Written tasks that request an explanation can offer detailed information concerning students' knowledge to the classroom teacher. The examination of students' written responses for the mathematical systems that are employed (referents), the connections that are displayed (relationships) and the communication methods that are utilized (modes) provides evidence that suggests how the student is making sense of a problem. The purpose of this article is to describe the constructs of referents, relationships and modes and to illustrate how these constructs may be reflected in students' written responses to a decimal task that requests an explanation. This article will also examine sets of responses from two classrooms using the proposed framework to illustrate the type of information that teachers may acquire through the application of this framework.
- Middle school
- Rational numbers