ABSTRACT
The term representation refers both to process and product- in other words, to the act of capturing a mathematical concept or relationship in some form and to the form itself. Representation consistently moves from concrete to abstract as new concepts are encountered and understood. All the meanings of representation are important to consider in school mathematics. The ultimate goal is to have students function abstractly with their mathematical understandings because that is the most convenient and accepted way to communicate about such things. If the work of a student reflects the understanding of the concept, teacher can help that student progress to a more sophisticated or acceptable representation of the idea. Technology comes into play as a means to represent ideas too. Young children represent numbers of objects via sets. Not all fractions are less than one. Fractions also represent the concept of a ratio.
