ably ways that can be systematically and reliably reduced to quantitative form. Knowledge and understanding also need to be probed in multiple ways, thus ensuring that a memorized definition does not mask misinformation or misunderstanding.

Assessments originate from different parts of the educational system, including administrators and teachers. But a particularly important form of assessment is students’ self-assessment. Engaging students in assessment of their own thinking and performance allows them to be more self-directive in planning, pursuing, monitoring, and correcting the course of their own learning. Self-assessment nurtures discovery, teamwork, communication, and conceptual connections.

In a review of more than 580 articles on formative assessment, Black and Wiliam (1998a) point out that “students should be trained in self-assessment, so that they can understand the main purposes of their learning and thus what they need to achieve.” Black and Wiliam also found that improved formative assessment — including self-assessment — was most effective in raising the performance of students at the low end of the performance scale, although students who perform well also benefit from better formative assessment. This approach to assessment therefore narrows the gap in performance between the highest and lowest achievers.

Involving students in assessment both reduces the burden on teachers and lets students know what’s expected of them. Unless students can see the criteria by which they will be judged and examples of successful performance, assessment becomes a game of guessing what’s in the teacher’s head. Students frequently fail to make explicit the connection between what they have just done and the question or problem posed. In this respect, it is not surprising that lower-achieving students benefit the most from learning the criteria for success and being shown examples of how to achieve these criteria.

One way of involving students in assessment is to engage them in devising the scoring guide for a task or project. Their first person statements, “I explain my ideas clearly and in detail,” and “I used words, numbers, drawings, tables, diagrams, or graphs to show my ideas,” are the students’ translations of the performance standards for inquiry abilities. Giving students the rubric before they start does not mean giving them the “correct answer” to their investigation. Rather, it is giving them the criteria by which the quality of their conclusions will be judged.

An example of such criteria can be