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.”

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.

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.]

Today I discovered and downloaded a new program, Google SketchUp. This program is free and is for drawing all sorts of 3-dimensional figures. The tools are very intuitive and the whole program is easy to use. You can save your work in a 3D file to come back to later, or you can export to a 2D image file (.jpg, .png, .gif, etc.). I wish I had this when I was teaching geometry a few years ago. My handouts and tests would have looked so much better!

Here are a few drawings that I made using SketchUp. All of these were made today, the first day I ever used this program. [Click on each thumbnail for a full-size image.]

Conic section - parabola.

Conic Section - bottom view.

Golden spiral.

Golden spiral in three dimensions.

Home sweet home. Yes, I do have stairs on the front of my house. They just were too tedious to draw.

My school is one that operates on a “block” schedule. That is, one that has only four classes per day, each of which meet for one hour and twenty-five minutes. Students will take four classes in the fall semester, and then four different classes in the spring. There are some advantages to this schedule (so I’m told), but from my perspective it is a detriment to mathematics education.

In secondary mathematics, the course of study is very sequential — each class building upon skills and ideas from the previous. But what often happens to students in a block schedule is that they will take a math class during the first semester one year and then not take the next course until second semester of the next year. If you do the math, that is a full twelve months that pass with the student not taking a math course. Therein lies the major fault of block scheduling. So much can be, and usually is, forgotten during that “time off” from math.

Recently, the English department at my school has seen the need for ninth graders to take a full year of English classes. They voiced their concerns to the school leadership team and were able to get 9th grade English converted to a full year course, even though every other class remains a one-semester course. I believe the math department is close to accomplishing the same thing for Algebra 2.

Ever since our school implemented block scheduling several years ago, we have seen a decrease in the number of students enrolling in Calculus. I believe this can be attributed to the fact that students are not receiving a “continuous” mathematics education. Even the administrator in charge of the master schedule, a self-proclaimed math phobic, is beginning to see the benefits that would come with teaching Algebra 2 (if not other courses as well) for a full year.