Reflections by Deborah Loewenberg Ball

It has been an enormous privilege to design the keynote address for this conference and to wander around the poster hall and listen in on the panels. I am still writing some comments and questions about the particular posters I visited, conversations to which I listened, and things I thought about as I read all that others contributed to this amazing event. I have never before participated in a virtual conference, and this event has piqued my curiosity in many ways. It is clear to me that the careful design and planning that went into this matter enormously. I know firsthand how much work Joni and Brian and their colleagues do to make this as smooth, aesthetically pleasant, and usable as possible. I know some – not all – of the behind-the-scenes work that goes on to make this happen. It took weeks of work to make it possible to share video with all of you, for instance. And that the site works so flawlessly is no small feat. The thing about a work like this conference is that if it is successful, a great deal of what makes it so remains invisible. I want to start with thanks and appreciation to the organizers and designers for all their hard and careful work, and to my colleague, Kara Suzuka, for all her support and work in helping me prepare my contributions to the conference.

But a conference like this would also lie flat and never become a conference were it not for all the contributions of the participants. The posters are amazing and provide views of the hard work that instructional improvement requires. I agree with my fellow discussants that the posters are a rich resource for considering the work of designers and professional developers in the change process, and how the environments of your work affect your efforts. The posters and the ensuing discussions also make visible the power of an emerging community of professional developers and innovators who too often work in isolation. The work of innovation can be learned, and having colleagues to talk with, and contexts in which to talk, get help, be questioned, and even have one's work critiqued, are all important parts of learning. Even more explicit discussion of the work of innovation and change would help. What are the core problems? What are strategies for their solution? Are some obstacles actually convertible to resources? What knowledge and skill are important for the work of innovators? Or of professional developers? Are we creating adequate learning opportunities for such work?

I'd like to raise four issues for our collective consideration, based on the reflections you have stimulated in me:

First, what do we mean by "practice"? I started this by referring to the importance of studying "practice" as a ground for understanding better what content teachers need to use in the course of their work. Jim Stigler correctly pointed out that we want to mean something more than lessons and interactive teaching when we talk about practice. I agree completely. In our analyses, we consider classroom lessons in detail, because we are convinced that much of the important work of teaching remains invisible and hence difficult to learn. My colleague, Jennifer Lewis, makes the point that while we realize that teachers' thinking, decisions, and reflections are invisible (because they are in teachers' heads), we fail to realize that a great deal of what is right in front of us is also invisible because we lack frames to see what teachers are engaged in doing. One thing that has struck me when I have listened to Japanese teachers discussing lessons is that they have a so much richer vocabulary for teaching moves, for the architecture of a lesson, for student contributions. This vocabulary also makes it possible to see -- and therefore study and learn – more of the work of teaching.

But lessons are also only one part of "practice." In our analyses, we examine planning -- for example, the details of task adaptation or design -- and reflection -- for example, analyzing where students are in a curricular territory and where they need to go. We study what is involved in clarifying goals. And we even examine what is involved in explaining and justifying one's curriculum to one's principal, or to parents. These, too, require mathematical knowledge, and can be studied and learned under the heading of "practice." I routinely ask my preservice teachers to design a letter to send home to the parents of their children in their student teaching placement about the unit they are teaching. I have learned that how they understand the content they are teaching plays a large role in their ability to communicate about it clearly in ways that parents will understand and appreciate. These are non-trivial tasks of teaching, and yet, we too often construe "practice" as only the in-class part of the work.

Finally, teaching is not the only site of practice with which we are concerned. The work of professional development, curriculum design, implementation, and innovation are all also practices. Too often we assume that people who engage in this sort of work simply do it, and we fail to talk about the knowledge and skill demanded. We don't analyze sufficiently the manner and style that matter, or the stance that can help in the chaotic and complex environments in which we work. Moreover, we do not even talk enough about design. What does it take to design a viable program, intervention, or workshop? What has to be considered, and why? How does one learn to do that? This has clearly been a large part of what this LSC community has been engaged in. But more explicitness about instructional improvement as a practice might help support and improve our efforts.

Second, what is the role of critique, dissent, and resistance in learning and change? The past decade has seen a huge wave of conflict around mathematics education, with challenges pressing on us from all directions -- -- from professional mathematicians, the public, and within the education community. We have often experienced these challenges as attacks, and they have resulted in difficulties in working for improvement. Yet, consider this: Our efforts in mathematics education have been of interest to the public. That there has been as much debate as there has means that people care about students' opportunities to learn mathematics. Science educators among us might covet that attention. Mathematics is considered important, and what students learn a crucial national issue. Science education still suffers from being too often relegated to the late afternoon, to being a lower priority.

Those of you who have had firsthand experience with the mathematics education conflicts might wonder how in the world I can see this as a resource! Well, first, it has been possible to gain resources for work in mathematics education. Yes, sometimes it is hard to make the case for a particular program or initiative or course of action. But there are resources, and the improvement of mathematics instruction is considered a priority. Second, we have been able to recruit leading disciplinary experts to work on problems of mathematics education. A wide range of mathematicians and others who use mathematics professionally have been willing to devote extra time to work on curriculum, professional development, and teacher education. True, their efforts have been at times destructive rather than constructive. But they are interested, and they actually (for the most part) care. Herein lies our challenge: How, in mathematics education, can we use this attention and concern as a resource for improvement? How can we use critique for useful improvement of our goals and strategies? We are not always right. We do sometimes advocate for goals that should be questioned, and revised. We have more to learn, and can profit from skeptics. But how to do this is not obvious, and is, in fact, one of the crucial skills of the practice of innovation to which I referred above. Too often we merely share war stories or complaints about our critics. Too rarely do we share ideas about how to use -- and even invite -- critique and skepticism. How can we convert ill-placed attacks to constructive engagement? And how, in science education, can we mobilize more attention and resources, more critique and concern, more intensity of public and disciplinary engagement? Third, teachers who "resist" may be sensing problems worth talking about. How often do we encourage resisters to express their ideas, to pursue them, to engage all of us in their worries? They may also be signaling, significantly, that the incentives for change are low. How can we take their "resistance" as a clue for what we have failed to consider, or design, or attend to? When we push out resisters, or argue back, we fail to take advantage of a set of fertile ideas that have the potential to strengthen, not derail, efforts to improve mathematics or science instruction. Again, however, the skills involved in doing this are not something we generally discuss or seek to develop.

Third, I want to underscore Jim Stigler's repeated comment that a common curriculum seems a crucial resource for constructive work on instructional improvement. To be sure, no curriculum is flawless. Still, the common engagement in planning, teaching, and analysis of particular lesson, contents, and approaches offer a concrete medium for detailed and productive work on practice. Many of the posters offer evidence for this. Because we have no national or shared curriculum in the U.S., using curriculum materials to provide the common working space for instructional improvement is likely an important element of successful change efforts. It is more than the common professional community that joint work on curriculum provides. We need to keep our eye on the fact that we are interested in improving the teaching and learning of mathematics and science, and in building shared professional knowledge and capacity for continuous improvement of instruction. Curriculum ensures that the details and the substance of the community's work will be about goals, about content, about students' understanding of that content, and about instructional tasks and representations.

Finally, I'll end with a puzzle, echoing George Hein's question. How do concerns for equity play a role in the design of our efforts to improve mathematics and science instruction? Is there something we need to be alert to that is more than good teaching and good curriculum? Are there strategic sites for work that would ensure that our efforts address the critical inequities in students' access, opportunities, learning, and development? Our relative silence on this in this context is a bit surprising, and makes me wonder what it means. My colleagues and I have been struggling to gain strategic leverage on the problems in our work with preservice teachers, to get past the rhetoric of "all students" or "high expectations." I would be very interested to learn how, in your work, you are conceiving and addressing the vast problems of educational inequity that permeate U.S. schooling. Working on the ground, in practice, where are the key points for attention inside of practice, that are concrete, and about what teachers and school leaders do? How can we be specific and provide scaffolds for such attentive work? And what is our evidence that what we seek to promote will actually make a difference in broadening access, participation, and success in mathematics and science?