By Kristin Klingensmith

IFL Mathematics fellow

Almost every school out there has tried to implement some sort of professional learning community, or PLC. Many of those schools started PLCs with the right intentions and provided time for PLCs to meet regularly to work collaboratively with the goal of increasing academic performance of students. And though implemented with worthwhile intentions, in many cases the exchange of ideas and the collaborative work did not lead to increases in student learning.

For a PLC’s collective efforts to result in enhanced student learning, the work of the PLC must attain these five characteristics (adapted from Vescio, Ross, & Adams, 2008):

• Shared values and norms about the group’s collective work

• Clear and consistent focus on student learning

• Reflective dialogue that is ongoing and relates content, instruction, and student learning

• Deprivatized practice through sharing personal classroom cases

• Collaborative solving of problems of practice

Though all of these characteristics are important for the PLC’s work, when it comes to growing and refining teacher practice in a way that results in enhanced learning for students, it is essential that the PLC engages in discussions that are reflective and ongoing and that relate content, student thinking, and instruction. Discussions that draw on the relationship among content, the ways students think about the content, and the pedagogy used to support student understanding of the content are focused on the instructional triangle (Ball, 1999). Using the instructional triangle to guide discussions and plan lessons reduces the “chanciness” of learning occurring because teachers are intentionally making connections among content, student thinking, and pedagogy.

The following transcript segment comes from a PLC of early childhood educators. The PLC has been working on using questions to elicit student thinking, one of the NCTM effective teaching practices, to increase the amount of student talk during mathematics explorations; this is their pedagogical goal.

The activity they are discussing involves transferring water between containers of different dimensions (from container A to B) so students can reason about the water maintaining its volume, even when it looks different, because no water was added and no water was lost. The teachers have already discussed the mathematical goal for the activity and are now discussing the inquiry they will pose to students.

T1: We will show the students the two A cups with water. Maybe we should ask them, “What do you notice about these two cups?”

T4: Haha, my students are going to say they both have water.

T4: They are probably going to push them together to see if the water is the same height.

T3: They’re clear. They are the same.

T1: We will show the students the two A cups with water. Maybe we should ask them, “What do you notice about these two cups?”

T4: Haha, my students are going to say they both have water.

T3: They’re clear. They are the same.

T2: I think mine will say they are the same too. I’ll ask them to tell me how they are the same.

T4: What if we asked, “Which cup has more water?”

T3: I’m not sure I want to ask that because it sounds like one cup has more water than the other, and it doesn’t.

T2: Maybe we should ask, “What do you notice about the amounts of water in the two containers?” instead of, “What do you notice about the two cups?” or “Which cup has more water?”

T4: Okay, that does sound different. It is not as leading as asking which of the cups has more water.

T1: I agree “What do you notice about the amounts of water in the two containers” draws their attention to the amount of water in each cup without leading them to more or less. They can respond a lot of different ways which means we can learn about their thinking.

T2: What do you think they will say and do?

T3: I think they’ll use their hand to show the water is the same height.

T3: So now we pour the water from A to B. We want them to think about the amount of water in each cup.

T2: Mine will say they are the same and maybe try explain why and how they are the same.

T2: Oh, yeah, so now that they have said the amounts of water are the same, maybe we can say “Tell me about the amounts of water in the two containers now.”

T4: A lot of my students are going to say that there is more water in A than in B because the water in A is taller than the water in B. What do you think your students will say and do?

In this short section of transcript, we see four teachers working collaboratively to refine the inquiry they will use throughout the activity to elicit student thinking.  In refining their practice, they considered the mathematical idea students were to explore, the conditions of the exploration, and various ways students might respond. 

PLCs that engage regularly in discussions similar to this one are more likely to enhance student learning because among other things they engage in

• Naming a mathematical content goal or a pedagogical goal linked to content,

• Discussing the underlying meaning of the mathematics, and

• Accounting for the specific ways students will solve tasks or demonstrate an understanding of mathematical ideas.

Whether you find yourself engaging as a member of a PLC or supporting the work of PLCs in your building, remember the value of using the instructional triangle as a guide and framework for collaborative discussions.  PLC’s may have many aims: increasing student performance, deepening student understanding, increasing the use of high-leverage practices.  When considering any of these aims, a PLC will benefit from ensuring that in all discussions, tethering deep content knowledge to student thinking around that content to teacher practice that supports student understanding of the content is critical and effective.


Vescio, V., Ross, D., Adams, A. (2008). A review of research on the impact of professional learning communities on teaching practice and student learning. Teaching and Teacher Education, 24(1), 81

Tagged with: High-Leverage Teaching Practices, Leadership, Math