In order for teachers to increase their effectiveness, it's helpful to explore how communication relates to developing understanding of mathematical concepts. Our own experience with fractions may have been limited to relatively simple operations -- we may not have explored fractions in situations other than those requiring computation.

In this section, we will examine your own, rather than your students', approach to a question. The following problem requires more than simply computing with fractions. As you do the problem, think about how you are approaching it, what difficulties you are encountering, and how you are communicating your thinking -- then read the solution to see how we approached the problem.

  Explore communication using the Shaded/Unshaded Circles problem