Room to Grow - a Math Podcast
Room to Grow - a Math Podcast
Celebrating Learning with Self-Reflection
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As we approach the end of the school year, this episode of Room to Grow addresses using self-reflection to celebrate the learning of the year. Our hosts use this definition: “Self-Reflection is the evaluation or judgement of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes (Damore, 2017),” and start with unpacking this quote from John Dewey: “We don’t learn from experiences, we learn from reflecting on our experiences.”
In the conversation, Curtis and Joanie suggest that reflecting at the end of a lesson, unit, month or school year provides the opportunity to be energized by and to benefit from what we’ve experienced and how we use that learning to continue to improve.
After making the case for self-reflection, the discussion shifts to specific ideas for student and teacher self-reflection. Ensuring that students understand the purpose of self-reflection is integral to making the process meaningful for students, and increases the likelihood that their reflective practices will contribute positively to owning their own learning, and to building positive mathematical identities. Some specific reflection questions and protocols are discussed, giving you ideas you can apply in your own setting as we all wrap up the 2021-22 school year.
We encourage you to explore these resources, mentioned and referenced in this episode:
- Dewey quote and Damore’s definition of Self-Reflection came from this post: Routines for Self-Reflection: https://thinkingpathwayz.weebly.com/routinesselfreflection.html
- Journal of Practitioner Research article on reflection as a tool for continuous improvement: https://digitalcommons.usf.edu/cgi/viewcontent.cgi?article=1044&context=jpr
- Edutopia article with specific ideas for engaging students in self-reflection: www.edutopia.org/article/frameworks-reflection
- Tuning protocol as a way for groups of teachers to reflect specifically on student work: http://essentialschools.org/horace-issues/the-tuning-protocol-a-process-for-reflection-on-teacher-and-student-work/
- Teachers and Change: The Role of Reflective Practice: https://www.sciencedirect.com/science/article/pii/S1877042812039870
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 was thinking about the power of that as like a formative assessment too. You know, that could be an interesting exit ticket to do. Because one of the things that I think happens is students don't always know, you know, we could have them self-reflect on what we did today, but they don't always have enough of the big picture of the mathematics to know, wait, what were really the important nuggets of what we did today? And what are some of the sort of secondary or tertiary ideas that we engage with that, you know, will come together to paint this big picture understanding. Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Funderberg. 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_03We 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. As we get close to the end of the school year, Curtis and I discuss the importance and power of self-reflection to celebrate our learning. We define what self-reflection means in our context, why it's important for us to do, and some tips and protocols for self-reflecting. We frame our conversation from a lens of student self-reflection and from a lens of teacher self-reflection and consider the value of reflecting on a frequent basis as well as taking a longer look back over a whole school year. We hope you enjoy it.
SPEAKER_00Let's get growing. Well, Joni, I am really excited to be here in the TI office again with you. Uh today, we're celebrating uh self-reflection this week. That's what we're going to be talking about. I'm really excited for this podcast episode. Um, we just recently come uh finished a uh summit with a whole bunch of teachers. It was really wonderful to be in person with them uh and chat with them a little bit. And I think this this episode we'll get a chance to um do some of our own self-reflection, perhaps. Um but uh let's go ahead and and kind of kick things off here uh for this episode. So um maybe some questions for us to kind of think about. This idea of self-reflection has been all around. People have been talking about it for a while, but why is it getting so much attention? Why should we be thinking about self-reflection?
SPEAKER_03Well, I I think it's an important part of the learning process, you know, and and nobody would argue that, yes, of course, we can learn by self-reflecting. But um, I I want to start us off, Curtis, with a really interesting quote as we were doing our background research for this discussion. Um, and this quote is from John Dewey, and he says, we don't learn from experiences, we learn from reflecting on our experiences. And it's such a, it's, it's kind of like a, oh, but wait, I learned from my experiences. But when you really slow it down, it's not the experience itself that necessarily results in learning, but it's the it's the looking back on the experience and analysis kind of and interpretation, like the intellectual work that goes into thinking about something that has already happened, um, where that learning potential happens. And I think um in some ways, sometimes that reflection happens so fast that we don't actually even realize that we're doing it.
SPEAKER_00For sure. I was thinking about uh thinking about that a little bit as we were preparing for this. Just um, you know, when you have some sort of physical experience, maybe uh I set my hand down and and uh there was a sharp object there and I got poked or something, there's an immediate response. My hand removes, but then I'm gonna be more naturally um attuned to looking for sharp objects when I put my hand down again. Right. Um and it's it's sort of this hey, that happened, but now I'm processing, hey, that that happened. So sometimes it's very instant. Um, but I think in the terms of of learning in our in our classrooms and things, I think it requires a dedicated uh time for me, for my students uh to be doing this, for for them to be thinking about it. Uh, right. And then so for for this episode, or at least some of this episode, we want to talk also about for teachers in the same way, thinking about not only daily what went well today in my lesson, but then close to the end of the year, let's think about what happened through the course of the year and what are some things that I can take away from both uh successes and then opportunities for success.
SPEAKER_03Right. And I think that's I I love that you've you sort of set us up that way because when we were first talking about this as a topic and thinking about the timing of the release of this episode being at the end of the school year. And of course, the end of the school year is a really natural time to reflect and think back and, you know, maybe have some structure to our reflection, maybe some, you know, maybe it's even reflecting back on goals that were set at the beginning of the year and uh planning for next year and, you know, shaping around the new goals. Um, but I think it again, as we developed, you know, the plan for our conversation today, it's really this is something we should be doing all the time. This should be a daily basis opportunity and it should be a big milestones opportunity as well. There's there's different benefits from reflecting in those different time frames.
SPEAKER_01For sure.
SPEAKER_03And to your point, reflection for students as well as reflections for educators. So I would love for you to, you know, kind of kick us off on the thinking around student self-reflection. So why is that what how what and how should we be thinking about in terms of students incorporating self-reflection into their learning?
SPEAKER_00So I think it's important uh as we as we think about that idea of self-reflection for students and how we incorporate that into the learning for our students. We might even want to kind of think about what a definition of self-reflection is. Um and and so naturally, I kind of just in my own terms had been thinking about uh getting quiet, concentrating back, rehearsing, maybe reliving the the examples or the things that had happened through the course of a lesson or through the course of a day, um, and and being able to reflect on, think about those things. But uh let's get a real let's get a definition from one of the articles that we uh looked at. So um self-reflection is the evaluation or judgment of one's performance and the identification of strengths and weaknesses with a view uh to improving the learning outcomes, one's own learning outcomes. So, so there's even a purpose in this self-reflection. It's not just thinking back uh on my day without some purpose, it's reflecting back and going, now what can I learn from that? What can I take away from that? And and moving forward, what are the things that I'm going to do uh differently? So, as we assume uh students have an opportunity for this, if if we give them opportunities for this in their classrooms, then what we need to probably be providing is is opportunities for and setting the expectation that when you're doing this self-reflection, when we're giving you this opportunity, and I don't know if it's daily, I don't know if it's weekly, whatever your your schedule, you kind of have to consider how your students are gonna do it. Um, but that they are doing it for a purpose of moving forward. What's my what's my next move going to be, or how is that gonna impact me moving forward?
SPEAKER_03Right. And the other piece I really like about that definition you just said, and we'll we'll put it in the show notes. I know there might be people like me that like hearing it isn't as powerful as reading it, or sure reading it and then hearing it, hearing, then reading it. But this idea of identification of one's strengths and weaknesses, right? So it's not just about what went wrong and what do I have to change or what do I have to do better, but what was good? What went well and what's a strength? Because I think there's I don't know if it's societally or maybe it's just a personality trait, but it's really easy to focus on the negative, the mistakes, you know, that whole trend of grading students' work in a green pen instead of a red pen, you know, all of those things contribute to uh trying to shift away from always focusing on errors or always focusing on weaknesses. So I think there's something really powerful about ensuring that focusing on strengths is part of that reflection process.
SPEAKER_00So let's let's dive in, let's get to the nitty-gritty, some details uh really for student self-reflection, maybe just a little bit. Um if we can, can we think about ways to build this in uh into a lesson? What would this look like for self-reflection at say the end of the class period? Um, are there questions that I can put out there for students um or to think about? Um what would what would it look like for a student to self-reflect uh at the end of a lesson?
SPEAKER_03Yeah, I I think that's such a great question. And it what pops up for me as another of these opportunities for me to think back to my classroom days and like, oh man, I was so not good at this. Um and the, you know, one of the I'm gonna I'm gonna go off on just a tangent for one second, but I oftentimes I would create really intentionally create these classroom experiences where I wanted students to engage really meaningfully with the mathematics. And it was, you know, I'm I'm thinking particularly about the lessons and activities where I I was not directing the learning, right? Where they're engaging in something separate from me and I'm sort of circulating around the room and you know, interacting with my my students in small group settings. But I so many times I would create these activities and they would, you know, take right up until the bell would ring and I'd be rushing to put the homework on the board before they they leave the room. And I would never take the time to summarize the learning. One of the things I when I learned about the importance of a lesson summary, I was like, oh, that's why. But I would I would be frustrated when come back the next day and it was like they didn't learn any of the things that I wanted them to learn through that activity. And thinking about self-reflection as a piece of that, I think that was another thing that I was missing. So I was thinking about the lesson summary as the opportunity for the teacher to lead reflection. But there's also this place that needs to happen, I think, where students are reflecting back to, okay, what did what did I do in class today? What did what sort of thinking did I engage in? What sort of mathematics was at the the center of my work today? And how does how does that contribute to what I know now that I didn't know at the beginning? Um, so I like this idea of um, you know, getting kids to think about what did I, you know, what got more solid in my understanding? Maybe what are the things I had an idea of that I got better at? What are things that I didn't even know about that came to me today? And then what are the things that maybe I dabbled in, but that are still lingering questions for me? I mean, that might be a very loose way to think about uh how students might self-reflect and some things that teachers might encourage students to think about on a regular basis to make self-reflection a part of their everyday learning.
SPEAKER_00It's a it's a real opportunity to do some of that cross-curricular piece and have students journal and write in math class. I know there's a lot of articles and things out there about having students write in math class. And so the prompts that you were just giving us are all ones that could be prompts for uh could be prompts for a math class to to do some journaling. And one of the articles that we that we have is uh here, even one that's maybe not directly tied to my classroom, uh, but this idea of family dinner protocol. That's kind of a cool uh idea of thinking about, well, what did you learn today? Uh what are some uh some things that you can can do? Here's a here's another one. Uh triangle, square, circle. What are three things? So the triangle that I learned. What squares with me? I love that. I like that too.
SPEAKER_03Little nerdy little you'd have to help kids understand. I don't know that a student's gonna know what squares with me means.
SPEAKER_00I don't know if that term is really used as uh as often anymore. And then what's still circling around in my mind? I I love that. That's just a really nice, well, sort of mathy way to get my students thinking about each of those uh each of those those kinds of things. But really just getting students uh to do that in either uh maybe it's we did the activity on on Monday, and so on Tuesday we have a moment to kind of self-reflect a little bit on what was happening yesterday um uh in the classroom. Sometimes I I too was often teaching right up to the bell. Um and so this might give me an opportunity to start the next day with remember yesterday. Right. Let's think back, concentrate. Now I know it's important to do it in the moment if you can.
SPEAKER_03Sure. But I don't think it's ever too late to self-reflect, though. Right. Yeah. And and just thinking about like even some of the simple, even sort of kitschy ones like the triangle square circle that you just talked about. I was thinking about the power of that as like a formative assessment too. You know, that could be an interesting exit ticket to do because one of the things that I think happens is students don't always know, you know, we can have them self-reflect on what we did today, but they don't always have enough of the big picture of the mathematics to know, wait, what were really the important nuggets of what we did today? And what are some of the sort of secondary or tertiary ideas that we engaged with that, you know, will come together to paint this big picture understanding? But that idea of prioritizing the content and prioritizing the learning of like what's important. So I could see using, you know, try triangle, square, circle, or some other self-reflection protocol, maybe even based on what my lesson content was, a specific prompt to see, you know, do they understand what the big idea is here, or are they stuck on something that's sort of tangential that I didn't mean for them to really think was important necessarily?
SPEAKER_00For sure. So you said something earlier that I I want to make sure that I go back to. Um, and that is this idea of students um doing the self-reflection um really gives them another an opportunity to uh generate and flow focus on the positive, the things that I that I did well today, or the thing that made sense to me today. Um, being able to point out those strengths is so important, I think, for building their own identity uh in mathematics. I know we talk a lot about this idea of students viewing themselves as doers of mathematics and kind of viewing themselves as people who can do mathematics and can learn it well. Um, pointing out the strengths and not always focusing on the opportunities for success really is a big important part of this process for our students. And so I just wanted to make sure that I called that out that there's more to this than just securing the learning and the knowledge, but there's also this reestablishment of my own self as an identity as a person who can do mathematics and who is doing mathematics at a high level.
SPEAKER_03I love that. And I really love too the opportunity that that would present to define multiple ways of thinking about success in mathematics. For sure. Like that's that contributes to the identity work is being, you know, reflecting back on my strengths is not just did I get the right answers. Like maybe a student identifies, well, today, man, that was really hard for me, but I really persevered. Um, or maybe today I did a good job of communicating with a classmate who didn't follow my thinking. So being able to have students self-reflect from a strengths-based approach really also helps us as educators broaden that definition of what it means to be successful and a strong mathematics learner and doer of mathematics.
SPEAKER_00For sure. So I want to I want to move also into so we've been talking a lot about um sort of the self-reflection and reflection on my activity or a particular lesson, or maybe it's a particular unit or week. But I think there's also a good opportunity, maybe as a class project um, or uh sort of a uh an overarching thing for us to do as a group, um, thinking about what we learned this school year. It's important, I think, to look back, because it's always amazing to talk to your students at the end of the school year and say, remember when you came in? And if I had mentioned some of these terms to you, or if I had said some of these things to you, they would have been, you know, just foreign language. But now reflecting back on this school year, look how far you've come and being able to allow students an opportunity uh to go back and reflect on the school year. What are the things that we've really progressed in uh this school year? Um, what are the things that maybe now I have an opportunity to improve upon for next year? Right. Uh those kinds of things as a whole in that sort of looking back on the school year. I think that's also an important opportunity.
SPEAKER_03Yeah. I like, and through the lens both of the mathematical content as well as myself as a student and as a learner. It reminds me of when my own kids were in elementary school and they did um, I I think a lot of schools still do this. They do uh student-led parent-teacher conferences, parent teacher-student conferences. That's so cool. So it was, and it it's almost like the students create a portfolio, right, where they show the per the trajectory of their learning through their own work samples and their own kind of writing. And then at the at the parent teacher conference, instead of the teacher saying, Well, here's how, you know, here's how Keegan did in terms of learning his multiplication facts in third grade, it was Keegan showing me, you know, here on this um, you know, this test of the facts that I took in uh in September, I could only get, you know, 15 facts in one minute. And then this one at the end of October, I got 55 facts in one minute. So, you know, to be able to have him reflect on his growth and you know, his opportunities to expand his learning over time.
SPEAKER_00That's wonderful. What a cool idea. That's really, really neat. Students aren't going to probably be listening to the podcast, I'm guessing. Uh, so this is all stuff that we as teachers can implement uh to help uh our students be able to self-reflect. But now let's move the conversation over to what about us as teachers? What uh is the big importance for me uh as a teacher thinking about uh my not only just this week and what went well or yesterday and what went well, but also uh in the whole school year and and thinking about um thinking about how things went and what are the things that I'm gonna implement next year that went really well this year that I tried that was new that was a big success. Maybe there's some things uh that I want to try again at.
SPEAKER_03For sure. And you know, one of the things again from one of one of the uh resources that I read in preparation for this, this idea that the power of self-reflection is I know myself better than anybody else knows me. And so I am I am the best at judging how what I was intending to do is what actually came out. So I think about my experience as a classroom teacher, there were years where I was really focused on, you know, something, whatever it was. Maybe it was, you know, this year my focus is really on engaging more students and not just calling on the kids who are the first to raise their hands or the kids that I know are gonna give me the answer I want to hear and move my lesson along quickly, but engaging the students whose voices aren't typically heard. You know, knowing that I'm gonna do that and knowing my students and the the interaction day-to-day with them, I'm the best person to reflect on that. So it might be something that I share with my administrator during an evaluation cycle process, but I'm not gonna be able to get that feedback from somebody else as meaningfully as I'm gonna get from my own, from my own self-reflection. So it's back to that idea of um uh, you know, your definition that you created where it's identifying the strengths and weaknesses with a view to improving the outcomes. And so so I think that's it's a really important piece about saying, here's where I'm at, here's what I'm working on, here are my strengths and weaknesses, and now I know something about what to do next.
SPEAKER_00So, so Joni, actually, I love I love what you were talking about there because and you actually wrote down in our notes here, and I'm looking at this going, I did we read this in an article? Or Joni, did you just write these yourself? But kind of a set of pro maybe a protocol for us at the end of the year. So we're we really are, we're releasing this at the end of the year with intent that. Um, that our listeners and you and I also will have an opportunity to think back on what have we done and how can we and and what can we do moving forward? Um, so you gave us three things to think about, which I think are really cool. So, something new that we implemented successfully. So, thinking back to this school year, or or in our case, thinking back uh just to to our work year, what is something that we have done new this year that I wasn't doing before? Right. That was implemented um with success. And and starting with that success, I think that's a really good, uh, really good thing to think about. Uh secondly, what is something that maybe I can let go of? Maybe it's something that was going well, but maybe it's gotten uh maybe it's run its course, or maybe it's something that's just too much and I need to simplify. I I don't think I can preach that enough to my own self about the need to simplify, both in my personal life and and professionally. Just kind of have this constant need to go back and reflect. Okay, I've collected this new thing on my plate. I've put this new thing on my plate. What else do I need to maybe think about letting go of so that I can do these things well? Uh, and then something that I've improved at, something that I've been doing for a while, but now I've made an improvement upon. Right. I think that's uh that that's a beautiful set of three questions to to kind of think about um addressing as I move forward.
SPEAKER_03Yeah, I I like those questions and how they appear in our notes. And it reminds me of another protocol that I've done engaging in other working groups. Um it it's the stop, start, continue, right? What should I what should I stop doing? What should I start doing? What should I continue doing? Um, so really some those those questions get a little more specific in terms of a uh a classroom application of that. But uh yeah, I think there's there's a lot of power in that. I I want to say too, while we're in this section of talking about teacher self-reflection protocols, um, for our listeners to consider maybe they have the experience with this and we'd love to hear from them on these experiences, but reflecting collaboratively with other educators, reflecting in your PLC. Um, you know, I I don't mean to be contradicting my statement earlier about I know myself best and I can reflect best, but I think there is some power too in in reflecting in a group. Um, that might be like a better protocol for the end of a unit or something where there's a structure around planning together with teachers. But, you know, hearing other people's self-reflection is also an opportunity for me to grow and for me to shine a spotlight on where I might have, you know, blind spots about my own practice.
SPEAKER_00For sure. That idea of ref self-reflection in a group, because as people uh reflect on their own things, they're gonna ask questions of themselves that maybe you wouldn't have asked of yourself. Uh, but then you kind of have a realization, right? You get an opportunity to go, oh, I hadn't thought about that. And now I can think about it in my own, uh in my own case and in in my own practice and thinking of the things that that I've done. And so yeah, that I th I love that idea of self-reflection uh in a group. So um, Joni, this is a really cool uh opportunity for us that to take some time. And I actually am looking forward to uh sitting back after this episode and doing a little bit of self-reflection uh on my own practice and and the things that that we're doing uh moving forward. So looking forward to that. But um I just want to kind of leave from here uh with what do we get, what are we gonna do uh with that self-reflection? Because this is a this is a thing. I I can do my self-reflection in May. And uh I can write it up, I can maybe put it in a note or uh put it in some folder or something. But I know that in August, uh things are crazy. It's back to school. We're you know, I'm trying to make sure that I get rosters inserted and I get all these. Yeah, I've got all of this stuff that's coming online. So in order to be productive, in order for that uh self-reflection to kind of have a reminder thing, I I put a little note in here to take take advantage of delayed delivery uh in your email inbox. So take your notes on your self-deflect reflection and uh send yourself an email with it, but don't send it immediately where it'll get lost in the in the thing. Send it so that your future self receives it from your current self uh as a delayed delivery for some time in August or even September. Uh and and that allows me to go back and see it a second time. And now that self-reflection, I'm put I'm removed from it and I can look at it and and benefit from it, make decisions and reflect on my reflection. Now that's a cool recursion thing.
SPEAKER_03Uh I'm seeing a fractal.
SPEAKER_00We're seeing fractals in our future here. But the idea being that that it's really difficult to implement things if we aren't reminded. And I know of my own self, sure, even if I do the reflection now, I'm gonna need the reminders as I go into the school year coming up next year. Right. I'm gonna need that sort of uh ping that says, hey, you thought about this. Uh what what's the next step?
SPEAKER_03Yeah, I think anything we can build in to set ourselves up for success uh is is definitely something we should always take advantage of. So great little tip there at the end, Curtis. And uh I feel like you we got the whole motivation about why I want to do this, and then the this is how easy it's gonna be to do for you. So thanks for that. Well, hopefully great way to end.
SPEAKER_00Hopefully, quite easy to implement. I know there's lots of times and things. So well, thank you, Johnny. This was a good uh good conversation. I enjoyed it thoroughly.
SPEAKER_03Me too. Looking forward to uh reflecting. 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.