 8 weeks of sins. It usually sounds something like this: “Mr. B, is there anything I can do to bring up my grade?” or “Mr. B, do you have any extra credit I can do?” or “Mr. B, I really need to get a C in this class. Can I clean your board or your desks for some extra credit?”

I sure would like to get my hands on the scoundrel who invented “extra” credit.  It’s almost like extra credit is a religion that students in which students blindy place their faith — they hope that it will save them from judgement for their sins.  I just tell my students, “Sorry, you should put forth a consistent effort throughout the entire course.  Then this wouldn’t be an issue.”

I thought this was pretty funny. So did my students.

Here’s an image I created — obviously playing off of the Nike logo and slogan. I have this posted on the wall in my classroom. Whenever my students start to become lazy, I just point to this sign.

Click for full-size image.

Here is an excerpt from an Associated Press report that was published in my local newspaper this past Sunday (17 Sept. 2006). Some of the information presented in it raises some questions in my mind. I’ve outlined the key statistics in red.

So from the article here’s a summary of the statistics:

In 2004, the percentage of certain borrowers that “paid a higher-than-typical interest rate on their home mortgages” are:

• 32.4% for blacks
• 20.3% for Hispanics
• 8.7% for whites
• 11.5% (all borrowers)

I’m wondering how such a small percentage of all classes are paying “higher-than-typical” rates. Doesn’t logic tell us that exactly 50% of all borrowers will pay a higher-than-typical rate and the other 50% will pay a lower-than-typical rate? Certainly this would be true if the definition of “typical” in this case was “average” or “mean.” So perhaps, “typical” indicates a range of interest rates. Then, the 11.5% indicates the percentage of all borrowers that had interest rates above that range. But if that is the case, it would be very helpful to know the size of that range. Any thoughts?

I’m thinking of a real number. What is it?

You’ve got 20 yes/no questions at your disposal.

Whenever you are ready, ask.

I tried something new today for a review over the basic probability chapter in my Statistics textbook. I created worksheets that contained approximately 50 exercises from the topics we have been discussing. I then assigned each problem a point value - easier problems were worth one point, harder problems were worth 3 points, and ones in the middle were worth 2 points.

Then I told the students that they had two tasks to complete today. The first was to complete 15 points worth of problems to be turned in and graded. This way, they could choose any combination of problems to solve whose combined point value was at least 15 points. The second task was for them to correctly solve a problem of their choosing and then present that solution to the class. If they chose to solve and present a 3-point problem, then they would earn 3 mythical extra credit points. If they chose to solve and present 1-point problem, they had an easier time at it, but the rewards were less (1 point extra credit).

This seemed to work very well today. The students enjoyed having the ability to choose which problems to solve. They also enjoyed listening to their peers explain solutions and rationale to the exercises.

[The phrase “mythical extra credit points” is one that I saw used by Dan Greene on his blog. As a math teacher, and I’m sure others can attest to this, I know that giving a student 3 or 5 or x extra credit points can mean as much or as little as you want it to. “Mythical” seems so fitting.]

On August 24, I posted an entry about a conversation with Andrew Jones.  That interview is now available to listen to or download at the Nick and Josh Podcast page.

Call 1, made at 4:22 pm while driving home from school.

Mr. B: Hello Mr. Schwartz. This is Mr. B, your daughter Jessica’s Statistics teacher. I’m calling because I’ve been having trouble with the amount of talking that Jessica has been doing in my class. Despite several one-on-one converstations with her about the importance of paying attention and not distracting others, she continues to create a disruption. If this continues, I will simply ask her to leave the class and spend the remainder of it in the principal’s office. If you are able to help the situation any from your end, I would greatly appreciate it.

Mr. Schwartz: Rest assured Mr. B, I will deal with this tonight. You will not have any other problems like this from Jessica.

Mr. B.: (Thinks to himself: Yeah, I’ve heard that before.) Thank you very much.

Call 2, made at 4:26 pm while stuck in traffic on the way home from school.

Mr. B.: Hello Ms. Clark. This is Mr. B, your daughter Markesha’s advisory teacher. I’m calling to let you know that I took Markesha’s cell phone from her today. She thought that she would try to be sneaky by hiding in the corner of my classroom and sending text-messages to her friends. She must have forgotten what I always tell my students: “You are not more sneaky than me. I know what you did, what you are doing, and what you will do.” If you would like to get the phone back for her, you may personally come by and pick it up in the main office at school.

Ms. Clark: Well, Markesha knows that she’s not supposed to use her phone in school. But I’ll speak to her about it again.

Mr. B.: Thank you. Please stress to her the fact that her phone needs to be turned off and put away in her locker while she is at school.

We’ll see if these calls actually make difference in behavior.  Sometimes they do, sometimes they don’t.