We received a query from a high school principal about the failure rate in algebra in his school. At the end of the first quarter, 44 percent of students were receiving grades of D or F. At the end of the first semester, the rate had increased to 55 percent. When the administration met with the teachers to offer support, teachers took the following positions:

1. The problem was caused by the fact that middle school teachers were not giving students the necessary skills.
2. The teachers had no aggregate data on the achievement of their students because there was no point in the team creating common assessments or reviewing evidence of student learning together. The teachers were already working very hard individually and did not have the energy to work together on this task.
3. There was no need to arrange for reteaching skills because if students did not learn the skills in the first semester they could do so in the second semester.
4. There was no easy way to aggregate data on student achievement because Scantrons, which could readily provide the data, are not conducive to math assessment.
5. Although the teachers agreed it was beneficial to have students make corrections on problems they had missed, they did not require students to do so.

The principal asked for advice. Here is what we said:

There are several things that the math team can do if it wants to reduce the failure rate. The first is to acknowledge that 1) reducing the failure rate is important and 2) changes in the teachers' own practice will contribute to reducing the rate.

Here are some of the things that are being done in schools around the country, all of which have teachers who work hard and are pressed for time:

1. The team should work with eighth-grade teachers to establish the prerequisite skills students must have in order to be successful in algebra and create an assessment to identify whether or not an individual student has those skills. Each middle school teacher should receive the results of the assessment showing how his or her students performed compared to the total group. Middle school teachers can then identify where their students struggle compared to other similar students and can begin to address those problems. If your teachers contend the problem is in the middle school, then you should establish a partnership with those teachers to address the problem rather than allowing it to continue.
2. It would appear from the notes that there is a pre-algebra course in the school. Students who are very deficient in essential skills should be assigned to that course to ensure they acquire the skills. It must be aligned with the algebra course so that exiting pre-algebra students are ready for algebra.
3. Students who are deficient in only a few skills should be placed in algebra, and the first few weeks of algebra should be a review of essential skills. Benjamin Bloom’s research on math classes showed that when teachers began with clarifying the most essential skills, assessing students on those skills, and then teaching the essential skills, they were ultimately able to cover more material and student achievement was dramatically higher.
4. The idea that if students don’t learn an essential skill in the first semester they can pick it up in the second (rather than arranging to give them another opportunity to learn in the first semester) is illogical and refuted by the team’s own evidence. The failure rate, which was horrible in the first semester, was worse in the second. Teams must begin to develop common assessments and review the data to identify immediately when students are having difficulty and who on the team seems to teach that skill better. Teachers must be willing to learn from one another, and there is abundant research on the benefits of common formative assessments in raising student achievement. The argument that Scantrons are not suitable for math is not valid. Adlai Stevenson High School math teachers, who have lowered the failure rate in their courses to 1 percent, use Scantrons constantly to get immediate feedback on where students are having difficulty. Teachers can use homework and individual teacher quizzes to review the students’ work leading to the answer, but students are constantly assessed in math (at the local, state, and national levels) in a format amenable to Scantrons.
5. The team’s argument that there is no benefit from looking collectively at evidence of student learning is only valid if they have no intentions of making any adjustments in their practice or creating plans for providing additional support for students who are struggling. The research on the benefits of this practice is abundant, and I would ask them to explain why that research does not apply to them.
6. I assume the greatest cause of failure is that students are not completing homework. Therefore, the school must create incentives for students who complete homework and require those who do not complete it to lose privileges until it is complete. For example, some schools make homework optional if a student is receiving an A or B. Students work to achieve those grades so they won’t have to do homework. All other students must complete homework as assigned, and if there grade dips below a C, they are assigned to a place where they must complete homework during the school day. In some schools, all freshmen are assigned to a study hall in recognition of the difficulty of the transition from eighth grade to high school. Those students are moved into an intensive guided study hall where someone monitors their homework each day. Others give up their lunch period and go to a working lunch study hall until they are passing. If your school gives students the option of not doing their work, many will choose not to do it. You must be more assertive as a school in taking away that option.
7. If the team agrees that correcting tests is an important tool for learning, it is inconsistent to then leave it up to students as to whether or not they will do the corrections. This should be a standard practice in all classrooms if it will help students learn, and students should have incentives for doing that work.
8. The school should have a process in place that requires students who fail a test to receive additional tutorial support on those skills. The team should have a process in place that allows students to take another assessment to demonstrate that they have achieved the skill. If a student fails a unit test after three weeks, he should remain in math class working on the next skill but be required to put in additional time on the skills he failed. If he can pass the test after continuing to work on the skills, then he should receive the higher grade. That is what formative testing is all about identifying students who don’t get it, requiring them to keep working on the skill, and giving them another opportunity to demonstrate proficiency. The team can’t make this happen alone. It will need the support of the school and structures put in place to ensure students keep working.
9. Instruction should engage students, and teachers must become more skilled at checking for understanding each day in their classroom. One observer said he did not see students doing many problems in class, but teachers said they are checking each student’s work multiple times during class. Which is it?

Here is the crux of the matter. Algebra has been called the single most important course in high school. It represents the window of opportunity through which students must pass to have access to higher education. The majority of students in your school are having that window slammed shut, and your teachers seem unwilling to accept any responsibility for doing anything about it. They call themselves a team, but they are not. They are not working interdependently to achieve a common goal for which they are mutually accountable. They are not developing common assessments to monitor each student’s learning and to inform and improve their practice. They are allowing students the option of failing and shrugging off their failure. They are rejecting suggestions for addressing the problem despite the evidence of the dire results of their current practice and the research in support of those recommended practices. My answer to the question about whether other departments were having secretaries call home would have been, "Other departments don’t have your dismal results, but you are right. This problem won’t be solved by a secretary; it must be solved by you." I would consider the situation you describe as a genuine crisis, and any school that is committed to the students it serves must work together to address that crisis. I have no doubt that the math teachers in your school are working hard, but they have abundant evidence that continuing to do what they have done in the past will result in failure for students. Working hard individually is not enough; the team must begin to work collectively at the right work.

Read Whatever It Takes: How Professional Learning Communities Respond When Kids Don’t Learn. Look at the math results from Stevenson described in Revisiting Professional Learning Communities at Work™: New Insights for Improving Schools. You will learn of a department that helps more students earn honor grades in calculus than any school in Illinois, a school where every BC calculus student earns an honor grade every year, a school where the mode grade is 5, and a school that has dropped the failure rate in all math classes to 1 percent. This did not happen because teachers were detached from the results. Read about Whittier Union High School District on the AllThingsPLC.info website. These schools have a student population that is much more challenging than yours, but they have been spectacularly successful in raising student achievement. Teachers in those schools believed their practices could help students learn to be successful in math, and they committed to searching for the practices that led to that success. A frank and honest assessment of the current reality in your school as depicted by the information you sent suggests your teachers have not made that commitment.