Gen Esmende Teaches the 95%
How to turn the abstract into the concrete and the alienating into the accessible.
Fantastic summer school session last week, folks. Several of you offered some great analysis of all the ways Colin Campbell supported the cognitive and social needs of a student named Zander, all in 90 seconds of class time.
Again, for the rest of July, I’m going light on original content, instead posting one of my private reserve classroom video clips with the goal of helping all of us understand what it takes to educate the kids that much of education technology writes off.
I’ll also feature some of your comments from last week, and offer a bit of commentary of recent edtech headlines, including this week a review of teacher concerns about being replaced by AI and an interesting set of data from Khan Academy.
What is Gen Esmende up to here?
In just 58 seconds, Gen Esmende takes mathematics that many students consider irredeemable—solving systems of equations—and manages to extract from that mathematics a lively conversation, a lively debate even. How did she do that? How do her curriculum, technology, and pedagogy work together in that moment?
Teacher (Esmende):
I'm gonna be passing out these cards and don't work on solving it, hold off from solving.
I would like you to take some time just to look at it and see which ones do you say is, watch this, do from here, talk to your partner about which ones do you feel is the least difficult, and which ones are the most difficult. So have a conversation with your partner right now about which one do you feel is least difficult, which one will be most difficult?
Class
(indistinct chatter)
Teacher
So least difficult, which one would be the least difficult for you to solve here, which would be easier for you to solve? Yes.
Student
A.
Teacher
A, so why do you say this would be the least difficult?
Student
It gives us our Y solution, so we just need solve.
Teacher
So you're already given your Y here. Okay, anyone else wanna show what you think is the least difficult and why?
Open thread with a conversation starter:
How does this approach to solving systems of equations differ from how you experienced the same math as a kid?
If you’re a member of the large group of students who feel unengaged when asked to work operationally on those numbers and variables (Is that group 95% of students? Who can say? But yes.) what does this question do for you?
Featured Comments
Fantastic analysis of Colin Campbell’s teaching from you folks last week. The fact that no two people shared exactly the same analysis of a 90 second clip of teaching points to the complexity of this work.
That "I believe in you" as he walked away from the table was so wholesome!
He actually listened to Zander. He gave him a heads up that he was going to ask him to share with the class.
This is often called “warm calling” as opposed to “cold calling,” an approach that I suspect would have the exact opposite effect on Zander.
When Zander reads the story, Colin is asking the class to visualize the story. That is also a good approach. Others are not passively listening when they visualize it.
“Visualize” is very different mental work than, say, “solve” or “calculate,” work that the larger group of students can engage and succeed in.
jwr:
The thing that stands out to me is using student-created stories to explore math concepts. While the verbal content of those stories might be similar to a traditional word problem, students are likely to be more engaged and develop a deeper understanding when they are the ones coming up with the stories.
An excellent ability to walk backwards through a sea of chair legs without falling over.
Odds & Ends
¶ An idea that seems both fun and fraught. A teacher sends the following into an image generator: a) a picture of the student, b) their career aspirations. The image generator creates a picture of them older and in that career. Generative AI: it’s neat!
¶ As More AI Tools Emerge in Education, so Does Concern Among Teachers About Being Replaced. Judging from Jeff Young’s sources, the “concern” here comes from policymakers and higher education exclusively, not from K-12 teachers at all. Young interviews two of them at the end of his article, and they are both like “yeah, lol, okay.”
“It’s not even on my radar, because what I bring to the classroom is something that AI cannot replicate,” said Lauren Reynolds, a third grade teacher at Riverwood Elementary School in Oklahoma City. “I have that human connection. I’m getting to know my kids on an individual basis. I’m reading more than just what they’re telling me.”
Christina Matasavage, a STEM teacher at Belton Preparatory Academy in South Carolina, said she thinks the COVID shutdowns and emergency pivots to distance learning proved that gadgets can’t step in and replace human instructors. “I think we figured out that teachers are very much needed when COVID happened and we went virtual. People figured out very [quickly] that we cannot be replaced” with tech.
¶ This research brief on generative AI from Goldman Sachs is pretty far from my usual edtech playing field, but I found it extremely fascinating. When confronted with the, shall we say, very slow build-up of killer apps and compelling use cases for generative AI, boosters will often say, “Well the internet took a long time to find its footing too,” and this Goldman Sachs analyst says, “well hold on.”
Many people attempt to compare AI today to the early days of the internet. But even in its infancy, the internet was a low-cost technology solution that enabled e-commerce to replace costly incumbent solutions. Amazon could sell books at a lower cost than Barnes & Noble because it didn’t have to maintain costly brick-and-mortar locations. Fast forward three decades, and Web 2.0 is still providing cheaper solutions that are disrupting more expensive solutions, such as Uber displacing limousine services. While the question of whether AI technology will ever deliver on the promise many people are excited about today is certainly debatable, the less debatable point is that AI technology is exceptionally expensive, and to justify those costs, the technology must be able to solve complex problems, which it isn’t designed to do.
¶ Pat Yongpradit is the Chief Academic Officer of Code.org, the sort of job that involves lots of travel, emails, the occasional appearance in front of Congress, etc. In spite of those demands, he has recently signed up as a substitute teacher locally to “keep my skills sharp and my perspective real.” Personally, I'm halfway towards my goal of teaching 12 classes this year, which I set for similar reasons. It's a large investment of time and energy (because few jobs are as time- or energy-consuming as teaching) but it is the best and perhaps only inoculation against the epidemic of magical thinking that is ripping through edtech right now. If you work in edtech, protect yourself! Teach a class! Pat: I’m gonna check in with you at the semester break to see how many times you answered the sub call.
¶ Khan Academy has released a fascinating data set—a non-random sample of ~200 student conversations with Khanmigo. It’s a test set meant to help the field evaluate the relative efficacy of different LLM-based tutors. That’s a valuable service for many in edtech, I’m sure. But for those of us who suspect there is a pretty low ceiling on the efficacy of chatbot tutors overall, this relative comparison is something like asking, “Which kind of bear—Black, Grizzly, or Polar—is the best babysitter for my toddler?” At this point, I would prefer instead to see some very basic descriptive stats about student interactions with chatbots. What does a random sample of 200 student conversations with Khanmigo look like? How many of them last more than a couple of turns? How many of them could we classify as something more productive than “just screwing around”? When students get an answer wrong and see the invitation to get tutored by Khanmigo, how many of them take up that invitation versus just typing in another answer and checking it? A lot of providers of chatbot tutors have assumed affirmative answers to questions of product-market fit that, for me, are very much unsettled.
¶ In “Exorcising us of the Primer,” Andy Matuschak writes about the Neil Stephenson novel that set him and so many education technologists on a path towards personalized learning. I appreciate how he’s reckoning with the appeal of that vision and using whatever was pure about it to imagine new possibilities for learning.
Emotions are powerful and immediate, so if you can harness an emotion -- any emotion -- and link it to mathematical insight, you create a visceral experience for the student: the initial insight is immediate ("ughh that looks horrible!"; "pffft, that one would be so easy!") and they can marshal reasons for justifying that insight *after the fact*; thus creating the sense of having intuition or natural insight before "learning" anything.
Now every student has some expertise. Now the stage is set: the student's feelings towards the easiest and hardest problems are *different* (e.g. confident about A but intimidated by X) but clearly of the *same* type. Suddenly there is a natural motivation to discover how the two are related ("can we transform X so that it would be more like A?"). I'll often follow this up by asking students if they could think of ways we could make A appear more like X, without affecting the solution; now they're thinking like a teacher.
Implicitly, it also reinforces an important lesson in learning: feelings *aren't* facts. You might be intimidated by X, it might look impossible but now you see it's on the same spectrum as A, which is not intimidating, so you know not be afraid of a new problem simply because it looks hard.
This is one of my favourite approaches to use. It is especially effective with intimidating content *because* of the strong emotional response. In some variations, I also emphasize to my students that this really is how mathematicians work: we look at a problem and notice what we don't like about it ("hmm, this would be a lot easier if we didn't have this part") and this emotional response can often be trusted to guide us towards an appropriate approach. Students learn that mathematical intuition and common intuition are not fundamentally different -- and who doesn't feel great about being "a natural"?! It feels wonderful knowing you can trust yourself.
Another variation on this approach is to ask "if you could change one thing about this problem, what would change?"; however, it's more appropriate at a later stage, when students have already developed a sense of the diversity of possible problems.
Giving students the opportunity to choose the "least difficult" of problems, offering student agency - giving them a choice and an entry into their learning. However, it also provides those who are confident to be looking for the most challenging to solve if they want. I recall advanced students who would jump to looking for the MOST difficult to answer, looking for that challenge, too. Ms. Esmende also includes the discussion between students giving voice, and then, I'm sure, she would use routines for students to explain the reasoning and continue with the lesson from there.