This project needs a name!
Please help. We'll give you chocolate, and Rodney will promise a home-cooked meal to the person who does this.
At ICLS '98 held here at Georgia Tech, I was fortunate enough to run into Dr. Nichole Pinkard, who is a professor at the University of Michigan. She's done work on using background knowledge and music to help teach kids beginning reading.
Her work was fascinating to me, and I was especially intrigued at the part about using prior knowledge and music to leverage learning new information, or at least applying this to better understand what is already known.
While she has done this with reading, I feel that it also has applications in math and science. Especially with math, there is a lot of music which uses principles of these in regards to patterns, rhythm, etc. I feel that by using songs that kids already know, we can help teach them basics of this.
Squeak comes into this in a big way, especially with using some of the new JukeBox work. With this, we can not only expose the kids to music they already know, but also allow them to compose new music and look at such things as combining music, creating new instruments and importing sounds to play with, and composing and completing new songs.
Hopefully, this will work on a number of levels. The beginning work should show them that much of what they listen to (and by extension, other parts of their daily lives) have many interesting and relevant links to science and math (and by extension, other parts of education). From this, we can show them how to manipulate these, and how changing sounds, tempo, etc. in music has direct correlation to mathematical properties. The hope is that this will give them a salient link to these and engage them in new and interesting ways.
Most of this is based off the work that Jean Piaget and Seymour Papert did concerning the ideas of constructivism and constructionism. Piaget coined the term "constructivism" for his theory that thinking is a process of active creation of knowledge in the brain, not of passive receipt of information.
Papert was a student of Piaget's, and expanded on his theory of thinking to create a theory of learning (called "constructionism"). If Piaget is correct about the nature of thought, then it follows that people should learn particularly well while working on personally meaningful projects. Learning through design and construction activities is better than learning by being told.
Using this, I believe that the kids will learn these ideas better if they are able to not only use music they listen to and like, but are also able to create new music and sounds to work with, and explore the subtelties of both music and math.