Season 4 Episode 11: 

00:00:00:00 - 00:00:02:00

Opening music

00:00:02:00 - 00:00:09:11

Curtis intro

Where, Curtis, have you grown this year or at least been more cognizant? 

00:00:09:11 - 00:00:43:06

Joanie intro

I really love that. And I think that's I would agree with you. That's something that I thought a lot more about this year than I think I had previously. In this episode of Room to Grow, Curtis and I reflect on 2024 and what we've learned this year from conferences we've attended, to, books we've read, to our podcast guests, and to our own self-reflection. 2024 has us both thinking differently about teaching and learning math. We know you've learned a lot, too, and hope you'll take the time to reflect and capture your own learning after you listen. So let's get growing.

00:00:46:17 - 00:00:59:11

Curtis

Well, Joanie, I am really excited, for today to be talking with you and recording the Room to Grow podcast once again. We are recording our final episode for 2024. 

00:00:59:11 - 00:01:04:03

Joanie

Yikes. The year is over. It just feels like it started. 

00:01:04:03 - 00:01:04:03

Curtis

It's unbelievable that we have been recording and made our way through another 12 months, which is just it's just mind boggling.

00:01:14:16 - 00:01:44:03

Curtis

Really. And so today, really, we've been talking about what are we going to do for our December episode? And we settled in on the idea of looking back, sort of a reflection upon, the places where we feel we've had an opportunity to grow in our own understanding of education and in our own practice, and just in the things that we think about when it comes to math, teaching and learning for students and teachers and administrators and that sort of thing.

00:01:44:03 - 00:02:14:07

Joanie

So, yeah, I think we, we have such great opportunities, Curt, in the work that we get to do to attend conferences and, you know, even on Room to Grow, we get to interview really interesting guests that have, you know, written books or been engaged in some really intriguing work. So I love that we picked this idea of sort of, you know, year end reflection and think back on our learning and kind of what, how 2020 for us has gotten us thinking differently. So, I'm excited to have this conversation.

00:02:14:07 - 00:04:55:04

Curtis

Yeah. Yeah. So, well, let's just let's go ahead and kick that off then, with some of the ideas maybe, that have given us, pause. And so for me, I will just say I was looking through and preparing this, this session and thinking about our podcast this year. And I was looking at the titles and the themes and who we've had on and, and really kind of the overarching theme, this year is something that I feel like I've grown in, in the idea of student centered instruction and environment. Nice. When I had to kind of think about, okay, so where Curtis, have you grown, this year or at least been, more cognizant? You know, sometimes we say, oh, we grew and all these things, and I'm not in the classroom anymore, so I don't get to I don't get to put these things into practice, save having conversations with my own, sons in their learning, in their instruction that they get from me at home when we're tutoring on their homework and, and trying to get them, moving along on those ideas that they're struggling with maybe from. Yeah, from their classes. And so I get to try to put some of this into practice just in a one on one basis. But really thinking about, what's important to our students. Right. And the, the place where they're coming from as they are attempting to learn and our classrooms. And when I looked back across our episode sort of line up for this year and I started thinking about, okay, you know, we started off the year thinking about, you know, thinking about this, this idea of how do we uncover student thinking, that conversation was very, very interesting. Yeah. Really trying to think about. Okay, so what is it that I'm going to do? The detective work that I'm going to do to try to to help my students expose their thinking, whether it's classroom routines, like when we talked with Amy and Grace last year, or if there are, you know, things that I can do to encourage my sons, as they talk to me in a one on one scenario.

What are the ways that I have, maybe focused on uncovering student thinking that was one maybe big area for me. As I reflected across the year, opportunities to focus on student thinking was, maybe one for me. 

00:04:55:04 - 00:06:56:00

Joanie

I really love that. And I think that's I would agree with you. That's something that I thought a lot more about this year than I think I had previously. And really thinking about the goal of instruction is just that. The goal of instruction is figure out what a student knows already about the math or concepts related to the math I'm teaching, and then figure out how do I help bring them along in their thinking and understanding. And you know, when you when you talk about that, it one of the things that in my reflection on this year that I really zeroed in on was our two episodes where we interviewed students and thinking like, exactly tying into what you just said, right? How each of the different students that we talked to so defined, like, not directly like, you know, we asked the question, what does it mean to be good at math? And they answered, this is what it means to be good at math. But as we were engaging with them and asking different questions about their experiences, so many of them, I heard them say not directly, but, you know, through their explanations that their understanding of what it means to be good at math is to give the answer the teacher wants.

Right. And and how that's in direct opposition to what you just said. That know what to be good at math is to make your own sense of the math and. Right. Have your own way of explaining and your own way of understanding and fitting it into your unique knowledge. Right. So I, I really appreciate that connection. And it was one of the things that struck with me most like, I would love to go back to the classroom, but in the opportunities that I have to work with educators and even to all of our listeners, I think helping kids to understand that what it means to be good at math is not try to

figure out the answer. The teacher wants me to say.

00:06:56:00 - 00:07:04:14

Music break

End of segment 1

00:07:04:14 - 00:09:02:02

Joanie

I have one quick story to share with you because, you know, you. I know you do. I can see it on your face. I, I know you have your opportunity to work with your sons, about this, but I and I work with my nephew Andrew. But one of the great things about this school year for Andrew is all of the legwork that I've done with him in the last four years is paying off because he calls me for help, like twice so far this year. Like that's fantastic. Yeah, he's just blossomed and he's doing so well in his algebra one class. But I took on a new, tutoring client this week, and it's a young man. He actually just turned 30, and he had a challenging high school experience, did not apply himself in high school and didn't graduate. And now he's interested in earning his GED because he sees, you know, not having a high school diploma as as blocking his opportunities moving forward. Sure. I don't want to go too long into this story, but I was really intrigued the first time I met with him this week of that same attitude of, you know, we started to look at some sample problems that he might encounter on the GED test and I could just see, like, oh, if I read the question and I don't automatically know what to do, then he just he just kind of shut down. He just kind of stopped like, oh, I don't know, this. So I spent this whole first session with him just trying to help him think about math as you know, you like you can draw on something, you know, even if you don't know how to get to the answer. Try to just make sense of the problem. Try to just go through in your mind of the things you do know and you do, understand. And it, it just reminds me so much of tying back to that kid conversation of math is giving the answer the teacher wants, like this narrow vision of math as being a thing, that there's one right way to do it, and you're good at math if you know that one right way. 

00:09:02:15 - 00:11:43:15

Curtis

Now, I think that to, to dovetail off of that, that's exactly what I was going to comment on, was this idea that, you know, I, I sensed it when I was talking with Teagan way back in January and we had that conversation, and then we listened to the student, conversations.

And then I listened. I was just listening to our conversation with Mike and Julie about, you know, this, this asset based, you know, thinking and learning and, and really the idea that mathematics is not about getting a right answer from a fixed method. Right. I think, you know, a lot of times we hear well math isn't about the right answer. Well yes and no. I mean we do need to have correct answers. There is ultimately we do need to be able to come up with solutions to problems. Yes. That's why we do. That's at least partly why we do mathematics is to, to like come up with answers to things. However, the fact that there are always multiple ways to think about, set up, compute, do the work, equivalent things that always there's always at least 1 or 2 others than just the one that a teacher has taught a student. I think that's the thing that we can reflect on and try to grow a little bit in our own practices. I know that that's one of the things I've been talking with with Teagan a lot lately about has been that, you know, I don't want to steal from Pam, but math is figure out a bill and you can figure this out. You can figure out how to do this because you've got certain tools, right. You don't have the tool. You don't have the procedure memorized right in your toolbox. You will eventually. Right. But utilize the things that you have right now. Engineer your little solution. Come up with the things that you do know, and then we can talk about what misconceptions or preconceptions that you might have that can help me to guide you along the process of making sense of this. And I think that's, you know, when we look at all of the things that we recorded this year, and I went to conference sessions and things, that was a big theme for me trying to, to learn about how do I change my perspective on what really the practice of mathematics actually is. 

00:11:43:15 - 00:14:32:06

Joanie

Yeah, yeah. You know, as I'm listening to you talk, I'm, I'm sort of flipping to the other side of the coin of this concept that you're talking about and thinking about by, by understanding and promoting in our classrooms. There's lots of correct ways to do and think about the math that, that creates what I think is one of the biggest challenges of being a math teacher, and that is to be able to effectively guide students in that way. I have to have really, really deep and broad content knowledge. Yeah. And I think, you know, probably like 15 years ago when blogging was cool, when blogging was like a brand new thing, I thought I might be blogging still cool. I mean, blogging is still cool. What I meant was when blogging first came out, when blogging was a new thing. Yeah. No. I thought it would be cool to do a blog. I tried to do a blog on. I respect bloggers because it takes a lot of dedication, a lot of work. But I thought really carefully about what would my blog title be?

And the title I picked was a quote from Lapping Mom, who wrote a book about teaching students mathematics, and it was my my blog title was A bucket for a drop, and it was an allusion to this quote from Lapping Ma that said, in order to teach students a drop of knowledge, the teacher needs a bucket of knowledge. And it just resonated so strongly with me and still does now. And what you're talking about. Right? Like this is what is so hard. I, I am most effective if I have a big enough understanding that regardless of where an an individual student chooses to go as they think about and explore and make sense of the math, I know where they are and how it fits into the bigger picture of what I'm trying to get them to learn, and that is just so hard and and quite frankly, unrealistic, right? Like, unless you're an educator, for sure. I mean, I started teaching 35 years ago, so I've got a lot of years to have filled my buckets. But certainly my first year teaching, if I was teaching kids a drop, I had a drop in half. You know, that being able to, build out your own knowledge, in order to support student learning and really student focused learning like you're talking about, is really complex skill. And I think is perhaps, maybe the never ending quest of math teachers.

00:14:32:06 - 00:14:41:00

Music break

End of segment 2

00:14:41:06 - 00:19:03:00

Curtis

Wow. Journey that, that leads right into another thing that I was thinking about. And it's related really to this idea of teaching as detective work, and instruction as learning and, and really this idea that I have to be curious enough about, the mathematics to engage in learning mathematics on my own. To have that bucket filled. Right. I mean, yeah, I certainly did not know anything about teaching statistics. Whenever I started teaching stats. Oh, you and me both. I didn't know anything at all. But the cool thing was, is there was lots of opportunity for me to learn. And I got to go. And when a student asked me a question, I got to say. Darn it, I, I don't know. Oh, can I figure this out? Yeah, I we can figure this. We can figure this out. There's, there's literally I mean, we can go find out. There's nothing telling us we can't do that. And so I really appreciated, my students grace for me in that. Right. And then I had to have the bravery to be able to tell my students, look, I don't know, today, tomorrow, we'll figure it out. Right? And, to be able to be brave enough to come back, and say that kind of thing that I think is another piece of the puzzle and that relates to, you know, when we were prepping for this and we were talking about, okay, so are we going to talk just about our comfort, our episodes, or what's going to be things that we learned from conferences?

And I attended a conference session in, Wisconsin at the Wisconsin Math Conference. And I really appreciated and kind of the generate curiosity theme, of the session that I, that I jumped into and, pardon me, I can't remember the name, the title, of the session. But Sunil Singh did the session, and I can go look it up and we can put it in the show notes. I might even have a link to some slides if I can find them, but I really loved this idea of, you know, sometimes we just need to get kids into a place where they're curious, right about something. And I experienced this often with my with my nine year old, you know, I, I, I came home immediately actually, after that conference and I said, “hey Tru I said, I learned something this weekend. You want to know what it is?” And, I talked to him about, a perfect number. Oh, yeah. What iswhat is the perfect number? And so I did exactly what, what Sunil did in that session. And he, you know, I said, hey, here's six is the first perfect number.

And I want you to try to think about why it might be perfect. And then I let him struggle with that for a little while. And then we talked about it. And so I told him eventually kind of guided him to what it was. And then I said, you find the next one nice, I love it. And I just left him to it and he played with it for a while. It was fun. It was really, really a cool, cool experience. But I think the idea of being willing to go and learn something, even if it's not necessarily directly related to the content that I'm trying to teach, just teaching students that, you know, mathematics really is about logic. It's about sense making. It's about developing processes and methods for determining answers. Sure. But it's about that exploration more than it is. Add to each side, right. Divide by seven x is equal to four. Right. Like there's that's not what this is about. Sure we eventually land on these sort of algorithms and these things that work, but it's more about the exploration and the logic and and determining coming up with mathematics that work.

00:19:03:02 - 00:24:19:02

Joanie

Right. Oh, I really like that. And I can, I remember you attending Smeal session in Wisconsin and how excited you were afterwards and not being the least bit surprised, because curiosity is something that I know is, is really paramount to you. It's something that that really matters and something that guided your own learning and researching when you were in the classroom too, and just your interaction with your kids too, and with people you know, when you when you do sessions at conferences, too. Curtis that's kind of how you anchor your work and, you know, making people curious about, the topic you want to discuss and that I'm going to kind of, segue a little bit, but, as you are describing there at the end how that is what math really is. I was thinking about a really great session I attended just a couple weeks ago at CMC South, and the presenter was one of our podcast guests, Rachel Lambert, and she was sharing about, you know, her work is around students with disabilities and, ensuring high quality math experiences for those students, in addition to students who don't have learning disabilities. And she, she kind of dove into something that I've heard lots of other folks talk about. I know I heard Kevin Dykeman talk about this at a conference once. This has been, you know, the topic of President’s Messages and CTM and, and threads we've seen on my NCTM discussion boards. But this idea around discovery or inquiry based instruction versus direct instruction, explicit instruction, teaching, teaching kids procedures versus letting kids sort of figure out the math on their own. And this session that, Rachel did at CMC was, was really powerful in that she focused on what the research says and she also just talked in general about how easily research can be twisted and presented in support of something that actually that isn't what the research says. But, it just it's one of those things that I wrestled with. And again, when I think back on the 20 years that I was in the classroom, I certainly was that type of teacher that believed in and, preferred to give my students some kind of discovery types of activities and sometimes even felt some inner turmoil when I had to do a lesson that was just teacher directed me giving them notes. You know, here's step by step how to solve this kind of problem. And I really think it's only been in the last couple of years that I've been able to start to pull together a belief about how those things work together. And, you know, I know I we've had this conversation before, so I know we share the idea that a balance is really what's needed.

And there are there are some things that kids just need to be told. And that's okay. Yeah. And there are other things that are great opportunities for them to explore their curiosity and their own sense making. And those things don't have to live in contrast or in competition with one another. And, and kind of alongside that one of the other big themes that I've been thinking about this year is mathematical identity. And how do we think about students mathematical identities and our own identities as teachers, and how those things interplay to one another? So, you know, even thinking back to our student interviews, right, like good at good at math means I, I know the answer and I know how to do it the way the teacher wants. And if I don't do that, then I have a negative math identity. And I think about, you know, the years of work that I've done with my nephew Andrew, who, you know, as a second grader came to me saying, I'm bad at math because I'm not fast. And everybody else gets the answer before I do. And, you know, really working with him to have him understand that speed is not your strength in math, but reasoning is your strength in math and understanding structure is your strength in math and that's why I think now that he's taking algebra, all of these structural understandings that he worked on through middle school, middle school, mathematics are all now coming together in algebra. And he just like it makes sense because he has this background. So thinking about how do we honor the different ways and the different strengths that students have? And I'm also circling back to the Mike and Jolie conversation, where if we can really focus on and help kids understand what their what strengths they bring, and then being able to utilize their strengths when they're challenged and when they're having a hard time, like when I know, hey, I'm really good at understanding and seeing structure. When I encounter a problem that I'm struggling with, I can take that step back and say, okay, what structures do I notice here? How does how is this problem like other problems I've done and understand and start to apply that. So this idea of identity and student strengths and making those explicit for the student for the benefit of their learning.

00:24:19:02 - 00:24:28:14

Music break

End of segment 3

00:24:28:14 - 00:26:49:15

Curtis

Now I love that. I love that a lot. I think, you know what one of the phrases that Jolie used in that podcast was, the focus on what is instead of what is not and, you know, helping the students realize that they bring things to the table. So I think that's I think that's really important. And, and I think that actually plays really well into what you were talking about, this idea that there is sometimes a balance between, you know, sometimes we have these, these procedural things that we kind of we start off with sort of a concrete procedural piece, and we can develop that conceptual thing from behind it, right in and in, in sometimes, you know, my preference, like you, I prefer to be able to demonstrate something and have it kind of be constructed, an constructivism sort of idea. Right. I'm constructing these ideas, these this, this learning as I go, but, sometimes that either I, as the teacher, don't have a broad enough understanding because sometimes that's the truth. I don't have a broad enough understanding to create a lesson or an activity or an environment where students discover something that sometimes is the truth. And so sometimes I just have to kind of rely on that. And some ideas really don't lend themselves to discovery, at least not at a level appropriate for our students. Right, right. And so we, we do have to kind of tell some things and then they go, oh, I see the pattern now, you know, it's, it's that idea. You know, it was fun for me the first time I actually recognized that a graph of equivalent ratios of things actually made, a line. Yeah. Right. That, that I could make this line. That was a realization for me. I had certainly held on to this idea of proportional relationships and reasoning and all of those things, but I had never made that one little connection, and that was one that I had to discover later on.

Right. That wasn't something that, I could , I could put together the first time I saw it. So, yeah, just thinking about those. 

00:26:49:15 - 00:28:43:11

Joanie

I was just going to say, I want to I want to stop right there and jump in because I think that's another one of the challenges to overcome as a teacher. Right? Like when we have all of this deep level of understanding and passion and excitement for the mathematics, we want kids to see all of that too. And I'm just thinking about what you were just saying, like you had lots of really solid understanding about equivalent ratios, about proportional relationships. Like you had a lot of good understanding about how all that worked before you made the connection to the graph being linear and passing through the origin. Right. And, and, and that idea of like, we don't have to teach them everything all at once. Like there's that's how learning happens, right? Like we get a little bit here and a little bit here. And a little bit there. And then I start to see the connections between them, and my learning becomes more robust. And it might be two grades after they're in our classroom. That's something we worked with students with, comes together in a way, because of a new experience that they've had. So I think that I know this was hard for me too. And again, I feel like I'm focusing on all the things that are hard about being a math teacher. I don't mean to, but, yeah, letting go of, like, they don't have to understand all of it right now, right? Like it's it. Learning happens in that accumulative kind of way. And just providing space for that to accumulate and even thinking to around, you know, I don't want to go back and teach content from previous grades, but if I can make connections to what I know students have learned in previous grades, I can actually try and tap into that cumulative learning effect and, and help to deepen previous understandings, just as I'm taking them into new ones. So I just I just had that kind of really strong visual. I wanted to share. 

00:28:43:11 - 00:29:59:20

Curtis

No, that's a good that's a great aha, and I think I'll wrap up that. With kind of pointing back to you, one of my mentors in teaching a Maryland Cob, and I don't know if she listens to the podcast or not, but, she used to talk about, this idea of, you know, teaching students, developing mathematical understanding is a little bit like building a candle. Yeah. And the idea of, of taking that wick and dipping it in the wax the first time and a little bit sticks. But not everything. Not the full candle. And then you dip it again, right? Yeah. And you actually have to have some time to let it dry. Right. And cool. You can't just keep dipping. There's, there's a process to building a candle. And the same thing is true with developing our math in a mathematical understanding and just really realizing and relying on the fact that, you know, students bring stuff to the table that some of the math can stick to. Right? Right. But it's not all going to stick the first time. And and it does take multiple exposures. It does take multiple dips, if you will. In the, in the candle wax, to build up that, that knowledge. 

00:29:59:20 - 00:32:22:02

Joanie

So I love that analogy and I love that visual. Yeah. That's just, that's just beautiful. So as, as we think about wrapping up, I wonder and stop me if there's more you want to share in terms of your learnings for 2024, but I thought it might be fun to just give our, kind of wrap up comments through the lens of what is it that we hope to learn more about in 2025? And if it's okay with you, I'll start, you know, again, in reflecting on the past year and getting ready for this episode, one of my favorites of last year was our February of 2024 episode, where we interviewed Rebecca Peterson, the National Teacher of the year. And one of the things that has really struck with me, you know, all these months later, was Rebecca talking about the joy in teaching and learning that happens when we can sort of let go of the pressure of getting through content and, you know, getting kids ready for the test and instead just let ourselves and them kind of savor the interest and curiosity and excitement of learning so that at the root, of some of the conversations that are happening for me locally here in Colorado in our math-ed community, are around, rigorous, relevant and diversified pathways. So really thinking about high school course offerings that allow more opportunity for more students to explore the mathematics that will be relevant to them after they graduate from high school, whether it's because they want to go into a Non-Stem major in college, whether they want to go right into a career or trade, the, the work around diversified pathways that we're talking about involves offering rigorous opportunities in high school that are not just about getting to calculus. So I'm really excited to learn more about that. And I think there's a lot of content from the NCTM high school book that we interviewed, Kevin Dykeman, later on the night in about. I see that coming together. But again, at the core of that being, this idea of creating more joy in teaching and learning mathematics. So, that's what I'm looking forward to in 2025. How about you Curt?

00:32:22:02 - 00:34:39:12

Curtis

 Well, that is a fantastic answer to the question. And actually, I really I can't just say me too, right? I mean, I can't just say ditto and call it quits. Although I'd really like to because, you really hit at the core of of what I want to continue. And then probably if you asked me this question over the last 20 years what, what do you want to know more about teaching and learning and mathematics.

 And it's going to almost always be, how do I drive? How do I do lessons? How do I do this act to this practice of teaching such that I can answer the question, is my math classroom? Are the activities I'm doing in my math classroom getting students to fall in love with the learning of mathematics?  And that's that's a quote from, from, our conversation with Julie, this idea of, of trying to get students to fall in love with the process of learning mathematics. Yeah, that's what I've always wanted to do. And I and I want to continue to do that. And really, to get specific, I was thinking about, really this idea of high school mathematics reimagined and revitalized and relevant that that book that NCT has just published, publicized, and released.I'm very excited about the work that is going into, the pathways, of course, but specifically just this idea of the modeling and, and the relevant mathematics answering questions the students are interested in answering in the context of mathematics that's on grade level. I, I just feel like there's this opportunity there to really, really push that kind of reasoning and relevant mathematics that I'm excited to learn more about, in 2025. So from the forever, I want to be curious about mathematics, and I want to help students be curious about mathematics and find joy in that. To the very practical, hey, let's see how we can do this in our math classrooms every day with a little bit more relevant questions and a little bit more modeling concepts and content.

00:34:39:12 - 00:34:53:00

Joanie

Love it! Well, this has been a great conversation, and I want to wish you and all of our listeners a very happy holiday season and a Happy New Year and look forward to talking again in 2025.

00:34:53:00 - 00:34:54:10

Curtis

 Thanks, Joni.

00:34:58:17 - 00:35:16:16

Joanie

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!