Until very recently, assessment was thought of as something teachers do at the end of a course; something teachers do to the students to evaluate them. Classroom assessments were few and far between, consisting of perhaps a few quizzes before the final exam. Feedback from the instructor came only in the form of a letter grade, and students were offered little opportunity to revisit or revise their work before moving on to a new topic.
Today, assessment is changing. More and more instructors are assessing students not just at the end of a semester, but frequently during class, as a part of instruction. Their goal is to make student thinking visible, both to themselves and to students, so that the understanding can be monitored before any grades are assigned. Formative assessment can be used to inform instructional practices and to give students advice without their worrying about grades. In this sense, assessments are done for the students and the instructor.
Formative assessment involves everything from pre-assessment to the many ways you might collect data about student understanding throughout learning experiences in a course. All this data is used to inform instructional decisions—what you need to review or teach from another perspective—and to help in assigning grades.