I like your analysis of this model. I teach new teachers and use the Gradual Release model . I will add this variation to my curriculum once they understand the basic structure. I have added one piece - I do, we do (guides practice), y'all do (partner or group work) and you do. Thank you for expanding my knowledge.
Thanks! Glad it's helpful. Those basic tools - including y'all do - are great building blocks. The key is to be a bit more flexible with how they fit together.
Your first bullet point under the benefits can't be overstated. One of the biggest pitfalls of the I/We/You that I see is that it starts and often times prolongs the centering of the teacher in cognitive engagement and not the student. When a simple "You" is placed first as in some of your examples, I see a myriad of benefits in classrooms. I don't know the neuro behind it, but I would hypothesize that it must activate/impact something in the student's brain differently, especially when the first You has a very accessible floor.
Yea definitely. I don't know the neuro either, but I think two of the positive effects are the confidence boost from starting with accessible questions, and activating prior knowledge. Which sounds obvious when I say it like that, but most of the curricula that are popular in the US right now often don't do a very good job with those two things (giving a nod to it very briefly, but then increasing the difficulty too fast).
Your first graph totally misrepresents how I/we/you works. "Task Difficulty" is not constant, and it ramps up throughout the lesson just as you suggest later on.
Not saying some teachers don't do it the way your graph suggests, but it's not how I was taught to design an I/we/you lesson.
I totally agree that the canonical sources (DI, Archer, etc) use I/we/you in a way more consistent with what I describe as a gradual increase in difficulty.
But I would bet you that if we walked into 100 random math classrooms of teachers who say they use I/we/you today, a large majority would be keeping task difficulty constant across the lesson. The heart of my criticism is that I/we/you lends itself to being used poorly, and if an idea is so easy to misinterpret I think we should use different language to describe teaching.
For what it's worth, I/we/you was taught in my grad program and it was taught as a gradual release and not a gradual increase. And I would argue that my program was above average! I think you may be an outlier compared to a typical teacher.
Curious if you would distinguish between “you” being an explore/inquiry task vs “you” being practice of something that’s been explicitly taught/modeled? To me these are different in terms of purpose and how they fit in with the I/we portions.
One shift in my teaching has been toward sequences of problems, rather than larger tasks. So in any given round of "you," it's often a sequence of 5-10 problems starting with something students have been explicitly taught, and getting gradually harder/building toward a larger idea.
So I don't know that I have a good answer to your question? In general most of what we're doing in math class is these constant cycles. Start with thing A that students (ideally) know how to do. Build gradually up to B and C. Is that inquiry? Then the next cycle there's some explicit modeling of B, and we build gradually up to C and D.
I do not try to explain everything or model every single little type of problem. I do try to start each chunk of practice with something students can feel confident with and that they've had modeled/explicitly taught. I make a lot of judgment calls around when I explain something first vs whether I want students to generalize themselves. All that is informed by lots of checking for understanding. But the differences feel pretty subtle to me, and can vary from one period to the next.
Interesting. I would definitely be intrigued to see this in action! I can see how this would make a lot of sense with 7th grade content. Maybe because the HS tasks take longer, I tend to start with review of what students know (you/we) followed by a longer (10 min) inquiry task that bridges from that to the new concept (you then we then I) that we debrief for students to generalize and then I formalize. After that we move into what you are describing with rounds of practice and modeling that builds in challenge but usually only 2-3 rounds because the problems tend to take longer.
The premise is that the first three problems are things they've seen before, and I questioned students through a similar sequence before we started. The next three are a bit harder, decimals and less mental math, and on #6 you can't just read the answer off the graph.
This type of thing is a huge chunk of what I do and I don't know how to categorize it in the explicit/inquiry binary.
The other thing I would say -- I previously taught high school (Alg II/Precalc/AP Calc). I think you can do a lot of this type of thing in HS by breaking skills down into much smaller pieces and building those pieces up. It requires some kindof contrived questions to break stuff down but I think that's fine. Happy to brainstorm an example if you're interested and want to throw something out.
Thanks for sharing. I’ll take a look! I imagine that it would make sense for certain lessons and not others. I think there are times when tackling the longer tasks in whole is important for building holistic understanding but other times when breaking into smaller skills could help build fluency.
A little off topic but how do you fit homework into your overall structure and what’s your view on homework? I’m asking as I believe homework should be compulsory and we have just implemented a compulsory homework policy (which I’m happy about as before I kept getting student complaints that other teachers weren’t making homework compulsory!) but take up is low and it’s been super tough to get some kids on board. I’ve never seen you post about homework … :)
Practice is essential, but practice doesn't have to be homework. Whether or not there's homework, there should be regular practice in math class.
Cheating is everywhere in middle school and high school right now. However much you think they're cheating, they're cheating more.
Homework works best with regular routines and collaboration between teachers. Which sounds like what you're describing! But there's still limitations because of cheating.
Ok practically speaking. I end ~every class with ~5-10 minutes to work on a DeltaMath (online) assignment. It's mixed practice, so multiple different skills. Kids who work quickly often finish it. It's homework for everyone else. Families are happy to hear there's homework they can check and get a sense of what we're learning. It's partly in class which reduces cheating. I can't justify the effort to print and keep track of paper-and-pencil homework. I also use that time to follow up individually with students who need extra help with something from the day's lesson, and digital work is good because students can be more self-sufficient while I'm doing those checkins.
I find Craig Barton's writing on homework has changed me to someone who puts more into homework as a teacher who struggles to find time for homework in lessons.
Basically his advice is to tie the homework into a weekly low stakes quiz to get the consistent buy in to actually using the homework as review and practice. I'm still struggling on the implementation though, mostly in finding the time to make the quizzes. My current plan is to have it consistent for my year 7s and hopefully year 9s all of next term, then check how it went.
I actually experimented with Carousel Teaching two years ago with similar goals. I honestly found it to be a lot of work to put together. I would love to revisit that idea someday, but it's just not that high on my list of teaching priorities -- there's a lot of other stuff that I find matters more.
I have switched to "revision for weekly 15 minute test" as homework instead of setting explicit homework for my sixth form this year. I felt that with AI getting as good as it is that they would be likely to cheat on homework, and so the benefits for me and for them were drastically reduced. This seems to be working ok so far, although some of the L6 still aren't taking it seriously yet. It's also a lot less marking for me and potentially more learning for them.
So does that look like a kindof "practice test" -- students try a bunch of questions similar to what they'll see on the test? Is it just once a week? One of my dilemmas is that I think homework is most useful if it is assigned every night for consistency, and kept relatively short. I would love to put together something like what you're describing, but I have trouble figuring out what the details look like.
Yes - it's past exam questions on the current topic. I only do it once a week so it doesn't impact too much on lesson time. In theory, they should be matching lesson time with time working at home and so working every day.
I wouldn't be trying this with younger students though - I don't think they would have the maturity for it.
I like your analysis of this model. I teach new teachers and use the Gradual Release model . I will add this variation to my curriculum once they understand the basic structure. I have added one piece - I do, we do (guides practice), y'all do (partner or group work) and you do. Thank you for expanding my knowledge.
Thanks! Glad it's helpful. Those basic tools - including y'all do - are great building blocks. The key is to be a bit more flexible with how they fit together.
Your first bullet point under the benefits can't be overstated. One of the biggest pitfalls of the I/We/You that I see is that it starts and often times prolongs the centering of the teacher in cognitive engagement and not the student. When a simple "You" is placed first as in some of your examples, I see a myriad of benefits in classrooms. I don't know the neuro behind it, but I would hypothesize that it must activate/impact something in the student's brain differently, especially when the first You has a very accessible floor.
Yea definitely. I don't know the neuro either, but I think two of the positive effects are the confidence boost from starting with accessible questions, and activating prior knowledge. Which sounds obvious when I say it like that, but most of the curricula that are popular in the US right now often don't do a very good job with those two things (giving a nod to it very briefly, but then increasing the difficulty too fast).
Your first graph totally misrepresents how I/we/you works. "Task Difficulty" is not constant, and it ramps up throughout the lesson just as you suggest later on.
Not saying some teachers don't do it the way your graph suggests, but it's not how I was taught to design an I/we/you lesson.
I totally agree that the canonical sources (DI, Archer, etc) use I/we/you in a way more consistent with what I describe as a gradual increase in difficulty.
But I would bet you that if we walked into 100 random math classrooms of teachers who say they use I/we/you today, a large majority would be keeping task difficulty constant across the lesson. The heart of my criticism is that I/we/you lends itself to being used poorly, and if an idea is so easy to misinterpret I think we should use different language to describe teaching.
For what it's worth, I/we/you was taught in my grad program and it was taught as a gradual release and not a gradual increase. And I would argue that my program was above average! I think you may be an outlier compared to a typical teacher.
Thanks! Will check this out
Curious if you would distinguish between “you” being an explore/inquiry task vs “you” being practice of something that’s been explicitly taught/modeled? To me these are different in terms of purpose and how they fit in with the I/we portions.
One shift in my teaching has been toward sequences of problems, rather than larger tasks. So in any given round of "you," it's often a sequence of 5-10 problems starting with something students have been explicitly taught, and getting gradually harder/building toward a larger idea.
So I don't know that I have a good answer to your question? In general most of what we're doing in math class is these constant cycles. Start with thing A that students (ideally) know how to do. Build gradually up to B and C. Is that inquiry? Then the next cycle there's some explicit modeling of B, and we build gradually up to C and D.
I do not try to explain everything or model every single little type of problem. I do try to start each chunk of practice with something students can feel confident with and that they've had modeled/explicitly taught. I make a lot of judgment calls around when I explain something first vs whether I want students to generalize themselves. All that is informed by lots of checking for understanding. But the differences feel pretty subtle to me, and can vary from one period to the next.
Interesting. I would definitely be intrigued to see this in action! I can see how this would make a lot of sense with 7th grade content. Maybe because the HS tasks take longer, I tend to start with review of what students know (you/we) followed by a longer (10 min) inquiry task that bridges from that to the new concept (you then we then I) that we debrief for students to generalize and then I formalize. After that we move into what you are describing with rounds of practice and modeling that builds in challenge but usually only 2-3 rounds because the problems tend to take longer.
Here's something we did today:
https://docs.google.com/document/d/1-g7QKZ6C3V5Do_Q45mJVQCuqnyA70WDDw2kkF4pUI0s/edit?usp=sharing
The premise is that the first three problems are things they've seen before, and I questioned students through a similar sequence before we started. The next three are a bit harder, decimals and less mental math, and on #6 you can't just read the answer off the graph.
This type of thing is a huge chunk of what I do and I don't know how to categorize it in the explicit/inquiry binary.
The other thing I would say -- I previously taught high school (Alg II/Precalc/AP Calc). I think you can do a lot of this type of thing in HS by breaking skills down into much smaller pieces and building those pieces up. It requires some kindof contrived questions to break stuff down but I think that's fine. Happy to brainstorm an example if you're interested and want to throw something out.
Thanks for sharing. I’ll take a look! I imagine that it would make sense for certain lessons and not others. I think there are times when tackling the longer tasks in whole is important for building holistic understanding but other times when breaking into smaller skills could help build fluency.
A little off topic but how do you fit homework into your overall structure and what’s your view on homework? I’m asking as I believe homework should be compulsory and we have just implemented a compulsory homework policy (which I’m happy about as before I kept getting student complaints that other teachers weren’t making homework compulsory!) but take up is low and it’s been super tough to get some kids on board. I’ve never seen you post about homework … :)
Here are a few random thoughts:
Practice is essential, but practice doesn't have to be homework. Whether or not there's homework, there should be regular practice in math class.
Cheating is everywhere in middle school and high school right now. However much you think they're cheating, they're cheating more.
Homework works best with regular routines and collaboration between teachers. Which sounds like what you're describing! But there's still limitations because of cheating.
Ok practically speaking. I end ~every class with ~5-10 minutes to work on a DeltaMath (online) assignment. It's mixed practice, so multiple different skills. Kids who work quickly often finish it. It's homework for everyone else. Families are happy to hear there's homework they can check and get a sense of what we're learning. It's partly in class which reduces cheating. I can't justify the effort to print and keep track of paper-and-pencil homework. I also use that time to follow up individually with students who need extra help with something from the day's lesson, and digital work is good because students can be more self-sufficient while I'm doing those checkins.
I find Craig Barton's writing on homework has changed me to someone who puts more into homework as a teacher who struggles to find time for homework in lessons.
Basically his advice is to tie the homework into a weekly low stakes quiz to get the consistent buy in to actually using the homework as review and practice. I'm still struggling on the implementation though, mostly in finding the time to make the quizzes. My current plan is to have it consistent for my year 7s and hopefully year 9s all of next term, then check how it went.
https://tipsforteachers.co.uk/low-stakes-quiz/
https://tipsforteachers.co.uk/homework/
I actually experimented with Carousel Teaching two years ago with similar goals. I honestly found it to be a lot of work to put together. I would love to revisit that idea someday, but it's just not that high on my list of teaching priorities -- there's a lot of other stuff that I find matters more.
I have switched to "revision for weekly 15 minute test" as homework instead of setting explicit homework for my sixth form this year. I felt that with AI getting as good as it is that they would be likely to cheat on homework, and so the benefits for me and for them were drastically reduced. This seems to be working ok so far, although some of the L6 still aren't taking it seriously yet. It's also a lot less marking for me and potentially more learning for them.
So does that look like a kindof "practice test" -- students try a bunch of questions similar to what they'll see on the test? Is it just once a week? One of my dilemmas is that I think homework is most useful if it is assigned every night for consistency, and kept relatively short. I would love to put together something like what you're describing, but I have trouble figuring out what the details look like.
Yes - it's past exam questions on the current topic. I only do it once a week so it doesn't impact too much on lesson time. In theory, they should be matching lesson time with time working at home and so working every day.
I wouldn't be trying this with younger students though - I don't think they would have the maturity for it.