Coaching Letter #220

This has been an exceptionally busy time. I have several writing projects that I’m behind on, I’ve done several workshops in several states, and we are just about to start what used to be Peter Week but is now Peter Fortnight, when we host two weeks of workshops presented by Peter Liljedahl, the author of Building Thinking Classrooms, in Manchester and Hamden. I have lots of thoughts to share about BTC, but those will have to wait. This Coaching Letter is in response to the news of the death of Assata Shakur.

I think you can be forgiven for not knowing who Assata Shakur was—she’s not exactly a household name, and I was surprised to see that her obituaryappeared in the New York Times. And I only came across her because a line from her autobiography showed up in a Linus Quotes cartoon : “No one is going to give you the education you need to overthrow them”. (Linus Quotes is a collection of quotations made to look like they appear in Peanuts cartoons—brilliant.)

So I read her autobiography, called Assata: An Autobiography. And she is not a particularly warm or sympathetic character; but I get the impression that she would not really care what I thought of her, and I can certainly respect that. But she does have a lot to say about what I would call troublesome knowledge.

I learned the term troublesome knowledge and a related idea, threshold concepts, from my friend and colleague Kerry Lord, who is frequently the source of useful ideas and pithy phrasings. Here is a full treatment of these constructs, but I’ve done my best to summarize them below.

Threshold concepts are core ideas within a discipline that, when grasped, transform a learner’s perception and understanding. They represent a gateway or threshold that, once crossed, fundamentally changes how a student thinks about and engages with the subject matter. These concepts are often transformative, irreversible, and potentially troublesome.

Troublesome knowledge refers to concepts or ideas within a subject that students find particularly difficult or challenging to grasp. These concepts might challenge their preconceptions, beliefs, or previously held understanding, causing cognitive dissonance. They are often essential for deeper understanding but can be initially perplexing or uncomfortable for learners. Here are some examples of things that kids have a hard time getting their heads around: the fact that it’s colder in winter is not because of the Earth’s distance from the sun (even Harvard graduates struggle with this one—see this very amusing but also disturbing video); matter is mostly empty space and particles are in constant motion; 1/5 is larger than 1/10; multiplying two negatives yields a positive (that’s one that I still can’t explain).

Threshold concepts and troublesome knowledge are closely related to transformational learning. Transformational learning involves a profound shift in a learner’s perspective, allowing them to think and perceive the world in new ways. When students grapple with troublesome knowledge and eventually grasp threshold concepts, it often leads to transformational learning experiences.

Here are just a few examples of threshold concepts that have led me to think differently about what I see in classrooms over the years:

1. Wait time (Rowe, 1974). Everyone knows about wait time. But in my experience, most educators do not know that the research distinguishes between wait time 1 and wait time 2, and wait time 2 is the one that really matters if you want students to expand their thinking. Here’s a slide deck with some useful findings/quotations from the research—including the finding that if you want a measure indicating expectations for student performance, wait time is a good one: teachers provide less wait time for students whom they perceive to be less capable.
2. Cognitive load theory (Sweller,1988). Once you understand that we all only have so much bandwidth, and anything that distracts us from the task at hand lowers the attention and processing power that we can bring to that task, you think differently about the visual landscape of classrooms. Don’t hate me, but that means that those sports posters need to go, and so do those bulletin boards with the Hallowe’en/Thanksgiving/St. Patrick’s Day decorations, and the clutter on desks and bookshelves. Same goes for noise, whether it’s traffic noise or the smooth jazz that is played during independent writing time. Nix it. See Tom’s blog post for a more elegant and deep discussion of cognitive load. And Zach Groshell’s new book, Just Tell Them, has a nice summary of the research on distraction.
3. Stereotype Threat (Steele, 1997): Once you realize that performance gaps are not just about preparation but about identity and expectations, you fundamentally shift how you interpret test results, classroom participation, and “grit” narratives. One of the counterintuitive ideas here is that students subject to stereotype threat care more about how they perform—it’s the caring that imposes additional cognitive load, reducing the bandwidth that students have available to devote to the task that’s going to be judged. Steele’s Whistling Vivaldi is a must-read, and so is this article on wise feedback, and Cohen’s Belonging also belongs in that category; see particularly what he has to say about situation crafting—the deliberate moves teachers make to reduce stereotype threat and increase belonging.
4. Cognitive demand (Stein & Smith, 1998). Tasks have an inherent level of difficulty, and teachers make choices all the time that either maintain or lower that challenge. For a really nice summary of this, see Tom’s blog post on the subject. One you know this, it makes you think differently about how teachers structure questions, to what extent they scaffold (see Juli Dixon’s great blog post on just-in-case versus just-in-time), and the cost-benefit ratio of differentiation
5. Productive struggle (Hiebert & Grouws, 2007). This one feels like old news now, but it wasn’t always. The idea comes from research in mathematics, summarized by Hiebert & Grouws: “We believe that two features of classroom mathematics teaching facilitate students’ conceptual development (and perhaps mathematical proficiency)—explicit attention to connections among ideas, facts, and procedures, and engagement of students in struggling with important mathematics. We believe both features are justified by not only the theoretical arguments but also the empirical data. We have not identified all of the teaching actions that might call students’ attention to relevant connections or engage them in productive struggle, but we have described a sample of strategies (e.g., posing problems that require making connections and then working out these problems in ways that make the connections visible for students).” This turns out to be a difficult concept for educators in two different ways. There are teachers who have a very, very hard time not stepping in to help students whom they perceive as struggling, frequently lowering cognitive demand unnecessarily and detrimentally. And then there are those who characterize productive struggle as teachers just letting students flail around, which they see as inefficient and malpractice—and indeed, if this was what productive struggle really was, they would be right. But it’s not so they’re wrong. There is nothing in the research that supports the idea that productive struggle is anything other than a planned instructional practice that requires teacher preparation, anticipation, and engagement (and therefore should not be confused with minimally guided instruction but, by the same token, just allowing kids to struggle without a plan for resolving misconceptions and successfully building new knowledge is just struggle—it’s the productive part that makes it productive struggle).

What makes some of these threshold concepts also troublesome knowledge is not that educators have a hard time understanding them from an intellectual standpoint (in the same way that young kids can’t grasp that the earth goes around the sun), but that they (the concepts) frequently challenge the mental models that educators hold about what good teaching looks like, like it’s the teacher’s job to make the classroom a cozy place, or to help kids as much as possible, or to keep up a brisk pace during instruction.

So what does this have to do with Assata Shakur? She was very astute in her writing about how educators/education deals with knowledge that challenges the prevailing mental models, about key historical figures in particular. Here she is on George Washington:

I didn’t know what a fool they had made out of me until i grew up and started to read real history. Not only was George Washington probably a big liar, but he had once sold a slave for a keg of rum. Here they had this old craka slavemaster, who didn’t give a damn about Black people, and they had me, an unwitting little Black child, doing a play in his honor. When George Washington was fighting for freedom in the Revolutionary War, he was fighting for the freedom of “whites only.” Rich whites, at that. After the so-called Revolution, you couldn’t vote of you were a white man and you owned a plot of land. The Revolutionary War was led by some rich white boys who got tired of paying heavy taxes to the king. It didn’t have anything at all to do with freedom, justice, and equality for all.

And Abraham Lincoln:

Little did i know that Lincoln was an archracist who had openly expressed his disdain for Black people. He was of the opinion that Black people should be forcibly deported to Africa or anywhere else. We had been taught that the Civil War was fought to free the slaves, and it was not until i was in college that i learned that the Civil War was fought for economic reasons. The fact that “official” slavery was abolished was only incidental.

But she is also deeply appreciative of teachers who were deliberate in what I think we could label schema-building—teaching about the richness of history and ideas and the myriad connections that help make meaning of the world and why it is the way it is. Here’s what she says about her fifth grade teacher:

She introduced us to art, literature, and philosophy. I remember studying the French Revolution in her class. She made names like Marie Antoinette, Charles Corday, and Robespierre come alive. She talked about philosophers like Rousseau who influenced the thinking of the period and about how the French Revolution was influenced by the amerikan Revolution. She even showed us pictures of the art and architecture of the period. She was the first teacher (one of a very few) who taught subjects as if they related to each other. Before i was in her class, i would never have imagined that history was connected to art, that philosophy was connected to science, and so on.

Assata understood that knowledge is power, but also complicated, contested, and fraught. And it seems to me that, at this exact moment in our profession and our society, we desperately need to be reminded of that. All our students deserve teachers like Mrs. Z, Assata’s fifth grade teacher, who taught a knowledge-rich curriculum and made it relevant to her students, giving them a thick and robust understanding of the world so that they gain, as Assata puts it, “the ability to think for themselves.”

As always, if I can help you at all, or if you want any other resources based on this Letter, please don’t hesitate to reach out. Best, Isobel