Inside the Non-Mathematical Mind

Part of what makes my job so interesting is trying to understand how my mathematically challenged students think.  Often when they do something that seems completely random there is an odd kind of logic behind it.

For example, one of the problems on the last Precalc test involved finding the cost of fencing for an oddly shaped piece of land.  Multiple students found the area of the figure instead of the perimeter.  When I reiterated that this was supposed to be a fence, several told me that "yes, I'm fencing in the area."  For students who are more verbal than visual, their mental use of the word area (it didn't appear in the problem) led them in the wrong direction.

In another question students were given that the lengths of the diagonals of a parallelogram were 8 and 14.  Several students drew the problem incorrectly as shown below.  They claimed that since the sides of the parallelogram were not perpendicular, they must be "diagonal."  Of course this is perfectly reasonable if they had not already had a course in geometry!

"I'm Confused"

Just two little words, but oh how I've grown to hate them.

Lately I've been pushing my IB juniors to do more problem solving without me, which causes a chorus of "I'm confused."  I think what drives me so crazy about the phrase is the inherent "I don't immediately understand so I want you to tell me how to do it."  I've tried to explain that being confused in math is okay and that not every problem will have an immediately obvious solution.  I've explained that my goal is to give them the tools that they need and then let them solve the problems.  In fact most of them do eventually solve every problem that I throw at them.  However, some students are just extremely uncomfortable with not knowing how to do something.  I need to keep in mind that these students have never before been pushed in this way and hopefully they will gain more confidence as the year goes along.

In the meantime I should teach them a new phrase.  I think "I'm pondering possibilities" has a nice ring to it.

Senioritis

Apparently the following equation is true:

2nd semester senior year + 49" of snow + 10 days off + Winter Olympics = A Major Case of Senioritis

I have a hard time understanding how students could be off for 10 days and not even complete 20 minutes of math homework.  Playing in the record-breaking snow all week and putting off the work until the last weekend is one thing (that's what I did!).  But showing up to class and having no idea if homework was even assigned is tough to understand.

I figured things would get better after they were back in school for a couple of days, but the next assignment was even worse because we didn't have time to start it in class.  In one class only 8 out of the 24 present students had completed the homework, which was only 4 of 19 seniors.  I could handle these statistics if they were doing any work in class, but that is not the case, and unfortunately it is rather difficult to solve trig equations without practicing.

Is it May yet?

Fear of Fractions

In Precalculus we just finished the first of the two most challenging units of the year.  Students had to draw graphs of sine and cosine functions that had been transformed in some way (stretched/compressed, moved vertically or horizontally, etc.).  The ultimate goal was to complete word problems that could be solved by writing a sine or cosine function to model the situation.  One would think that the most challenging part of this would be the word problems, but those actually went fairly well.  No, it was the fractions required to correctly label the scale on the x-axis that caused meltdowns even among some of my better students.

Note that if you just look at the fractions this student thinks the order should be 5/2, 1/4, 3/2, 1, 2/2, 2/3.  Yes, my high school graduates students who think that 3/2 is less than 1, 2/3 is greater than 1, and 2/2 is a different number from 1.  I just hope when they go to college they don't mention who their last math teacher was.

Red Badge of Courage

Some of my IB juniors have been struggling lately. It's tough to go from always being the best math student in a class to working hard just to get B's. I give them a lot of credit because they are rising to the challenges that I set for them and learning both math and problem solving. I can see a big difference in their ability to explain what they know, which is often very difficult for gifted kids who intuitively understand things.

To commemorate their completion of Precalculus on Tuesday, I decided to give them an award. I printed out this image onto 3" x 4" mailing labels to make giant stickers. I wasn't sure if they would think it was a dumb idea, but earlier in the year I had made them unit circle stickers which were a big hit, so I figured it was worth a try. I thought they might stick them to their notebooks, but half of the class immediately put them on their shirts! One kid claimed that "this is the nerdiest thing I've ever worn." (I should hope so!) I figured they would take the stickers off as soon as they got in the hall, but at least a few minutes later they were still wearing them. I'm so proud of my little nerds! :)

Report Cards

The end of the quarter is tomorrow which always brings a flurry of last minute makeup work as well pleas for me to bump up grades. It can also bring some amusing conversations, such as this one that occurred with one of my seniors last year:

Student: Could you please stop writing comments on my report card?
Me: Well, we have to write comments for anyone who got a C or lower. Why?
Student: It makes it very difficult to Photoshop!

Yes, the student who rarely completed homework spent several hours Photoshopping her report card to improve her grades and comments. I guess her parents never figured out how to log in to the online gradebook??

Back to Work

After a 16-day hiatus, we finally started back to school on Monday. Boy was that a tough day! I tried to keep my classes very interactive to help the students ease back into things, but they were too tired to do anything even quasi-fun. They were supposed to make graphs on poster paper and usually the mere mention of markers gets them excited. On this occasion they were too lazy to even hang up their posters and tried to complete the project without moving from their desks. It's a good thing I had already moved the desks into groups or we might not have gotten anything done!

Today was not much better - they seemed even more exhausted and looking at the class gave me flashbacks to zombie movies. On the plus side we got a ton accomplished because they were sitting quietly and dutifully taking notes. We'll see if they remember anything next class.