Leading Learning

David Brazer's blog discusses practical issues in education leadership while linking to theory and research

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A Persistent Problem: Factoring Polynomials

Today, I pick up the conversation with Sandra, the Algebra 1 team leader, where we left off last time. She comes to see me about a week later, having thought more about her aborted attempt to introduce a new method of factoring into the Algebra 1 team’s teaching.

Sandra begins, “I thought a lot about your comment that my solution was searching for a problem and that my approach was putting the problem all on the shoulders of the students. It seems to me that our teachers are not fully taking responsibility for the factoring problem because they are not yet thinking about what they should do differently. If my idea didn’t happen to grab them, for some unknown reason, then they would forget about it as soon as they left the meeting. So, what do I do?”

The truth is, I don’t know how to solve the factoring problem. I probably can’t factor a polynomial myself. But my job is not to give Sandra the answer, even though that is the role into which most of us cast leaders. “You’re in charge, you fix it.” I can’t accept that role even if I were tempted to do so. I simply don’t know enough about high school math curriculum and instruction. Instead of taking on the responsibility of giving teachers “best practices,” I am better off remembering my aspiration to lead learning for lasting results. I need to think through how to help Sandra move from problem articulation though action planning, assisting her along the way.

“Sandra,” I ask, “do the Algebra 1 teachers think that factoring polynomials is a problem?” “There you go again,” she replies. “The problem is so obvious. We’ve got large proportions of students earning D’s and F’s and we complain in nearly every meeting that the students don’t know how to factor.” “Ok, let me put this differently,” I say. “Do the teachers on your team own the problem? Do they think they have a role in creating it?” “Oh, no way!” Sandra bursts out. “They think it goes back to middle school and the kids not learning basic operations, math concepts, and on and on. They can fill an entire 45-minute meeting pointing out what our students didn’t learn in middle school. In the last few minutes they will all agree that the Algebra 1 curriculum is a mile wide and an inch deep, so they need to rush on and can’t deal with students’ learning gaps along the way.”

The puzzle for Sandra is to get her teachers to stop blaming circumstances outside of themselves and their classrooms for the factoring problem. The student context is real and must be considered, but progress will not be made until teachers look at what they do influence. Preaching won’t work. The teachers will not listen or, worse, they will stop attending team meetings. Here is where data become important. Osterman & Kottkamp (2004) write persuasively about how to use data to unpack teaching problems that no one wants to own. The collaborative processes involved make the work a little more complex than it may seem on the surface, but for now it is important to give Sandra an anchor for working with her teachers.

“I would like to suggest,” I say, “that you mine the data on factoring that you have from the past couple of years of Algebra 1 common assessments. If you find little or no growth in students’ ability to factor after they come to our high school, then it seems to me that puts your team on the road toward understanding the teaching problem.”

Sandra sits in silence for several moments, then replies soberly, “I think we have the information sitting around, but getting access to it and organizing it is a big job. I don’t know where I’ll find the time. I’m not the department chair so I don’t even have a released period.”

Now we come to a point of reckoning for me as principal. I’m brought face-to-face with the fact that I may be asking teachers to do something—analyze common assessment data for a specific learning problem—without having built the organizational and personal capacity for them to do so. I have a responsibility either to wrest some additional full-time equivalent (FTE) for my teacher corps from the central office or find it within my existing staffing formula to provide on-site data assistance if I want busy teachers to do this work. In the meantime, I’ll need to patch something together to help Sandra.

“Sandra, I understand your time dilemma and I want to help. If you trust the mathematics curriculum specialist from the central office, I’m going to ask the assistant superintendent for instruction to give us some of her time to help you mine the data. She knows how to use the district’s data warehouse and I think she could save you a lot of time. I don’t want her to give you answers. I just want her to give you data you and your team members can analyze, possibly with some additional help from the specialist.”

“That would be great,” Sandra replies, “but I see this taking a long time. Everyone has a busy schedule and meanwhile large numbers of kids continue to fail in this all-important gateway course.” “I understand the urgency, but it will take time to bring your teachers around to understanding the problem anyway and we know we won’t do any worse in the meantime. Let me rough out a timeline for working on this problem and you let me know if it makes sense. It’s now just past the middle of February. I think if we can get the specialist working with you in the next week or so, there is enough meeting time for you and your team to gain a deeper understanding of the problem and maybe some of the root causes by the end of the school year. I will pledge workshop money to you and your team to spend a couple of intensive weeks during the summer to create a strategy for strengthening teaching and learning of factoring by the beginning of the next school year. How does that sound to you?”

Sandra smiles. “You’re ever the optimist, David. I’m willing to give it a try. I think that one or two of my teachers will work with me on understanding the problem and we might pull in one or two more with the incentive of workshop pay. If you get me some help, I’ll take another run at this. I really think we can do better.”

As Sandra leaves, I pick up the phone to call the assistant superintendent for instruction. Fingers crossed, I’m hoping I can deliver.


Osterman, K., & Kottkamp, R. (2004). Reflective practice for educators: Professional development to improve student learning (2nd ed.). Thousand Oaks, CA: Corwin Press.


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Group Inertia: Where Promising Ideas Go to Die

Blogger’s note: When I started this blog last year I was worried about being able to keep it up. As you can see, my concerns were warranted. It has been nearly 10 months since my last post. My apologies to anyone who might have been waiting for the next one. I am committed to doing better.

Two people responded to my April 27, 2014 post (though they did so to me personally, rather than by leaving a comment) with essentially the same frustration. Having read my vignette from research they wanted to know what might have been done to make the learning experience more meaningful for teachers and more impactful on student learning. In response, I’ve decided to put on my principal’s hat for a few weeks. What I am about to say may seem simplistic to some, but it represents how I think about these kinds of problems from a principal’s perspective.

I’ll begin where the story left off with an imagined dialogue between the chair of the teacher collaborative team, who I’ll name Sandra, and myself. Let’s imagine that Sandra made an appointment to see me and walks into my office:

“David, I just don’t know about our effort to work with collaborative teams. I presented my Algebra 1 team with a great new way of factoring polynomials and they just sat there with no response. Only Mary, my special education co-teacher, and myself even tried to implement the idea. No one wanted to talk about. This is just so discouraging. It feels like such a waste of time.”

I respond, “Do you want to improve the situation or disband your Algebra 1 team?” “Of course I want to improve the situation,” Sandra replies, “I really believe in the power of collaboration to improve teaching and learning.” “I do, too,” I say. “As principal, I am striving to make this a powerful lever to improve student learning and overall school performance.”

Sandra, in her eagerness, short circuited the collaborative team process by presenting a solution to a problem about which no one had thought seriously. This is a common difficulty for energetic teachers (or anyone, for that matter) who want to make a difference and are convinced they have a good idea. Short on time and strong in their passion to implement ideas that have caught their imagination, teachers and administrators often fail as advocates for their pet ideas. The result can be resignation that change will never happen, or private trial and error in one or two classrooms. My challenge as principal would be to help Sandra see that she needs a different process to bring along teachers who presently are disengaged from her team. But I cannot simply tell her what to do. I need to help her discover a new path and I need to provide the time and resources she needs to follow it.

“Sandra,” I begin, “What is the problem your factoring method was intended to solve?” “What are you talking about? Of course the problem is that many Algebra 1 students cannot factor polynomials, preventing them from succeeding in this course and beyond.” “Ok, I understand, but that is only the student’s problem. What is the teaching problem?” “Oh, you mean pedagogy, I guess,” Sandra replies. “I hadn’t really figured that out. I just know the students cannot do it.”

Sandra has fallen into a trap that has been set by more than a decade of high-stakes, high publicity accountability. The way into the trap is a bit convoluted, but it starts with the disaggregation of student data. Knowing which clusters of students are not meeting standards is certainly helpful. Some districts, such as the one featured in the research discussed in the last post, insist that teachers understand and work on the achievement of individual students, another potentially positive step. But now the trap is set.

With a sharp focus on student achievement, teachers we have observed in our research tend to think and talk about students alone. They ask, “What does the student know and what is she/he able to do?” and “Why didn’t the students absorb what I taught?” Good questions, but the next one is equally important, and rarely asked. When teachers know that students are not succeeding on tasks such as factoring, an important question follows: “What could change in my teaching that would improve these students’ knowledge and skills so they can perform the task?” In fairness to Sandra, she tacitly asked that question and explicitly answered it with her new factoring strategy. So, why didn’t the other teachers go along?

No one joined Sandra in the new factoring method because they did not see or agree with the link between the problem and what Sandra proposed to solve it. Skeptical, or perhaps never even interested, they endured the meeting and dispersed to their classrooms, doing what they always do. Sandra’s new method requires effort and may actually fail, thus reducing motivation for anyone else to move away from their more comfortable routines in the absence of compelling reasons to do so.

I believe that what Sandra needs is a longer timeline and an inquiry-based approach to collaboration in order to address the complex teaching problem of factoring polynomials. She may benefit from a strategy I will begin to describe in my next post.