Richard DuFour

Richard DuFour, EdD, was a public school educator for 34 years. A prolific author and sought-after consultant, he is recognized as one of the leading authorities on helping school practitioners implement the PLC at Work™ process.

Teachers Key to Reversing High Failure Rate in Math

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 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.


Michael Bresk

Thank you very much for this Blog and for the information contained. If you had made a personal visit to our school and to our Math department you could have made a report that was virtually the same as the contents of this blog! I believe that the teachers in our department are highly qualified and highly motivated to succeed. I also believe that communication is what is preventing us from having a world class math department.
All of the excuses offered in the school are excuses I have heard myself at my school and I am sad to say frequently emanating from my own mouth. From this point on the excuses stop. I can see on other blogs that the implementation of a PLC environment into a school will have dramatic effects on student outcomes. Therefore I am making it my personal mission to establish a PLC for my school. The seeds are all there, we do have meetings to discuss the use of common tests and curriculum meetings to discuss book selection and adoption of new state standards. Our ‘meetings’, while fruitful, can be much more effective and numerous if all members are able to contribute via electronic submissions.
As a new teacher of some four years, I believe that the improvement of the math department can be made with the sharing of teaching methods, the sharing of skill set needs and the improvement of dialog with each other to have a cohesive approach to teaching the subject. Virtually all of what I use in my classroom in the way of strategies, I have learned (stolen) from other teachers. My proposal is to make the sharing of ideas more streamlined. Several teachers have adopted practices I use in my classroom and I see this as the particular answer to improving the delivery of our services to our students.
I was particularly impressed with the recommendations discussed of requiring the students to make corrections to the errors made on exams. I encourage my students to make errors a learning tool. I offer ten points of grade improvement when students make corrections to all problems the miss on a test. It works and the students make gains.
I would like some help implementing a PLC for my school and, how to specifically make the PLC a positive experience for all of those teachers who would like to use it. Yes, I believe it can be created from the ground up giving ownership to the teachers!
Thank you very much and please send me the blog names of any Math teachers that have created a ground up approach to this process. Thank you for the blog….it is very motivational.

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Tim Kanold

Dear lmarcellin,

The response is simple and I will place it in terms of an Equity and Access issue as well.

The practice of offering students an Algebra 1 option over a two year period, although well intended, is actually a violation of Equity and Access opportunities for all students. Slowing the Algebra curriculum down not only sorts out the best students from the rest - it also prevents the 2 year students from ever catching up. ( Thus, widening the Access GAP for kids). The better response for students struggling in algebra 1 is the typical PLC response. Keep them in the one year course, but provide additional time and support. In Algebra, the best RTI is a daily required support course tied directly to the prior knowledge skills needed for the lesson that day. Which means the Algebra team of teachers must be willing to teach the same lesson each day and coordinate their calendars.

The second choice for additional support comes through a GAP analysis for the struggling students in order to identify the exact basic skill outcomes that are causing them to fall behind. And then remediating the skill. moreover, though is a change in the teaching of the Algebra itself. As a "Skills Based Course" (Algebra is a series of "How to's" - how to solve, graph, write , etc.) and thus it require a lot more than just a teacher "model " of the skill - it really requires a development of student understanding and development of strategies to perform the skill.

Finally, there is absolutely no research that would affirm a 2 year Algebra course as an effective educational practice and there is a lot of anecdotal evidence against the practice. The current movement in the US is away form the two year Algebra models.

Dr. Timothy Kanold

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I believe the key is teachers and how they use time, both in a collaborative manner as well as in providing student support. Schools that implement the PLC concept understand the necessity of providing support to students during the school day. When students reach the level of algebra 1, they are encountering math in an abstract manner, possibly for the first time. There are two common issues that students have: first, they lack the understanding of basic math concepts, so they are unable to transfer those skills to algebraic skills that are similar in concept. Second, they struggle with the need to actually prepare for math class, since many of these students were able to pass with little or no extra effort prior to the algebra 1 year.

How can teachers work together to address this? It is vital that there is vertical communication between the algebra teachers and those who teach the pre-algebra course, but it goes beyond that. Teachers in grades 8 and below must be including algebraic concepts and vocabulary in their lessons, and hopefully the school has included this in the math curriculum for each school year.

If the teachers are meeting and communicating in a collaborative manner, then I suggest considering a two year algebra class that beings in grade 8 and finishes in grade 9. The advantages are numerous: students in grade 8 are exposed to the rigor of algebra within the structure of a middle school year, not when they are also adjusting to high school; the one variable we do not control - time - is built into the schedule and allows the grade 8 teacher to address remediation needs within the class time; students can complete a year of algebra by the end of grade 9, allowing them time to take a second year of algebra as well as geometry, usually required for college acceptance.

What is the key to accomplishing this? Teachers who collaborate and who set high standards for students while also providing support for them during the school day.

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Robert M

Have the teachers had the opportunity to reflect on the results and explore (alignment of standards between curriculum and tests, curriculum and assessments) why these results occur year after year?

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Thank you for the clear guidelines for developing a powerful and functioning PLC to support students in our Algebra courses. I'm curious about a practice at our high school. Students take Algebra A for one year and then Algebra B for the next year. The practice seems to have a strong historical foothold in the dept, but the data shows that the longer students take Algebra, the worse they do on our state assessments. Are there models of moving a dept from a long-standing practice with questionable/unimpressive results to one that will impact student achievement?

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