## Defining Formal Formative Assessment

*formal*as meaning a planned opportunity for all students to share what they know and can do. These activities can take many forms, including homework assignments, exit tickets, and handouts. As an example, in one of the 6th grade math classes we observed, the teacher asked students to complete an exit ticket with the following task: Draw two shapes—one rectangle and one square—so that each has a perimeter of 12 units.

## Windows into Student Thinking

*how*students arrived at an answer, we can be more precise about our next instructional steps. For example, knowing that a student has incorrectly identified which of two fractions is larger is not as informative as knowing that the student only considered the denominators in making her decision (Wiliam, 2011). Only the latter information can help us know where to focus our time and efforts. The key is to create activities and ask questions that make students' thinking explicit.

## A Prescription for Feedback

*descriptive*and

*prescriptive*. A

*descriptive*comment, such as, "Good explanation. You are providing data as evidence to support your claim," lets the student know why something was correct or incorrect. A

*prescriptive*comment, for instance, "Do you have a claim? Where is your evidence? Provide some justification that supports your claim," helps the student know how to improve.

## Moving Forward with Instruction

*why*an answer is correct or incorrect than to provide only correct answers or to hand students their reviewed products without further discussion.

## Balancing Efficiency and Effectiveness

*When you administer formal formative assessments to get a sense of students' thinking, choose a few well-designed questions or prompts.*If you won't review all of the questions, there's no point in asking them. A few well-designed questions are better than many superficial ones. You will want to be able to quickly review students' work and identify their strengths and weakness.In our study, a middle school math teacher asked students to solve one multiplication problem: 2 1/9 × 11/16. The teacher selected this problem because it requires students to complete all the potential steps that might occur when multiplying mixed numbers, including converting a mixed number to a fraction and multiplying two-digit numbers in the numerators, as well arriving at a product that is an improper fraction and deciding what to do with an improper fraction that can only be reduced to a mixed number. With just this one question, she could very quickly see where students were getting hung up.*Briefly review the students' work to determine whether a number of class members made the same mistakes or displayed the same misunderstanding.*If all or almost all students made the same mistake, consider taking action the following day with the whole class by reteaching, modeling, or assigning a new or modified task. In our study, we found that in 92 percent of work samples in which all or almost all of the students missed the same question or questions, teachers left repetitive comments on the work. The teachers could have instead spent that time planning whole-class instruction targeted at the area of misunderstanding.