Room to Grow - a Math Podcast
Room to Grow - a Math Podcast
Giving Meaningful Feedback
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In this episode, we discuss considerations for providing meaningful feedback to our students. We think this is a great follow-up to our last episode on grading! In preparing for our discussion, we learned about the research supporting effective feedback for learning, which includes suggestions around the type of feedback to give, when to give it, and how meaningful feedback is separate from grading.
Our research articles suggest that feedback is not advice or criticism, but information that helps the receive to understand their next actions. Although it makes sense that students must engage with feedback in order for it to be meaningful, we were intrigued by the suggestion that the receiver of feedback should work harder as a result of the feedback than the giver of the feedback! In other words, our students should work harder than us, their teachers!
We explore some concrete ideas for making your feedback more meaningful, reflect on our own mistakes around providing feedback, and emphasize the fact that in all aspects of a teachers work, relationships matter most.
We encourage you to explore these resources, mentioned and referenced in this episode:
- Blog post from Edutopia. The five suggestions here are backed by research. https://www.edutopia.org/blog/tips-providing-students-meaningful-feedback-marianne-stenger
- Article from the South Carolina Center for Teaching Excellence. This resource is general for all content areas, is a quick read, and includes a list of specific ideas for effective and efficient feedback. https://sc.edu/about/offices_and_divisions/cte/teaching_resources/grading_assessment_toolbox/providing_meaningful_student_feedback/index.php
- Article from ASCD (free if you haven’t already accessed your limit of free articles). Grant Wiggins authors this article that Curtis and Joanie refer to multiple times during this episode. https://www.ascd.org/el/articles/seven-keys-to-effective-feedback
- Article/research summary from the Tang Institute. Although this resource appears longer than the others, the summaries and graphics make it very readable. This would be a great resource for a PLC or professional learning setting. https://tanginstitute.andover.edu/files/Feedback-in-Practice.pdf
Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.
I I think appropriate and effective feedback can always be meaningful, even if I'm not, you know, I'm not going to be able to see the student apply that feedback. But I think the point of this actually is ensure that you give feedback, but you time your feedback in such a way that it gives the student the opportunity to adjust course. Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Fenderberg. We work together at Texas Instruments, and we're glad you're here.
SPEAKER_00We're looking forward to continually improving our practice, and we understand that you are too.
SPEAKER_02We hope that you'll find this podcast as a room for you to grow along with us as we wrestle with and explore ideas about teaching math even better. Today, Curtis and I talk about giving feedback. We explore what feedback actually is and what it isn't, and how it can and should be separated from grading. We discuss ways to provide feedback, even for procedural skills, and how important it is to leverage our relationships with our students to ensure the feedback is most meaningful. We were both taken by the idea that feedback should require more work by the receiver than the giver. So let's get growing.
SPEAKER_00Well, hello, Joni. Hi, Curtis. We're back in the office again. We get to record uh another day in uh in person, which is fantastic.
SPEAKER_02Sitting across the table from one another. Right. This is so cool. It is cool.
SPEAKER_00I'm really excited for today's episode where we're gonna talk a little bit about giving feedback, um, talking about what is meaningful feedback, um, and addressing maybe some strategies for uh doing this in our classroom today.
SPEAKER_02Yeah, I really love this topic as a follow-up to our previous episode on grading. Um, and I think, you know, one of just to frame again, in the last episode, we really took some time to say, hey, we're not here to say we know what's the best way to grade or here's how you should set up your gradebook or any of that. Um, it's kind of fun because for this particular topic around giving meaningful feedback and effective feedback, sure. We really do have research to back up the things that we're gonna talk about, and we'll be able to point our listeners to some of the articles that you and I looked at in preparation for this. So it's it's really exciting because this one's a little more concrete and we're able to say, no, there's actually data to show that this is most effective for student learning. For sure. Yeah, so it'll be good. So why don't you start us off, Curtis, and talk about, you know, what do we really mean by feedback? Like, is that just writing comments on my students' papers in addition to grading them as right or wrong? Is that, you know, giving them, you know, you got a 84% on on this quiz, but the person next to you got a 77% on this quiz? Like, what do we mean by feedback? Can you like call that out for us?
SPEAKER_00One of the articles that uh we read in preparation for this actually called out um sort of the difference between uh what you might call advice or guidance uh and and feedback. And um, he described the uh like if I'm hitting a tennis ball uh into the other side of the court and I watch to see if it lands in or it lands out, or if I'm telling a joke, I watch my audience and I see sort of whether the joke um lands and people really laugh, or if they maybe smirk or give me sort of a strange look on their face. Like those are feedback, like those kinds of things are feedback. It's what happened as a result of my action. Or in the case of my classroom, I might be able to describe to a student here's what you did, or here's what you didn't do, in regards to the goal, the learning goal. So one of the things is is thinking about what is the end game, what are we trying to accomplish. Right. And so feedback is given in the context of that and what I did or didn't do uh that worked for or against me getting to that goal. So that's that's the idea of feedback. I I really attached to that because it separates um the feedback or what happened or or what I did or didn't do to accomplish the goal from the guidance that I'm going to now as a teacher give uh to the student to help them learn a little bit more, to teach them uh in regards to that. So um just thinking about what is feedback. Um, for me anyway, that was one of the things that I took away from what we read.
SPEAKER_02One one of the things I really like about what you just said is, you know, when you think about the tennis ball example, or even you were starting to say as a teacher, and I was thinking, as a teacher, it's almost like the stand-up comedian analogy, right? As a teacher, I get feedback from my students as I'm teaching. Um, but the thing I like about those examples is the feedback doesn't necessarily require an external evaluator, so to speak, right? I can get feedback just from engaging if I know what the target is. So, you know, one of the things that is a theme I think across our podcast is engaging students more in their own learning. So if we're gonna define feedback as progress toward a goal or or um a reflection back on the progress toward the goal and the success or what, you know, success towards that. Um, I think an important component is that students really understand what the goal is. And how much more meaningful is feedback when you get what you're trying to do and then somebody gives you those um, you know, comments that help you get closer to the goal versus, well, I don't really understand what I'm gonna do. So this person gives me comments and I don't really know how to put them into context.
SPEAKER_00For sure. For sure. I uh I mean, what a cool uh thing for us to think about how students are going to need to engage with uh the feedback that we give them. I think that's one of the things, one of the articles that we that we pointed out, in fact, probably our favorite one, yes, for sure uh articles, started off with four big ideas. And I think we could go through um some of those. But the first one is that students must engage with the feedback uh in order to learn from it. So the kind of feedback that we give, and and now I'm probably blending the the two concepts of of what is feedback and what is uh coaching or advice or guidance based upon the things that I saw, right? So I I think that students can then uh action on those things. And one of your favorite phrases from that is that students needed to, what was it?
SPEAKER_02The the receiver of the feedback should work harder than the giver of the feedback.
SPEAKER_00Yeah, for sure. That's a very interesting concept. I mean, uh really, so what that was one of the that caused me to really think about the feedback that I used to be able to used to give to my students, right? You write a little, okay, this is what you missed here, or this should be a negative instead of a positive, or so some of the comment comments that uh I gave to my students, but then what what are the next steps uh whenever I give them that comment? What is something else that I can give them to make sure that they are actually having to engage now uh with that feedback? Do you have some ideas?
SPEAKER_02Yeah, I mean, I think it it kind of comes back to really fleshing out what you said before, like how does feedback differentiate from advice or even praise, right? So it's not the the feedback needs to be specific enough and related to the standard enough and actionable. So it's all of those things together, right? And whether it's feedback, I think one of the other things that strikes me about this is that feedback isn't always just pointing out the negative or pointing out what's wrong. Right. It's also giving, you know, yes, this part you nailed it, or this part you're mostly there. Um to get all the way there, here's what you what you need to add to. So I think it's that specificity and it's also this taking back the the value. Okay. You know what I mean? Like it rather than saying good or bad, it's there or not there. And in what ways are you there and in what ways are you not there? And in the ways that you're not there, it's not necessarily, I mean, I'm thinking specific to math, right? And one of the things about this article that we'll share in the show notes is I think it's it's really general. It's meant for every content area. But feedback in math, I think we have to really be careful to think about how do we give students something that's actionable that's not just telling them, you know, here's what you do, here's what you did wrong, and here's what it should be instead.
SPEAKER_00Yeah.
SPEAKER_02Um, and and our focus on right answers too. It's easy to say, well, this is right or this is wrong. Um, where really right or wrong is often not the target of our standards.
SPEAKER_00Right. It's more about the concept or or the skill or the practice. The case or the thinking behind it, right? Yeah. So I see that you uh took this action here. Now, what was your thinking or consider your thinking as you approach the next three practice problems or the next time you uh see this kind of a problem or or this kind of skill being asked for? Yeah.
SPEAKER_02I'm thinking of um just the way you said that made me think of working with my nephew, our our listeners who have listened already know I work with my fifth grade nephew uh frequently. And we were um just last week working through um thinking about mixed numbers and improper fractions. Okay. And he wrote down, I'm trying to remember what it was exactly. I think it was four thirds. And he was explaining to me how he understood what that meant and what an equivalent um mixed number would be. And he was just kind of writing, uh, wasn't speaking, he was just writing, and he wrote one and one half. Well, we had just done several examples with a denominator of two. So I knew I know this about him having worked with him for a year and a half now. Like he just his brain gets going super fast and he writes faster than he's thinking, and he'll make those kinds of mistakes all the time. So my I and I had this moment where I didn't want to say, no, it's not one and one half, you know. But how do I give the right feedback that helps him not make that mistake again or be more intentional as he's progressing through? Because it's funny, it's funny. And I think this translates to middle and high school as well. When kids are confident, then I think they get more careless. Sure. Right? Like there, there's not this like slow methodical thing. I did too, right?
SPEAKER_00Like when I get confident, I just kind of get floppy.
SPEAKER_02And you're more likely to make those kinds of errors. So my question to him was um tell me how you got that one, that whole number one. Then tell me how tell me where that one half part came from. And so, like slowing his thinking down. And the feedback was, you know, slow down and tell me how you're thinking about this so that he could actually reflect back on his thinking and then catch his error himself.
SPEAKER_04Perfect.
SPEAKER_02And get to that. And then it was like, why do you think you did that? And he's like, Oh, well, I just subtracted one, so I subtracted one. And I don't know what the subtract. I think he was thinking four. There's only one difference between four and three. So he thought that he needed to subtract again. Yeah. Um, but anyway, I, you know, just as an example about how does the feedback help get closer to what the goal is.
SPEAKER_00Well, that's that brings up the I I think uh just your story. You said a couple of things there that struck me. Um that brings up the second big idea in that article, which was uh that relationships matter. Um and and the fact that you know where he's at, that you know him as your student, right, uh, and and also as your nephew. I think that helps also as well, right? The relationship there. But just being able to have worked with him over some period of time, you know sort of his tendencies, you know some of the things that he uh does do. Um, and so you you had the ability to give him actionable feedback because of that relationship. And he was able to respond to it because of his relationship with you, right? He trusts you, he knows what your your goals are and and kind of uh believes in what you are trying to do for him. And we've had plenty of conversations on this podcast about how relationships matter uh for giving students feedback or for teaching students or for engaging them in the learning of mathematics. And so, uh, but that is the second big idea, right? That that was in this article. And I think that's I think that's pretty cool.
SPEAKER_02Yeah, I I I just want to linger on that for a minute because it's sort of a duh, you know, like of course relationships matter. Like really every teacher I've ever known has said the most important thing I do is build relationships with my students, or the my students are the most exciting and wonderful thing about being a teacher, and that's true. But I think taking it a step further and connecting relationships to feedback, it it is that like take advantage of the fact that you have these relationships and take advantage of what you know about your students when you think about giving feedback. And I remember, you know, there was uh we'll we'll talk about this in a minute, feedback being separate from grading. But I remember when I was at one point in my career, like just overwhelmed by grading. And I thought I made up this little strategy where I would have general comments about an assignment, and then I could just code them. And then I could give my students like um the code, like, oh, on this problem, your error is aligned to comment number two. And on so so I had these like really what I was doing was giving, I was grading. Um, but I wanted the grading to go beyond that's wrong to identifying common errors. So I thought it would save me all this time. But what I found was like it wasn't kids could see it was very transparent that it wasn't personalized anymore.
SPEAKER_00Okay.
SPEAKER_02Right? It wasn't, I wasn't able to say, you know, to to a student who I have kind of a light-hearted, jokey relationship with that didn't translate.
SPEAKER_03Sure.
SPEAKER_02Um, you know, I didn't put the smiley face I would put next to that comment. Or or a kid that would be, you know, get anxious and feel criticized, you know, that kind of cold structured comment just wasn't effective. So I it it's not, of course, relationships matter. Relationships matter in everything we do as teachers, but it's leverage those relationships in giving your feedback, and that will make it more effective.
SPEAKER_00That your story reminds me of uh uh one of the stories that was in these articles where a teacher said that it was an English teacher, I think, uh, and at the end of a semester that a student came up. You kept giving writing the same word on top of my papers over and over again, and I still don't know what this word means. Vagoo. The teacher, vague was what the teacher was writing out. And but I mean, what a contrast of like, I mean, whoa, the feedback was also vague. Um, and so just making, but anyway, so I thought that was kind of a nice little piece. That's such a great analogy, right?
SPEAKER_02And when it's too general, then that it's also not helpful. And when students don't understand it and students don't know how it connects to what the instructional goals are, like all of that.
SPEAKER_00I want to transition us uh into this uh idea of um should we be giving feedback only on errors? This was kind of an interesting thought for me when I started to think about what do I give or what do I expect feedback on? And if you take it back to the tennis uh court or even the telling of a joke, or in my classroom, I get feedback from my students, like you mentioned, uh seeing their reactions, if their eyes are rolling to the back of their head, or if they're sitting on the edge of their seats, their brows are furrowed, like or if, or if if you listen to the last podcast where I mentioned or a couple of podcasts ago, where I mentioned that there was motivational stuff on the walls, and kids are staring off and looking at why does he have that so crooked? Um like we get that feedback from the students, right? So should we be only uh doing things on errors? And if you think about the tennis court, well, no, I get feedback whenever I did well as well, right? I get feedback from telling a joke or the the audience laughed, and there was a big like do more of that, right? Yes. And so when a student does a great job or has an interesting thought or a nice justification uh on a particular problem, and I think this becomes more difficult when we're doing things that are skills-based. Yes, right. I mean, it's pretty difficult to tell my first grader or my kindergartner when they're adding three and three and they come up with six. Like, great job.
SPEAKER_02Like you added really well.
SPEAKER_00Like what are the comments? And I would love to know more about that. I'm certainly not an expert because I've one, I've got a six-year-old, so I'd like to be able to tell him great things and help to encourage his learning, but I also I just want to know more. So if somebody out there has advice, that would be awesome. Yeah, but then thinking about it when I'm in algebra one and I've got a student who is solving uh, you know, one or two step equations that we call one and two step equations, right? That's I mean, that's a that's another point, another rabbit hole that we could go down at another time. But just this concept of solving equations, they do it perfectly. They do a beautiful job of executing the skill. What do I say to that student? Yeah, you know, that could be an interesting thought. Like, do we just give feedback on errors or on good things?
SPEAKER_02It's a it's a really interesting thought. And I love that you sort of touched base on to how much more challenging that can be for skills-based learning objectives, right? Um it makes more sense to say, you know, we both taught AP statistics, and when you're, you know, constructing an argument about whether the null hypothesis is true or or not true, there are other components there where you can say, well, you know, you calculated the correct p-value, but your argument isn't structured correctly, or something like that, right? Where you've got the, you know, feedback that gets closer to the goal, even if the answer is partially correct or mostly correct. Um, so I I think the interesting thing about the procedural ones where it's really skill-based, and I want to go back to your, you know, kindergarten, first grade, three plus three equals six, where my mind goes is being cautious not to just say, Yep, good, let's move on. And I mean, maybe there is a time for that. But when we're thinking about how do we give feedback that deter that that even that feedback should be more actionable for the student than it is for the teacher giving it. So I would say I would follow up with, you know, a kindergartner saying three plus three equals six. Great. Tell me how you thought about that. And then the feedback can be around the thinking rather than around the correctness or incorrectness of the procedure or the answer. And I would say that same thing, even if they had an incorrect answer, three plus three equals seven. Well, tell me how you thought about that because it's uh I I I think this is a really interesting nuance between teaching for conceptual understanding and teaching for procedures, is really identifying how is the student thinking about this? And is the thinking aligned with the the concept, the bigger mathematical idea? And especially in such a way, back to your algebra example, solving equations, like I want to give feedback in such a way that sets students up to be successful as that concept gets more complex and more complicated further down the road. So it's it's bringing up something for me that I didn't necessarily see, Kurt, in the articles and the preparation that we did. But and you know, this is kind of one of my this is one of my hills to die on. How important it is that teachers have really deep understanding of the content that they're teaching.
SPEAKER_04Sure.
SPEAKER_02And how important it is to know so much more about the content than you're trying to convey to the students, because you can give them that meaningful feedback that they can then take beyond your classroom.
SPEAKER_00Sure. I think that's important. And I I was thinking about what do I say to my six-year-old when he adds three and three and gets six. And I was wondering if there are good ways to maybe pull that into, okay, well, let's get out, let's get out something tangible, uh manipulative, and and let's pull this together and we can talk through why what you did was right and and what you did was correct, and you you uh came up with the appropriate sum. Um, I th you know, using that opportunity as a as another teachable moment, right? And and yes, here's the positive feedback and C three and three do make six. So we can see them here tangibly and do the, you know, I could see uh sort of a space for for that kind of feedback, right?
SPEAKER_02Yeah, or or even sorry, back to my nephew. Like when I first started working with him, I remember him. We were doing, you know, multiplication was kind of the thing that was the impetus to me working with him. My brother called and is like, he just doesn't know his multiplication facts and he's feeling like he's not good at math because he doesn't know them as fast as his classmates. And as we were, you know, we're engaging in problem solving that requires him to apply his mathematical, his, his multiplication tables, not just, you know, rows. Sure. But at one Point, I would see him like, you know, he's counting the multiples of three, for instance, and he's three, six, nine, twelve, fifteen. And I see the paws, you know, his eyes kind of go up, and then I see he's counting on his fingers, but he's hiding them in his lap. And my feedback to him was to acknowledge that. Like one of the things I wanted to do with him early on is get rid of the shame around not knowing your facts. And so I said, Well, can you tell me how you thought about that as you listed those numbers? And I noticed that you slowed down here. And you know, tell me more about that. And and then I saw you count it on your fingers, and that's great. Our fingers are a great tool and resource. And but that that slowed you down, didn't it? So, so being able to um, that feedback I think helped him to not feel judged by his procedure. So that getting to what is your thinking and giving feedback related to the thinking rather than to the answer.
SPEAKER_00And that actually leads us right into um the third uh piece of that article, the big ideas. So we've we've talked a little bit about uh engaging, students need to engage and how relationships matter, but then also just being specific around the instructional goal. And I think, you know, I keep tying it back to the tennis court and the joke, but you know, we know what the goal of those things are, right? We want to make people laugh, we want to make sure that the shot goes in. Um and I think that having students be able to engage with the feedback, having uh having that happen has to come from students knowing those specific goals. And then my feedback needs to also be tied to whatever the action was that we were trying to accomplish, right? Right. I mean, that's that's a big, a big idea. Um, the last one um that we've briefly touched on as we started the conversation, but I think I'm gonna uh do a little bit more here is this idea of um making sure that feedback is separate from grading.
SPEAKER_02Right.
SPEAKER_00Um, and that's not something that I did a really good job of when I was in the classroom. I know that um I, you know, I was trying to be instructional, I was trying to be uh guidance giving and being actionable for students so they could go and practice the next one. One of the ideas um that one of the articles put out was uh, you know, okay, so the next time you you see two uh exponents uh with equivalent or the same bases uh multiplied together, you you need to recognize that that what happens is you need to add the uh the exponents instead of multiply them or whatever the the mistake was that the student was made. Why don't you practice that on this next two here? Right? So so give them an action that they can go and do, which is awesome. Uh I didn't do a really good job of that piece. Yeah. It was often tied to so here's what your score was on this problem, minus three or minus five. Right. So I wrote the here's what you did wrong, but then it was immediately tied right next to the number of points that were taken away.
SPEAKER_02Yeah. Yeah. And that ties back to something that I kind of took pause at when I read one of the articles too. Maybe it was the same one, but it was that idea of give feedback before you give the grade. And I thought, wait, how do I how do I do that? Like, if if I'm handing back a an exam that students took, like, where do I write the grade if I want them to read the feedback before they know what the grade is? So I wrestled with that a little bit, but I think it's connected to this idea of separating feedback from grading. So thinking about what's the timing of the feedback, right? And you know, with both of us having our experience as high school math teachers, we're not the feedback, the idea that it should be actionable, it's really important to give it all along the way so that that assessment, that assessment, the purpose of the assessment is grading. The purpose of the assessment is not feedback, although it's an always an opportunity to give feedback. But um that I I think that's different, right? Sure. I think that's back to our original question of what do we mean by feedback? It's not the same thing as grading. So sure if you're if you're writing a comment that justifies the points you allotted or didn't allot, that's not feedback. Right. That's that at that point, that's grading. Yeah, and scoring that's grading. So so yeah, this idea of keeping them separate is like, okay, that makes sense, but logistically, how does that play out? And I'm intrigued by the idea of being able to give students the opportunity to to practice and you know, try their hand at expressing where they are towards a standard and and the opportunity for me to give feedback that's not tied to something that's gonna go in the grade book. Okay.
SPEAKER_00Well, at the risk of uh getting us into another podcast episode here, um, I'm gonna ask a question, or I'm gonna at least I want to dive into that a little bit deeper because you've given me some things to think about uh here with this idea of um you know separating feedback from grading and uh when assessments are given back, uh, what does that mean? And so I I'm thinking about when I give an assessment, the point is to figure out what students know at this time. Uh especially when it's at the end of a semester or or at the end of a class, right? Where we're at the end of the course and it's summative and they don't really have an opportunity now to take an action on that, right? So that's when those things uh that's when those things aren't. We're moving on when it's a test, right? We're moving on uh to the next uh topic or to the next uh thing. And so it's really difficult to call that feedback. So I'm thinking about uh what does this tie back to our conversation uh about uh grading and what should be graded and what shouldn't be graded? And is the primary opportunity for feedback when we give students opportunities for practice and draft, things like homework, things like quizzes, uh things like early in the in the year tests on a topic that is going to be.
SPEAKER_02Like even a diagnostic test.
SPEAKER_00Right. Or on a on a semester exam, right? I'm not I'm preparing for the semester exam, right? So I I give smaller exams throughout my course. Uh those could be potentially opportunities for what we're calling feedback. Right. But that semester exam is kind of at I'm at I'm at the end. Uh it's kind of a challenge to give actionable feedback at that at that point because we don't we don't get to see them again next time, right? Exactly. I mean, maybe we're giving them advice for next semester or next year uh when they go to to their next teacher or next subject, but in terms of us being able to carry that on for their learning.
SPEAKER_02Yes. And I think the point is not don't give feedback on a summative, you know, semester exam or end of unit exam or whatever it is. Like I think appropriate and effective feedback can always be meaningful, even if I'm not, you know, I'm I'm not gonna be able to see the student apply that feedback. But I think the point of this actually is ensure that you give feedback that you time your feedback in such a way that it gives the student the opportunity to adjust course.
SPEAKER_00I would love, I would love to be able to go back and see the reactions on my students' faces when I handed back an exam with uh feedback on it and no grade. Yeah. Um, and then either shortly after or later, you know, the next day or two days later, give them the actual grade once they've had an opportunity to, you know, process the feedback, action on it, do some maybe even a draft piece of this. I don't I uh and again, I don't want to like dive into all the different strategies that could come out of this because uh we could spend all day talking about well, what if, what if, what if, but uh just something to think about.
SPEAKER_02No, I think it's a really compelling idea because you know, in terms of grading, I think this is connected to the one of the things we talked about in terms of grading. Like what if a student's learning is just a little bit slower? So what if on exam day they they weren't they weren't there in terms of the standard, but they so they get meaningful feedback on the exam and then they have the opportunity to retest or to show you know a second time or a third time or whatever it is to show again later down the road that they actually have made improvements on that topic and they are closer to the standard. I mean, I I was a big proponent of exam retakes. Sure. Um, but and I think this feedback component, you know, could have been a really useful part of that. Like I would have given better actionable feedback and then required students to show that they took action before they earned the privilege to retake the test. Yeah. Yeah. Yeah.
SPEAKER_00I d there's so many things that are just boiling up in my mind right now. I'm going, man, I really want to, I want to go back and teach a class now. I want to go back to the classroom and teach because I'm just excited about these opportunities. And so uh, well, Joni, we've given uh we've had a lot of conversation today. Um, we've got some ideas for different things we could take back uh to the classroom and uh, you know, ideas for thought for what do I do and how can I do it. Um so hopefully uh our listeners can engage with that and and move uh on and and be able to go and do some of these great things.
SPEAKER_02I hope so. And I really hope that they can take some actions in a way that actually results in stronger learning and more enjoyment on the part of their students. So great conversation, as always, Kurt. Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us, consider leaving a review to help others find us and share the podcast with a fellow math educator. See you next time.