You can download an mp3 of the podcast here.
Michael Pershan’s tips:
- Begin your explanations as a series of questions that everyone can answer (03:12)
- The best feedback is a learning activity, and it’s much better than written feedback on the page (16:28)
- Get used to asking “what if” after explaining something (31:02)
- Use partner work as a chance to recruit quiet kids to share their thinking (42:05)
- End every conversation with the student saying something smart (51:21)
Links and resources
- On Twitter, Michael is: @mpershan
- Michael’s website is: michaelpershan.com
- Michael’s book is: Teaching math with examples
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View the videos of Michael Pershan’s tips
Podcast transcript
Craig Barton 0:00
Hello, my name is Craig Barton and welcome to the tips for teachers podcast. The show that helps you supercharge your teaching one idea at a time. This episode I had the pleasure of speaking to a math teacher, an author all the way from New York, Michael Persian. And if you’ve heard Michael on my podcast before, you know you’re in for a treat. Four quick things before we start up, sponsor spots for the podcasts are open. So if you want to let the world’s most interesting listeners know about your books, product or event, just drop me an email. You can view videos of all Michaels tips on the tips for teachers website. These are great to show in a departmental meeting or a training session, you can sign up to the tips of teachers newsletter to receive a tip in your inbox most Monday mornings to try it with your classes in the coming week. And finally, if you find the podcast useful, I will be ever so grateful. If you could take a moment ideally now, just pause the podcast and give us a lovely review on your podcast player of choice. Thanks so much. Okay, let’s get learning with today’s guest the wonderful Michael Persian spiral spiral spoiler alert. Here are Michael’s five tips. Tip one, begin your explanations as a series of questions that everyone can answer. That’s kind of the opposite of what I do, which I like as what I like about. Tip two, the best feedback is a learning activity and it’s much better than written feedback on the page. Tip three get used to asking what if after explaining something, I absolutely love that one tip for use partner work as a chance to recruit quiet kids to share their thinking. And finally, Tip five and every conversation with the student saying something smart. absolute cracker this one I promise you. So if you look at the episode description on your podcast player, or visit the episode page on tips for teachers that communicate you’ll see the timestamp teacher the tips so you can jump straight to anyone you want to listen to first or re listen. Enjoy the show.
Well, it gives me great pleasure to welcome Mr. Michael Persian to the tips for teachers podcast. Hi, Michael, how are you? I am great. Right, Michael, for the benefit of listeners. Can you tell us a little bit about yourself ideally in a sentence?
Michael Pershan 2:21
Absolutely. My name is Michael Persian. I live in New York City where I work as a classroom mathematics teacher for children. And I’m also a writer about math, mathematics, teaching and others.
Craig Barton 2:36
Fantastic. Well, let’s dive straight in what is technical on today?
Michael Pershan 2:41
Tip number one is something that I only realised a couple of months ago, I think. And it’s to begin explanations is a series of questions that most people can answer. Maybe everybody in the class can answer.
Craig Barton 2:59
This is an intro.
Michael Pershan 3:01
That was a complicated sentence.
Craig Barton 3:03
No, I’m living in my car. I’ll let the dramatic pause your left there. It’s perfect. Because it’s ideal. It’s because it’s as we often chat about explanations, we have similar things but different things. And this is definitely different. So So tell me how this plays out and tell me why you do this.
Michael Pershan 3:19
So here’s what I’ve realised what I realised is it was during a lesson for I teach young kids and older kids just as a funny thing about my school. So I teach third graders here is one of the classes I teach. And those kids are, what are they eight, maybe nine? Or is it seven or eight? No way, my son is seven. So let’s say eight or nine. So they’re on the young end. And I was getting ready to teach a lesson about symmetry. And the first thing I tried, the first thing that came out of my mouth was today we’re studying symmetry class. And symmetry is and I immediately, I backed off in my head this is I saw their poor ashen faces, how sad they were that I was dieting like that. I took a step back then. And I said, Okay, wait a second, tell me a shape that you could fold in half. And that was much better. Because then all the hands went up. And I suddenly had a class that was thinking and thinking in the right direction also, and thinking about things that would be necessary to think about before you could understand what symmetry is. I so so then I started doing that more often I was doing a lesson about algebra with some older kids. And it was about systems of equations. And I said, Oh, I know what to do now. And I said, Tell me two numbers that add up to 10. And they did. They told me and everybody in the class could do that even the students who would have found it hard for me to start with variables and an equation would have found that that hard if I had written x plus y equals 10. What are two numbers that satisfy this equation? There are some students by class who would have been able to answer that so so so that’s what I started thinking Oh, what I should really do is, before I explain anything, I should think I should try to translate basically, as much of the explanation as I can into questions. And ideally, it’s questions that at the very beginning, everybody can answer so that I have given everybody kind of a clear signal that they can be part of this. And there’s probably cognitive benefits to that also, right? Besides the kind of engagement stuff. I imagine, I love. Because, you know, you’re saying to kids, you’re reminding kids of things. So that’s, that’s, that’s my tip.
Craig Barton 5:33
Right? Well, let’s dig into his marks. I love this. But as I say, it’s different to what I do. But I think I get the feeling you’re right. And
Michael Pershan 5:41
I’ve read your books, and yet I can’t remember. I’m sorry, I, it’s please.
Craig Barton 5:46
Well, I’m very much kind of, you know, this is the way you do this. Listen to me really carefully. Now you do it as in a nutshell. But what I want to dig into here with with with yours is, are these questions your kind of prerequisite knowledge check? Or is this a different thing? Are you so it’s like systems of equations is a good example. Are you assessing the find they know what a variable is? They know how to, you know, add two equations together? Has that come before? And then these questions are kind of to engage and get them into it? Or is this? Are they much the same?
Michael Pershan 6:19
I don’t know. That’s a great question. I feel they’re very similar territory, right? I think that’s what you’re picking up on. There’s, it feels like a lot of different types of lessons benefit from a slow ramp up, right, where you have something like this, even if it’s not exactly this, I don’t think of them as the same way. But maybe I should write maybe I should think of this as the preamble, a kind of a check for understanding a prerequisite knowledge before I dive into, you know, a worked example or an explanation or modelling something. But that’s not how I think about it. The way I think about it is, when I’m about to explain something, I need to slow down. When I’m about to open my mouth and explain something to kids, I need to translate that. And maybe what that’s doing is, is like you’re saying, reminding myself maybe the reason why that works is because it’s checking prerequisite knowledge or kind of reminding kids of prerequisite knowledge. But I think it might be more, I think it might be also because it’s an invitation to join in, it’s a clear signal, you are going to understand this, it’s a way to I love how in English, we say pay attention, as there’s like, oh is if there’s currency involved, it’s almost like you’re putting down some money on attention. And now you’re invested, if you want to take the metaphor further. So that’s kind of how I think but you know, the thing is, is that a lot of things in teaching, it feels like when they don’t work, it’s because of a couple of reasons. And when they do work, there’s a couple of ways to see it, you can see a lot of things socially or cognitively. You know, so should we see this as reminding students of prerequisite knowledge? Or should we see it as inviting students to participate? I don’t know. They kind of sometimes feel like very hard to separate, they always happen together and teacher, or most of the time they do, I guess you can tear him apart at the edges.
Craig Barton 8:08
It’s really interesting. This Michael, it feels to me like if I was to build this into the way I do things, then it feels to me like it is it is a little bit different to prerequisite logic in a really good way. Like I think your symmetry runs a good example of this, like asking kids, can you think of a shape that you can fold in half that feels to me a very different than a prerequisite knowledge check that feels to me as you say, I like this idea of this invitation that you’re part of what’s about to happen this this new knowledge. So it feels like this could kind of sandwich in between a my my concern with making this a prerequisite knowledge check, is the thing that prerequisite knowledge checks that I think anyway, is you need to get mass participation, you’ve got to get all the kids responding. Because if you don’t, then there’s a real danger, you start making assumptions that just because one child knows this, everybody knows this. And that’s bad news anyway, but particularly for prerequisite knowledge, because then the whole the whole deck of cards could could fall apart. So I’m interested in how you’re kind of collecting responses in this what I would consider kind of this middle phase where you’re where you’re asking questions, as part of your explanation. Is it one to one Is it white board? What how does that play out my call?
Michael Pershan 9:17
It’s not systematic. I mean, it could be systematic, but I’m thinking about this third grade class where they were often transitioning between things I was I the way this works is for these little kids, I come into this classroom, and they’re in the middle of doing something with their homeroom teachers. And then I come in, and I say, hey, it’s math time. Mathematics time, maths time. It’s time to you know, to do some arithmetic or whatever. And so I’m really sensitive to gathering attention and having it feel as fun and communal as what was happening before. So often what Oh, the other thing about this though, Have to say just one response to your question is my addled brain sort of like, remembers things that I wanted to say in the wrong order. So I’m sorry about that. But the other thing I wanted to say was part of asking a question that everyone can answer is that it’s an easier question. So so how do you deal with that it’s not engaging for a very sharp child to be asked a question that’s much too easy for them. So. So the way this would often work is I would say, maybe that symmetry question, tell me a shape that you could fold. Actually, I’m gonna go with the other one. Tell me two numbers that can add up to 10. And I would look at my around the room, and I’d try to see as many hands up and I’d be like, Daisy, because I’m calling on Daisy, because Daisy never raises her hand. And she, you know, often has a hard time in math class. So DAISY, go first aid into brilliant, who’s got another one? And picking another kid. Okay. And, and maybe that’s Mark and Mark is five and five, amazing Mark. I’m reading on the board. And then I see, you know, oh, Oliver, Oliver has his hand up. And Oliver is an all star. So I call on Oliver. And Oliver says, you know, five and a quarter, and four and three quarters, and I say, great. And then I write that down. And I want to honour the fact that he’s thinking, so I would sometimes ask a follow up question. In that case, I would say, Oh, that’s amazing. And how did you know that? How did you figure that out? How did you decide that it was going to be that? I mean, I noticed that that’s smaller than five, you went four and three quarters? Can you say a little bit about that, trying to show that to those kids in the class that, that cuz there’s this contract that you need to have, right? Of the promise I’m sort of making here with this activity is, I’m promising kids who often have a hard time in math class, that they’re gonna be able to understand what happens. And I’m promising also, to kids who feel sometimes as if the class is moving too slow for them. Or if they got it already, I’m promising you’re gonna learn something, too, you’re gonna have to think hard also. So I’m trying to promise everybody that the good stuff is coming.
Craig Barton 12:17
This is great, Michael. But just one final question on this. You know, I’m always intrigued by the way you do work to examples where your students study their completed work, to example, read it, then answer the self explanation prompts, and so on. How would that fit in with this? Would it be a kind of series of these kind of what almost kind of warm up or participation questions and then it’d be okay, now, here’s, here’s a new thing for you to study. What’s What’s the transition between the questioning to the studying the example of like?
Michael Pershan 12:47
I think it’s exactly like you said, and it ties to what we were saying earlier, which is that things like this, things like these invitations or these open or questions, more open questions are a frequent part of, of instructional models. When you look around, it’s almost like a part of the everybody’s paradigm, it’s a good idea that a lot of people have is in one way or another, you want to start with something more accessible either for cognitive reasons, or for social. So with worked examples. I’m thinking, hey, there’s a lot of I know where we’re heading. And I want us all to notice stuff that is going to be necessary for the work example, I want us to remember the things that are going to show up in the work example, perhaps so it might be more tightly tightly connected to prerequisite knowledge. And then I would say, well, everybody, we’ve just found a bunch of numbers that add up to 10. Now, what if I also told you that the difference between I’m thinking of two numbers that add up to 10? And the difference between them? Is eyes? Three? How would you find that let’s study an example. Let’s look at how one student did that. And then we’re, you know, we’re on to the next thing. But in a way, that’s, that’s right, because worked examples are is what we do, I think, typically for when we want to teach a procedure, right? Or a strategy, and explanations, I think of is, oh, we want to explain what a category is or what a concept is. And that’s part of like the parallel worlds thing here. Like in the world example, procedural world, the way I think of it is, if I’m trying to teach kids a skill or a procedure or strategy, I’m in the worked example world, and I want to start with some sort of prerequisite question that will help them notice and remember knowledge, and then we’re gonna go to a worked example. And then I guess what I’m saying with this tip is, it’s broader than that, right? The same kind of two part thing applies more broadly, whenever you’re trying to explain anything. It’s good to start with some questions that everybody is able to answer. Because of all the reasons we’ve been saying, so So if I wanted to teach kids what a triangle was, I With I don’t know, I don’t know what I would the concept of a triangle. I don’t know I, I, I kind of just committed myself to something that I don’t know how to do. I got young kids. But I suppose what I do is I’d say, you know, what can you what are all the things you don’t know Maybe? What are all the things you can make with three, three lines? What are all the shapes you can make with three lines? And I’d say n cubed, raise their hand and say a triangle and be like, Great, I’ll draw on the board. And then I’d say, what else can you do? And maybe some would say, I don’t know, just like three lines at the centre. And we knew that and we’d say, okay, these things. Now I want to teach you some of these things are triangles, and some of them are not just just being rigorous about in my head remembering to open up the question, the beginning, is, I suppose, with a little bit
Craig Barton 15:46
likely, it’s definitely one I’m going to need to reflect on this. I don’t think I involve my students enough. I like this almost this invitation, this is definitely something I need to reflect on loving Michael. Alright, what is tip number two, please?
Michael Pershan 16:00
Tip number two is another hard one. hard one? One, a hard one tip? Okay. All right, it’s day number two is the best kind of feedback, in my experience, the best kind of feedback to offer a student or a class when there is mistakes, or when there’s errors or when there’s things that they haven’t done, right, the best type of feedback is a learning activity. And it’s not even close. It’s much better than written feedback on a page of their work. That’s my, that’s my, in my experience learning activities is or better feedback than writing comments on a page. And it’s not even close.
Craig Barton 16:43
I like it. I like I love no hasn’t had any kind of definitive answer. This is good. Michael, good. Give me some give me some examples of this, how you might use this in to sell your argument?
Michael Pershan 16:53
Absolutely. Well. I started reading research. Ah, okay. I’ve been a teacher since 2010. And I try in my own way, I was reading research. Back then, I think I ramped up over the first couple of years, I went from reading. Like Paul tufts books, I don’t know if you know who he is. pop psychology, mindset things. I got kind of ramped up to like, find my way around research papers and stuff. And then I’m okay, so I said, I’m going to understand now I want to understand all the research about feedback, and I want to think about, I know I can be doing better. So I want to understand this. So at first my project was I’m going to learn how to write the best comments ever on pages, I’m going to understand how to take a stack of quizzes or a question that I’ve collected from the class, and I’m going to write the thing, the thing that will work, and I will write it on that page, and it will lead to learning. That’s what will happen. Because I read that feedback was immensely impactful. And super important. And I wanted to do it, I wanted to do the thing that is the best I wanted to, to master that part of teaching, it would lead to better learning would turn mistakes and for learning. And so I started reading. And I started looking for things that I started writing them. And I would take a lot of time and I read a lot of comments. And inevitably, they’d still go into garbage, the comments on the papers after I was done. Students wouldn’t always read them carefully. And I said, why is that? Why is this at all and that I kept reading research. And I read dealing Williams, writing about research and formative formative assessment. I know he’s a friend of the podcast. And and he pointed me to cougar and Denise’s writing about research, reading on feedback. And from them, I got really something that what I took to be like, a very direct question about feedback, one that made me basically give up on my project of writing comments. Because the question was, how does feedback work? And how could it work? Really? Right? You don’t usually teach a class the first time by writing comments on the side of the page, right? You don’t do that. I don’t do that. I don’t say Okay, class. Here’s some comments. Here’s just a piece of piece of paper that says how you’re supposed to do this. You don’t do that. I don’t do that. It’s a bad idea. No one would pay attention to that. So. So what are you doing? So you’re either cougar and Denise, he said, in terms of understanding feedback. And really they were trying to understand why feedback sometimes backfires so often, and so many of the research studies that were done at the time, and why so why work sometimes and what they ended up saying which was very clarifying to me is like look at it’s funny what you pick up from research, right? This is not the point of their paper, but this is what I took out of it. They said conceptually, you’re either teaching by giving feedback, that’s one thing that you could be doing probably Adding new information to students helping them understand something they didn’t understand before, or you’re motivating them. Literally, what else is there? But what else could you be doing? When you’re writing a comment on a page? So your comments on the page must either be teaching kids something, or motivating them to study harder or to pay better attention or something like that. And I’ll say, just on the side, there is a third purpose that comments can have, I think, which is, you’re showing that it’s not directly tied to learning, right? You’re showing, I read your paper, I value what you did. You put in a lot of time to this project, or you wrote this essay, and I read it, and I valued it. And, and there’s good things here. And there’s things that could be better. But we’re learning it could it could have a different role is what I’m trying to say. But if it’s just about teaching and learning what it has to be, there’s not much helps. You’re either providing instruction or motivating. And I asked myself, What am I doing with these comments, and I wasn’t good instruction. And it was clearly on motivating. So I said, What else can I do? And then I started thinking, Wait a second, how do I teach? How do I teach? If it’s instruction motivation? I don’t really know how I motivate.
I don’t I don’t have a systematic thoughts about that. But I do have a pretty clear idea of how I teach things. So I said, Okay, so what do I have to teach? And that changed things for me that I changed the questions I was asking, when I saw a pile of quizzes with mistakes, I started asking myself, what can I teach? What is the thing here that and there’s always something to teach more or less. So I started looking at the kids papers, their their quizzes, their homework, whatever it happens to be, and I started looking at it for the I have, I would like to do a follow up lesson tomorrow to get feedback. I would like to. I mean, I guess I would also Okay, well, I would prefer if everything was perfect, and they understand that and they’re like, Oh, you’re the best teacher in the world. We love you. Yeah, fine. But realistically, I love to teach a follow up less than the next day with a learning activity of some kind. That could be easily modifiable. So I get like Mega specific about what I need to teach. And I would teach it. So that changed what I started doing. I started looking at these papers, and I tried to get very specific on the assumption being they understand some things. I shouldn’t just repeat the instruction I did before I tried to focus in on say, okay, they know how to solve Pythagoras theorem problems. In these cases, perhaps this is a common thing that I think a lot of teachers experience, perhaps when the hypotenuse is missing. But a lot of the mistakes are when a leg is missing, they still squared both sides and add them. It’s maddening. So that’s the thing that they need to learn. So my lesson tomorrow will be a quick lesson about that. And there are easily modifiable formats worked examples are one of them. But there’s others too, where I’ve got instructional activities that I can do and I can just kind of like slot in the thing I need to teach. And I started doing that. And I started seeing learning more, which made sense because I was now doing teaching the way I usually do it not the kind of weird way where you kind of write down in a sentence 40 times and, and hopefully kids learn from that sentence. And I think that’s much better and you can’t throw out, you can’t crumple up and throw out my lesson. Because you’re there for it. And you can’t throw it on the floor. I don’t have to pick up my lesson that I’ve taught, you know, from from from from the garbage and look at my carefully crafted comments. Like sitting with a very sad face, like the toys and Toy Story at the end in the garbage as kids left the room so that it’s a
Craig Barton 23:53
winner, like, well, I’ve got one reflection and then one question for you on this one. So my reflection is when I read similar research, my I thought, right? If I improve my written comments to set kind of follow up work for kids to do like, almost like, come up with a worked example for one of the questions they’ve got wrong in their book and then set them almost like a your term that will be great. The problem is it took so long to do. And still some of the kids weren’t particularly engaged in doing it. So just like you, I thought, Okay, I need to scrap this. It’s not working. So let’s go to what we probably call in the UK like a whole class feedback model. So we look for these kinds of common trends and issues within you know, a set of assignments or homework, and we address the big ones in front of the whole class. But I’ll tell you the kickback I always get on this mic when I start talking about this and I’m hoping you can answer this for me is what do you do about the kids who who don’t need that whole class feedback? What do you do about the kids who have nailed their assignment? They’ve got it all sorted. They’re ready to move on and yet you are spending valuable lesson time with the rest of the class. Well, what’s what’s your response to that?
Michael Pershan 25:00
do we How much time are we devoting? And what are we doing? Is I guess the question. When I have done this, what I’ve tried to do is not repeat instruction. But to give more specific instruction on a more specific aspect of the mathematics, or whatever the skill happens to be right. My model for this is that you were always trying to teach, I’m tracing a circle, a blob area, with my with my pencil, right? If we’re always trying to nail in original instruction, like, if we’re trying to teach kids a skill of a constrained area, and it’s not the biggest we could possibly do. And it’s not the smallest either, because we’re trying to find the right size skill to teach the right you know, we don’t want them to just be able to write one kind of essay, one kind of paragraph one kind of sentence, one, be able to solve one type of equation, multiply specific types of numbers, but we don’t want it to be everything, we’re teaching a certain thing. And so we guess on that size, and the way I think about it is sometimes we what’s revealed on one of these things is that we guess, too big, too small, we taught most of the territory, but not a little corner of it. And very frequently we’ve taught, you know, you’re trying to the kind of weird thing about teaching, I guess is you try to teach a blob by teaching specific points inside. And you try to build this territory out from the inside, usually. So you’ll learn through certain things reflect on why they’re true. And you’re kind of hoping to sketch out this area, but you inevitably fail, or leave areas blurry. And that’s what I’m trying to do in the follow up thing. So I don’t think of it as repeating any instruction, I think of it as new instruction, that is flushing out an area that we hadn’t really properly flushed out before. And so I think that, you know, I can go to your podcast and say anything. And you have to either believe me or not, right, I could save you. There’s no reason why you have to believe me when I say I think you know, it’s worked out, okay, with my students, they don’t seem bored, even the kids who got it, right. But I can tell a story about why those kids don’t react in that way, why they’re engaged, as engaged as they are, you know, usually, and it’s because what’s happening when I say, teacher worked example lesson about some more specific area, you know, kids are having a chance to explain why something’s wrong, apply, you know, their knowledge to a specific type of question that maybe they already know how to do, or, but they’ve never, we haven’t featured it in the lesson yet. Really, because of how that was revealed. By, you know, it’d be a little bit weird, if I know weird, I guess this happens all the time. But I wouldn’t devote this kind of, I wouldn’t choose to do it. Again, if it was just a clone of something we’ve done before, I’m always trying to hit it in a slightly different way, have a different kind of learning activity than when we did before? So that’s the hope. I don’t know. I think it usually works out. But the other thing is that you keep it short. There’s only so long the kids can get bored for so, you know, this is a 1015 Minute activity that you’re doing to give feedback on a crucial matter, then, then, then, how bad can it be?
Craig Barton 28:20
Yeah, I completely agree. Michael, I’m always intrigued by this, the more I work with teachers, the more I hear differentiation being used as a way to scrap a load of really good practices, like because it’s perhaps not suiting the needs of every single child where we can’t do it then. So that gets kind of thrown out the window. But but like you if it’s a relatively short time, and it’s not reteaching I think it’s super powerful. I just am really worried about this kind of almost like the like, it’s like a game as soon as you say some people just sort of like differentiation, and you’re like, alright, well, I can’t do anything about that. Because it’s impossible to differentiate perfectly. And it just, yeah, it concerns me. So I’m just interested to get your take. But that’s great.
Michael Pershan 28:58
That’s fantastic. Yeah, it’s interesting, like because it because if it’s a game, it’s always possible to do that, right? It’s like, Ah, I found it. What about kids from New Jersey, they already know. They already know, this bridge, less. And I don’t know anything about New Jersey, New Jersey, for those in the UK is right next to New York is where Bruce Springsteen has fun from, and other musical acts subsequent to Bruce Springsteen, and it’s very close to New York. I’m not actually as provincial as many New Yorkers, because I’m from the Midwest of the country. This is a little bit of American spice just
Craig Barton 29:38
promotes the idea. We’re a global podcast, Michael. So I like that. That’s good.
Michael Pershan 29:43
That’s great. The the, the pushback I get from teachers when I talk about feedback is typically what do you do when there’s a million mistakes across a long test? And there’s no great answer to that because it’s not easy to get fit. Back on a big test with a big exam that’s got like 40 questions on it and five kids got this one wrong? That’s That’s a harder question for me because I because I kind of want to say, well, there’s no good way. It’s hard. Like, how are you going to figure out what to focus on you, there’s AI and there’s things you can do but but your learning activity needs to get much cleverer, because it’s much more difficult to give feedback on something so varied. So that when you started, I thought, you’re going to tell me that
Craig Barton 30:29
it was some ballista as well. But when you when you’re back on in a couple of years time when I start having to re invite guests on, Michael, you can answer that question. That’d be fantastic. All right. Michael Walker, what’s your third tip for us today, please?
Michael Pershan 30:44
My third tip is get used. I said, used get used to asking what if? What if questions after explaining something almost constantly and the way when I say get used to get accustomed to, I think there’s, in my own teaching life, there’s two. There’s two things about teaching that helped me get better. And I think that this, you know, goes to the heart, a little bit of what makes teaching a challenging profession. It’s some some ways that I get better at teaching or by understanding more things. Better understanding some aspects of teaching or mathematics or whatever. Or children, and another. But even the things that you understand about your subject, the classroom, pedagogy, research, whatever, it’s so easy to forget them during the course of a busy year, right, and then that goes along, it’s almost like a think of it as a sports analogy. As some more American colour, you know, in basketball, you can be a student of the game and understanding it, but part of it is, is is trying to it’s, you know, it’s a performance thing. If you can’t bring it to the court every day. You’re you’re not performing at a high enough level. And so there’s, there’s kind of an intellectual side to why I think asking what if questions during explorations is very powerful. But for me, I have to kind of like, put a sticky note on my computer remind myself that this is something that I want to be accustomed to. Because if I forget, I sometimes after a couple of weeks be like, Why don’t I stop doing that? It’s such an easy, small thing. And I’m constantly like, trying to keep it together and make things second nature that are not naturally second nature to me. So I’m trying to get accustomed to it.
Craig Barton 32:46
Can you give me give us some examples of these what ifs, Michael?
Michael Pershan 32:50
Absolutely. Absolutely. So what what do you think? Should we tell the story of like the intellectual story? Now let me just listen. Okay. You said to give an example of this, so, so I’ve just finished explaining. A student has just finished explaining. I don’t know. No, I had to go back to a previous thing. My student raises his hand to answer How do you make? How do you add two numbers to make 10? And says, I hear what I said before five and a quarter and four and three quarters? And I say that’s great. And what if we were trying to make 15? Or what if we were trying to make 14? Maybe that’s the question I’d rather answer because, because just thinking quickly here, you know, five plus five is 10. But you can go up and you can go down. And maybe what I would like to nudge this child to think about is to make a generalisation. Oh, seven plus seven is 14 go up and down. And what if we’re trying to make 100 Whatever trying to make 1000. But the broader point being that what if questions are ways of supporting people and making generalisations? It’s, it’s, it’s, it’s poking precisely on the generalisation button in your mind. And in going back to this kind of blob that I was tracing out in front of this camera. You know, not so long ago, right? We try to teach a blob, we try to create a blob like skill out of particular things. And in my vision there, you know, each particular thing is a question that a child successfully understands or has answered. And when I asked that child, what if I’m trying to draw a kind of a blob around that? I’m trying to get that kid to explore more territory build a generalisation around that particular point? So I’m trying to flesh out each particular question example, idea that a child is having. We’re understanding I want to get a little more territory. I want to get a little bit more I want to build that into a generalisation. Otherwise, it’s just a question. It’s just a isolated bit of knowledge. It’s just a lonesome fact.
Craig Barton 35:10
It’s really, really interesting as Mike, let me just reflect on this for a moment. So one change I’ve made to when I’m working with kids these days, is I like to do a lot more kind of learner generated examples. And I never used to do this, everything used to come from from me, but I reread thinkers by and Watson, John Mason, and Chris and Liz, Bill’s recently, and they have some really good structures in there for learner generate examples. So a good one is, give me an example of and another and another. So something like, give me an example of a fraction that’s equivalent to four fifths, and give me another one, and give me another and I tend to chuck a little twist at the end, make that last example as interesting as you can. So to try and get kind of boundary examples, I really like that one. And I also really like they have one called additional constraints, which is something like, think of two fractions that are together to make one. So that’s the first one and then the constraint comes in, but the denominators need to be different. And then another constraint for you next, and the numerators need to be the same, and so on. But what I like it feels like this will slot in nicely along there, it feels like it’s kind of it’s kind of like a learner generated example, because you’ve asked, you’ve asked one question, they’ve come back with an answer. And then it’s okay, well, what if I changed it a little bit? What would you need to do to your answer? So I really like this, because what I like about learning generated examples is they lead towards generality. They also show students understanding really clearly because particularly if you push towards the boundaries, you can really see whether they grasp the concept or not. But after that big, long ramble, my question is, when do when do these come in to like a learning journey, Michael? Because my fear is, if these are coming in the explanation part, it may be too much too soon. But they come in after an explanation or come in after a bit of practice. When When do the what if questions work best for you? Do you think?
Michael Pershan 37:00
Well, I think about it in terms of distraction, right? I wouldn’t want a what if question to distract from our understanding of going back to this analogy that, for whatever reason is stuck in my head this morning. If we’re trying to draw a particular point, on this map, we want to make sure to actually get the point. And we want to make sure everybody gets the point in the room before we start expanding. So so there is a bit of a constraint there, right? We don’t want to if, if, if we’ve just explained something, and I assess that in the room, not everybody has had it, and the first student that I call on seems to understand it, I’m not going to push What if, because I don’t want to distract from the learning in the room. We can’t generalise from something that we collectively don’t yet understand. Well, now it when I do a worked example, routine, the way that I’ve kind of incorporated this is I think about this as a self explanation prompt. In other words, I think about this as a, it’s very hard. So self explanation prompts, are supposedly, are supposed to not supposedly supposed to help students. support students from learning from examples. So if you have an example of something, a model paragraph that you’d like students to write, to write in the style similar to or if you have a procedural way to solve some problem, and that is an example of that on the board, self explanation prompts are supposed to help students, you know, find a way around that. And what if questions, I think, are examples of those things. And they’re just easy to say. They’re easy to, they don’t require tremendous creativity to come up with so. So when I’m doing a work example, just to straightforwardly answer your question, students will analyse the example. And then they will discuss it and often, I will say kids, okay, go ahead. Your first analysis question is about making sure that you can, your first explanation question is make sure that you understand everything here and make sure that you understand the particulars. You’ve paid attention to everything you’re you’re not dropping the ball anywhere here. And then the second question is, okay, now generalise it. So I guess the way I think about it is, once we once we understand this thing, why not generalise? It doesn’t need to wait until practice.
Craig Barton 39:31
Really interested in again, I’m going to need to is one of those things, I’m going to need to think where they fit in for me, I’d never thought of putting them in the self explanation. For me, it feels like something that comes after some kind of teacher directed practice. But to take your point, I don’t see why it shouldn’t come in. Early on. That’s interesting.
Michael Pershan 39:47
Well, let me make the case a little bit further. Craig. Yeah, doctor puts pressure on you. Okay, but just just to make the case. How are students supposed to use an example for practice? Right, there are different trials. We’ve all experienced students who perfectly seem to understand an example and then are unable to apply them in practice. So how I think some people think, Oh, you just copy it, you just you just do the thing. But But you and I know that even the slightest differences in surface level details are often meaningfully different to students when they’re beginning learning. So it’s not enough to say just do the same thing, an equation that looks ever so slightly different, makes it impossible for them to do the same thing. So we are talking about generalisation through and through. We are necessarily when we when we say apply this example to this problem. We are talking about generalisation, so some amount of generalisation has to happen. And we do need to support students in making those generalisations whether what if questions are, are you know, we could talk about that we could talk about whether that’s the right way to do it. But something needs to be done to help subsume these things under the same framework.
Craig Barton 40:58
It’s interesting this and just so I’ve got that said,
Michael Pershan 41:00
I think I think one thing that in your work, you would very, very slightly right, you do very small variations between between examples and practice. And I think that we could do that also with what if questions? I think that’s not so you know, very different from what you do. Right? We could say, whatever variation you would do in a sequence of problems, in your approach, Craig, where you’ve got like, minimally different practice. We can do that too. Right? We would say what if instead of 12, it’s 13? You know?
Craig Barton 41:30
Yeah, this is fascinating. This, Michael. Yeah, I’m going to need to, I’m going to need to ponder where this fits in. Because when you when you were saying this, I’m thinking, yeah, that’s. So what happens if this six was a 12? What happens if the length doubled? It’s, it’s this kind of thing that I would fit into the practice. But I wonder whether you can slot in a bit early, you always made me think Michael which, which is why I wanted you on the show. That’s, that’s brilliant stuff. Whilst what’s Tip number four, please.
Michael Pershan 41:55
Okay, tip number four, is to use partner work as a chance to recruit quieter kids to share their thinking. So, so the idea is, is that we all have students in our classes that are reluctant to share their thinking for whatever reasons, and it’s good for them to share their thinking for various reasons. And we can talk about those various reasons on both ends. But one way of bridging that gap for the kids is, I think, if you ask a question, and then ask partners to talk about it, or to work on it, that gives me a, a very clear picture of what they’re working on. And I can see them, hopefully being successful. And I can go up to them and say, hey, great job. Great job. Craig, you, you did a wonderful job talking about this just now. Would you mind? If I called on you? I’d like to call on you, actually. Now, would you mind? I’d like to call on you. Greg, this is brilliant. I’d like to call on you to share your idea with the class when we’re discussing. I’m going to do it okay. And every once in a while a child will say no. And you know, that’s okay. I’ll say are you sure? It’s great. I’ll just call me it’s no big deal. If they say no, it’s fine. I’m not gonna get into a weird power thing about it. But But, but sure, you know, that often works. That often works for me. Right? They’ll say yes. And then I get to feature them in front of the class.
Craig Barton 43:27
dishy Great. Well, let’s let’s dig into this. Michael, I’m always fascinated by the practicalities, what what would be an example of the kind of question you would ask to get them to then start discussing? I’m assuming it’s not just the kind of straightforward? The answer to this is seven or or is it? Is it those kind of right or wrong questions? Or is it more kind of discussion based ones?
Michael Pershan 43:47
Well, it you know, it could be, there’s no reason why it can’t be if I asked students to solve problems, and they’re doing it with partners, and we’re on mini whiteboards, or whatever it happens to be i There’s no reason why I can’t call on a child and say, can you tell us what the first steps going to be? I’d like to call on you for that. That’s fine. It’s also more discussion based things. And you’re right. I mean, I find more value in asking partners to discuss things that are more discussing based because that, you know, it’s right there in the title discussion based. It goes better if you ask partners to do something that needs partners works for. And it’s also easier, you know, more seriously, I want kids talking to each other very frequently. Very, it’s very often the case that I’ll have kids in class that think, oh, I don’t belong here. I am not as smart as the other kids here. I can’t do the things the other kids can do. I’m just going to keep my head down. I’ll do my work. And just going to this is not something where I’m going to speak up. And I had students like that in my classes this year, my 1314 year olds this year. I had this child and and there’s tremendous benefits for getting kids talking to each other in this way because it builds confidence. I think giving explanations is a great way to learn. And if you are terrified to share your ideas, you will learn less. And also feeling like you belong in a classroom. This is this is every I think every classroom teacher would agree that’s often very important for some kids to feel as if they belong socially with a group. It changes their ability to take intellectual risks in the classroom. And it allows it makes it much easier for the teacher to talk about mistakes that might have been made or, or to support their learning in various other ways. It just feeling like you belong matter. So so I will ask kids to talk about stuff together, I going back to work examples, self explanation prompts are a great thing for partners to talk about taking turns explaining things to each other. Okay, everybody, here’s your questions to we just study this example up here on the board. Here’s what I want you and your partners to talk about. First of all, talk to your partner, make go through each step, make sure each person is understands everything that’s written on the board for each step. And then what I’d like you to do is, first of all answer this first question over here, which is why did they choose to do this? Couldn’t they have done that? And then what if instead of 12, the number 13, was in this president plus 12, it could have been plus 13, but would have been similar or different. If they’d done that ready, the sign partners go. And then here I am walking around the room, kind of like looking very casual. Kind of just like I’m not paying attention, just hands in my pockets. Walking around people. I’m not even paying attention. I’m just enjoy. I’m sipping my drink. I’m good. You know, and then I Oh, here I am. I happen to be standing next to the quiet child. I’m like, Oh, wait, I was just I was just happened to be standing here. That’s a brilliant point. Hey, could I call on you during the discussion? Just to share that it’s a really good point. People should hear it. Oh, yeah. Okay, great. Okay, then. All right, class. Welcome back. Okay. So they’re great discussions, everybody we’re gonna call on Tony. First, Tony. Why do you say, you know, what would have been different it was plus 13, instead of plus 12. Tony. All right. And then Tony talks and and then 10 years past, and he writes me a heartfelt letter about how that lesson changed his life. And he one day becomes a congress person in America. And he dedicates a museum to me. That’s the goal. That’s the plan, at least unlike in step two of that plan.
Craig Barton 47:47
That’s what we’re all in it for. Because my question I wrote down was, was exactly what you respond to. They’re like, what do you do whilst this partner talks happening, because there’s a real danger we can get in the way, right? Particularly if you’ve got a quieter child, a shy child, a less confident child, we call as we walk round, they they’ll tend to shut down a little bit, or maybe even I don’t know, if you see this, like kids, when they see you close by, they want to almost perform so they stop there kind of natural rhythm that they were having in their conversation. All of a sudden, it’s, it’s a phoney dynamic, it’s different than not having that one to one conversation that we’re having. So aside from kind of walking around casually, with with your drink, how do you not get in the way, if that makes sense, but still be able to listen? So you can pick up on these these key insights? It’s tricky, isn’t it?
Michael Pershan 48:35
It is tricky. I mean, this, I’d say the thing that I try not to do is I try not to, I know that we’re going to have a discussion. So I try to be thoughtful about when I interrupt. I try to only interrupt if if there’s a real need. Not just to correct a mistake that I’ll be able to correct in the whole group in just a moment. You know, I think a lot of the the other thing that I was there’s a there’s an educator in Canada, who has a book that is a hit in the United States. It’s called Building thinking classrooms. And one of the things that he identifies in this book is the concept of I think he calls it proximity questions, questions that students wouldn’t ask, but they only asked because you’re, you’re nearby. Like you’re standing nearby, so like, I might as well ask, we don’t know this. We’re talking about it, but he and he’s right there. So so I’m trying my body language is not. I thought about different body language and ways of attending. When it’s clear that I’m looking for questions to answer. And when I’m trying to give room for people I’m standing a little But farther back, I’m not really making as much eye contact. And basically, I’m not not doing the things that I’m not acting the way I am. I’m not like poking my head. And all the time, though the way I am when I’m looking for questions to answer, I do have those different modes in the classroom, I do have a, you know, attention. Question seeking mode, where I’m saying, who’s got questions, I want to answer your questions. I want you to ask questions, please ask questions. And this is a different mode. I’m standing back, I’m trying to think about how far I am. I’m not. I’m trying to train them to be a little bit more independent in this way. That again, I’ve had classes where they need me to be a little bit more attending, and, and any independence, any student independence is something that you’re trying to help them become more independent, but they might not be ready for it yet. So it’s a balance in that way to tastic. I don’t know. All right, Michael. Yeah. Whenever you ask a hard question, I just talk and it’s because because that’s the way teaching is right. There’s, there are there are things that are hard and solvable. And there are things that are hard, and they’re just hard.
Craig Barton 51:12
Got it. Brian, Michael, fifth and final tip, please.
Michael Pershan 51:17
Alright, so my my fifth and final tip. Now I am looking at my notes. And there’s four tips here. Now you think I’m looking at my document, the fifth one has been deleted. So so you’ll have to tell me I before we talked, I shared this fifth one. It does exist of bad news. So I remember I think I remember it. Okay, because I have bad news for you. But
Craig Barton 51:43
you said one of them was bad news for you because I am looking at your same document because it’s a shared one. You’ve caught it off. So I it’s a mystery to me. I can vaguely remember it. But it’d be a nice surprise for me what the fifth one is.
Michael Pershan 51:56
What you I remember before you told me that one of my tips wasn’t as good as the other. And so we deleted one. So I’m hoping I remember the right one. If this tip doesn’t make sense, it’s my fault. I mean, obviously, it’s my fault, but it’s my fault in a bigger way. Anyway, I think what I wanted to say is I think that tip number five was when you call on a student do not move on from that student. Until they have said some felt
Craig Barton 52:23
sorry about that.
Michael Pershan 52:25
Yeah, okay, good. That’s the good one. Okay, good. Right. And that’s another one of those habits that I’m trying to constantly remind myself on, because I think it’s a good one. I think it’s something that I tried to hold on to it’s one of those things that I when I don’t do it, I’m like, Oh, I did it again, I moved on from a kid. And the last thing they said was wrong. And that didn’t feel right.
Craig Barton 52:44
How would you how would you do it, Michael to talk talk us through this as an example.
Michael Pershan 52:49
What I, what I used to do is I’d call on a kid and I’d say, you know, some of the times I asked questions like the ones before, like what are what are two numbers that add up to 10? That seems to be the one that that’s safe territory for me in this interview, I can always go back to that question. And so I say that and you know, kids like one and three, like so. So a very easy thing to do that I find myself falling into sometimes is is I’ll say, No, that’s not right. Anybody else? Who else has an idea? Which just trying to like steer away from the one plus three idea, which is not true. One plus three is not 10. So what do you do in those situations? And so what I’ve tried to do is I’ve tried to, and because and just to add on to why, like what’s going on there, right? Because teachers are good people. I think what’s going on there is at least psychologically, for me, I hear a one plus three is not 10. And I think to myself, Oh no, I need to get away from this situation. This is an embarrassing situation for this child. The more time I dwell on this child’s mistake, the more embarrassing it’s going to be. This child is going to I’m going to write and there’s so many bad ways to do it. Right one plus three. I’d say no, no, what is one plus three though? And then they say 10? Because they just said that one plus three is 10. And I’ll say no, no, but but can you Okay, start with one. Let’s walk you through it. And what one plus 121 plus and it’s gonna it’s gonna go badly and everybody will there’ll be Snickers there’ll be kids going while this kids doing you know, there’ll be whispers and then like a kid behind will be like st st watching your pastime. You know it’s a far because kids are trying to save because they’re all so nice trying to save their friends from embarrassment. Okay, so how so but But so every instinct in my head is saying get away from the situation. And yet I think that that’s sad, because then the lat you haven’t given this kid a chance to be smart. And then the last thing they’ve said is something wrong. And we don’t even know if they’re gonna learn anything from it. So what can we do? So my goal now, in those situations, I try to remind myself, let’s get this kid to smart territory. And let’s end when this kid says something smart, because if you say something smart, doesn’t matter what he said before that was wrong. That’s fine. You’ve learned something and you said something smart, you’re part of the community of smart people. We’re all we all understand math. We’re all working on this together, but we’re ending in the same direction. So how do I do that? How do I get this kid to say something smart? That’s what’s what’s in my head, and I’ve got a couple moves. I don’t have a tonne. But But one thing I do is I corrected for the kid. And then I shift to explanation. So I’ll say actually, one plus three is not 10. It’s four, can you prove that it’s four? If I think that the kid can do it. Why Why does it make sense that it’s four, actually. And a lot of that’s, it’s a little bit risky still, because the kid might not know. But very often, if you choose your battles correctly, the child, in my experience has been able to say, oh, right, it’s four. Oh, yeah. Because Frey because because one, and then two, and then three, and four. And that, and I like, there we go. Yes. Brilliant. That’s absolutely right. So can anyone build on what Ari has said, He’s proven that one plus three is four. So one plus one wouldn’t be 10. You know, and I can kind of, it feels better. It feels better. The kids learn something, I’ve corrected it. And I think that’s an example of how, what feels like it might be meaner in some ways to say No, that’s wrong can actually be be kinder if it as long as it’s not the end of the story. So So quick correction. And then new question. Or sometimes that explanation is, is powerful in my experience? So the paradigm is like, wrong answer from a kid, quick correction for me. Quick follow up question that the kid can successfully answer now that they’ve hopefully realised something from feedback. And, and then we move on.
Craig Barton 57:22
I love it. Michael, did you say you had a couple of moves? Was that was that the two moves? Is it kind of quick correction, followed by a follow up question and quick correction, followed by asking them for an explanation? Or is there another move? Obviously, there?
Michael Pershan 57:34
That’s the one that works the best. You know, I think the other things that I do I think more teachers would would, I think recognise as like, familiar territory, you know, you say? What’s the other one? Yeah, like, you know, kid says one plus three. So you know, what’s one plus two? That kind of thing is, is I think,
you know, trying to get a kid to realise a mistake that they made by asking a question that they think that you think that they can answer on their own. And I think more familiar territory, though, the, this is new to me, this is this is this is this is something that, that I don’t know that I need to keep my eye out for in my own teaching and see what comes up and try to kind of see what other moves I do have.
Craig Barton 58:36
A lot more, Michael. And just one final reflection for me on this. One of the things that I find myself doing a lot or found myself doing a lot is what Doug Lemov says, calls rounding up. So this idea that the students has a wrong or an incomplete answer. And you as a teacher have the critical part to make that answer. Right. And it feels great in the moment, but then you think you know what, this isn’t good this because the kid thinks they’ve actually understood something when in fact, they haven’t really they’ve given like the the incomplete answer. And then you’ve added the kind of key bit and it’s not checking for understanding, it’s kind of a bit of a bit of a cover up where everyone’s involved. But the thing about rounding up is the kid feels good at the end of it. But what I like about what you’re saying here is you’re not you know, you’re making it clear that that answer is wrong. You’re also not moving on to say okay, I’m going to come back to you let me ask some of the child because that the kids feeling a bit bad about themselves. They’re, I like this idea that you’re being really open and genuine. But you’re given them that other opportunity to feel successful in a in a genuine way. It feels really powerful. It’s it’s not rounding up. But it’s not kind of almost like no opt out. It’s not like you’ve got it wrong, but keep listening. So I’m going to come back to it feels like this is a different strategy to that, that has the best of both worlds. You’ve got your kind of understanding, but you’ve also got the kind of motivational positive feeling. I don’t know if I any of that makes sense at all.
Michael Pershan 59:59
No It makes sense. The thing I would add is that I think what makes this possible for me is when I started realising when I start having a better understanding of the types of questions that I asked, it opened things up, because if the only question you’re asking is the only learning question you’re asking is, what’s the answer? Yeah. What what’s an answer? Then Then a new are kind of stuck if a kid says something wrong. Because, or you can try to find the right answer. But when you expand things to explanation questions, or generalisation making questions when you have a repertoire of right, another thing that I’ll do is a quick correction. And then, so if the kid seems to be like, oh, yeah, I’ll be like this. So why is that wrong? What’s wrong with that? You just realised that it was wrong. Share that, please. That’s another once you have, you know, once you can rattle off, which I feel lately that I’m better able to do like, Okay, well, you can answer a question, you can explain why something’s right. You can explain why something’s wrong. You can extend a question you can do a What’s if what if question, when you have a repertoire of questions that you ask, then, okay, we’ve knocked down one possibility for a kid there. So, you know, four or five others that we could ask this child to answer that they are potentially capable of, and potentially now, especially capable of now that they have realised, oh, that’s wrong. So, so, so, so I do agree, I do kind of the, I think you you nailed it. We’re trying to have kids rounded up, I suppose. I mean, rounding up is is not the image I guess I would use here at all, if we’re trying to orient everybody in the same positive direction, towards learning towards understanding towards contributing to our collective understanding. And a tool for doing that is giving feedback. And here’s an here’s a lobbying thing and normalising error. I mean, that’s not just him, but but normalising error is, is is part of the tool here, right? If error is a big deal, then we have to kind of rear away but if it just like, No, that was wrong, but let’s talk about something, you know, something related to that. Yeah, and but and just this just add on, because I kind of waffled a little bit earlier, because I don’t have a perfect understanding of how, I don’t know if you feel this way. I feel like when I’m teaching things come up, and then I have to kind of like sift through it over the course of the subway, ride home or whatever. And try to be like, did I do that? Does that work? Should I try that again? So I think another thing that I’m realising as we’re talking about this, and I’m reflecting on this is write a quick correction sometimes works. But in the situations where that doesn’t work, sometimes a longer correction still sets things up for the child, right? Right. One plus three is not. There’s not 10. It’s four. There’s no AHA that I hear there’s no oh, I’m like, right, because one plus one is to one plus two is three, one plus three is four. So what would one plus four be? Child? Right? Right. I’ve got a better shot there. If I’ve said a little bit more so so I can, My correction can be quick, it can be longer, but I’m always trying to end with the child saying something true.
Craig Barton 1:03:20
Fantastic, Michael. Love that. Love that love these five tips. So just before we say goodbye, what should listeners check out of yours? Well, what do you want them to take away?
Michael Pershan 1:03:31
Well, I do have a book if you wanted to buy it. That’d be very nice. The book is teaching mathematics, teaching math with examples from John cat. And, again, if you wanted to buy it, that would be very nice. I do have children. This would support us in buying Honey Nut Cheerios for them, which is their favourite food. They eat so much honey nut cheerios. Other than that, there’s nothing really in mind that if you’re interested in more of my things, by all means, I have a website Michael Pirsch n.com. I’m on Twitter. And for Michael followed by person, but that’s all good. You follow me or not?
Craig Barton 1:04:15
That’s great. Twitter habit. I’ll put links to your Twitter, your website, your books will all be in the show notes. And again, we’ve spoken before on my podcast you know, I’m a huge fan of your work and especially if your book I think it’s fantastic. So Michael, all that remains me to do is thank you for giving up your time to be able to tips for teachers podcast, always a pleasure speaking to you. Thanks so much, Michael.
Michael Pershan 1:04:38
Absolutely, Craig, have a great day.
Transcribed by https://otter.ai