Thursday, August 18, 2011

Set Mathematics and iTunes

Set mathematics, Venn diagrams, Union of sets... Are your eyes glazed over? What possible application could this have in your students' lives?

Depending on the socio-economic status of your school's population, it's likely that many classrooms are filled with students who are familiar and comfortable with iTunes, iPods, and mp3 players in general. They likely use them on a daily basis, but there's a high chance that they haven't seen the math that iTunes is capable of harnessing to their advantage.

If you've got iTunes on your computer, take a look at the smart playlist. It's a playlist that contains songs that meet user-defined criteria. You can use any of the fields of meta-data that iTunes stores for each song (such as song name, artist, genre, play count, skip count, last played, album artist, and so on). iTunes is free, and at most of the school computers I've used in the past, it is installed or easily added.

Now here's where things can get interesting: you can define sets of songs in order to create a playlist that updates itself. I use a complicated algorithm to compile a playlist of music that shuffles automatically, drops songs I've heard or skipped, and makes sure I listen to higher rated music more often than lower rated music.

This is all calculated through set mathematics. It's a convoluted algorithm that's tricky to get into here, but a few years ago I put together a prezi detailing how to go about creating a playlist like mine.

This might be an interesting way to motivate students to think about set mathematics and set operations. A real-world application and real-world problems that students want to solve can help cement their understanding of what could be an otherwise abstract and dissociated topic.

Enjoy! And, as always, comment or email if you want to find out more or need clarification.

Monday, August 15, 2011

Math in Real Life

I really enjoy it when math reveals itself in facets of everyday life. The golden ratio, the distribution of prime numbers, and fractal patterns are all really neat concepts that can show students how math can be found everywhere you look.

Dr. Ron Eglash of Rensselaer Polytechnic Institute has developed an interesting website. His project shows a myriad of ways that math can be found in different cultural designs. My personal favourite is the way he relates grafitti art with principals of cartesian and polar geometry.

It may be too advanced for most elementary students, but secondary students may find it a good motivator to start looking at the world through a mathematical lens. The site contains tutorials and lessons, as well as information about the history of each cultural feature.

Take a look at the culturally situated design tools website, or post a link on your classroom web page to let your students investigate their own interests.