Last week, educate4life posted the following comment on Grading Formative and Summative Assessments by Rick DuFour:

I am new to this forum but stumbled upon this thread. I am a high school mathematics teacher. I have a few comments and am interested in your response. The school I am teaching at has an “open access” policy. That is, any student can take any class regardless of their previous performance. In addition to this, I teach closer to 200 students, not 150. That is, five (5) sections at forty (40) students. Does formative assessment work when students are misplaced? In theory, formative assessment sounds spot-on. However, when we (teachers) are dealing with increased class size and students without an adequate foundation, does the formative process give us information that we do not already know? I guess what I am asking is, what are the requirements in order for this model to be successful/meaningful? In mathematics, do the students need to “pass” the summative assessments in previous classes in order to have valid formative assessments?

Rick DuFour’s response to educate4life’s comment follows:

The common formative assessment process in a PLC is effective only if the school has a plan for providing students who are lacking in skills with additional time and support for learning those skills in a way that is timely, directive and systematic and does not remove the student from new direct instruction. It is unrealistic to assume that an individual teacher with 200 students can provide intervention in the classroom at the same time that he or she is also expected to be moving forward with teaching the knowledge and skills students are expected to acquire in the course. Without a plan for systematic intervention, your school will not realize the benefits of common formative assessments.

That being said, Benjamin Bloom’s research in the teaching of math found that teachers get better results when they begin the course with a brief pre-assessment of the skills students must  have in order to be successful in the unit they are about to teach. They discover areas where students are lacking those skills, and then instead of beginning new content, the begin with several days of instruction aimed at the prerequisite skills. They repeat this process for every unit, asking, "Which skills must students have in order to be successful in this unit, and how do I know if they have them?" The process works best when it is done by a collaborative team of teachers and the schedule is designed to have some of them teaching in the same period. They give the pre-assessment, look at the results, and then divide the students between them. One might take the group that needs support in learning the new skills, another works some students to practice those skills, and another presents practical problems to students who are called upon to apply the skills. After several days of this, the students return to their homeroom teacher and the new unit begins.

One might think that this process would have an adverse impact on student achievement because teachers couldn’t cover as much content. In fact, Bloom found just that opposite. The fact that students had acquired the necessary skills enabled teachers to move through the content more quickly and the results were dramatically higher. You can read about this in an article Bloom wrote years ago for Phi Delta Kappan magazine called "The two-sigma effect."