Episode #112: There’s No Wild 3 Times 5’s Running Around – Where Are They Now Math Mentoring Moment
In another “Where are they now?” episode series we bring back on 3rd grade teacher Bill Zbozny Del Percio from Pittsburgh. Bill’s back to talk about the changes he made in how he managed student learning with trying problem based tasks. He also chats with us about how he can embed the math process standards/expectations into his daily routines.
This is another Math Mentoring Moment episode where we talk with a member of the Math Moment Maker Community who is working through struggles and together we brainstorm possible next steps and strategies to overcome them.
- How to paint a picture of what you value in learning for your students;
- How to use purposeful questions to elicit thinking in your students;
- How to balance helping students with too much help.
- The importance of learning mathematics through context instead of through “bare” or “naked” problems;
- Building the Standards for Mathematical Practice (CCSS) or “Process Expectations” (Ontario) into your math class;
- How we can connect the Practice Standards to our formative and summative assessment practices; and,
- How to hold yourself accountable for your own math pedagogical and content knowledge growth.
Math Practice Standards
Process Expectations →
Bill’s first episode
Episode 44 with Christina Tondevold
Make Math Moments Academy
Wooly Worm Race: Fractions 6-Day Unit of Study
Bill Zbozny: As I've been picking apart standards, those are the threads that run through all the grade levels. Because they don't have content attached to them, it's easy to overlook them. In my textbook, they'll be like, oh yeah, this is mp3, and give me a little blurb on it. That's really easy to overlook, because nobody has infinite time to plan for all these things. That's where I'm noticing, is that a lot of the things I want my students to do really comes into play with these standards and practices here of how to learn math or ...
Kyle Pearce: In another where are they now episode, we bring back on third grade teacher, Bill Zbozny Del Percio, from Pittsburgh. Bill is back to talk about the changes he's made in how he's managed student learning with trying problem-based lessons through task. He also chats with us about how he can embed the math process, standards, and expectations into his daily routine.
Jon Orr: This is another math mentoring moment episode where we talk with a member of the math moment maker community.
Kyle Pearce: Who is working through a struggle, and together, we brainstorm possible next steps and strategies to overcome them.
Jon Orr: Let's do it.
Kyle Pearce: Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce from tapintoteenminds.com.
Jon Orr: And I'm Jon Orr from mrorrisageek.com. We are two math teachers who, together ...
Kyle Pearce: With you, the community of math moment makers worldwide who want to build and deliver math lessons that spark curiosity.
Jon Orr: Dual sense making.
Kyle Pearce: And ignite your teacher moves. Welcome, my friends. Jon, are you ready for another where are they now episode with the awesome Bill Zbozny Del Percio?
Jon Orr: Of course, Kyle, of course. Before we get to our interview with Bill, we want to remind you that you too can join us for a math mentoring moment episode on this podcast. In these episodes, we talk with teachers about real issues that arise in the classrooms. Together, we work through possible solutions. We know that our listeners, math educators, like you, will also get a lot of value out of the conversation by listening in on that conversation.
Kyle Pearce: Yes, my friend. If you have a struggle or an issue that you're working through, and let's be honest, we all are working on something, head on over to makemathmoments.com/mentor and fill out the form. We won't be able to talk to everyone who fills out the form, because there have been a lot. What we're trying to do is we're trying to pick out different ideas that many have struggles with and also trying to give a variety of classroom issues for all of our math moment makers to think about and reflect on. Again, head on over to makemathmoments.com/mentor to toss in that pebble in your shoe, so we can work through that problem together.
Jon Orr: Yeah. We're looking forward to chatting with more members of the math moment maker community. I'm sure that before too long, we're going to have someone jump on a call with us to discuss a concept that tends to be a huge pebble in the shoe of educators and students everywhere. Luckily, we've been busy adding new full units to our make math moments website, including a six-day unit of study that was created specifically to help remove that very big pebble, the wooly worm's race.
Kyle Pearce: Yes, you're so right. What is that concept that the wooly worm race unit is going to help us address? Well, in the day one lesson of that unit, student curiosity is going to be sparked by watching a short clip of a bunch of the wooly worms or caterpillars erasing up a string. What are students going to notice out? What are they going to wonder?
Jon Orr: After acknowledging student voice and addressing as many notices and wonders as we possibly can upfront, we'll challenge them to first estimate and then determine how far the winning caterpillar collide.
Kyle Pearce: The part I love about this unit is that throughout each of the six days, students are prompted to represent the distances traveled by each caterpillar using a concrete or visual model to help them compare, order, and even add fractional amounts without rushing to the algorithm.
Jon Orr: Throughout the unit, we even get students converting between fractions, decimals, and percentages to help build fluency and flexibility with these fractional representations that tend to be proceduralized a bit too quickly in a learner's journey.
Kyle Pearce: Best of all, you can access all six days of this unit and run them in your classroom straight from your web browser by visiting makemathmoments.com/wooly, that's W-O-O-L-Y.
Jon Orr: Yes, that's right. The content is openly accessible for you to run from your classroom and even the full day one teaching guide and planning supports are available for you to gobble up.
Kyle Pearce: Get on over to makemathmoments.com/wooly to get started with this fantastic six-day unit to put an end to the frantic fraction frenzy that so many of us face when we're trying to overcome this huge conceptual struggle for so many of our students.
Jon Orr: Yeah. See you over at makemathmoments.com/wooly to run this task in your classroom today.
Kyle Pearce: Alright there, Jon. Let's get into this awesome where are they now mentoring moment episode with Bill. Hey there, Bill, welcome back to the Making Math Moments That Matter podcast. We are so excited to have you back for a where are they now math mentoring moment episode. How are things going in Pittsburgh?
Bill Zbozny: They're doing well as you can expect. We had the whole teaching online thing and that we've all had to deal with, but lots of fun there.
Kyle Pearce: New learning, eh?
Bill Zbozny: Yeah, absolutely.
Jon Orr: It is definitely something that is a struggle for all of us. We chatted about it lots here on the podcast, but also in our live Q&A sessions for our academy members. It's a ongoing growth for us how to manage this crisis for our kids and our students. Looking forward to chat with you here, Bill. Maybe we can even talk a little bit about that later on. We gave you a little intro in our introduction. Remind all of our listeners here, what's your role in education? What are you going to be teaching? Or what are you teaching in? Just fill us in a few details just to remind everybody who have not listened to Episode 23. Now again, listeners, if you have not listened to Episode 23, head over there, listen to that, and check out Bill's first episode. Bill, what's your role?
Bill Zbozny: I'm still a third grade teacher, self-contained classroom. While I focus a lot on math, I have to teach everything, which is fun. I found that some of my math practices are bleeding over as best practices into other curriculum areas, which is exciting. Other than that, my plan is really to stay in the classroom. Started work on a math education master's degree and really focus on elementary problem solving as a vehicle for introducing and teaching through problem solving, is my passion.
Kyle Pearce: Fantastic, fantastic. For those people who did have the opportunity, go back to Episode 23 and listen in. They may remember that we were talking a lot about how we might select worthwhile tasks to elicit mathematical thinking that was something that was on your mind you want to riff on a little bit. We talked about efficiency, if you recall, and this idea that what's efficient for one student or in particular, what's efficient for us, as the educator, may be very different for what's efficient for students along their journey.
Then we started talking about how we can maybe approach pushing our students to be a little more ... We quoted Cathy Fosnot in her line about being more clever with mathematical strategies and thinking. There's an art to that, this idea. We explored this idea that you don't want to force students into using a certain strategy or a student type of mathematical thinking, but we want to actually emerge them. Then finally, we talked a little bit of how math develops conceptually to help them with sense making.
A lot of really good nuggets, at least in both Jon and my opinion that came out through that episode. We're wondering, take us through the last ... Oh, geez, when was that episode? Probably close to a year, once this one goes live, probably about a year ago since then. While this is a lifelong journey, we always say that. It's not like we can ever cross all of these ideas off of a list. How have things been going since we last chatted? Has there been any progress? We'll get into maybe some of the new hiccups that might be arising along the way. Help us understand how things going.
Bill Zbozny: Well, overall, I think it's been a very positive process as reflecting from what we talked about last time. I really did dive into the standards and eligible content for my grade level and bookend ones for me, like the three to five band and a little bit of what second grade does, to try to get a clear roadmap of ... We had talked about the continuum and being able to do all the things on a continuum and not just trying to get to the end of the continuum, getting as far to either sophisticated, clever, or I think we use a couple of different words to describe students problem solving strategies.
As I went through that and started really to develop, I think at the end, you talked about, hey, here's the benchmarks. Well, what's the steps in between those benchmarks? Start really looking into the things really with multiplication and fractions a lot, because that's the majority of the third grade work. It's not everything. If the students come out with the ability to really understand multiplication and then the inverse division and fractions, they're in a pretty good spot going forward for the rest of their math careers. That's been a lot of my free time, reading up on things like that.
Kyle Pearce: Going down the rabbit hole.
Bill Zbozny: Yeah, a little bit. It was a journey there. Like you said about the efficiency, that's really a moving target for students. If you can get really good at a strategy, while it might not on paper, be as efficient as the algorithm. If you can really do that strategy and you really own that strategy, it's going to be more efficient for that student and moving towards more abstract models away from concrete examples of things like that as we get through the third grade year, trying to take multiplication from skip counting and repeated addition into partial products, and things like that, decomposing numbers.
It's fun, at least for me, to see all the little step that they make. As we spiral through our curriculum, really having a much clearer roadmap of what that looks like in multiplication and what that looks like in understanding fractions are numbers, and how to prove that to the students. That's really where a lot of my time has been. That's really helped me select better problem solving and put better context. Another takeaway I got from our conversation was that, I would do this great context rich task with the students and that we'd go back to doing bare problems or problems that had minimal context.
I couldn't understand why they couldn't transfer it. Well, the context is gone. Their vehicle for understanding was taken away from them. More context is what I've been doing. That sounds awkward, but I try to keep the context and relate the context and show like, hey, look, this is why we're dividing. Even like, look, this is the story problem here. We don't even take the numbers out of it. Let's just talk about the context here. Why would you want to divide? Oh, we have a large amount of things and we're trying to give it to a group of individuals, things like that. I'm really trying to help them under the nuts and bolts going on behind and not just like, okay, you need to divide. Let's go. Those types of things.
Kyle Pearce: Plug and play.
Bill Zbozny: Yeah, absolutely. Somebody joked one time in a PD I was in and it was like, yeah, there's no wild three times fives running around.
Kyle Pearce: Right. You don't just encounter three times five.
Bill Zbozny: There's a context for it.
Jon Orr: It's such an interesting way to learn in a sense that I taught like many teachers teach by frontloading and teaching how to add fractions, how to add integers and divide, and just by just numbers, and no context whatsoever, because you think it's easier. You think that it's like, I don't have to have context, because people will say, they'll say like kids struggle with word problems, kids struggle with the application problems. When you actually introduce those problems through the context, from my experience, and it sounds like your experience, and I know it's Kyle's experience, is that kids can intuitively see what to do.
Then what you can do is, they'll know how to put these things together. Then you, as a teacher, can mold that into what it might look like without context. I think that's a gradual thing. I find that such a weird flip that so many people think you need to go numbers, numbers, numbers first, no context. Then because they think they'll be easier when they bring in context, but it's actually the reverse for most situations.
Kyle Pearce: Actually, Jon, there's something too like popping into my mind this idea, and you alluded to it there, Bill, this idea of I think you were saying bare problems. I always call it like naked problems, where you just give them these facts. I vividly remember that was how I was taught and that in some ways, for memorizers, it's easier to give them bare facts. Because you just say, okay, every time I see that ... I love that, by the way, the wild three times five, it just showed up in your world. You're like, oh, every time I would just know what that is, I would know it's 15.
I never really thought anything about it even when I got into teaching. Now we realize that context is what helps kids, and we say it all the time, this fueling of sense making. Without that context, it's very challenging for them to make sense of why it matters. Think of how many times kids said like, "When will I ever use this?" If I'm giving them bare problems and you're using multiplication as an example, but we could do this for pretty much any concept in math. Where we strip it down, we just say, hey, do a bunch of these and then we'll try to fit it in.
It is so much harder because now they're saying, "Well, I'm really good at just doing these ones over here, but I have no idea how it connects to this context over here." When we build out our tasks and our make math moments problem based units, we'll add a link in the show notes for those who haven't checked them out yet. We leverage and we savor the context. That context is so important. It's one of the biggest reasons why three act math tasks, in my opinion, are so helpful. Because it's so easy for students to hang on to that context and build off of it.
I'm so happy that you've had this revelation or this epiphany to be able to realize how important that is. Then I'm going to even argue too, that we want to almost, once students are good with the context, maybe come back and challenge them to take some bare problems and wrap a context around it themselves. It's like, how do you now take that three times five and build us a context? Can you build me two different ones? Especially when we get to division, as I'm sure you're quickly realizing as you go down this content rabbit hole, that these two types of division pop up a whole lot more obviously when we're using context than when we use bare problems.
This is really, really great. I'm excited over here because I feel like, Bill, you and I are on a similar journey. I'm way into the content and trying to unpack especially some of the early content now that I'm in my role as a K to 12 math consultant. I get to play in that land, that three to five land like you're describing a lot. Even earlier, a lot of really powerful things happen in that grade band. A colleague of mine, her name is Yvette Limon, we call it the band of despair in some ways, because there's so many things happening. Yet, if we just give bare problems, we miss it all.
Then we wonder why students start spinning their wheels as they start moving into those middle grades. Really exciting stuff. I'm wondering if you had to summarize it, what would you say is your biggest success? I know you've already mentioned a few ahas that you've had here. Which one do you think would be the biggest success that you feel you've witnessed or you've experienced over this past year as you're moving through this journey, the one that you feel like it's maybe most important. Describe it to us or help us unpack it a little bit.
Bill Zbozny: This is a really exciting topic for me. Again, that epiphany of realizing how important a context is, but also then we talked a lot about ... I was focusing on my moves last time and really just how can I keep pushing the students. Really, understanding that what I'm actually trying to do is build some patient problem solvers, some resiliency, some sticktoitiveness, came up in one of your podcasts, I think, with Christina Tondevold who's pretty awesome on how not failing and being a rule follower and always getting right made it hard when the first time you fail, but really letting students explore strategies that they're trying.
We talked in my past episode about a child who was not using scale to make their tiles and it was like, maybe I should have just let them fail a little bit at that to see if they would change your strategy on their own. Go over ask a question. It's like, "Hey, is that working for you? What is, what isn't? Talk to me about it." Then let them make the decision instead of pushing. My biggest takeaway is to be ... I don't want to say less hands on, but to interfere less, to just ask and get them to talk about their thinking with me or with other students, and just letting them really explore, and that it's okay if we spend a class period working on a problem and not getting there.
Because that can be more valuable than them actually solving whatever the equation ends up being at the end, to let them lead and have more ownership. Before, I was using to problem solve a problem tasks two, three act tasks and other versions of those to push my agenda of the content and letting them be like, "Okay, well, this is your task. If you're going to work through this, you need to decide, are you doing what you need to do? My job is to question you along the way using different models and things like that, and to check in, but not necessarily try to push you forward or back on the continuum every single time." It doesn't need to be done in one task, I guess, is what I'm trying to say. I think that was a powerful understanding for me.
Jon Orr: I'm so glad that you seen that as your powerful understanding, is that you've got this course and your job is to help students move along this pathway to understand the standards or demonstrate the standards. You've got a full year to help them along. I really like that you have questioned kids and are questioning kids instead of just jumping in to help. Because there's this definitely a balance there. Dan Meyer's phrased that he said, "Be less helpful." It's like we want to be less helpful in a way where kids can be put into a struggle on their own.
Because we know that if you're less helpful and they are in a productive struggle in a sense, that they can check a strategy and you can talk to them about it. Then they are going to have a little bit more ownership in their learning, in their understanding. Then that sinks in deeper. Instead of you just saying, hey, let me just help you fix this or let me just show you what to do, then that's when we get kids, they're like, "Why are we learning math?" They just don't get that sense of accomplishment or sense of ownership in their own math. I think ownership is a huge thing.
The balance is, if you're not helpful enough, then you get an unproductive struggle. Kids just start spinning. Then you know those kids are sitting there going like, "I have no idea how to even get started." It's like, what is the right balance to help them enough so that they feel the productive struggle and they can feel eventually that ownership of the math, but we don't want to help them too much. It's definitely a balance. People are like, "Well, what is the right balance? Or how do I do that right?"
I think, Kyle and I said this lots of times, it's like you just have, as a teacher, give it a go and learn what questions are going to work. These purposeful questions are so important. You can find some of those and learn about more of those in the principles to action for effective teaching practices. There are some really good stuff in there to help you along the way. It's one of those things you can't just learn it by listening to us on the podcast right now. You can't just learn it by reading the book. You actually have to give it a try and see what is going to work with the kids. It sounds like you're doing that great. I'm glad that you've brought that up.
Bill Zbozny: Yeah, I'm pretty lucky to have had pretty supportive administrators the last five years that I would say, "Let me experiment with this stuff." They're like, "Hey, this sounds like there's potential here. Try it." Have them come in and observe in a non-threatening way like, hey, just here to see, get some more eyes on it as the different tasks have evolved. As I've somewhat dipped my toe into trying to make some problems from my textbook into more problem rich activities for us to solve. One of the thing is like, I can usually tell, end of a lesson if I helped a kid too much or not.
Because you can see the ones that are excited, feel accomplished. You see the ones that are sitting there like, okay, I checked it off. It is definitely, like you said, I think you really have to do it. If anybody out there still isn't sure, try it. This really is something I think the more experience I've got, more enabled and more empowered I feel to do it.
Kyle Pearce: Yeah, for sure. I love how you've mentioned that because I'm picturing too. This is where I think reflection is so key that if I'm just barreling through my lessons day after day and I'm not pausing to reflect. It sounds like you're definitely doing that right when you can say that you can tell if you've been too helpful. Sometimes too, maybe you can tell, I know when I've been not helpful enough. When I say helpful, I don't mean like telling them or funneling them in a certain direction. It's like you had mentioned this idea of asking kids questions.
Jon articulated how we want to keep the struggle productive. Our questions, I think, are what keep that happening, keeps them in that zone. I'm picturing the zone of proximal development. That productive struggle is like a similar zone where you want to keep them from helping too much, but you also want to keep them from feeling like completely on their own. That's where our questions come in. It sounds to me like you're doing a great job with reflecting on that. I'm picturing myself when I go into classrooms. I'm in classrooms and I'm asking questions.
I feel like more times than not, I'm trying to ask a question. You've tried to plan what might happen in the lesson. We all know that that's only part of the story. There's going to be a surprise solution, strategy, or approach that I didn't anticipate. Then now I'm trying to ask a question without giving too much, without giving too little. Oftentimes, my go-to move is, I say, "Huh, I wonder about that. I wonder if you can convince me." Or I say, "Oh, interesting." Then I walk away. As I'm walking away, I make it appear as though I'm going to check out other students.
I'm actually thinking about what to ask. This is definitely an art form. I'm sure we can riff on it all day. I want to give you the opportunity here. What are you working on now? Is it that purposeful question? I'm sure you're going to forever be working on these things that you're sharing. If we were to zoom in on any particular problem of practice that you're working on now, as we mentioned at the beginning, as you dig into your teaching practice, especially content knowledge, as you had mentioned, you've been working on that and really thinking about how the content connects and how it develops. I'm wondering, is there anything in particular that you wanted to discuss and riff on with us now in the math moment maker community?
Bill Zbozny: Yeah, absolutely. I've gone down that rabbit hole, as you said earlier, with the content and learning about. Maybe I reaffirm it with myself, that context is important. The mathematical practice standards have popped up. They're written in a way that they're entwined with the Common Core standard. Sometimes it's hard to tease out. What I've noticed, especially I said about like patient problem solving, is that that's where the standards come in.
I'm asking students to make sense of a problem and reason abstractly and do those types of things like, what models are you going to use? Are using your tools strategically? Are these problems structured the same way? Those types of things. It's my challenge that I'm having now. Or the next, I think, hurdle for me is to make those practices not be the cute little teacher, pay teacher posters that are up on the corner of the wall, that you go over and you point to every once in a while. We say, "Hey, we're going to try to do this." Then it gets lost in the shuffle.
How do I make those be ... Actually, I want them to be the center of my math classroom and the skills that we're working on, whether it's decomposing shapes or fractions or data. The vehicle we're using is going to be these eight standards of practice to build mathematicians, if that makes sense. That seems to be my next frontier.
Jon Orr: It's definitely something that I think gets overlooked. I think we get bogged down as educators in the curriculum standards, the content standards, and thinking like, I have to make sure I teach these, I got to cover these, I got to cover these. Then you assess those. It sounds like you're in this shift of like, what really matters in my math class? What do I value? Do I value the process standards? Or do I value the contents there? In truth, we value both. In one sense, we don't evaluate both.
Sometimes when we don't evaluate things, we tend to focus on the thing we evaluate on. Students pick up on that. It's like, I got to focus on understanding this and demonstrating this, which is great. We also want to show our students and paint them a picture about what we value in our math class. Sometimes we say these things, like we say we value problem solving. We say we value resilience. We say we value these process standards. We don't show it in a particular way the students pick up on that.
It was something that I'm on a learning journey too, Bill, is to figure out how can I embed those standards, those process standards, into showing students that that matters. Like giving them feedback on those standards above and beyond the content standards. That's something that's in the process, for me, as well as you. I think a lot of teachers, I think, are starting to make that shift. That's something that I think it's going to be great for the kids because they're going to start to see like, yeah, resilience matters and my mindset actually matters.
Bill Zbozny: Yeah, exactly. As I've been picking apart standards, those are the threads that run through all the grade levels. Those practices and processes, because they don't have content attached to them, it's easy to overlook them. In my textbook, they'll be like, oh yeah, this is mp3, and give me a little blurb on it. That's really easy to overlook, because nobody has infinite time to plan for all these things. That's where I'm noticing, is that a lot of the things I want my students to do really comes into play with these standards and practices here of how to learn math or how to be a mathematician.
The content can be adjusted to that. That's what I'm trying to get my head around, I guess, at the moment. It's how to do that. Because my report card does have the standards on there. It's like a plus and a minus, not even like a check. It's like, oh. I'm not saying it needs like a letter grade or needs to be called out much more than that. It's like, it's there, but it's like one of those a do, do thing. We do, do this. Check, check, check, check, check. Okay, can my kid divide? It's like nobody is paying attention to that part of the report card, not the part that I'm finding more value in as I'm going through this, I guess.
Kyle Pearce: Yeah, for sure. Jon, as you mentioned, we're all on journeys. We're all trying to improve. Obviously, anyone in the math moment maker community who's listening to the podcast, or engaging in our Facebook group, or in the academy, or wherever people are engaging, clearly, like you, Bill, are trying to continue building their math practice and continuing to push forward. Just to set a little context, for those of us that are not from the US, the standards for math practice, there's eight of them. We have something similar in Ontario. We call them the process standards.
There's eight of them in the US, in the Common Core. We have seven here in Ontario. Most curriculum or curricula around the world have something similar in some way, shape, or form with maybe different names. For example, the first Common Core practice standard is make sense of problems and perseverance solving them, and reasoning abstractly and quantitatively, construct viable arguments and critique the reasoning of others. As we go through this list, in Ontario, we have some ... Actually, we have a new curriculum coming out this fall here.
On the top of the whole COVID thing, they decided it was a great idea to just flip the curriculum for grade one through eight teachers in Ontario. They've actually included social-emotional learning skills with the math process expectations. They're taking things like reasoning improving, which was a process expectation from the past. Now they're saying they want students or they want us to be helping students to, for example, identify and manage emotions and recognize sources of stress and cope with challenges.
Then it says, as they apply to the mathematical process expectations, which I think is awesome, but we're going to have to do a lot of work. Just like you're saying here, Bill, of like, so what does this look like and sound like? I'm picturing in my mind, I read through these, and I'm almost thinking, wow, wouldn't it be awesome if the report card was only this stuff, where it was all feedback driven, not grade driven. Imagine we lived in a world where we could be providing students and their families with some feedback on how they're doing with these social-emotional learning skills, as well as these process expectations.
The curriculum, the content curriculum was just a guide for us on what kinds of tasks and experiences we would use to elicit these ideas. In my mind, I think that would be amazing. I know that's not the world we're living in in most places. In some places, things are shifting in that direction. Clearly, here in Ontario, we're shifting. Still, we still have content at its core is still maybe overemphasized in how we report and evaluate. My wonder for you, Bill, if we dive a little deeper here, you had mentioned some of the challenges here.
This is on your mind that you want to essentially work to help ensure that you're pulling at these ideas, these mathematical practice standards. I'm wondering for you, what do you think might be holding you back from doing that? I'm hearing, making assumption that how we report obviously isn't helping. I wonder if we were to put reporting to the side, and we know we still have to report on what we have to report on, but if I'm in my classroom, where are you feeling that maybe there's a disconnect between your want to focus on these mathematical practice standards and your actual ability to actually follow through and do that?
Bill Zbozny: That's a good question. I think, assuming COVID and all that stuff goes away and I can get back into the classroom in the way I'm used to, because online has presented its own challenges, which we don't really need to talk about at this moment. I think we've all experienced them. Getting back to the question. I don't know that if I know enough about them. They're things I know how to do in my own problem solving, the methods that I use. I know how to make sense of problems. I know how to restate questions and do those types of things.
I don't know that I have the expertise or knowledge or experience yet to really know when I'm using, well, say, model with mathematics and what the difference between using an appropriate tool strategically. That's math practice four and math practice five in the US here. They sound like they could be very similar. By using, I don't know, connecting cubes to show repeated pattern, is that using the tool appropriately or am I modeling math with that. I know I'm probably doing both, but how to choose which one to focus on. A year ago or so, just like, okay, I'm selecting tasks.
One of the issues I think I have was like, did the task I select line up with the goal I had? Now it's like, okay, the practice that I'm attempting to demonstrate here, does it fully aligned with this? I'm sure we'll get to the place where like, oh, each student is using a different practice at the moment. I think my issue is being able to identify when I see those practices and being able to have that level of comfort to why I have ownership of the practices at this moment. I don't believe I have that yet.
Jon Orr: I really like that you brought up the tasks and how the tasks might not be hitting exactly one standard or another or this exactly aligns with the standard. Did you notice when you are selecting those problem-based tasks that sometimes they bring out more than one content standard?
Bill Zbozny: Yes, absolutely. I've gotten better at looking, okay. Again, the big job in third grade is really understanding multiplication and division, but that also entails a lot of addition and subtracting. Sometimes I'll notice students who may be using some kind of additive strategy end up with place value issues. While that isn't necessarily what I was going for, well, obviously, we need to address that. Because place value is infinitely important to what we do. I'm assuming that my standards of math practice issues are also the same way. I'm hoping that there's to focus on some kind of tool, but maybe it ends up for that. Maybe it ends up being like, they can't make sense of the problem. They're stuck in practice one because they can't understand this task.
Jon Orr: I'm looking at it the same way for my classes, my students. It's that like when we talk about a problem and bring it up, that problem is going to bring out a couple different standards. We might want to focus on one. That's because we're going to move through that curriculum. When I think about the process standards or the process expectations, I'm thinking about them as a whole. That sometimes I get one or two or three that show up in a lesson or I'm going to model one, two, or three in a lesson. Thinking about that, they should show up regularly.
In an ideal world, you should see all of them every day in that particular lesson. When I'm thinking about ours with reasoning, improving, I should see that right along with communicating and representing and connecting. We should be definitely seeing all of those. Now, do we have to give feedback or make notes on every single one for every single kid every day? No. You might want to have a look for these on a regular basis. I used to get in a rut where I didn't look for a particular student for a particular process standard or expectation and I would miss it.
Now what I do is keep a checklist of, who am I seeing stuff from? Am I seeing good work from over here? Am I seeing good insight on this idea over here? I'm thinking of both content standards and practice standards very similarly in the sense that we're going to see them multiple times a day. I do want to track who's using what, but I don't want to overwhelm myself. I don't think we have to select a task to just get at one or two. What we want to do is model. Think about how you want to model it. Then you can give feedback when you notice it from your students.
Bill Zbozny: A good first step for me with this, maybe especially early in the year looking at that first one for US. Basically, it's like makes sense of the problem and start teaching right away. We do the notice and wonder routine for pretty much everything. That just probably been the most powerful tool I've ever found for teaching, because it works in so many other subjects too. Like just what do you notice in science? What do you wonder in social studies? Just generating questions and things is great. Not to get down that rabbit hole either, but to start with that.
I start that pretty much from the very first math class. I think that's a way to help students make sense, because it gets them questioning and restating what information they have. Maybe what I need to do then is focus on a math standard and model it for a few lessons, look to see how the students are doing that. Then I let it spiral through the year. That way, I would with my other standards. Because you're right, if they're being a mathematician, air quotes, around it, then they should be doing all these things.
Reasoning abstractly in third grade is very different than what it would be in middle school. They're still doing it, especially if they're using a number model or they're finding different strategies and things like that. Unless somebody does something, I guess, that jumps off the page in one of them, maybe just spend a week looking for one of these. Like, hey, can I use repeated reasoning? Can I transfer this skill to other problems, which was a problem I was having in the past? Maybe I just look for that. I like that checklist idea.
Maybe week five is, hey, I'm just looking at this now. This is what we're trying to do. I'll model this a few times, see if I see it, and keep coming back to it. Because I think it would be a lot for me, especially with, like you said too, all the questions you have to answer and how you buy some time by saying, "Oh, that's interesting," and you walk away, and you're chewing on this student's strategy to see if it works and probe in your mind where it may fall apart. You can try to help that student see that. Then add this on top of it.
Then for your case, adding social emotional goals too, which is awesome, but also going to be a challenge. I think maybe what I would tell my students to do would be like, "Well, don't do the whole thing, do one piece at a time." Maybe I need to try to do that, not tackle all eight at once.
Kyle Pearce: Right. Going back earlier as well, as I was envisioning, if we could wave the magic wand and change how we assess and evaluate, I'm picturing those content standards as, again, that conduit to get students to the standards for mathematical practice. For us, I'm thinking about our math process expectations. Again, if we read through them, they're very similar to the Common Core like ours, our problem solving, reasoning, improving, reflecting.
Obviously, each of these, they give you an explanation of what they mean by that by connecting, communicating, representing, selecting tools and strategies. When I think about that, if in my mind, if I'm approaching that today's lesson, sure, the task is likely going to elicit certain big ideas. If today I'm working with this idea of the two types of division and I've strategically given a context that's going to elicit partitive division, and I then flip the context, the extension task is to flip the context. Now what will emerge is this idea of quotative division.
Then we're giving kids this opportunity to compare and contrast like, what did you do over here? What did you do over here? They'll realize that mathematically, how they approached it is actually different. That idea of reflecting for us here in Ontario, this practice standard or this process expectation is right at the forefront there. I'm wondering if it's almost like when you envision planning your lesson, that we tend to start with content, we tend to start with like, so what's the topic that I want to be using today and emerging today? Then, for what? Why?
We could say the why that like, well, so that they know how to divide with the two types of division. That's an obvious one. Okay, that's great. Why? Then I go, oh, because I want them to be able to develop, select, and apply problem solving strategies. Because I want them to develop and apply reasoning skills and to justify their thinking, to investigate conjectures, and to construct and defend arguments. As we're planning these lessons, I love Jon's idea of the checklist, and I'm trying to, in my mind, envision how this might be manageable for you.
I think one thing that we might want to also focus or think about moving forward and not saying it's going to happen tomorrow or the first day of the next school year, but trying to work towards this idea that I'm not just going to give you feedback on how you're doing with this specific content standard, I'm going to actually give you feedback with how you're making out with these practice standards. Whether that's through conferencing or whether that's through a rubric with some feedback spots there.
Or however it is that you choose, but to really bring it to the forefront so that both you and the students, it's like you're putting yourself on the hook and you're putting them on the hook that we care about this. We're not just looking for you to bang out a bunch of bare or naked problems as you had referenced earlier. I think one of the other struggles we hear a lot that comes out in our Q&A calls with academy members, they talk about this idea of shifting from a procedures first approach to mathematics, which many of us have a lot of experience with.
The way I was taught, the way Jon was taught, it sounds like you probably had a very similar experience. Shifting to a concepts first experience is very hard. One of the big major roadblocks that teachers always share with us is, kids, when they get an answer, especially that student that traditionally has excelled in that procedures first mentality, that memorizer, or that one that could just basically mimic problems, they really struggle with getting them to show more than just an answer or to do anything more than just get that number at the end of the problem.
They have a hard time. What they're having a hard time with is pulling at those practice standards, like pulling at these ways of them representing problems and being able to use that repeated reasoning. How come that works? How come it works here and it works here, and getting them to reason through that. I'm wondering if that shift, if you're shifting that in your mindset, clearly, you're committed to doing it, if we can make it more visible for our students, I wonder if it'll also help reduce some of the other roadblocks that tend to come up as we shift from this procedures first mentality to a concepts first mentality and start moving towards that problem-based learning lesson.
That's what's going on in my mind. I'm wondering if we throw it back to you, any thoughts on what Jon shared, what we've discussed here today. We'll move into any takeaways or maybe next steps that you see in your own mind. Do you have any ideas of where you might go next? Then obviously, we're going to definitely have to check in with you because this one's a juicy one. I'm actually very curious to stay on top of this with you and learn with you here.
Bill Zbozny: There was a lot that both of you said. I definitely put note down like checklist, again, to help me chunk. I also liked how you hit at that by having a rubric and giving feedback to the students in that way on those topics, on those practices. I think you guys call them the processes. It puts it as this is what the classroom is about and builds the culture around that, instead of building the culture around content or that ... Our job is to learn the stuff. This shifts it to be the job of our classroom is to become good learners.
Because that's how I view the standards here, the math practice standards and process standards that you guys have, is that this is what good learners do. I think by having saying, I'm going to give feedback, however, I decided to do it, will hold me accountable to make that accountable. Because I think I started off every year, again, I said, hey, I go over to the poster on the wall and I talk about it. Then by the second quarter, I'm bogged down and all the minutia that comes with the job looking at, again, like because I'm not just math focus.
I'm also looking at like, oh, well, Johnny has some trouble reading. What do I need to do for this? Does the kid need an evaluation or the data that you get is a mess. Especially in my district, we do different types of tests to tease this stuff out of kids. It's really easy because now, I don't want to say you're going to survival mode, but you go, these are tasks I usually do at this time of the year. Let's go back to them. I need to focus on this and not focus on the standard. Making that the priority is what I'm taking away. Because that's really what I want.
It reminded me of that 80/20 rule, where 20% of the stuff, 80% of the results. If you ever heard that, like if I focus on these standards and using the content to get to those standards, those practice standards, then I don't want to say 80% of it will be done. Then it's like, hey, I still have to do the content. Now that I'm focused this way, I will get to the content through that vehicle.
Jon Orr: That's a great way to put it there, Bill. I think that's a great takeaway, that if you focus on 20% of these things, that 80% of the other things will follow. I think that's a fabulous thing to focus on for your next step. Also, you mentioned a couple of things here, Bill, that relate to your takeaways. Earlier in this chat, you talked about your progression of where kids are on this learning journey and helping them along that. We just wanted to remind you or let you know that in the academy, which I have just unlocked for you, you had an account in there.
You're going to go back in and you can access our academy courses. We've given you also premium access to one of our bigger courses, the concept holding our students back, which is about proportional reasoning. Kyle dives in on that course on, basically, that whole journey on just proportional reasoning. Like from start to end, what we should be thinking about? What's it look like before, after, in the middle on that kind of progression? He's done lots of work there. We've got that course. That's inside your academy membership, plus all of the other ones.
We got another one that's on the fundamentals of math that helps along this exact idea of like, where should kids be on this progression. That's all unlocked there for you. It will be as a podcast guest. You can get in there and head to learn.makemathmoments.com to get access to that. That's going to be there for you to help you on your journey. We'll stay in touch through the message board in there, but also through email. Bill, we want to thank you so much for joining us here on the podcast. We definitely will be, as I said, touching back later. Because this idea of process standards is a big one, I think, for us too on our journey. We wouldn't mind keeping in touch with you on that.
Bill Zbozny: Yeah, awesome. This was great. Definitely helped me solidify next steps for me as I continue on this, trying to teach through problem solving and trying to develop learner mathematicians. Awesome. Thank you, guys.
Kyle Pearce: Bill, it's been awesome. It's a great way for us to start our day. It's early in the morning here. I'm feeling really energized walking out of this one. I just want to say I'm very proud of you, the journey you've been on and the journey you're continuing down. It's really easy for us to just sit back and hope that everything's going to work out okay or get better over time. Clearly, you care about teaching, you care about mathematics, you care about your students. Really, it sounds like you care about being the best version of yourself that you can be as an educator.
On behalf of all of your students, but also on the math moment maker community, I know that a lot of people right now are feeling good after listening to this episode. I'm hoping that they'll join you along that journey. Thanks so much for hanging out with us. We can't wait to catch up with you again soon. Thanks a ton.
Bill Zbozny: Yeah, thank you.
Jon Orr: Well, there you have it, Bill Zbozny Del Percio, from Pittsburgh. We know you're listening to this, Bill. We want to say one more time, thanks. We appreciate you and we look forward to having you back on the show in the future to see how you progress in your journey.
Kyle Pearce: Yes. This was another math mentoring moment episode with many more to come where we're going to continue these conversations with members from the Making Math Moments That Matter community, just like you who's working through a challenge or a struggle. Let's be honest, we are all working on something. If you're not, then you got to start thinking about that. Like what is that pebble in your shoe that you want to work through? Let's work together to brainstorm ideas and next steps to help overcome them just like we chatted with Bill about here today.
Jon Orr: If you want to join us on the podcast for an upcoming math mentoring moment episode, you can apply over at makemathmoments.com/mentor. That's makemathmoments.com/mentor.
Kyle Pearce: Awesome stuff. My friends, have you checked out the wooly worm race six-day unit of study yet? If you're seeking ways to make math moments while exploring fractions, decimals, and percentages with your students, then you've got to get over there.
Jon Orr: There are many big ideas that emerged through this unit. We thought we'd share just a couple of them like fractions can be represented in a variety of ways. How you partition the whole determines the fractional unit. As you partition that whole into more parts, the smaller the size of each part, and many more.
Kyle Pearce: Yes, that's right. There are ton of big ideas that we intentionally attempt to emerge throughout this unit. Best of all, you can access all six days of the unit and run them in your classroom straight from your web browser by visiting makemathmoments.com/wooly.
Jon Orr: Yes, that's right. The content is openly accessible for you to run from your classroom and even the full day one teaching guide and planning supports are available for you to gobble up.
Kyle Pearce: Get on over to makemathmoments.com/wooly to get started with this fantastic six-day unit to help put an end to the frantic fraction frenzy that so many of us face when we're trying to overcome this huge conceptual struggle for so many of our students.
Jon Orr: See you over at makemathmoments.com/wooly to run this task in your classroom today.
Kyle Pearce: In order to ensure you don't miss out on new episodes, make sure you smash that subscribe button and do us a huge solid by helping us grow this podcast, by leaving us a rating and review on Apple podcasts.
Jon Orr: You don't know how much it means to us, so take a pause, hit subscribe, click our rating. If you're super awesome, leave us a short review. Every one definitely makes our day.
Kyle Pearce: Yeah, that's absolutely right there. Remember, friends, show notes and links to resources including full transcripts from this episode can be found at makemathmoments.com/episode112. Again, that's makemathmoments.com/episode112. Well, math moment makers, until next time. I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr.
Kyle Pearce: High fives for us.
Jon Orr: And a big high five for you.
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