The Core of the Matter Issue #8
What is the mechanism?
My work as a consultant takes me into classrooms in a number of districts. And a frequent observation when on these travels is that students are doing a lot more of their work standing at vertical whiteboards. This is of course in response to Peter Liljedahl’s revolutionary Thinking Classrooms framework, which has blazed through the K-12 landscape over the past 4 years. Yet, this influx of what Peter calls vertical non permanent surfaces (VNPSs), has not necessarily led to drastic shifts in the way teachers teach and students experience mathematics. Now don’t get me wrong, my work routinely affords me the pleasure of seeing plenty of fantastic educators brilliantly delivering equitable and adaptive instruction; however, I am also frequently in the position of viewing a lesson featuring students working at VNPSs where the instruction does not necessarily leverage the potential of the board structure to engage students in cognitively demanding work.
This tension between the ideal version of an instructional reform versus the way it is implemented in practice has historically been one of the largest barriers to sustainable instructional improvement. One of the most vivid examples of this phenomenon is illustrated in David Cohen’s 1990 account of Mrs. Oublier’s perceived instructional transformation in teaching mathematics. After informing us of Mrs O’s recent attendance at a workshop based on California’s recently released math reform framework, Cohen tells us:
“Though her revolution began while the framework was still being written, it was inspired by many of the same ideas. She reports that her math teaching has wound up where the framework intends it to be. Yet as I watched and listened in Mrs. O's classroom, things seemed more complicated. Her teaching does reflect the new framework in many ways. For instance, she had adopted innovative instructional materials and activities, all designed to help students make sense of mathematics. But Mrs. O seemed to treat new mathematical topics as though they were a part of traditional school mathematics. She used the new materials, but used them as though mathematics contained only right and wrong answers. She has revised the curriculum to help students understand math, but she conducts the class in ways that discourage exploration of students' understanding (p. 312).
He continues:
“That melange is part of the fascination of Mrs. O's story. Some observers would agree that she has made a revolution, but others would see only traditional instruction. It is easy to imagine long arguments about which is the real Mrs. O, but they would be the wrong arguments. Mrs. O. is both of these teachers. Her classroom deserves attention partly because such mixtures are quite common in instructional innovations-though they have been little noticed. As teachers and students try to find their way from familiar practices to new ones, they cobble new ideas onto familiar practices (p. 312).”
The last sentence in the above quote, “...they cobble new ideas onto familiar practices,” is precisely how we get a classroom where students are standing at vertical whiteboards, yet not necessarily collaborating with peers to negotiate meaning about mathematics, or engaging in novel and challenging tasks.
This is of course because BTC is not about the boards! Rather, the essence of Building Thinking Classrooms is about getting more students to think harder for longer amounts of time. This is accomplished through giving students challenging things to ponder over, the space to make meaning, and creating the conditions for collective and individual knowledge generation. The boards are certainly a key component of a larger catalyzing process, but they are not the star of the show.
In statistical terms the boards are considered a moderating variable. In other words, if the goal of BTC is to increase mathematics learning, working at the boards is not powerful enough to do this directly. However, they are important in that they make it more likely that the mediator, or the variable that does directly influence the goal, has a better chance of working. In the case of BTC, the mediating variables are mathematical thinking and meaning making.
In order to avoid the creation of future Mrs Os it is important that educators are supported in deconstructing a new instructional reform in order to separate what components are moderators, which can be categorized in terms of format and characteristics, from the mediator, or the actual mechanism that leads to increased student learning. Two things that a district can do to help educators to successfully identify the mechanism in a given instructional practice are to create a shared understanding of high quality instruction across the system, and to make sure that all staff have a deep understanding of how learning happens.
A shared vision of what good looks like is essential. Without a shared target you are creating a space where everyone will operate according to their own mental model of what good teaching is, with no guarantee of alignment across classrooms, grade levels, or schools. This is part of the Mrs. O conundrum. In reading the article it is quite evident that Mrs.O and the piece's author, David Cohen, have two different pictures in their heads of what high quality math instruction looks like. This is why I cringe every time I hear an administrator or coach say something to the effect of, “you are already doing most of these things” when addressing a group of teachers regarding some kind of instructional reform. I try to point out nicely: “No, they are not already doing it, because if they were we wouldn't be having this conversation right now.” What they are doing, by trying to provide reassurance that the change they are asking for is going to be easy, is actually attempting to minimize the conceptual distance between current practice and desired practice. I am also reminded of the wisdom of my colleagues in these situations, who often use the line, “you cannot talk someone into a new mental model.” Instead people need experiences that have the potential to push on their existing schema and force them to think differently. As such, part of cultivating a shared vision of effective instruction must include multiple experiences where people can see and experience the shared target.
Relatedly, having an understanding of how students learn is crucial in being able to decipher the mechanism from form and characteristics when it comes to effective instruction. Once again, the case of Mrs. O provides a particularly salient example. Cohen explains:
“The teacher used a new mathematics curriculum, but used it in a way that conveyed a sense of mathematics as a fixed body of right answers, rather than as a field of inquiry in which people figure out quantitative relations. It is easy to see the framework's ideas in Mrs. O's classroom, but it also is easy to see many points of opposition between the new policy and Mrs. O's approach (p.313).
It is evident from the above quote, that Mrs O views learning as transmission and thus teaches in accordance with that belief. However, learning involves integrating new knowledge with old. It occurs when deep schemata are developed and encoded into long term memory. Schema acquisition is the result of a meaning making process facilitated by the act of thinking. Therefore, if you want learning to occur you need to employ instructional practices whose mechanisms engender deep thinking.
Classroom Connection
What is the mechanism? This is the question that needs to remain top of mind as we work to shift and improve existing practice. More specifically, we need to be able to connect the mechanism of a given practice to current models of learning. To accomplish this will require major shifts in how we currently approach instructional reform. For example, rather than individual teachers trying these things in isolation, we need structures that allow teams of teachers to work collaboratively on instructional improvement. Further, in order to avoid Mrs O’s fate of improvement at the margins, we need teachers to have ample opportunity to experience ambitious and equitable instruction for themselves, as well as with their own students, in order to challenge potential limiting beliefs about what certain students are capable of achieving. In addition, we need to stop using evaluation tools and look-for docs, which often contain detailed descriptions of the moderators of a given practice (i.e. students standing at whiteboards), with no mention of the mediator. This tends to lead to follow-up actions and conversation focused on things that are easy to measure, but have limited impact.
Mrs. O serves as a cautionary tale. She teaches us that the process of transforming instructional practices requires more than just the adoption of new tools and techniques, such as vertical whiteboards. True transformation occurs when the focus moves toward understanding and fostering the mechanisms that drive meaningful learning. The story of Mrs. O illustrates the complexities that arise when teachers simply layer new practices over traditional ones without fundamentally changing their underlying beliefs about learning. To avoid such outcomes, districts must support educators in distinguishing between the surface-level changes (moderators) and the core mechanisms (mediators) of effective instruction. This requires fostering a shared vision of high-quality instruction, providing teachers with ample opportunities for collaborative learning, and ensuring they have a deep understanding of how students learn.
Related Reads
Here is the full story of Mrs O. Definitely worth a read.
In this article, Chris Argyris, describes the heuristic of single and double loop learning, which is a useful frame when thinking about the power of experience to shift practice.
This post from, Evidence Based Education, discusses the idea of lethal mutations and how to avoid them.
In this post, my talented colleague Isobel, lays out why it is so important for districts to develop a shared understanding of high quality instruction.