Sixty-seven third-graders were assigned by class twice a week, for twelve 45-minute sessions in all, either to regular mathematics instruction or to "academic music instruction" taught by regular classroom teachers. Students in the music class learned the values of quarter notes, half notes, and whole notes. They clapped, sang, and drummed, and they filled out worksheets using the time values of the notes to add up to a full four beats, or whole note, in every bar.
At the end of the six weeks, students in the academic music section outscored their peers on a fraction test by 50 percent, a significant difference.
Getting a strong "fraction sense" is an important first step in learning to understand fractions, and it makes sense that a tactile and auditory fraction sense can help strengthen a more numerical or logical sense. Besides, clapping and singing are fun. On the other hand, it's important to remember that this is a small study. Because students were assigned by class, there were probably only one or two teachers in each experimental group. The difference in outcome might be because the teachers in the music group were more enthusiastic. It's hard to say from one small study.
Of course, the connection between music and mathematics is a well-established one. Euclid and Pythagoras were both great believers in the connections, and even today many top mathematicians are more than competent at playing musical instruments, not to mention understanding musical theory.
The Ice Castle: An Adventure in Music, I explore the connections through the investigations of one of my characters, Ivan. Ivan can't sing, and he's never done more with music than listen to his i-Pod, but he does have an interest in math and experiments. In the Land of Winter, where music matters more than anything, he uses his understanding of fractions and logic to learn about musical scales, intervals, octaves, and even how to build musical instruments. As with Lost in Lexicon, there's a brainy aspect to the book, though wrestling with it is completely voluntary. Kids who choose to do so will be able to read the book just for its adventures: bears, kidnapping, slavery, prison, competition, and a castle made of ice.
As for me, I'm working on extension games and activities that will allow kids to experience more fully the connection between math and music.