Man, there's a lot to chew on here (as per usual), but I'll confine myself to the one piece I know a little something about: "Much of what I’m describing in my critiques of personalized learning depend on 'heroic individual teachers' like Liz Clark-Garvey. This is a concern that worries me too and I’m hoping to find some time to write about how we can ensure that teachers like Liz are made, rather than born."
I founded an organization dedicated toward this goal (Deans for Impact) that was/is premised on two basic ideas: (1) We will have more great teaching if teachers have a better understanding of the science of how students learn. (2) Initial teacher education is a good place to focus effort on ensuring (1).
Both of those propositions are debatable, though I'm prepared to defend them still. But I am also happy to *complicate* them with some additional contextual claims borne of lived experience:
(3) Understanding the science of learning means a lot more than just "read about basic ideas from cognitive science." The key is in the *application* of that understanding in real classroom settings with kids. Learning science doesn't tell teachers what to do, but rather, gives them a "mental model" that helps inform the many thousands of pedagogical decisions that they'll have to make.
(4) Most -- I'm tempted to say all -- programs that prepare teachers aren't designed with (3) at their core. Modeling effective teaching is haphazard, feedback is unstructured, and end goals are uncertain. This is a design flaw, and I'm not sure it can be solved by trying to reform existing institutions that prepare teachers, though I am glad Deans for Impact is still trying (I no longer work there).
Interestingly, Dan, when you wrote recently about the blinkered view that ed-tech funders have about "Terra Mathematica" I found myself thinking everything you argued there applies with equal force to "Terra Teaching." A few years back there was a well-funded effort to create a wholly new teacher-training program that would be "competency" based (High Meadows Graduate School, for the curious). It failed spectacularly, and I'd argue in part because thinking about teaching as a series of discrete competencies is as misguided as thinking about mathematics as a set of discrete skills.
That said...the idea that we might design an entirely new and different program to foster great teaching holds great appeal. I've come to believe this has to be done from the ground up -- grafting it into existing institutions is a hard slog. What would this new Institute of Inspiring Teaching consist of? Well, instead of a disparate set of unconnected courses and basically random student teaching experiences, this new organization would be designed with near-constant opportunities to practice teaching (including lots of approximations of teaching); have a faculty comprised of cognitive scientists, practice-focused researchers, and expert veteran teachers; would provide ongoing support to novice teachers in their first few years of practice; and would make use of all the tools that learning science indicates are effective for learning.
Dare to dream. Also sorry for the essay/pitch in the guise of a comment.
The decision to focus on preservice education vs inservice education seems consequential to me. I can see a lot of appeal with preservice. It's the start of a teacher's journey, sort of, depending on how you define it. They have dedicated time to learn about their craft. On the other hand, inservice teaching offers a longer timeline and the opportunity to apply learning to practice.
I agree. But one problem here may be the bifurcation of these worlds -- many teacher-ed programs see their work as finished once their candidates graduate (understandably, tbh). There are alternatives. The Boston Teacher Residency, which I think is excellent, provides on-going support and feedback to the teachers it prepared for years -- even decades -- after they've entered practice. What if that was the norm rather than the exception?
Yes. The Boston Teacher Residency sounds awesome. On-going support and feedback seems like it would be quite helpful. I also think a network of support could be part of the puzzle.
Ongoing support and feedback would be awesome. Or even regular scheduled check-in questions coupled with something like Angela Watson’s 40 Hour Teacher Workweek and a voluntary network of local teachers willing to observe each other and provide positive constructive feedback.
See my comment directly on Benjamin's comment above. I agree this is a consequential decision. I find significant appeal of getting "upstream" to preservice teachers at the beginning of their game -- and I worry about them going into schools that are inhospitable to their approach. If they are frustrated at every turn, this might make them leave the profession earlier which would be worse than where we started.
This is exactly what jumped out at me -- "I’m hoping to find some time to write about how we can ensure that teachers like Liz are made, rather than born." I gravitate toward the theory of change that has teacher training *making* a bunch of iconoclastic teachers rather than waiting for them to be born.
Right now, the first 2 big things that come to mind are these:
1) Teachers who graduate from these new evolved preservice programs will go into schools -- with school leaders and colleagues -- that may have evolved very little. This is a tough landscape in which to innovate. Perhaps there needs to be additional training in "rocking the boat" and support groups for teachers who are doing just that. We need to train teachers differently AND we need to develop environments (schools) where those skills are embraced. This probably includes working with both pre-service and in-service teachers.
2) Related to 1, we need a meaningful way to stitch together the Liz's of the world who are out there so they feel supported and can see themselves as part of a network rather than as solo unicorns.
Additionally, I 100% agree that the shift in training is not as simple as just making sure folks know cognitive science. I think we need to focus more on adaptable principles and practices that can be metabolized by individual teachers, adapted to their students, subject, content, and then integrated into their own practice in ways that make their job better -- and more joyful.
Thanks for the comment, Becca. "Metabolized" is a critical way to understand teacher development IMO – both how teachers metabolize ideas they learn (in the context of surrounding structures like curriculum, colleagues, policies, etc) and how their surrounding environment metabolizes the teacher (your point #2 about institutional support). That idea of metabolization, more than any other, is why I'm most excited to develop PD in the context of a core curriculum, the thing that metabolizes teachers more than most other elements in their work.
One essay related to environment that I think every new teacher should read is something like, “Find your marigolds” by the writer of blog Cult of Pedagogy.
My interpretation (7th year high school math teacher, Algebra 1) is that in the limited prep time I have available each day, I usually look ahead to the next lesson in our curriculum. Especially as a new parent, I’m grateful to have access to a curriculum made by a thoughtful team (Desmos/Amplify, which Dan works with). And one thing I love is a preview email they send out which is like a three minute mini PD, which has not only good teaching ideas but also how they can be directly linked to the next day’s lesson. Concise plus sense of humor for the win. Example, in a lesson that values student skepticism (correlation does not equal causation), telling students this lesson will be the most fun they have all week (even including sports and video games). Such a good reaction from my students haha.
Ooh...tell me more about what you mean when you say 'core curriculum metabolizes teachers' - I'm super intrigued. Feel free to point me back to previous posts - I'm relatively new here on Mathworlds. And I'd be excited to see your thoughts on this in future posts as well. Thanks.
Well, I think principles of cognitive science are, fundamentally, adaptable in the ways you describe. At root it's a scientific theory of how we think and learn, and I don't think there's a better one to inform how teachers teach.
I agree with you that existing school environments can be tough on great teaching. A support network for new teachers is great in theory, perhaps challenging in practice. As I replied to Dan, I think teacher-training programs should not see their job as ending when someone formally graduates; there should be ongoing coaching and collaboration along the lines I think you're imagining.
Love your point "Great teachers are often quite impatient. They do not wait for the demand for their teaching to arise naturally in a student. They see it as their job to create demand, oftentimes quite impatiently."
Thanks for sharing Jenna Laib’s article. Really enjoyed reading the kindergartners’ responses. I may try this with my high school ninth and tenth grade students for something like “What is pi? Can you be pi miles away from something? Is pi infinite? What does that mean?” Any other good questions to ask high school students about math come to mind that could have answers as intriguing and helpful to read as the “is 0 a number?” was for younger students? Maybe something along the lines of “what is the sun of the internal ‘angles’ of a circle?”
A student teacher once told me I had the patience of a saint. This helps explain why I had mixed feelings about that and did not feel exactly complimented. It’s good to read some urgings that it can be helpful to be impatient too.
1. Both Khanmigo and ChatGPT currently use a text interface. When I tutor a math student, we can talk and listen to each other. Also, we can see each other’s work. I do not think many students will have the patience to do all the typing and reading that is required with Khanmigo and ChatGPT.
2. I wonder how meaningful the Kahn “0.20 standard deviation” study is. Aren’t they really comparing a more motivated group to a less motivated group?
That Fordham link is pure gold. And the point about impatience is excellent. Curious if you've looked at Manifold Markets as a way to follow through on you point about betting?
Loved so much about this essay. I especially appreciate the acknowledgment of teachers inpatient demanding selves that think long and hard about how to connect to students' prior knowledge and create demand for Curiosity and can see in real time student thinking and students' eyes shine. Thank you.
Man, there's a lot to chew on here (as per usual), but I'll confine myself to the one piece I know a little something about: "Much of what I’m describing in my critiques of personalized learning depend on 'heroic individual teachers' like Liz Clark-Garvey. This is a concern that worries me too and I’m hoping to find some time to write about how we can ensure that teachers like Liz are made, rather than born."
I founded an organization dedicated toward this goal (Deans for Impact) that was/is premised on two basic ideas: (1) We will have more great teaching if teachers have a better understanding of the science of how students learn. (2) Initial teacher education is a good place to focus effort on ensuring (1).
Both of those propositions are debatable, though I'm prepared to defend them still. But I am also happy to *complicate* them with some additional contextual claims borne of lived experience:
(3) Understanding the science of learning means a lot more than just "read about basic ideas from cognitive science." The key is in the *application* of that understanding in real classroom settings with kids. Learning science doesn't tell teachers what to do, but rather, gives them a "mental model" that helps inform the many thousands of pedagogical decisions that they'll have to make.
(4) Most -- I'm tempted to say all -- programs that prepare teachers aren't designed with (3) at their core. Modeling effective teaching is haphazard, feedback is unstructured, and end goals are uncertain. This is a design flaw, and I'm not sure it can be solved by trying to reform existing institutions that prepare teachers, though I am glad Deans for Impact is still trying (I no longer work there).
Interestingly, Dan, when you wrote recently about the blinkered view that ed-tech funders have about "Terra Mathematica" I found myself thinking everything you argued there applies with equal force to "Terra Teaching." A few years back there was a well-funded effort to create a wholly new teacher-training program that would be "competency" based (High Meadows Graduate School, for the curious). It failed spectacularly, and I'd argue in part because thinking about teaching as a series of discrete competencies is as misguided as thinking about mathematics as a set of discrete skills.
That said...the idea that we might design an entirely new and different program to foster great teaching holds great appeal. I've come to believe this has to be done from the ground up -- grafting it into existing institutions is a hard slog. What would this new Institute of Inspiring Teaching consist of? Well, instead of a disparate set of unconnected courses and basically random student teaching experiences, this new organization would be designed with near-constant opportunities to practice teaching (including lots of approximations of teaching); have a faculty comprised of cognitive scientists, practice-focused researchers, and expert veteran teachers; would provide ongoing support to novice teachers in their first few years of practice; and would make use of all the tools that learning science indicates are effective for learning.
Dare to dream. Also sorry for the essay/pitch in the guise of a comment.
The decision to focus on preservice education vs inservice education seems consequential to me. I can see a lot of appeal with preservice. It's the start of a teacher's journey, sort of, depending on how you define it. They have dedicated time to learn about their craft. On the other hand, inservice teaching offers a longer timeline and the opportunity to apply learning to practice.
I agree. But one problem here may be the bifurcation of these worlds -- many teacher-ed programs see their work as finished once their candidates graduate (understandably, tbh). There are alternatives. The Boston Teacher Residency, which I think is excellent, provides on-going support and feedback to the teachers it prepared for years -- even decades -- after they've entered practice. What if that was the norm rather than the exception?
Yes. The Boston Teacher Residency sounds awesome. On-going support and feedback seems like it would be quite helpful. I also think a network of support could be part of the puzzle.
Ongoing support and feedback would be awesome. Or even regular scheduled check-in questions coupled with something like Angela Watson’s 40 Hour Teacher Workweek and a voluntary network of local teachers willing to observe each other and provide positive constructive feedback.
Side note: I can't thank you enough for pointing me to the gorgeous comic in The New Yorker about human cognition and generative AI. It made me weep.
See my comment directly on Benjamin's comment above. I agree this is a consequential decision. I find significant appeal of getting "upstream" to preservice teachers at the beginning of their game -- and I worry about them going into schools that are inhospitable to their approach. If they are frustrated at every turn, this might make them leave the profession earlier which would be worse than where we started.
This is exactly what jumped out at me -- "I’m hoping to find some time to write about how we can ensure that teachers like Liz are made, rather than born." I gravitate toward the theory of change that has teacher training *making* a bunch of iconoclastic teachers rather than waiting for them to be born.
Right now, the first 2 big things that come to mind are these:
1) Teachers who graduate from these new evolved preservice programs will go into schools -- with school leaders and colleagues -- that may have evolved very little. This is a tough landscape in which to innovate. Perhaps there needs to be additional training in "rocking the boat" and support groups for teachers who are doing just that. We need to train teachers differently AND we need to develop environments (schools) where those skills are embraced. This probably includes working with both pre-service and in-service teachers.
2) Related to 1, we need a meaningful way to stitch together the Liz's of the world who are out there so they feel supported and can see themselves as part of a network rather than as solo unicorns.
Additionally, I 100% agree that the shift in training is not as simple as just making sure folks know cognitive science. I think we need to focus more on adaptable principles and practices that can be metabolized by individual teachers, adapted to their students, subject, content, and then integrated into their own practice in ways that make their job better -- and more joyful.
Thanks for the comment, Becca. "Metabolized" is a critical way to understand teacher development IMO – both how teachers metabolize ideas they learn (in the context of surrounding structures like curriculum, colleagues, policies, etc) and how their surrounding environment metabolizes the teacher (your point #2 about institutional support). That idea of metabolization, more than any other, is why I'm most excited to develop PD in the context of a core curriculum, the thing that metabolizes teachers more than most other elements in their work.
One essay related to environment that I think every new teacher should read is something like, “Find your marigolds” by the writer of blog Cult of Pedagogy.
My interpretation (7th year high school math teacher, Algebra 1) is that in the limited prep time I have available each day, I usually look ahead to the next lesson in our curriculum. Especially as a new parent, I’m grateful to have access to a curriculum made by a thoughtful team (Desmos/Amplify, which Dan works with). And one thing I love is a preview email they send out which is like a three minute mini PD, which has not only good teaching ideas but also how they can be directly linked to the next day’s lesson. Concise plus sense of humor for the win. Example, in a lesson that values student skepticism (correlation does not equal causation), telling students this lesson will be the most fun they have all week (even including sports and video games). Such a good reaction from my students haha.
Ooh...tell me more about what you mean when you say 'core curriculum metabolizes teachers' - I'm super intrigued. Feel free to point me back to previous posts - I'm relatively new here on Mathworlds. And I'd be excited to see your thoughts on this in future posts as well. Thanks.
Well, I think principles of cognitive science are, fundamentally, adaptable in the ways you describe. At root it's a scientific theory of how we think and learn, and I don't think there's a better one to inform how teachers teach.
I agree with you that existing school environments can be tough on great teaching. A support network for new teachers is great in theory, perhaps challenging in practice. As I replied to Dan, I think teacher-training programs should not see their job as ending when someone formally graduates; there should be ongoing coaching and collaboration along the lines I think you're imagining.
Love your point "Great teachers are often quite impatient. They do not wait for the demand for their teaching to arise naturally in a student. They see it as their job to create demand, oftentimes quite impatiently."
Thanks for sharing Jenna Laib’s article. Really enjoyed reading the kindergartners’ responses. I may try this with my high school ninth and tenth grade students for something like “What is pi? Can you be pi miles away from something? Is pi infinite? What does that mean?” Any other good questions to ask high school students about math come to mind that could have answers as intriguing and helpful to read as the “is 0 a number?” was for younger students? Maybe something along the lines of “what is the sun of the internal ‘angles’ of a circle?”
A student teacher once told me I had the patience of a saint. This helps explain why I had mixed feelings about that and did not feel exactly complimented. It’s good to read some urgings that it can be helpful to be impatient too.
Another great observation: most students need an impatient demand teacher! Amen!
Liked this a lot. Two additional thoughts:
1. Both Khanmigo and ChatGPT currently use a text interface. When I tutor a math student, we can talk and listen to each other. Also, we can see each other’s work. I do not think many students will have the patience to do all the typing and reading that is required with Khanmigo and ChatGPT.
2. I wonder how meaningful the Kahn “0.20 standard deviation” study is. Aren’t they really comparing a more motivated group to a less motivated group?
Dan, the penultimate paragraph of this article is one of the best things you've ever written.
That Fordham link is pure gold. And the point about impatience is excellent. Curious if you've looked at Manifold Markets as a way to follow through on you point about betting?
THIS! THANK YOU!
Loved so much about this essay. I especially appreciate the acknowledgment of teachers inpatient demanding selves that think long and hard about how to connect to students' prior knowledge and create demand for Curiosity and can see in real time student thinking and students' eyes shine. Thank you.