Principles for Classroom Assessment

The following list of principles for classroom assessment:

1. The main purpose of classroom assessment is to improve learning (Gronlund, 1968; de Lange, 1987; Black & Wiliam, 1998; and many others).

2. The mathematics is embedded in worthwhile (engaging, educative, authentic) problems that are part of the students’ real world.

3. Methods of assessment should be such that they enable students to reveal what they know, rather than what they do not know (Cockroft, 1982).

4. A balanced assessment plan should include multiple and varied opportunities (formats) for students to display and document their achievements (Wiggins, 1992).

5. Tasks should operationalize all the goals of the curricula (not just the “lower” ones). Helpful tools to achieve this are performance standards, including indications of the different levels of mathematical thinking (de Lange, 1987).

6. Grading criteria should be public and consistently applied; and should include examples of earlier grading showing exemplary work and work that is less than exemplary.

7. The assessment process, including scoring and and grading, should be open to students.

8. Students should have opportunities to receive genuine feedback on their work.

9. The quality of a task is not defined by its accessibility to objective scoring, reliability, or validity in the traditional sense but by its authenticity, fairness, and the extent to which it meets the above principles (de Lange, 1987).

These principles form a “checklist” for teachers who take their classroom assessment seriously. But the journey from principles to practice can be long. So we will now turn to a discussion about several key issues in designing and implementing a classroom assessment system.

In the list of principles, the content was mentioned in different ways (relevant, real-world mathematics) and at several levels of mathematical thinking and reasoning because our goal for mathematics education is to enable individuals to deal with the mathematics involved in realworld problems. This is needed for each individual’s current and future private life, occupational life (work or education), and understanding and appreciation of mathematics as a scientific discipline. In other words: We want our students to become mathematically literate.