People often talk about how teaching a subject gets you to understand it much more deeply – it feels like elaboration is probably a big key as to why. I'm not quite sure how you would structure a classroom to get the students involved in teaching, but it would be really cool if there were a way to do so. I taught at a math camp in Michigan last year that was designed for middle school students who were struggling with math, and they were effectively mostly being taught by high school students who had previously attended the camp as middle school students. It was pretty interesting to see this kind of cascading teaching effect and the impacts it had on their understanding
Yea there’s a whole world of research on this, it’s often called “reciprocal teaching.” It’s one of those things that works well in a lab study but is hard to do in a real classroom. One of my colleagues is trying this year and it’s been a ton of work and a pain to deal with. I don’t know how to square that, it’s not something I’ve ever put effort into.
I get that! Admittedly, it is harder with some groups than others- and the post-Covid lack of maturity/ social skills makes it much more difficult to manage some students when they are out of their seats. One of my classes this year spent the majority of their time doing very explicit atomized instruction— seated as far from each other as possible. We have simultaneously been slowly working on some of the skills they need to be successful in BTC. I am starting to see progress in their ability to work together (or really even be near each other without losing their minds ;) ) and more importantly, only in the last few weeks- I’m starting to see some small glimmers of the thinking behaviors I am aiming for.
Many of the practices behind Building Thinking Classrooms do exactly this. Done right, using sequences of thin sliced tasks (which your progressions model well) in random groups at whiteboards, accomplishes the aims of reciprocal teaching. Many who have never tried BTC characterize it as “repackaged discovery,” and I will be the first to admit that perhaps I’m doing it wrong- but for me, it’s anything but. In fact during my session at the first BTC conference, I taught a lesson and then projected the elements of explicit instruction as outlined in Anita Archer’s book on explicit instruction, and I asked participants to identify the elements in the lesson I just taught. I expected them to find at least half- to my surprise, they identified them all. For a far better explanation of how the BTC practices can be used while also adhering to the “science of learning,” I highly recommend Doug Doblar’s blog. (If you haven’t already discovered him because he recently referenced you in his piece about technology.)
Yeah I agree with this. BTC done well is highly structured and has a lot in common with explicit instruction. A lot of the hate it gets is either caricaturing or focusing on a narrow slice of the framework. I do think it depends a lot on how well a teacher can structure the group work aspect of it. I have used it in the past and moved away from it because I struggled to consistently get all groups functioning well enough for everyone to learn. Doesn't mean it's broken, just that it's a different set of skills that are necessary.
I get that! Admittedly, it is harder with some groups than others- and the post-Covid lack of maturity/ social skills makes it much more difficult to manage some students when they are out of their seats. One of my classes this year spent the majority of their time doing very explicit atomized instruction— seated as far from each other as possible. We have simultaneously been slowly working on some of the skills they need to be successful in BTC. I am starting to see progress in their ability to work together (or really even be near each other without losing their minds ;) ) and more importantly, only in the last few weeks- I’m starting to see some small glimmers of the thinking behaviors I am aiming for.
"Done well" does a lot of heavy lifting here. In my neck of the woods, we see teachers go to regional trainings on BTC, some led by PL himself, and come back embodying those caricatures. I suspect it's a framework that needs more job-embedded support than our service districts are set up to provide.
I get it, but I also think some of the folks who are critical of BTC like to take potshots that don't engage substantively with the good ideas. "Thin slicing" is a good idea whether you're doing BTC or something else. Vertical whiteboards reflect the importance of accountability in group work, which is a good lesson for the many teachers who ask students to work in groups. BTC puts a lot of emphasis on students doing math. I've talked to plenty of teachers who say that the approach has helped them get students doing a lot more practice.
In education people love to argue about labels without getting into specifics. I associate what I do with a lot of the Anita Archer, Rosenshine's principles style of explicit teaching. I avoid that label because I know there are tons of people who also label themselves with "explicit teaching" or "direct instruction" and mostly lecture at students. I think it cuts both ways, and my answer is to try to write a lot about the specifics of what my teaching looks like and not attach myself to any given label.
Any method of teaching takes far more training than it usually receives. I think it would be nearly impossible to attend a one or two day training and come back as a skilled practitioner, no matter who taught it. While using BTC, I have had 3 student teachers. I tried to resist taking on a student teacher because I knew that not every student would be willing or able to teach this way. I only accepted student teachers with the understanding that they knew what they were getting into. It took an enormous amount of coteaching and coaching before they were ready to teach this way on their own. I am a believer in BTC, but I don't think it should ever be "forced." I honestly don't think it can be "done well," by anyone who isn't committed to it and who isn't willing or able to put in a LOT of extra work (initially) to make it work. On the flip side, once that initial work has been done, at least for me, it is soooo worth it. By this time every year, unlike many teachers, I am not counting down the days. I am still enjoying almost every lesson of every day and watching what the students are now capable of, makes everything worthwhile!
Glad you clarified the hypothetical nature of the world of cheese you describe, I was troubled there for a while. Hard agree on the centrality of elaboration and eliciting is a challenge and best done with an on ramp
I haven't seen it worded like this before, but mathematically playing "what if?" with the kids seems like a very low floor/high ceiling way to approach this thing.
Yea that's a great way to put it. The questions are tricky - the example I gave could be either too easy or too hard depending on the students and the spot in the curriculum. But getting it right is a great way to provide access while also challenging students.
Yeah, they are. It feels good when you choose the right "lead-up" questions, and when you don't you feel it IMMEDIATELY lol (or at least I do). I think this is an underappreciated skill as a math teacher, and it's one of those things that I don't really know how to get better at other than just getting reps in day after day with the kids in class. It's hard to practice, replicate, or know whether you've chosen wisely without having the real audience in the room with you. It's challenging, but pretty fun when it goes right.
A related term in cognitive neuroscience, particularly memory literature, is "encoding depth" in a "cognitive map". Which is a slightly mysterious sounding term, but basically it refers to the number of connections you form between a new concept and established concepts. The more connections you build, the easier it is to retrieve the new concept, because there are more "routes" from the things you already know to the thing you just learned.
In these terms, the 200% sequence seems to be building a connection between "200%" and "doubling", and more generally between percentages (the new concept?) and integer multiplication (the old concept?).
Interesting! I haven't heard that term before but it makes total sense.
In the example I gave it's a link with multiplication, but also with the idea of a proportional relationship (another grade-level standard) which creates even more encoding depth.
What I think is really interesting about your thought process is that it sounds like you start with a question (based on a key understanding) that you want students to be able to engage with or answer and then design a task or series of problems that intentionally builds students toward the question. This feels flipped from how I think teachers often think about question-asking which is to design questions to follow a task that already exists in curriculum to try to draw out key understanding. It seems like your approach has clear benefits of making questions more accessible for all learners and tasks more targeted to the question. I’m definitely interested to play around with this flipped approach in my classroom.
Interesting! I had never thought about it that way. Yea, I definitely put a lot of effort into what comes before the curricular tasks I give students. I do think part of that is the reality of where I work and the skills students do or don’t have.
Recently, attached to one of your other posts in the comments, was a brief discussion of problem strings. This feels similar but a little different (am I right on that?).
Yea I think problem strings definitely fit here. I'm trying to both be a little more specific about different ways to sequence multiple problems, and to connect to this broader idea of effortful thinking.
Great post, and I love the progression questions, where you have a carefully designed sequence of questions designed to elicit thinking. They sit in a space between repetitive worksheets and "rich tasks" that I think is insufficiently explored.
By the way, I think the "explain your answers" trend predates the Common Core by a long way. What happened sometimes was that people latched onto the practice standards to validate what they were already doing.
I agree there's a ton of space between repetition and rich tasks. I've felt pretty disillusioned by rich tasks as stand-alone entities for all the reasons I describe in my post. They just haven't consistently engaged my reluctant students.
re: "explain your answers," I don't know... There were definitely some folks emphasizing explanation before Common Core but I think it's gone mainstream in a way that's become watered down and unproductive. A typical pre-Common Core textbook didn't put much emphasis on explanation, but now textbooks are mostly dead and most of the popular curricula ask students to do a ton of explanation. It's not just the practice itself, it's asking students to explain things without scaffolds or instruction on what good explanation looks like.
Explanation is tough because it seems very easy to get stuck on it. The space of possible "explanations" is infinite and poorly defined, and it is not always obvious what counts as one. It seems like a good way of taking a marginally-motivated student and completely shutting them down.
There is a huge bank of these sorts of resources here https://variationtheory.com/.
Oh, just saw this after posting my comment, looks great!
People often talk about how teaching a subject gets you to understand it much more deeply – it feels like elaboration is probably a big key as to why. I'm not quite sure how you would structure a classroom to get the students involved in teaching, but it would be really cool if there were a way to do so. I taught at a math camp in Michigan last year that was designed for middle school students who were struggling with math, and they were effectively mostly being taught by high school students who had previously attended the camp as middle school students. It was pretty interesting to see this kind of cascading teaching effect and the impacts it had on their understanding
Yea there’s a whole world of research on this, it’s often called “reciprocal teaching.” It’s one of those things that works well in a lab study but is hard to do in a real classroom. One of my colleagues is trying this year and it’s been a ton of work and a pain to deal with. I don’t know how to square that, it’s not something I’ve ever put effort into.
I get that! Admittedly, it is harder with some groups than others- and the post-Covid lack of maturity/ social skills makes it much more difficult to manage some students when they are out of their seats. One of my classes this year spent the majority of their time doing very explicit atomized instruction— seated as far from each other as possible. We have simultaneously been slowly working on some of the skills they need to be successful in BTC. I am starting to see progress in their ability to work together (or really even be near each other without losing their minds ;) ) and more importantly, only in the last few weeks- I’m starting to see some small glimmers of the thinking behaviors I am aiming for.
Many of the practices behind Building Thinking Classrooms do exactly this. Done right, using sequences of thin sliced tasks (which your progressions model well) in random groups at whiteboards, accomplishes the aims of reciprocal teaching. Many who have never tried BTC characterize it as “repackaged discovery,” and I will be the first to admit that perhaps I’m doing it wrong- but for me, it’s anything but. In fact during my session at the first BTC conference, I taught a lesson and then projected the elements of explicit instruction as outlined in Anita Archer’s book on explicit instruction, and I asked participants to identify the elements in the lesson I just taught. I expected them to find at least half- to my surprise, they identified them all. For a far better explanation of how the BTC practices can be used while also adhering to the “science of learning,” I highly recommend Doug Doblar’s blog. (If you haven’t already discovered him because he recently referenced you in his piece about technology.)
Yeah I agree with this. BTC done well is highly structured and has a lot in common with explicit instruction. A lot of the hate it gets is either caricaturing or focusing on a narrow slice of the framework. I do think it depends a lot on how well a teacher can structure the group work aspect of it. I have used it in the past and moved away from it because I struggled to consistently get all groups functioning well enough for everyone to learn. Doesn't mean it's broken, just that it's a different set of skills that are necessary.
I get that! Admittedly, it is harder with some groups than others- and the post-Covid lack of maturity/ social skills makes it much more difficult to manage some students when they are out of their seats. One of my classes this year spent the majority of their time doing very explicit atomized instruction— seated as far from each other as possible. We have simultaneously been slowly working on some of the skills they need to be successful in BTC. I am starting to see progress in their ability to work together (or really even be near each other without losing their minds ;) ) and more importantly, only in the last few weeks- I’m starting to see some small glimmers of the thinking behaviors I am aiming for.
"Done well" does a lot of heavy lifting here. In my neck of the woods, we see teachers go to regional trainings on BTC, some led by PL himself, and come back embodying those caricatures. I suspect it's a framework that needs more job-embedded support than our service districts are set up to provide.
I get it, but I also think some of the folks who are critical of BTC like to take potshots that don't engage substantively with the good ideas. "Thin slicing" is a good idea whether you're doing BTC or something else. Vertical whiteboards reflect the importance of accountability in group work, which is a good lesson for the many teachers who ask students to work in groups. BTC puts a lot of emphasis on students doing math. I've talked to plenty of teachers who say that the approach has helped them get students doing a lot more practice.
In education people love to argue about labels without getting into specifics. I associate what I do with a lot of the Anita Archer, Rosenshine's principles style of explicit teaching. I avoid that label because I know there are tons of people who also label themselves with "explicit teaching" or "direct instruction" and mostly lecture at students. I think it cuts both ways, and my answer is to try to write a lot about the specifics of what my teaching looks like and not attach myself to any given label.
Any method of teaching takes far more training than it usually receives. I think it would be nearly impossible to attend a one or two day training and come back as a skilled practitioner, no matter who taught it. While using BTC, I have had 3 student teachers. I tried to resist taking on a student teacher because I knew that not every student would be willing or able to teach this way. I only accepted student teachers with the understanding that they knew what they were getting into. It took an enormous amount of coteaching and coaching before they were ready to teach this way on their own. I am a believer in BTC, but I don't think it should ever be "forced." I honestly don't think it can be "done well," by anyone who isn't committed to it and who isn't willing or able to put in a LOT of extra work (initially) to make it work. On the flip side, once that initial work has been done, at least for me, it is soooo worth it. By this time every year, unlike many teachers, I am not counting down the days. I am still enjoying almost every lesson of every day and watching what the students are now capable of, makes everything worthwhile!
Glad you clarified the hypothetical nature of the world of cheese you describe, I was troubled there for a while. Hard agree on the centrality of elaboration and eliciting is a challenge and best done with an on ramp
I think it reflects poorly on how much school resembles the real world, but I find that students generally take this kind of thing in stride.
I thought you might enjoy this rather old blog post of mine about elaborations of a slightly different kind: https://edgeoflearning.com/elaborations-for-creative-thinking-in-stem/
I haven't seen it worded like this before, but mathematically playing "what if?" with the kids seems like a very low floor/high ceiling way to approach this thing.
Yea that's a great way to put it. The questions are tricky - the example I gave could be either too easy or too hard depending on the students and the spot in the curriculum. But getting it right is a great way to provide access while also challenging students.
Yeah, they are. It feels good when you choose the right "lead-up" questions, and when you don't you feel it IMMEDIATELY lol (or at least I do). I think this is an underappreciated skill as a math teacher, and it's one of those things that I don't really know how to get better at other than just getting reps in day after day with the kids in class. It's hard to practice, replicate, or know whether you've chosen wisely without having the real audience in the room with you. It's challenging, but pretty fun when it goes right.
A related term in cognitive neuroscience, particularly memory literature, is "encoding depth" in a "cognitive map". Which is a slightly mysterious sounding term, but basically it refers to the number of connections you form between a new concept and established concepts. The more connections you build, the easier it is to retrieve the new concept, because there are more "routes" from the things you already know to the thing you just learned.
In these terms, the 200% sequence seems to be building a connection between "200%" and "doubling", and more generally between percentages (the new concept?) and integer multiplication (the old concept?).
Interesting! I haven't heard that term before but it makes total sense.
In the example I gave it's a link with multiplication, but also with the idea of a proportional relationship (another grade-level standard) which creates even more encoding depth.
What I think is really interesting about your thought process is that it sounds like you start with a question (based on a key understanding) that you want students to be able to engage with or answer and then design a task or series of problems that intentionally builds students toward the question. This feels flipped from how I think teachers often think about question-asking which is to design questions to follow a task that already exists in curriculum to try to draw out key understanding. It seems like your approach has clear benefits of making questions more accessible for all learners and tasks more targeted to the question. I’m definitely interested to play around with this flipped approach in my classroom.
Interesting! I had never thought about it that way. Yea, I definitely put a lot of effort into what comes before the curricular tasks I give students. I do think part of that is the reality of where I work and the skills students do or don’t have.
Recently, attached to one of your other posts in the comments, was a brief discussion of problem strings. This feels similar but a little different (am I right on that?).
Yea I think problem strings definitely fit here. I'm trying to both be a little more specific about different ways to sequence multiple problems, and to connect to this broader idea of effortful thinking.
Thx!
Great post, and I love the progression questions, where you have a carefully designed sequence of questions designed to elicit thinking. They sit in a space between repetitive worksheets and "rich tasks" that I think is insufficiently explored.
By the way, I think the "explain your answers" trend predates the Common Core by a long way. What happened sometimes was that people latched onto the practice standards to validate what they were already doing.
I agree there's a ton of space between repetition and rich tasks. I've felt pretty disillusioned by rich tasks as stand-alone entities for all the reasons I describe in my post. They just haven't consistently engaged my reluctant students.
re: "explain your answers," I don't know... There were definitely some folks emphasizing explanation before Common Core but I think it's gone mainstream in a way that's become watered down and unproductive. A typical pre-Common Core textbook didn't put much emphasis on explanation, but now textbooks are mostly dead and most of the popular curricula ask students to do a ton of explanation. It's not just the practice itself, it's asking students to explain things without scaffolds or instruction on what good explanation looks like.
Explanation is tough because it seems very easy to get stuck on it. The space of possible "explanations" is infinite and poorly defined, and it is not always obvious what counts as one. It seems like a good way of taking a marginally-motivated student and completely shutting them down.