#### Answer

As the study did not mention randomly selecting 2nd-graders of similar math
levels to begin with, it is an observational study using inferential techniques.
There are several possible explanations that piano lessons could improve a
student’s math ability in fractions and proportions.
1. Piano keys are separated and yet grouped together which may improve
a student's sense of fractions and proportions.
2. Music has rhythm and beats, each note (long or short) is part of a whole,
this resembles math problems of fractions and proportions.
3. While playing a piano, a student uses a sheet music or imagines one in his or her head,
the structure of a sheet music contains multiple lines which divide the different regions of notes
both vertically and horizontally. This may improve a student's visualization and understanding of
fractions and proportions.