Embedded Formative Assessment. Dylan Wiliam

that some statements might be more than a single type of figurative language. Once the students realize that there can be more than one answer, the class responds correctly to statements two, three, and four. About half the students, however, indicate that they think statement five is a simile. The teacher then leads a whole-class discussion during which students give their reasons for why they think statement five is a simile or a metaphor, and after a few minutes, all the students agree that it is a metaphor, because the statement does not include like or as.

      8. An AP calculus teacher has been teaching students about graph sketching and wants to check quickly that the students have grasped the main principles. She asks the students, “Please sketch the graph of y = 1 over 1 + x².” Each student sketches the graph on a whiteboard and holds it up for the teacher to see. The teacher sees that the class understands and moves on.

      In each of these eight examples, the teachers use evidence to elicit and interpret student achievement and make a decision about what to do next, but whether this is enough to make each of these an example of formative assessment is a matter of some debate.

      I often ask teachers which of these eight cases they would regard as formative, and there is rarely any consensus. In example 1, assessment modifies instruction, especially if you regard the supervisor as the teacher and the teachers as her students, but many people are unhappy that it is two years before the changes occur. Similar concerns are raised about example 2, especially since the students on whom the data are collected do not benefit from the process, and, moreover, it is not clear that next year’s algebra 1 students will have the same problems. Example 3 raises concerns for many teachers that assessment is being used in a punitive way, but as Harvard economist Roland Fryer (2014) points out, some students need more instructional time to reach proficiency on their state’s standards. He calls this the basic physics of education: “If your students are falling behind, you have two choices: spend more time in school or convince the high-performing schools to give their kids four-day weekends. The key is to change the ratio.”

      Requiring students to attend additional classes on Saturdays may not be ideal, especially in rural areas where transportation requirements create additional difficulties. However, a school that provides additional instruction on Saturdays for students who need it has at least found a solution to the problem of how it is going to get more instructional input to the students who need it. Any school that hopes to “close the gap” without having a way of getting more instructional input to the students who need it is just paying lip service to the idea of equality.

      Example 5 is interesting because it is a districtwide policy in which the formative assessment process is hardwired into the school year. To create the slack needed for the system to work, teachers have to prioritize content, which is difficult because teachers and administrators are generally told that all the state standards are essential. The problem is that most state standards contain so much material that only the fastest-learning students have any chance of mastering the required material in the time available. Robert Marzano and his colleagues asked teachers how much time they would need to cover all the content in their state standards for each year, and the average figure was twenty months (Marzano, Kendall, & Gaddy, 1999).

      While that figure may have been reduced somewhat in states that have adopted variants of the Common Core State Standards, the fact is that most states specify considerably more content for their students to learn than can possibly be achieved by most students in the time available. The teacher could, of course, cover the required material at a rate that guarantees all the standards are covered, but that would mean that most students would be floundering. In Philadelphia’s school system, as discussed previously, teachers have to make choices about which of the standards are essential and which are desirable, teach the prioritized standards, and then assess. If students have made enough progress, then the teacher can spend some of the “re-teaching week” on new material, but if a substantial number of students have not made enough progress on the essential standards, they remain the priority. The defining feature of this system is that the teacher does not know what he or she will be teaching in the re-teaching week until she sees how the students have done on the assessment.

      Most teachers, in my experience, are happy to regard example 5 as an example of formative assessment, although some teachers suggest that twelve periods is a long time to wait to find out whether students are learning anything. On the other hand, many teachers are disturbed by example 6 because the teacher discarded the students’ responses, rather than giving students individual feedback. However, this rather misses the point, because the reason that the teacher used exit passes in this situation was because she did not want to give students individual feedback. Her aim was to decide how to start the next lesson, as I discovered when I asked her why she had discarded the cards.

       Me: Why did you discard the exit passes?

      Teacher: Because I know where to start tomorrow’s lesson.

       Me: What did you decide?

      Teacher: They mostly got it right. I’m moving on.

       Me: What would you have done if they weren’t ready to move on?

      Teacher: I would have taught it again, but slower and louder. I’m joking of course. I would have taught it again, but in a different way.

       Me: What would you have done if half the students had answered correctly and half of the students had answered incorrectly?