Professional Knowledge

Saphier imagines a situation where a teacher tells you about a successful classroom practice that’s different from the one you’ve been using. If you believe there’s generally a right and a wrong way to teach something (the effectiveness or “best practices” paradigm), your reaction may be that this colleague is trying to show you up or is patronizing you. But if you view teaching as a vast repertoire of practices that need to be matched to individual classroom situations, you’ll have a different reaction: Hmmm, that’s an interesting alternative. I might want to try it. “That view of professional knowledge not only accepts the legitimacy of different ways of doing things,” says Saphier, “but also encourages debate and professional problem solving.”

Kim Marshall (the Marshall Memo) summarizing Jon Saphier’s article in The Learning Professional, “The Equitable Classroom: Today’s Diverse Student Body Needs Culturally Profiicient Teachers”

I wonder if the perspective that Saphier describes is a distinguishing feature of the teaching profession. He argues that a “best practices” perspective is disconnected with the realities of teaching. A more productive perspective is looking at teaching as a broad repertoire of skills matched to the vagaries of classroom situations. I don’t know much about anything besides teaching, but that seems like a defining feature of the experience of teachers, and one that is less present in other respected professions like medicine and law.

Another point Saphier makes is that, once teachers move away from treating teaching as a set of best practices to be learned, they need to constantly ask themselves what’s working and what’s not, and use assessment evidence to back up their decisions. I find this fascinating. I think formative assessment, broadly speaking, is one of the most important things I can do to improve student learning. Saphier argues that formative assessment can also be an important tool for teacher learning.

I’m curious about the experiences that cause teachers to shift perspectives on skillful teaching, and the school cultures that help to facilitate this process.

Student Engagement

My work on this paper began over 10 years ago with my research on the AHA! experience and the profound effects that these experiences have on students’ beliefs and self-efficacy about mathematics (Liljedahl, 2005). That research showed that even one AHA! experience, on the heels of extended efforts at solving a problem or trying to learn some mathematics, was able to transform the way a student felt about mathematics as well as his or her ability to do mathematics.

-Peter Liljedahl, Building Thinking Classrooms: Conditions for Problem Solving

A convergent observation across psych applications is that behavior change->belief change is easier to accomplish than belief change->behavior change.

-Brian Nosek on Twitter, references here

I often feel confused by student engagement. What does it look like? What creates it? What sustains it? How can I better understand the subtleties of how it plays out in different classroom situations? Engagement feels like a black box. Some inputs go in, engagement may or may not come out, and I don’t have a great understanding of what happens inside the box.

Despite that pessimism, here are two things I think I understand:

  1. Convincing students to be more engaged is really hard
  2. Facilitating situations where students feel successful helps improve that student’s engagement in the future

Students often come to class with deeply ingrained beliefs about who they are and what they are capable of. Convincing them they can reason mathematically is an uphill battle because it goes against the weight of their experience — by the time I teach them, over a decade of it — in math classrooms. If instead I can provide new experiences where students feel successful, where they feel their voice and their ideas are valued, where they have those AHA! moments, I can create a new foundation to build off of and positive momentum for the future.

Where I get confused again is how to facilitate those experiences for every student in class, and to sustain those experiences over time, while meeting the demands of the curriculum. I have some strategies, but when I look honestly at my students and their growth over time it feels like I make progress far more unpredictably than I would like.

“Natural” Teachers

“What explains America’s love affair with the untrained, the unschooled, the uninitiated?” – Peg Cagle

Peg Cagle’s ignite talk above masterfully takes down the trope of the “natural teacher”, arguing that painting some teachers as natural is unrealistic and demeans the teaching profession. I want to expand on her argument and unpack what people often seem to mean when they describe a teacher as a natural.

Walking into a classroom, an average member of the public might describe a new teacher as natural based on surface characteristics that actually aren’t essential to helping students learn. Speaking confidently, explaining ideas clearly, having some content knowledge, and getting students to like you are all things that many humans get good at outside of teaching contexts, and at first glance someone with those skills might appear to be a natural teacher. That’s not to say those skills aren’t important, but if a teacher stops growing there, they are falling short of the potential of impactful teaching.

The heart of teaching is much more subtle, much harder to learn, and much more counterintuitive. Where else but classrooms do people ask questions not to learn the answers, but to provoke thinking in others? Where else do people try to figure out how someone thinks about an idea that they don’t yet understand? Where else do people design an experience with scaffolds for someone who is struggling? Where else do people have to manage a room by both maintaining a thread of instruction and paying attention to the motivation, engagement, and understanding twenty-five individuals? Where else do people design experiences where, multiple times in an hour, they need to react on the fly to something a participant said or understood and possibly change course? These are skills that new teachers are extraordinarily unlikely to find “natural”, and they are only a small subset of the skills that make great teachers great.

Teaching is not natural. And, for many of the uninitiated, seeing someone as a natural means focusing on surface-level features of teaching, cutting away the complexities and challenges that lie under the surface and simplifying the profession down to the lowest common denominator that those outside of it can understand.


Because “Real World”

I’m tired of arguments against a particular practice in education, using the logic that “this would never happen in the ‘real world’, so why are we doing it in classrooms?”. Classrooms, and learning environments more generally, should not be designed to imitate the activities students will do in the real world. They should be designed for learning.

I try to teach my students that the goal of math class is learning, not performing. I caution against focusing on right answers at the expense of what can be learned from a problem or series of problems. In the real world, it is the quality of the work produced — the performance — that matters. In an environment designed for learning, the performance is far less important and can distract from learning.

Research in cognitive science has explored “desirable difficulties” — situations where performance is worse in the moment, but the cognitive demands and deeper processing as a result of those difficulties actually optimize learning. This research suggests that optimizing learning environments for performance in the moment can actually detract from learning, and points to only one of many examples where improving learning can actually be counter-intuitive.

A focus on performance can be more insidious. Anyone who has witnessed teachers taking problems from department- or school-wide assessments and giving them to students the day before a test with a few numbers changed can attest to this. The goal of the workplace is to produce high-quality work, but in that instance, a focus on producing high quality work degrades learning.

I don’t mean to say that education can learn nothing from the workplace. I just mean to say that, as arguments, “students will never experience [x thing] in a job, therefore schools shouldn’t do [x thing]” or “in the workplace, [x thing] happens, therefore schools should do [x thing]” seem to me insufficient to guide teaching and learning.

What’s Next?

When I started teaching, I didn’t enjoy my time in the classroom very much. During hard classes I could barely wait for the bell. And when I sat down to plan my next class, I would stare into space, stumped, stuck thinking about everything that went wrong with the last lesson and unable to plan what to do next.

Now, by the time I get back to my desk after a class the next lesson is often mostly planned. There’s lots of reasons for that, but one shift I’ve noticed is that when I teach, I spend a lot more mental energy thinking about the future. When an activity falls flat or I realize that students understand less than I thought, I respond both by figuring out what to do next in the moment, and thinking about what I’d like to do the next day or the day after to build from where students are based on what I’m seeing.

Noticing this shift reminded me of Lani Horn’s writing on an asset orientation. When thinking or talking about students who struggle, a deficit orientation focuses I can focus on shortcomings and blames the student’s past or experiences out of their control. An asset orientation focuses on their strengths and how they can move them forward from where they are. An asset orientation is forward-looking and solution-oriented. In the same way, I can think during class about what I wish I had done differently, what I wish students had known, or what I wish I had changed. Or, I can focus on what I’m learning about my students in that moment and how I will use that to move forward with their mathematical learning. This doesn’t mean hiding from my mistakes or pretending that a lesson went better than it did. It just means looking at my classroom and students with the perspective of “what’s next?”.


Note to self:

Some words take on meaning as pejoratives, used to denigrate a different perspective without engaging with the substance of that perspective. “Worksheet”, “traditional”, “rote”, many more. Without context, these words aren’t very useful. If I give my students a piece of paper with three problems on it, I might be labeled as giving them a worksheet devoid of understanding. If I cut those problems up and tape them around the room for students to work on in groups, suddenly I’m at the pinnacle of progressive pedagogy. The substance is the same, but the surface features are used to label one approach as better than the other, regardless of the specific context or my goals in that moment.

It’s easy to put someone else down by labeling their teaching with words that have been weaponized by a particular ideology. It’s much harder to speak in specifics about how different pedagogies play out in different classrooms — who they support, who they leave behind, how they build off of each other, and what they actually look like on a minute-by-minute and day-by-day basis. To do so means to value reality over rhetoric, and substance over style. I want to do more of that.

Scientific Knowledge for Teaching

Daniel Willingham writes in a recent article:

[R]esearchers have argued that teachers’ learning should not be limited to practical classroom strategies. The teacher who understands the psychological principles undergirding the recommended strategies will presumably find them more sensible and will see ties between seemingly disparate strategies. Perhaps most important, that teacher will also generalize strategies to novel situations. Teachers need what might be called a mental model of the learner: knowledge of children’s cognitive, emotional, and motivational makeup.

So teachers will benefit from knowing some things about how students learn. But what exactly, would teachers benefit from knowing? Willingham distinguishes between three types of knowledge in science: empirical observations, theoretical statements, and epistemic assumptions. The whole paper is worth a read, but I’d like to focus on one element of his argument that was particularly compelling for me. My paraphrase:

Teachers can benefit from bottom-up knowledge that is built on concrete observations, whether those observations are from research or their own practice. Top-down knowledge that begins with broad theories or generalizations about learning are likely to be less useful.

If teachers focus on bottom-up knowledge, they have the opportunity to buttress their everyday observations in classrooms with additional examples from research into how humans learn, building a rich and experience-based model of how their students learn. This type of knowledge is more likely to be humble; learning is fickle, and a certain practice may work in one context but not in another. Teachers are always learning, observing, and developing a more robust understanding of learning. If teachers focus on top-down knowledge, they come to their experience with broad statements about how students learn that can be adapted to justify a range of practices, separate from any evidence that they are effective for students. Willingham writes:

A statement like “learning is social” could be taken to mean “children learn best in social situations,” which is actually a very different statement–it is a statement about how children behave. But confusing it with “learning is social” could easily lead to thinking that because group discussion is more social than teacher instruction, it is a settled matter that it is more effective for learning, whereas the empirical reality is far more complicated.

In short, top-down knowledge about teaching can be twisted to support a range of ideas, and distances itself from everyday experience. Two examples of where I see this happen:

Cognitive Load Theory 

From a top-down perspective, cognitive load theory is a theory that, in problem solving situations, students’ working memory becomes overloaded, preventing them from learning. This statement could be used to justify any number of teaching practices, and to foreclose entirely any problem-oriented learning. But from a bottom-up perspective, cognitive load theory is a set of experiments in which, under certain conditions, students become overwhelmed by the demands of problem-solving and unable to learn from that experience. This perspective, while only subtly different, sets teachers up to incorporate that knowledge with their own experiences and to approach new situations with some humility — cognitive load theory doesn’t prescribe a course of action, but offers evidence for a practice that seems not to work in some contexts.


From a top-down perspective, constructivism is the perspective that learners actively construct new knowledge. It is often used to support inquiry-oriented approaches to learning, with the justification that if learners are to construct their own knowledge, they need to be active participants in that process. From a bottom-up perspective, constructivism is the recognition that what students learn depends on what they already know, and incorporates both teachers’ experience and research into how prior knowledge can have a large influence on future learning.

In both cases, the shift is away from prescriptive theories that try to make broad statements about best practice, and toward a focus on building a broad base of knowledge for teachers to draw from in their instructional decisions. Rather than coming into the classroom with preconceptions about what learning must look like, a bottom-up approach emphasizes concrete experience, the importance of context, and humility.