Episode #240: How Can I Engage My Students Consistently?

Jul 3, 2023 | Podcast | 0 comments



Today we speak with Cara Carbone, a high school teacher from Bellingham Washington. Cara is here to share a pebble in her shoe around engaging her high achieving students with rich tasks. She implements some low floor/high ceiling tasks but struggles to do this consistently due to time constraints and the large number of preps she has during the year. 

Stick around and you’ll hear how we help Cara reshape the resources pulled from online sources and Teachers Pay Teachers into meaningful, engaging experiences for her students. 

This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them.

You’ll Learn

  • Engage your students using resources you already have;
  • Modify textbook problems and exercises so that they spark curiosity in your students;
  • Use the Make Math Moments Curiosity Path so that your students will not only love math class but also learn to think deeply;


District Math Leaders: 

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? 

What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

Book a short conversation with our team now.

Start your school year off right by downloading the guide that you can save and print to share with colleagues during your next staff meeting, professional learning community meeting or just for your own reference!


Cara: I really love the school. The thing that I’m missing though is that collegial support because as you read, I’m kind of a lone ranger, and after the pandemic… Our kids, they’re very smart. They just don’t love education, and they’re very reluctant learners, I guess I’ll put it that way. And so I’m just kind of struggling to come up with something to hook them back.

Kyle: Today we speak with Cara Carbone, a high school teacher from Bellingham, Washington. Cara’s here to share a pebble in her shoe around engaging her high achieving students with rich tasks. She implements some low floor high sailing tasks, but struggles to do this consistently due to time constraints and the large number of preps she has during the school year.

Jon: Stick around, and you’re going to hear how we help Cara reshape the resources pulled from online sources and Teachers Pay Teachers into meaningful, engaging experiences for her students. This is another math mentoring moment episode where we chat with a teacher just like you who’s working through some problems of practice, and together we brainstorm ways to overcome them.

Kyle: Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pierce.

Jon: And I’m Jon Orr. We are from makemathmoments.com.

Kyle: This is the only podcast that coaches you through a six step plan to grow your mathematics program, whether at the classroom level or at the district level.

Jon: And we do that by helping you cultivate and foster your mathematics program like a strong, healthy, and balanced tree.

Kyle: The trunk of your tree represents leadership in your organization or the classroom pillars in your math classroom. The roots of the tree represent mathematics content knowledge, and what it means to be mathematically proficient.

Jon: Like a tree requires soil, water, and sunlight, your mathematics program requires a productive educator mindset and the belief that all students can achieve at high levels. Your professional learning structure or your professional learning plan is represented by the limbs of the tree.

Kyle: The branches of your tree represent the development of educator pedagogical content knowledge including effective teaching and equity-based teaching practices. And the final section of the tree are the leaves, which represent the resources, the tools, and the classroom environment.

Jon: If you master the six parts of effective mathematics program, the impact your math program will grow and reach far and wide.

Kyle: Every week you’ll get the insight you need to stop feeling overwhelmed, gain back the confidence and get back to enjoying the planning and facilitating of your mathematics program for the students or the educators that you serve.

Jon: All right, let’s jump into the conversation with Cara. Hello, there we are. There we are.

Kyle: How are you?

Cara: Good.

Kyle: Awesome, awesome. Glad that we have a opportunity to chat here. It looks like you took some time and completed the organization math program assessment and are looking for a little bit of some guidance on some next steps here. So why don’t you tell us a little bit about yourself? I know you’re at a school, you’re a bit of a lone ranger it sounds like, and it sounds like there might be this potential for a math coaching position. Take us down that rabbit hole and let’s learn a little bit about you.

Cara: Okay. Well, I’ve been teaching for quite a long time. I live in Bellingham, Washington, and I’ve made pretty much a lap around the city. I taught at one public school for 11 years, and then I taught at a different public school for 11 years, and now I’m teaching at the tribal school, and I’ve been there for 11 years. I really love the school. The thing that I’m missing though is that collegial support because as you read, I’m kind of a lone ranger, and after the pandemic… Our kids, they’re very smart. They just don’t love education, and they’re very reluctant learners, I guess I’ll put it that way. And so I’m just kind of struggling to come up with something to hook them back into learning, especially after COVID because they’re super disengaged.

Jon: Yeah, I feel like a lot of the gains I think we were making before COVID feels like we not only went back one step, we went back a few steps and maybe haven’t kind of gained back what we had beforehand. That’s how I kind of felt with my classroom. I know that the teachers that I was supporting as well, I noticed that with that group as well. It’s like, “Hey, we were making a lot of gains, but we are not back yet to where we were I think before.” I don’t know if you’re feeling similar to that.

Cara: Yeah. I want them to enjoy being there. I’m not super hard driving on, “Oh, we’ve got to cover all this ground because we’ve missed so much.” At the same time, we’re releasing them out into the world and they’re not math fluent, and they don’t see the value, and they’re not having fun. I’ve listened to your podcast a little bit. You guys are the fun guys making math fun, and I feel like I used to be the fun person, and I’ve lost a bit of that, so I’m just trying to find something that can help fill the gaps in the students’ learning, but also just get them excited about math and see the relevance of what they’re learning.

Jon: Got it. Got it. Cara, we always have to ask this question. Every guest gets asked the question about their math moment. So when I say math class, what pops into your mind as sticking with you through all these years?

Cara: I had a student, and this is just recent, it was an amazing question that he asked of me that I shared with some of my former colleagues. He said, “Ms. Carbone, if math was a person, who would it be?”

Kyle: Now, I’m wondering, did you have a response or were you just taken by the question?

Cara: I was taken by the question, and I did not respond immediately because I wanted all of the other students in the classroom to think. I go, “Hmm, that’s a super interesting question. I bet it would be a different person for every single individual in this room.”

Jon: I love it.

Cara: And so then I threw it back at the class and I said, “I want you to tell me who would embody math for you and why?”

Kyle: Did any stand out? Maybe positive ones, maybe some that either surprised you or maybe even saddened you a little bit? I’m sure there might be some.

Cara: That’s like a two headed beast.

Kyle: Yeah, I love it. I’ve done the verb question with some students saying, “If math is a verb, what is math?” And some are like, “It’s hard work, it’s determination, it’s a climb.” Things like that. Others are like, “It’s drowning,” and things like that. Talk about what a great conversation for those students to be able to at least reflect on it. Because I think a lot of times too, we just sort of go through school, and it’s just a thing we do. It’s like, well, it’s the school year and we get up and we go to school and we learn these things and we come home, and we don’t really think about our relationship with a subject area. So I think that’s a really interesting question. And I have a funny feeling if the student who asked that question, how would you describe maybe their relationship with math? Is it a positive one? Are they kind of the joker of the class or are they just the creative one that sits there and thinks about interesting things during class?

Cara: Well, he is definitely an out of the box kind of thinker, very creative, and at times he doesn’t think he’s a very good math student, but then he’ll latch onto something and then just announce, “I’m so smart.” It’s delightful to have this young man in my classroom.

Kyle: Awesome. That’s fantastic. Well, thank you so much for sharing.

Jon: So what would you say you’ve done so far to gain back that engagement level, that fun you’re looking for in your class to get students who may be achieving at high levels but need to enjoy math and see math in a different way? What would you say you’ve done so far to achieve that goal you’re looking for?

Cara: Well, I try to give them interesting problems to think about. And Dan Meyer, right? What I learned from him was to pose an interesting question and don’t give the kids all the information that they need, require them to ask for the information that they need. And we were doing geometric probability, and I have a big Promethean board, and I had created kind of a fun geometric shape. I gave them little rubber chicken darts that they could shoot at the Promethean board and try to land in different zones. And so I posed the question if it was completely random, if rather than aiming at the dart board, if you were to hit the dart board at random and your rubber chicken lands on the Promethean board, what’s the probability that it would land in each of the given regions?

Cara: And it was a pretty deep problem. They had to find the area of an octagon inscribed in a circle and also a square inscribed in the octagon. So they got into that. So those types of things where it’s a pretty rich problem, but wrapped in a lot of stuff that we’d learn on trigonometry and areas and fractions and percentages and things like that. So kind of do those sorts of things.

Kyle: How would you say that the students responded to that activity? So you’d kind of highlighted a few things, and Jon and I talked about this withholding information to try to keep that curiosity going. I also like that you didn’t necessarily pick a task that was super animated or had all kinds of shining lights and all of these things. You picked an idea, an interesting problem, and you sort of held back on the problem even at first, sort of just made it about this random shape, but then presented that question involving the probability piece. So how would you say that students responded? And then also on top of that is what do you think maybe is holding you back or maybe holding other educators back from making more math scenarios similar to that one?

Cara: Well, first they responded favorably. Of course, they were super into these rubber chicken darts that I gave them, so it got them excited about the problem. For some of them, they got lost with the rubber chickens. They were so excited about that they didn’t step up and do the math right away. So they were excited to do the problem. They were excited to play with the little darts, and then once they settled down, they dove into the problem. I was pretty satisfied with their engagement with that problem. As I mentioned in what I’d written to you, I’m the only general ed high school math teacher. And I know our middle school teacher, she’s super structured. I think my classroom tends to be a little bit wild. And so I think a more conventional teacher would shy away from some of those things just because it does create a little bit of chaos.

Jon: I’m imagining that teacher walking in going, “What is going on in here?” And when they’re used to having this very controlled environment versus a classroom that is thriving in a way. I like to use the word thriving. That gives off a very visual of what my classroom should look like, and that’s something that we’re always striving for in our classes. How can I make this class thriving instead of just the sitting and getting? And it sounds like that lesson had your students thriving. I’m curious about two questions, I guess, about that. One, did you feel like it opened the gateway for you to get at the math at either a quicker pace or a deeper pace with your students, and then also what is preventing you from doing more of that? Or is there a deeper problem that you’re looking to get guidance on here? Because it sounds like you’re starting with an engaging problem, and we’re trying to get that class thriving, but it’s like, “Whoa, what’s happening next?” And what’s preventing you from going with that process to create that thriving year?

Cara: I spend a lot of time coming up with my own problems, and I think my biggest hindrance is time. I have five different preps, and so maybe I need to take something like that problem and more fit into things that can be used in a variety of my different classes to minimize the amount of time that I’m spending prepping for these little activities. Time is a huge deal.

Kyle: I’m guessing there’s a ton of people who are feeling the exact same way. They’re going, “Hey, if I had all the time in the world to sit and think and craft and all of those things, every math class would be much more engaging.” So I’m wondering what would you be relying on, let’s say, in a scenario where you’re tight for time, you’re like, “Oh, my gosh, tomorrow I’m teaching. I’ve got five different preps, and I just don’t have enough time to sort of fully craft the experience like you just described.” What would be sort of the go-to resource in that perspective? And then I’m wondering maybe there’s a place where we can help you with the next step as to how do we maybe get a little bit of both without necessarily feeling like you’re way over here throwing out those other resources. So what would that look like? You’ve got no time, and you’re going to go into class tomorrow to teach this specific group. What does that look like and sound like? What sort of resources do you have access to, and what would the lesson sort of look or sound like?

Cara: Well, I don’t know. Gosh, when I get desperate, I go onto… Well, I love Desmos. I always find some cool stuff there. I think when I get kind of desperate, I go to Teachers Pay Teachers for just a fun little engaging activity.

Kyle: Now, here’s a question for you because I think there’s this general sort of sense or feeling that educators have out there that Teachers Pay Teachers is bad. And I’m going to go ahead and say it right here that there’s a ton of great resources on there. There’s a ton of maybe not so great resources out there too. But ultimately at the end of the day, I guess why I wanted to know a little more about that if you had, let’s say, a textbook to rely on, it sounds like maybe you don’t have a curriculum resource that’s provided by the school or the district, so you’re kind of left to your own devices to kind of go out and find something, right? Let’s say it’s Teachers Pay teachers, I could go and find a resource, and it might be a really great resource, but the part that I’m wondering about, and I’m going to throw this at you and have you maybe think about this a little bit, is what if I went and I found a Teacher’s Pay Teachers resource for that day, and maybe there’s an activity involved in there, and I’m wondering, is it possible that you might be able to put some of those same thoughts into what you did in the previous activity to maybe transform that Teacher’s Pay Teachers activity?

Kyle: And for other people that I’d be talking to, whether it’s a textbook, it doesn’t matter what the resource is, is there a way that maybe it’s like, “Hey, I’ve got that as a starting point, and then I just focus to the first 10 minutes of that lesson. What could I do to craft that one prompt?” When you described your scenario… Now, I know throwing darts and things is fun, but I would argue that the more important piece of the activity that you described to us was that withholding of information and asking a good question, and I wonder about that, if it’s possible that I might be able to kind of hit two birds with one stone.

Kyle: I get this lesson to maybe fall back on to make sure that there’s enough content there for me to feel like I’m going to meet the goals for that lesson, but then it’s like now I just have to focus on what is the thing, the prompt? Here in math moments land, we like to call it the spark of the lesson. In Singapore math, they might call it the anchor task. Right? Now, of course, maybe there isn’t a great first initial problem, but even if I have this lesson and I look to the lesson and I go, “Okay, it’s helping me meet all these expectations or standards or the specific standard I’m after really focusing on today,” and I go, “What is the one question I can ask students at the front?” And it might simply be a Googled image, it might simply be a verbal statement or a story or a context.

Kyle: I’m wondering, do you feel like that would be more manageable than, let’s say, starting from scratch and coming up with the entire idea all on your own? Does that reduce anxiety? Is it increasing anxiety or are you sort of going, “Nah, it’s not really helping me out here?”

Cara: If I know on a given day this is what I want to be teaching, these are my learning goals for the day, and oh, here’s a really cool question that I haven’t had to think of on my own to launch the activity, that would be pretty cool. I think that might be what I’m looking to you guys to maybe supply, I don’t know. I kind of figured that’s what you were all about.

Jon: Well, when we craft lessons that’s going through that activity, that kind of thought exercise that Kyle just outlined is exactly how we’ve crafted all the lessons on our website when we create them. I think there’s always power in knowing that process so that we can repeat that over and over and over again and not always going to that exact lesson every single time because it might not fit for this group of students, it might not fit for the next year, and maybe I’m teaching a different course and I can’t find those lessons that are out there. It’s always, in our opinion, a stronger skill to kind of think about the elements that are easily implementable so that what he’s saying, you can take any resource and quickly add or change some elements to create that thinking type task. Another way that we usually think about starting those tasks is that’s a little different than trying to go the curiosity route is, could I put my students in a situation that creates a productive struggle that leads to the thing that we need to teach that day?

Jon: This usually is a way when we’re working with high school students in a situation that might help build their understanding of where this math needs to come from and why this strategy works or why that strategy is better than this strategy is to kind of put them in these struggling situations that at the end, either this new strategy comes out on top or it puts you as the teacher in a position to say, “We’ve all struggled on this joint venture for the last little bit, but there is a strategy here that maybe I haven’t seen yet, but maybe last year’s student tried this strategy, and it looked like this.” And all of a sudden that’s the new teaching element for the day. So it’s like you interject after everyone’s had this shared experience with a strategy that was on your learning goal list the whole time, and now it’s a way for them to kind of like, “Oh, I see that connects with what I was doing,” making those connections very clear.

Jon: We call that tying the bow, that this is a great strategy to help in this situation, and, hey, why don’t you try my strategy or that last year’s student strategy next on this next problem? And kind of increment the work after that. That’s another way to think about taking any lesson, any resource, and kind of thinking about it slightly different so it transforms into more thinking than say let’s just do I do, we do, you do model.

Cara: You’re right. Well, and that is one thing that I’m really trying to grow with them. I have signs up in my room that we are thinkers, we’re leaders, we’re not followers, and curiosity, creativity, perseverance. And I think as I reflect over my past 11 years, there is much greater willingness on the part of the students to think and engage in a little bit of struggle. When I first started teaching there, if they didn’t get something instantly, they would actually throw their papers off their desk. It was really interesting. Or if there was a little mistake made, they would wad the paper up and throw it away or erase absolutely everything. And some of the things that you’re saying are speaking to me and reminding me of where I’ve come from and their willingness to struggle with a problem.

Cara: And when you talk about the strategy that a student used on a previous year and trying to wrap that in with what I’m doing with a student on a given year, the beautiful thing about the size of my school is that the student from last year is my student this year. And remind them of their own strategy that they employed to solve a particular problem maybe last year or two years ago and say, “Hey, look, how about when you did this?”

Kyle: I love it.

Cara: Let’s build on that.

Jon: Or when I say last year’s student, a lot of times it’s not last year’s student. It just makes them look like somebody else did it this way, but it’s the strategy that no one else has yet come up with. So I usually say last year’s student, but not necessarily. It is a strategy of that last year’s student. I kind of pull the wool over their eyes a little bit sometimes.

Kyle: Yeah, I love it. I love it. It sounds like you’ve had little takeaways. I want to offer two thoughts or two suggestions maybe as for some next steps that you might consider. One is we actually have an open training on what we call transforming your textbook into a curiosity machine. So it really highlights some of what we described here. We call it the curiosity path of really trying to take any old problem and trying to essentially draw out the four key components that are really important. You mentioned it, the withholding of information piece. We want to actually create some anticipation which causes some noticing and wondering, and then we always try our best to incorporate some sort of estimate or prediction of some type. And there’s nothing better than getting people when they don’t have enough information to get their gut opinion on something, right? Why do we always have these guess how many gumballs are in the jar as a prize at an event, right?

Kyle: It’s because everybody wants to get their thought in there. Everybody wants to guess. Everybody wants to win the prize. And if we can do more of that in our math class, which again doesn’t have to mean staying up late every night and making it the perfect problem or the perfect start to your lesson, it’s just about considering those four things. And what you’ll get in that training is you’ll get this opportunity to kind of check out a couple problems and examples of what they look like prior and then what we did to sort of shift them. And there’s no perfect way to do it. The way you’re going to do it might look different than the way I would do it. The way I would do it might look different than John and so on and so forth. So that’s a great start. And the other thing you might want to consider doing is checking out on our website, we have over 60 problem-based units, and day one of every single unit is open for you to explore.

Kyle: Now, they range in grade from K all the way through high school. We really have honed in on some of those upper elementary through middle grades. That’s sort of the wheelhouse of where most units are, but I’m not saying to go there to necessarily grab tasks and use them. You could use them as exemplars to go through and sort of analyze how we use the curiosity path as a means to try to get students to kind of engage in the problem and help us get towards what we call the sense-making portion of the lesson, which is going to be where students are actually doing the thinking, where they’re actually trying to understand what’s happening. They’re going to pull out those strategies that maybe they’ve used in the past or that they have available to them, and it’s going to give you information as the educator to go, oh, this student is here in the developmental trajectory, and I want to help nudge them along to get them further along that path.

Kyle: Those are the things that we’re trying to do through our units. So you’ve got two thoughts or two next steps that you can dig into, and we’d encourage you to let us know how things are going, what your big takeaway is after you complete them. But before we let you go and kind of dig into those, I’m wondering, are any sort of key takeaways from today, a big takeaway that has maybe resonated with you to help you feel like that pebble in your shoe is either getting smaller or maybe, heck, maybe we even knocked that entire pebble out for you?

Cara: Well, I think some of the things that you said, I guess, reinforce what I am doing in my own classroom, and I think I might have misled you. We do have a curriculum, and I think it’s pretty decent. In fact, I picked it 10 years ago, but it’s 10 years old, and it is kind of overwhelming for our students. Anyway, I guess I just feel validated in the things that I am doing, but I’m also encouraged that there’s some stuff that you guys have out there that’s published that might give me some support and then things that I can share with the rest of our math teachers, which would go all the way down to kindergarten because I would like to grow these kinds of notions about that productive struggle starting at an earlier age. I think they do a lot of rote mathematics in the elementary grades, and that builds confidence.

Cara: Knowing your multiplication facts gives you confidence because I do have high school students that pick up a calculator. They reach for the calculator when they’re doing zero times three. Of course, I have a big fit. And I snatch it out of their hands and throw it across like, no, use your brain, you can do this. But there needs to be a blend. And so I would like to be able to share with some of the other teachers at the lower grades the kind of work that you guys do.

Jon: That sounds like a great plan. And the younger you can engage students in that productive struggle in changing the mindset of what mathematics is and what mathematics should be at school will eventually pay off. And eventually, by the time those students get to you in high school, maybe they’re not whipping out that calculator. Maybe they are using the strategies, the models, that they’ve built up over time. So I’m excited for the work that you’re going to engage in in this next little bit and share with your fellow educators. So Cara, I want to thank you for joining us here today.

Cara: All right, great. Thank you.

Kyle: Awesome. Thank you, my friend.

Kyle: Well, my friends, Jon and I learn a ton from these conversations, and it’s clear that Cara has a lot of awesome things going on. However, time is always a factor. And something I sensed here, Jon, was that Cara knows much of the pieces to put in place, but that time piece seems to be getting in the way. And I think sometimes we feel like it’s an either/or, right? We can only have this really effective, really rich, really exciting lesson or we have something we may have pulled out of the textbook or maybe something that we pulled off a website or Teachers Pay Teachers as we heard here today, when in reality, starting with what you have and making some adjustments might be just what you need. So for me, I guess, the part of the tree that I’m thinking about right now are the leaves, right?

Kyle: And we’re looking at these leaves as you may have a curriculum that’s been selected by your school, your district, or maybe you’re left to fend for yourself. In either case, whatever you’re finding as sort of the start, the backbone of your math program, there are things that we can do to adjust and ensure that the branches of the tree are being leveraged, which are the pedagogical practices that we’re putting into place. So as we mentioned here, there’s some great resources that you can leverage. The one that came to mind for Cara today was our Transforming Your Textbook into a Curiosity Machine. We’ve got an awesome, awesome self-paced and freely accessible mini course that you can go check out over at makemathmoments.com/transform. Once again, that’s at makemathmoments.com/transform so you can strengthen those branches and ensure that those leaves are green and flourishing.

Jon: Awesome stuff there, Kyle. So is this the first time you’ve listened to a podcast episode? If so, hit the subscribe button right now so that you don’t miss out on new episodes. And if you are returning and you’ve listened to a few, you’ve listened to some, you’ve listened to many, then we want to welcome you back, and we encourage you to share the podcast with a friend, a neighbor, a person of interest, a person that you know is going to get a lot of value out of the particular episode you are thinking of right now. Please share that podcast with that person so that we can reach as many educators as we can where our goal is to help a million students with the work that we do. And we can only do that through folks like you by taking action on what you’ve heard here today. So make sure that you share. You can also engage with us over on any of our social media accounts at Make Math Moments, and hopefully we’ll see you over there and keep the conversation going.

Kyle: Friends, show notes, links to resources and complete transcripts, including the link to that Transform Your Textbook Into A Curiosity Machine mini course that you can dig into right now are available over on makemathmoments.com/episode240. That’s right. We are at episode 240. Makemathmoments.com/episode240. Well, Math Moment Makers, until next time, I’m Kyle Pierce.

Jon: And I’m John Orr.

Kyle: High fives for us.

Jon: And a high five for you.


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