Fostering students' ability and understanding depends greatly on how teachers communicate about mathematics and help their students develop communication skills. By improving your own ability to read about, write about, and discuss mathematics, you improve your students' ability to do the same, as well as your effectiveness in the classroom.

One point to remember is that, for teacher or student, communication is part of all the Process Standards. Using Cuisenaire Rods to help solve fraction problems enables you to communicate your thinking about the relationships between the fractions. For example, you begin to see the need for equivalent fractions and common-size pieces in order to combine fractions. You also see that the unit whole may vary from one example to another; for example, in one problem, the light-green rod may represent "1," whereas another problem may use the purple rod to represent "1." These are important fundamental ideas in understanding fractions.

As we work with the rods, we are likely to use a combination of both informal and precise mathematical language -- just as our students do when tackling similar problems. Like them, we may find some aspects of a problem difficult to communicate about precisely. Turning visual mathematical insights into clear communication is often a challenging task -- but it's a very rewarding one, for student and teacher alike. As we communicate about varied aspects of mathematics -- representations, methods, results, and even mistakes -- our conceptual understanding becomes richer.

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