students. One necessary step is to be able to analyze and interpret students' responses to questions, or their actions in problem situations. In short, teachers need to use data from assessment in order to make appropriate inferences that form the basis of their feedback. This can require careful analysis to probe the meanings behind what students say, write, or do. Questions of good quality are those that evoke evidence relevant to critical points of understanding, but students may often respond in ways that may be hard to interpret. There are many studies that show that seemingly incorrect responses to questions are evidence of a misinterpretation of the question rather than of misunderstanding of the idea being questioned (NRC, 1981). Difficulties with language or in the contexts or purposes of a question are often the cause. Although such difficulties can undermine the validity of formal tests, they need not undermine formative work by the teacher, provided that follow-up questions are used to check, as will happen if question responses are shared and explored in discussion with the teacher or with peers.
A teacher's interpretation of a student response, questions, and action will be related to that teacher's understanding of the concept or skill that is at issue. Thus a solid understanding of the subject matter being taught is essential. Performance criteria need to be based on authentic subject matter goals and on a depth of understanding of the subject matter. For formal tests, sound scoring requires careful rubrics—assessment tools that articulate criteria for differentiating between performance levels—that help the assessor to distinguish between the fully correct, the partially correct, and the incorrect response. Such rubrics are even more useful if the variation of common ways in which answers can be partially correct are identified, inasmuch as each partially correct response requires a different kind of help from a teacher in helping a student to progress in overcoming particular obstacles. For an example of a rubric, see Table 4-3 in Chapter 4.
Similarly, less formal assessments also may benefit from a rubric-type tool for interpretation. For example, during a classroom discussion, a teacher can draw on her previous experience with a student's particular difficulty in order to formulate the most helpful oral response.
Underpinning such appropriate rubrics or frameworks will be the teacher 's conception of how a student learns both generally and in the particular topic of study. A vision of learning will inform teachers' guidance to students. Addressing issues related