Friday, October 8, 2010

What is an application?

A couple of years ago I was reading a problem in our college algebra text, and it made me laugh out loud.  The first sentence is below.
 Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo (bison) hear that spends falls and winters in the park.
The problem then gives the logistic growth formula for the herd, and then asks the student to compute the number of buffalo in the herd in 2002.

What made me laugh is the thought that Canadian buffalo is just as abstract for my students as the formula.  This is a word problem and it does give students the opportunity to practice skills for translating between the word problem and the computations.  However, I would not call this an application because it is not relevant to the lives of the students.

With the multimedia technology of today, it is possible to find applications in the real world and bring them into the classroom.  Dan Meyer gave an amazing talk about this topic at TEDxNYED.  The video is linked below.

I have been trying to incorporate more applications in my classes.  My focus is working on phenomenon that are difficult to see with the naked eye due to time frames that are too long or too short for use in the classroom.  To date, I've created three PowerPoint files that track the motion of a ball in the air, a weight oscillating on a spring, and water boiling.  The spring and the ball are videos that were reduced to individual frames so measurements can be taken at intervals of 1/30 of a second.  The boiling water is a twenty minute experiment with photographs taken every minute.  Some stills are below.
Ball Video (Spring 2007)
Boiling Water (Spring 2010)
Spring Video (Spring 2010)
These videos are useful in every mathematics class.  I use them to teach the students to build a mathematical model and then use the model to find more information that we can check using the media.  The complexity of the model changes from one class to the next.

I encourage you to come up with your own media applications for your classes.  I feel that the impact on the students is stronger when they know that you produced the video.  It would be best to let the students make the media themselves, which would have to be done outside of class due to time constraints.

If you have an application that you want to share, please share in the comments.