Supporting Instructional Growth in Mathematics (Project SIGMa)

Good news to share: another research grant has been funded by the National Science Foundation. Yay!

For this project, my research team and I will be working with Math for America in Los Angeles to design a video-based coaching method for their Master Teacher Fellow program.

sigma logo

This is what we pitched to the NSF:

This study addresses the need to develop processes for adequate and timely feedback to inform mathematics teachers’ instructional improvement goals. In this study, we propose using design-based implementation research to develop and investigate a process for documenting mathematics teachers’ instruction in a way that is close to classroom practice and contributes to teachers’ ongoing pedagogical sense making. The practical contribution will be a framework for formative feedback for mathematics teachers’ learning in and from practice. The intellectual contribution will be a theory of mathematics teachers’ learning, as they move from typical to more ambitious forms of teaching in the context of urban secondary schools. Both the practical and theoretical products can inform the design of professional development and boost other instructional improvement efforts.

In a recent Spencer study, my team and I investigated how teachers used standardized test data to inform their instruction. (That team was Mollie Appelgate, Jason Brasel, Brette Garner, Britnie Kane, and Jonee Wilson.)

Part of the theory of accountability policies like No Child Left Behind is that students fail to learn because teachers do not always know what they know. By providing teachers with better information, teachers can adjust instruction and reach more students. There are a few ways we saw that theory break down. First, the standardized test data did not always come back to teachers in a timely fashion. It doesn’t really help teachers adjust  instruction when the information arrives in September about students they taught last May. Second, the standardized test data took a lot of translation to apply to what teachers did in their classroom. Most of the time, teachers used data to identify frequently challenging topics and simply re-taught them. So students got basically the same instruction again, instead of instruction that had been modified to address central misunderstandings. We called this “more of the same,” which is not synonymous with better instruction. Finally, there were a lot of issues of alignment. Part of how schools and districts addressed the first problem on this list was by giving interim assessments –– basically mini versions of year end tests. Often, the instruments were designed in-house and thus not psychometrically validated, so they may have not always measured what they purported to measure. Other times, districts bought off-the-shelf interim assessments whose items had been developed in the traditional (and more expensive) manner. However, these tests seldom aligned to the curriculum. You can read the synopsis here.

Accountability theory’s central idea  ––  giving teachers feedback –– seemed important. We saw where that version broke down, so we wanted to figure out a way to give feedback that was closer to what happens in the classroom and doesn’t require so much translation to improve instruction. Data-informed action is a good idea, we just wanted to think about better kinds of data. We plan to use a dual video coaching system — yet to be developed — to help teachers make sharper interpretations of what is happening in their classrooms.

Why did we partner MfA LA? When I reviewed the literature on teachers’ professional learning, they seemed to be hitting all the marks of what we know to be effective professional development. They focus on content knowledge; organize their work around materials that can be used in the classroom; focus on specific instructional practices; they have a coherent and multifaceted professional development program; and they garner the support of teacher communities. Despite hitting all of these marks, the program knows it can do more to support teachers.

This is where I, as a researcher, get to make conjectures. I looked at the professional development literature and compared it to what we know about teacher learning. MfA may hit all the marks in the PD literature, but when we look at what we know about learning, we can start to see some gaps.

*Conjecture 1 Professional learning activities need to address teachers’ existing concepts about and practices for teaching.

 

Conjecture 2 Professional learning activities need to align with teachers’ personal goals for their learning.

 

Conjecture 3 Professional learning activities need to draw on knowledge of accomplished teaching.

 

*Conjecture 4 Professional learning activities need to respond to issues that come up in teachers’ ongoing instruction

 

*Conjecture 5 Professional learning activities need to provide adequate and timely feedback on teachers’ attempts to improve their instructional practice to support their ongoing efforts.

 

Conjecture 6 Professional learning activities should provide teachers with a community of like-minded colleagues to learn with and garner support from as they work through the challenges inevitable in transformative learning.

 

*Conjecture 7 Professional learning activities should provide teachers with rich images of their own classroom teaching.

 

The conjectures with * are the ones we will use to design our two camera coaching method.

We need to work out the details (that’s the research!) but  teacher’s instruction will be recorded with two cameras, one to capture their perspective on significant teaching moments and a second to capture an entire class session. The first self-archiving, point-of-view camera will be mounted on the teacher’s head. When the teacher decides that a moment of classroom discourse illustrates work toward her learning goal, she will press a button on a remote worn around her wrist that will archive video of that interaction, starting 30 seconds prior to her noticing the event. (As weird as it sounds, it has been used successfully by Elizabeth Dyer and Miriam Sherin!)  The act of archiving encodes the moment as significant and worthy of reflection. For example, if a teacher’s learning goal is to incorporate the CCSSM practice of justification into her classroom discourse, she will archive moments that she thinks illustrate her efforts to get students to justify their reasoning. Simultaneously, a second tablet-based camera would record the entire class session using Swivl®. Swivl® is a capture app installed in the tablet. It works with a robot tripod and tracks the teacher as she moves around the room, allowing for a teacher-centered recording of the whole class session. Extending the prior example, the tablet-based recording will allow project team members to review the class session to identify moments where the teacher might support students’ justifying their reasoning but did not do so. The second recording also captures the overall lesson, capturing some of the lesson tone and classroom dynamics that are a critical context for the archived interactions. Through a discussion and comparison of what the teachers capture and what the project team notices, teachers will receive feedback on their work toward their learning goals. We will design this coaching system to address the starred conjectures in the table

Anyway, I am super excited about this project. I am working with amazing graduate students: Grace Chen, Brette Garner, and Samantha Marshall. Plus, my partners at MfA LA: Darryl Yong and Pam Mason.

I will keep you posted!

 

 

 

Instructional Activities and Core Practices for Teaching

This past week, I had the great pleasure of spending a few days thinking with some very smart people about issues in teacher education. They included Judith Warren Little, Magdalene Lampert, Elham Kazemi, Nicole Louie, Jessica Charles, Lynsey Gibbons, and Britnie Kane. We had a few other folks interested in teacher education drop in and chat with us too.

From left to right: Nicole Louie, Jessica Charles, Lynsey Gibbons, Elham Kazemi, Magdalene Lampert, Judith Warren Little, me, and Britnie Kane

From left to right: Nicole Louie, Jessica Charles, Lynsey Gibbons, Elham Kazemi, Magdalene Lampert, Judith Warren Little, me, and Britnie Kane

Right now, debates rage about the value of teacher education. The folks around this particular table take teacher education very seriously. We all aim for what is currently called ambitious teaching — ambitious in the sense that it aims to engage all students in rich and complex forms of content.

To pull a couple of examples from their work, Magdalene currently works with the Boston Teacher Residency. Borrowing the idea of residency from medical education, she and her colleagues work to figure out effective ways to use long-term partnerships with practicing teachers and schools as the grounds for teacher education. Elham has been working with in-service elementary teachers in the Seattle areas, focusing her work with one particular school on mathematics instruction.

Both of these projects have had some impressive successes. BTR has done extremely well in recruiting and retaining teachers, and Elham’s project has dramatically improved math instruction on multiple measures.

Magdalene and Elham are a part of the Core Practices Consortium, a group of scholars from University of Washington, University of Michigan, UCLA, Notre Dame, University of Wisconsin, University of Colorado and the Boston Teacher residency.

If you want to read more details, here is a description of a conference session they did describing their work. Here is a journal article and here is a website cataloging some core practices by content area.

The basic goal of the Consortium is to identify practices that capture specific, routine aspects of teaching that require professional judgment and stand to raise the quality of content-specific instruction in K-12 schools. Because teaching requires thinking and doing, these activities create focal points for the work of teacher education.

Some examples of instructional activities include things like interactive close reading in elementary literacy or pressing students to construct evidence-based explanations in secondary science.

I purposefully used the examples above because I think they are smart choices for this work, but my reservations remain nonetheless.

As we discussed and shared and learned together, I still wonder if it’s possible to adequately capture teaching practice –– in the broad meaning of the word that I know my colleagues intend — through the specification of routine activities.

Let me explain.

I’ll start with a definition of teaching. I’ll extend David Cohen’s formulation slightly and claim that teaching is the deliberate cultivation of learning in others in distinctive teaching situations. The “in others” highlights its relational dependence. The “teaching situation” part points to is context-dependence.

This elaborated definition cuts to the very heart of my concern. While aspects of teaching are undoubtedly routine, their meaning comes out through the particulars of relationships and situations, with all the complexity of that setting and those histories.

My favorite example to illustrate this idea comes from a conversation I had with Peg Cagle. We were talking about whether to put names on publicly displayed student work.

In my working class high school where many of my students’ had histories of struggle in mathematics, I visibly put my students’ names on the work I hung on classroom walls. They needed to have ownership of their mathematical ideas, even in their formative stages.

Peg, on the other hand, taught in a magnet program for gifted students. Many of her students worried about being discovered as an impostor in the gifted track, making them fearful of others’ judgments. She kept her students’ names off of work-in-progress in her room.

Did we have different practices? At a certain level of description, yes. I put names on and she kept them off.

However, on a deeper level, we were attending to the same issue: the social vulnerability of asking students to share what they think. We both wanted to encourage our students to do so in ways that were attentive to their prior histories with mathematics.

So while what we did was different, at a deeper, conceptual level, however, we were alert to the particulars of our teaching situations and modified our practice to meet the goal of students sharing their ideas.

I don’t offer this example to negate the idea of instructional activities. I am convinced that there is value in this approach. I share the example to point out that teaching, because of its contextuality, may not operate like other professions where the meaning does not so depend on the relationships among the people involved.

More than Reflection: How Teachers Learn from Each Other

I have had a really interesting twitter conversation this morning with Luann Lee, a science teacher who is thinking hard about instructional coaching. Luann wrote a post suggesting that, instead of instructional coaching, it might make more sense to use resources to buy an assistant teacher for her and her colleagues to free them up to do more visits to each other’s classrooms.

While I agree that this may be a great idea for Luann and her colleagues, I do not think it would work in every circumstance. Recently, my graduate student Britnie Kane and I did an analysis of teachers’ collaborative conversations. They were all math teachers working in urban schools and involved in a professional development project. The key difference among the three groups of teachers was their level of accomplishment in what we call “ambitious teaching” — the kind of instruction that involves all students in high levels of content.

So we spent a year (I am not kidding) analyzing and coding 17 hours of video to make sense of the differences in how they talked about problems of teaching.

Using quantitative and qualitative analyses, here is what we found:

  1. Time spent on problems of practice increased with sophistication in ambitious teaching.
    While the average length of conversations about any one problem in the Sophisticated and Emergent Groups were relatively similar (11 min 26 s versus 9 min and 4 s, respectively), the average time spent in both of these groups was more than twice that of the Beginning Group (4 min 15 s). The differences between the Beginning Group and the other groups were significant (Sophisticated Group, p=0.0055; Emergent, p=0.0003).
  2. The Sophisticated Group consistently considered broad ideas of teaching in light of particular instances of practice.
    Their talk was neither overly vague (e.g., “we need to do more spiraling”) or overly specific (e.g., only telling stories). If they introduced a teaching idea like “spiraling”, it was always linked to examples from the past (what happened that makes them think that) and plans for the future (what will more spiraling look like in their classroom). The linking of general ideas to particulars was a hallmark of their talk, as was the constant pivoting between past and future classroom events.
  3. The Sophisticated Group typically linked discussions of students to issues of instructional decisions and content-specific learning. 

    The other groups might have a good debrief about why a lesson did not go as planned, but then the analysis would not be taken up in subsequent conversation. The Sophisticated group consistently linked any discussion of student learning to instructional decisions and content issues, while the other groups might reflect on these issues but not connect them back up.

In the end, we saw that all reflection is not created equal. The analogy we drew was to the differences between learning from a text when you are a strong versus a weak reader. Good readers can make inferences and extend their understanding, while weaker readers struggle to decode text and can’t see the larger implications. In other words, there is more to gain from reflective discussion once you have already learned quite a bit about teaching, making it an unequally valuable resource for different teachers.

When we looked at conversations with a strong facilitator, a lot of these differences disappeared. For this reason, we think that good facilitators and coaches can make for better conversations. (We know that they don’t always — but that is another post for another day.)

We also think our analysis sheds light on what it means to understand a concept in teaching. You can’t just have an abstract idea of student learning, scaffolding, cognitively demanding tasks, or status, and then know how to use it in your classroom. You need to see multiple examples, in different situations over time. By understanding the connections across these examples, you can really dig into what these things mean.

I guess this is why good teaching is so hard.