In this section, we looked at problems that were solved using different forms of representation. Consider why each type of representation was appropriate for the given mathematical task. Remember that one of the goals in working with representations in the middle grades is to help students move from their own non-conventional forms of representation to using conventional forms. These problems are good examples of how we can introduce students to conventional forms of representation by using situations that have meaning for the students.

As we think about how to encourage students to use representations in their mathematical work, we should consider the process we use to show our own thinking through the use of appropriate notations. We begin by creating a representation from the given data -- whether geometric, algebraic, or even a story with two variables. We then select a representation to model the problem. This is the tricky part -- are we going to draw a picture, make a table or graph, use technology? Often, there is more than one representation to use for a problem, such as in the Building Viewpoints task. If this is the case, we need to choose the one that works best for the given situation. Finally, we need to use our representations to communicate the mathematical knowledge to others.

  Add to your journal