Episode #126: My Students Aren’t Engaging and Struggling! What Do I Do? – A Math Mentoring Moment
Today we speak with George Garza – a high school teacher who strives to make a difference in his students’ lives is struggling with engagement, pacing, and reaching his students who are falling behind. In this conversation you’ll hear George reflect on his practice and realize where he needs to focus his efforts. Stay with us to hear his epiphany!
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 Help Students At Varying Levels.
- How do I structure my lessons early in the course so students become better problem solvers?
- How can I use the curiosity pathway in my classroom?
George Garza: So, I think the biggest issue I'm having is trying to square two ideas that seem very separate from each other, but I know they can be unified and I don't know how it is. I think that's what it comes down to crosstalk
Kyle Pearce: Hey there, Math Moment Makers. Today, we speak with George Garza, a high school teacher who strives to make a difference in his student's lives and is struggling with engagement, pacing, and reaching his students who are falling behind. We can definitely relate. We hear this struggle all the time and we feel this struggle often. In this conversation, you'll hear George reflect on his practice and start to realize where he might want to focus his efforts. Stay with us to hear this epiphany in action!
Jon Orr: This is another Math Mentoring Moment episode where we talk with a member of the Math Moment Maker Community, a person just like you, who is working through struggles and together, we brainstorm possible next steps and strategies to overcome them.
Kyle Pearce: Let's hit it!
Speaker 4: (Singing)
Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr. We are from Make Math Moments and we are two math teachers who, together...
Kyle Pearce: With you, the community of Math Moment Makers worldwide, who want to build and deliver problem based lessons that spark curiosity...
Jon Orr: Fuel sense making...
Kyle Pearce: And ignite your teacher moves! Welcome, my friends, to episode #126. Jon, holy smokes.
Jon Orr: Whew!
Kyle Pearce: 126 episodes and you know what? We get to spend it with an awesome Math Moment Maker here. George Garza.
Jon Orr: We are excited for this and we have a jam packed episode! But first, we want to say thank you to all of you Math Moment Makers from around the globe who have taken time to share feedback and leave us reviews over on Apple Podcasts.
Kyle Pearce: Yes, that's right, Jon. This week we want to highlight Mashka88, who left us a five star rating and review. That is so awesome! The rating and review this person left says, "I love it on my drive to work. Kyle and Jon are absolute gurus. Listening on my morning drive allows me to come to work inspired and motivated to try something new each time. While I've always considered myself a 'math person,'" using the little bunny ear quotes, "listening to their approaches puts a new spin on my techniques and allows me to access even more of my kiddos!"
Jon Orr: They also add, "Pro tip: Go back and listen to older episodes, too. The info and advice is just pertinent now as it was then. Thanks for all you do, guys." Wow! That is a prot tip. The older episodes of this podcast... As we said, this is episode 120... What did we say, Kyle? 126.
Kyle Pearce: 126! Holy smokes!
Jon Orr: And you're right! If you go back and look at the titles of the episodes in you podcast player, pick one that stands out to you, for you at that time. Like we've got so many episodes for everyone on different parts of their journey. So you don't have to go and listen to every single episode! That'd be crazy because there's 126 hours worth of episodes or about that. Go back and choose one that's like, "Yes, that's for me today. Let me listen to that one."
Kyle Pearce: Yeah. For sure, for sure. So if you haven't taken a moment, go back and listen to some of those episodes and really importantly, really helpful to help us reach more Math Moment Makers around the globe, leave us an honest rating and review. In particular, on Apple Podcasts, as that is where we get most of our Math Moment Makers who are listening in. But whatever platform you're on, we certainly appreciate it. And remember, you're not only helping the show, but you're also helping other Math Moment Makers make some of those important shifts in their own teaching practice.
Jon Orr: Totally, totally. All right, let's jump into our conversation with George. Here we go!
Kyle Pearce: Hey there, George! Thanks for joining us here on the Making Math Moments That Matter Podcast. We're super excited to dive into a another Math Mentoring Moment with you, actually, a long-time Moment Maker. How are you doing today there, George?
George Garza: I'm doing really good. I'm doing good. Today's been a great day. So...
Jon Orr: Awesome stuff, awesome stuff. Like Kyle said, I think I first saw your name like over a year ago inside the academy and we've been anxious to chat with you, George. But before we get going, why don't you tell our listeners a little bit about yourself? Where you're coming from, how long you've been teaching. What's your journey look like and what role to you hold right now?
George Garza: So, I think I've got a little bit of a unique store here. Everybody's unique, I guess. So I've always enjoyed helping people. And in high school, I was tutoring people in math all the time. Graduated high school and wasn't sure what I wanted to do. So I became a draftsman and just worked for architects and engineers. And I was chipping away at college during this time. I wound up getting married, having kids, and stayed in that field a lot longer than I intended to. So a couple years ago, I finally got my Bachelors in Math Education. So that was really cool and super excited to get out there.
So while I was finishing that up, I did some student teaching at the local high school and that teacher was a very, very traditional teacher. But that year, the principal had installed whiteboards around the classroom for everybody, for all the math teachers.
Kyle Pearce: Nice.
George Garza: And he had kind of signed up with this program, so the teacher was trying to comply with the program and it was basically lecture for 10 minutes and then have the kids do their... We'd normally give them a practice sheet. Well, instead of a practice sheet, they go to the whiteboards and do their practice there. And then, you come back for another round of 10 minutes and then they go back to the boards. But just being able to... having them at the boards, I just saw how powerful those boards were for getting them moving and getting them engaged. That was the first little thing I kind of saw that really stuck, clung to me.
But I also saw the problem with traditional teaching there, too. And so after that, I just kind of started digging around, trying to find out what I could about problem based learning because I'd heard a little bit about it through my college program and didn't go very much into depth into it, so I was trying to research everything I could. That's how I found Making Math Moments That Matter, found you guys, and yeah, I've been listening to you guys since, I think, episode 2.
Kyle Pearce: Oh, nice!
Jon Orr: Wow! You're a long-time listener, George.
George Garza: Yes.
Kyle Pearce: Yeah, that's awesome. That's amazing to hear.
I want to dive into this a little bit more, but before we do, you may have said it. If so, I want to apologize because maybe I missed it, but where are you coming to us from? So whereabouts is this taking place? Just so I can kind of put a pin on the map somewhere in my mind here.
George Garza: Sure.
Jon Orr: We got a map, actually, over here and we just put pins in it for inaudible-
George Garza: Oh, that's cool.
Jon Orr: ... for all the people we talk to.
George Garza: That's awesome. I am in Visalia, California.
Jon Orr: Oh...
Kyle Pearce: Nice! Awesome.
George Garza: So, it's Central Valley of California.
Kyle Pearce: Super cool. And I'm just kind of picturing this, your journey and following along with your journey. It sounds like that you almost knew, but I'm not sure if you knew it consciously, but you had mentioned you were always helping in high school, tutoring. And it's almost like you maybe had that itch there. Was it something that you actually considered early on? Or was it something that took you a little while to kind of clue in? That like, "Wait a second, I'm enjoying this, helping this." And I guess my wonder is like what about that did you enjoy? The whole helping part. Was it when those lightbulbs went off? Was it just being a friendly person, someone people could turn and count on? What sort of got you down that road of helping students in high school? And then, I guess, what called you back? Did you always plan on getting into teaching or was that just something that sort of happened after maybe your job as draftsman sort of wasn't cutting it for you?
George Garza: So I had toyed with being a teacher in high school. And I think what it is is... knowing that I'm leaving somebody better off than when I met them. Just knowing that their lives are better for having interacted with me. I would say that's what it comes down to. So... after high school, like I said, I had briefly considered being an actuary or an engineer or... just all these things that I had that strong math proficiency. But I think through my job as being a draftsman, I saw I needed to be interacting with people. Just I needed to be helping people. And so I would get in trouble for training newbies when that wasn't really my job. Because I just gravitated towards that. So, like I said, I just wound up there.
And it's funny because once I wound up deciding, "Okay, I think I want to become a teacher," I wanted to be a history teacher at first. Because I love history and I think history's critical to know. But I was like, "You know what? There's a severe shortage of good math teachers and I'm going to try to be the best math teacher I can." The number of math teachers I had growing up, I had some that they just phoned it in. And so, I just knew if I could be that one person that reaches out and helps these kids and gets them to realize math isn't that terrible, I could change their trajectory, I could change their family tree.
Kyle Pearce: Yeah.
Jon Orr: When you said, George, that every interaction you want to leave someone better off than what they were or you wanted to leave like a positive impact on them, it just clicked for me. I just watched a show that... it just reminded me of this character on this show. It's called Ted Lasso, it's on Apple+ right now, it's relatively new. It stars Jason Sudeikis. I'm just going to go on a tangent here, just for a sec. Because it's got this main character who's a coach and he's just super positive all the time, like always uplifting, always thinking on the bright side and he's in a situation where everyone's kind of out to get him. And I just finished watching it with my wife. It's like, in my opinion, the most heartwarming show I've seen in a long time and I can't stop thinking about it. But, George, it just popped into my mind that when you said that, because it just embodies this character and it sounds like it's embodying you and some of the things that you do. So if you haven't watched that, I would recommend it to anybody. It's such a great, great, heartwarming, funny, inspiring show about a coach. So check it out.
But George, let's keep moving here on that note with kind of your... almost feels like your big why. And let us know, like we got to ask this question, you know it's coming if you've been listening to all the episodes, about your Math Moment. So if you think back to something that's kind of... And maybe this is the thing that sparked why you want to do what you do in your classroom or maybe it's just something that changed your trajectory. I don't know what your Math Moment is, George, I want to hear all about it. But when we say "math class", there's always something that just pops into people's heads as one of their first memories of math or a defining moment about math. Sometimes it's great, sometimes it's not great. But I'm eager to hear yours, George. Tell us.
George Garza: So, I think about math and I think about math class. The thing that sticks out the most to me is an instant in my eighth grade algebra class with Mr. Price. Every day, he would stand at the door, he'd shake your hand, he'd greet you, he'd frequently find something to compliment you about. It was cool because you didn't get into his class without shaking his hand. So even if you were late, he'd stop teaching, and you'd walk to the front of the classroom and shake his hand, and he'd give you a warm greeting, and then you went back to your desk. But that was also a little bit embarrassing, so I kept us not wanting to do that.
I remember he looked at me and kind of patted my shoulder and he says, "You know, when you get to high school, the football coaches aren't going to be happy to hear that you just want to be smart." I had stopped growing at about seventh grade. I'm about 6'2".
Kyle Pearce: Oh, wow! Sprouted up quick.
George Garza: Yes. I grew about 12 inches in a little over a year and it took me a couple years to get used to my body, just how awkward it was. I was constantly tripping over things and I think that he told me that... Like it made me realize like, "Oh, there actually is a bright side to being a really big guy." So... But that's just what I think about math class. That relationship there is what I think is core to math.
Kyle Pearce: Yeah. And I'm definitely hearing that and I'm sort of sensing that theme going back to, again, this idea of you're trying to help and really leave someone in better shape than before they had interacted with you. And this piece here where that's your memory, that having a teacher who sort of connected with you in that way. And we talk a lot about relationships on the podcast and I know a lot of our webinars, we talk about like culture building and those are so important, it's so easy for us to miss. Especially if you're really like into math. I was one of those teachers for a very long time, that it was like math, it was all about the math. And in many ways, you can easily forget the human, the person that's there that you're trying to work with and help and shape and mold and we're hearing that in so many Math Moments out there. So it's awesome to have another one to add to our repertoire of all these different moments. And it's always great to hear a positive moment as well because sometimes the moment that people remember isn't always positive. So I'm happy for you that you had one that was positive.
So let's keep on with this positive train. And we're wondering, what's a quick win you can share with us? Maybe it's something recent, it could've been today, maybe this week, or maybe it's this school year. What would be maybe a quick win that you can reflect on here and share with the group? To give them some more positivity to fill their math hearts.
George Garza: So at the beginning of the week... I'm learning Desmos and I'm learning how to incorporate it more in my teaching, especially with this online format. And so I did a couple things. The topic was binomial multiplication. And at the beginning of the Desmos, I just started out by asking them to draw the most exciting thing they did for the weekend and then we took like five minutes and just talked about, "Hey, you did this, you did that." And we joked about the funny drawings and I think that got a lot of kids' engagement up and it built relationships.
And then, through the lesson, I just kind of did that progression. So we started out with just, "Hey, here's a rectangle. Just a 3x5 rectangle. What's the area?" And then just kind of moved on from there until by the end, you got the binomials on both sides. At the end of the lesson, the majority of the kids had it down. It really wasn't very frustrating for them, overall. I got a lot of compliments from the kids saying they had fun and they enjoyed themselves. And I walked away from that thinking, "Okay. I can do this. This is what I was looking for." Right? I just noticed the engagement was way up.
Jon Orr: Right.
Kyle Pearce: And that online, it sounds like you're online teaching right now-
Jon Orr: Is that true?
Kyle Pearce: ... and that obviously throws that extra wrinkle into things.
George Garza: Yeah. Yeah, it does. It really does because I don't know, I can't see what they're doing. Because I've got kids that sometimes Mom asks them to watch the baby for 20 minutes while they go out shopping. Or Mom asks them to go wash dishes in the middle of class or whatever. And they don't always let me know, so I ask, "Hey, Suzie, what's this?" And I don't get anything back.
Jon Orr: She's gone.
Kyle Pearce: Are you still there, Suzie?
George Garza: Right.
Jon Orr: That's the reality, George, right? What grade are you teaching? Is it eight? Nine?
George Garza: Ninth grade. I'm teaching Math 1, so I have all the way up to juniors in there.
Jon Orr: Awesome stuff. The way you started that binomial distribution is exactly the way that I have started that skill for a number of years now. And actually, this week has been... George, I'm not sure if you know what my schedule looks like, but we're teaching week A, week B. So week A, it's all one class all day, we're face-to-face, but we're cohorted. So it's all day, so for 300 minutes with the kids in a class, all that class. So like all grade nine math and then... for the whole week. And then it switches to a different class. So the kids will go to a different class, teach a different class for the second week, and then we flip flop between week A and week B for until... we're almost done, actually, until the first week of November, second week of November.
But since one of my weeks is actually my prep week, like when I would normally have a prep period during the day. And so, that week corresponds to me kind of moving from class to class to give every other teacher an hour break or an hour prep period. So I kind of go into a class, they say, "Hey, we're doing this. Can you pick up where I left off?" Or, "Can you teach this lesson on the fly?" Or, "Can you help them do their homework?" That kind of stuff. And they're all math classes, luckily. But I walked in... this is why I'm telling you this, George. But I walked into a lesson where they had just finished the distributive property. You know, binomial multiplication, and they did not start... Like they were starting with...
I think some people are like... they get hung up on algebra tiles and this is, I think, why algebra tiles sometimes get a bad name is people are like, "I don't see the use of algebra tiles," or, "I don't see the use of the area model." And it's because I think when teachers teach the area model, they draw the box, right? They call it the box instead of, say, a rectangle-
Kyle Pearce: Yeah, the box method.
Jon Orr: ... or... Yeah. And it's when they teach that, I feel like the kids still are like, "Well, why are we doing... and what is this? And I'm still memorizing steps." And this is what I kind of walked into and realized that they had shown the box method, but not really shown you like why you're drawing a box. And you're just kind of filling in gaps or filling in spots and that adding all back up. So, it was like on the fly, had to kind of pick up on where that teacher left off, but then, in my mind I was like, "I can't keep talking about this without going back and going, 'Let me do 3x5,'" like you did, George, "and then 35x6 and then like 42x67, and then bring in X and then..." You know? So it was like I had to redo the multiplication, then you could see the kind of lightbulbs flick on.
Yeah, sometimes we teachers get thinking like that tool is going to be great, but if we don't talk about where that idea comes from or why are we representing it as a box, but we're really representing it as the area of a rectangle and we've got different ways to represent area and length and width and all that stuff. So I'm excited that you had done that lesson. I just love doing those lessons.
George, I just kept talking for a long time, but it's time for you to chat a little bit and we want to chat about what's on your mind lately. What's a challenge for you? What's a struggle for you? What can we dig into here so you can go back tomorrow and help your kids feel better than where they were? What's a pebble in your shoe lately?
George Garza: So I think the biggest issue I'm having is trying to square two ideas that seem very separate from each other, but I know they can be unified and I don't know how it is. I think that's what it comes down to.
So last year, I was at a high school and it was based off of Bob Marzano's academy models of teaching. So basically, every kid is working completely at their own pace. It's mass customization. So every student is working at their own pace, setting their own goals, it was all about the students and helping the students where they were. It took me a while to learn to work within that, but then they had a budgeting shortfall and they had to let me go.
So now I'm at a more traditional school and we're doing CPM curriculum and the CPM... it's a lot of like what you talk about with the group learning and the problem based tasks and it's got the... interleaving into it and the spiraling, all that kind of stuff built into it. My problem is I'm not sure how to have the kids work in these homogenous groups. Because the idea about the sharing ideas with each other, but then at the same time, working with what they're ready to learn. Because when you're working with the whole group, you're going to have kids who that a little bit behind and kids that are ahead. And I understand the thinking is the kids that are ahead, they learn it deeper by helping the kids that are behind. And maybe I'm just too inexperienced to see it. I'm noticing as I'm getting more experience, I'm able to make a lot more connections with all these different ideas that I have, but it's just like... I've got these two different things and they've both got really awesome traits to them and very powerful ideas that run in both. And I want to figure out how I can combine them.
Kyle Pearce: Nice. Now, I'm wondering... So you had mentioned about Bob Marzano and mass customization. Now, was that at a previous placement, were you saying?
George Garza: Yeah, that was last year. That's where I was working.
Kyle Pearce: Awesome, okay. So and then this year with CPM, which Jon and I are familiar with and, as you mentioned, the very, I would argue, problem based as well. So kind of matches, or aligns with much of the Make Math Moments philosophy. And then, when you had mentioned about grouping, I think, or at least I thought I heard you had mentioned like homogenous groups. So is that homogenous by like skill level or were they heterogeneous groups? Like they're kind of like mixed up skill levels? Or how were those groups being polled?
George Garza: It's heterogeneous groups.
Kyle Pearce: Heterogeneous, got it.
George Garza: Yeah. That's what my school is pushing really hard is to make sure everybody's... You've got the different ability levels grouped.
Kyle Pearce: Perfect. Awesome. So, I'm hearing that there's maybe some struggles there. Now, I'm wondering when these groups... And actually, I'm wondering a little more about how the groups happen. So is it something that you just sort of put different groups together? Do you randomly select groups? How is that taking place? And then, I guess, where do you feel that some of those struggles are arising? Like when you're actually getting the groups started? Once their into a task? Or kind of paint us a little bit of a picture about where those struggles are arising for you.
George Garza: So, I'm going to say I haven't done a lot of group work this year because of the format.
Jon Orr: Mm-hmm (affirmative).
Kyle Pearce: Oh, yeah. That makes sense.
George Garza: I tried for... three weeks. I tried doing breakout rooms because we're using Google Meet at my school, so I basically had to make separate Google Meets for the groups. But when I was doing it, it was all randomized. So I just randomly picked kids to put in the groups. And I guess as you were talking, I'm reflecting back on the experience with that and the experience I had was some groups where they were just flying through and some groups, they couldn't even begin to start their very first problem, not without a ton of support. And of course, then you've also got the kids that just checked out. But that's just a problem with the online format.
So that's been my experience with it so far. I thin if we're in a classroom and I could do it right now, I would definitely try to group them by the ability level, kind of average out... so the highest with the lowest... I'm trying to remember. I met with a teacher recently and she was trying to guide me through that. But this problem, I just haven't been able to practice as much.
Jon Orr: Right. Right, right, right. So one thing that when teachers come on and they share what they're working through and I think I get a sense of what you're working through. I think a clarifying question or something that can help you think about it is like what's the real struggle here is one thing. And the other thing that kind of I always want to ask is like... because it could help you clarify or think about it is why do you think you're not doing a good job? You know what I mean? Like when you bring up like, "Here, this is something I want to work on." But like what's telling you that it's like this needs to be better? And I think you did say something along the lines of you thought one group was fast, one group was slow. Like I've had that experience, too, but I didn't think that I was doing a bad job at it. So I'm wondering like what makes you think you're doing not so great at that part?
George Garza: So part of it is... the engagement with the students. I feel like if I do my job well, the students will enjoy the material and they'll enjoy learning. So when there's poor engagement, that tells me that... that's important feedback for me. And the other on is... I think the pacing guide that the department uses and I'm having a lot of trouble trying to catch up with how fast everybody else is going. And I know that's a more arbitrary thing. The fact that I'm having to spend more lessons than the other teachers to try and teach the same material because it's not sticking, again, tells me that I need to change something up.
Kyle Pearce: Something interesting about that with pacing guides, this is something that comes up quite a bit. I mean, there's this worry we all have. We put this pressure on ourselves. The curriculum or the standards that we're abiding by or we're trying to teach to, they provide this sort of weight on our shoulders. And there's something that's really rough because I find that you sound a lot like I think what Jon and I were doing in our classroom, where we were trying to gauge were learners were and we still do this. We still try to gauge were learners are and we try to teach at the speed of learning. Graham Fletcher says that quite a bit. It's you have to teach at the speed of learning and just because another class is ahead, a question that you'll always have to remind yourself, or at least as yourself, is, "I wonder whether the students are any further ahead." And what we mean by that is are the students actually... Is it really sticking? Or does the content sticking and the understanding sticking just maybe mean something different to you? And those are tough when you're up against a pacing guide.
This is the first year our district's using a pacing guide, but only it's less about a pace and more about a when to teach concepts simply because we have a lot of students at certain times of the year that can go to our face-to-face school and our virtual school. So there's going to be a lot of movement throughout the year, so we're really just worried about students being transient across different courses and trying to be able to kind of settle into a new class without them being in a completely different spot. But it is providing some pressure for the teachers in our district as well. Like I'm getting many e-mails and we're doing online calls with teachers, trying to help them work through that.
I heard you had mentioned about engagement as well and it sounds like you're teaching conceptually. When you go back to your binomial example, starting with that 3x5 and then kind of working your way and building towards and almost... the word I love to use is emerging. Emerging new strategies, emerging new models, and then, essentially, emerging new learning as you go. So I love that. But when it comes to engagement, I'm wondering what might it look like or sound like when you're leading a new lesson and you're taking a trip down a new concept? What are you leaning on in order to try to sort of spark that curiosity for a student or for the class?
George Garza: That's a trouble area for me. The podcast you guys had last week, that's a really critical part, to put this in like some kind of context, for the kids to help them understand. And typically, the best I've been able to do so far is just trying to tie it to something they already know. So again, like tying it to finding the area of a rectangle, right? They know how to do that. But there's some ideas that doesn't work well for, so...
And again, just this whole year like with how inexperienced I am and with the novel format, I mean... And this is new for everybody, but I'm trying this, I'm trying that. I think I introduced the school year to the kids just by saying, "Hey. We're both going to be learning how to learn online this year." So...
Kyle Pearce: Yeah, for sure.
Jon Orr: Yeah, yeah. We all get that. I think everyone is not in their heads to say that when you are new to the building, new to the course, new to the curriculum, new to the teaching role or that class, that things take time to gel. And so sometimes, it's like you're comparing yourself to the teacher down the hallway because they're progressing faster than you. I think you always have to tell yourself, "Well, this is maybe the first year that I've used this. This curriculum, this CPM, I've not used it before and most likely, they've already kind of felt the ins, what lessons are going to work with their style, and where they can draw from this area. And they kind of like have build around that." And that takes time. Year after year, you build up what your course looks like over time and if you're teaching a course for the very first time, sometimes you're like, "We got to do this, we got to do this, but I want that engagement," just like you've said. You're like we want that and we just have to also remember that it's going to take time.
And there's a couple ways I want to give you some suggestions here, George, and one of them is thinking about that lesson where you introduce with the rectangle and thinking about... in two ways. In the first way, I want you to think of that... sometimes we think of we're going to go into these lessons and we're going to be problem-based and the kids are going to develop everything. And then, I'm going to put them in groups, they're going to do the math, and then that'll be it! And some groups are done and some groups aren't. And I think when you first try this strategy, and what I felt has worked great especially at the beginning of a course, because it takes time. It's like a progression of skills. Like kids aren't just great at all of a sudden being thrown at the walls or saying, "Hey, here's a math problem. Go ahead and solve it on your own," because most times, that's not been their experience in math class. Most times they're shown how to do it and they're kind of lost when you're like, "Okay, well, what do you mean I'm just going to do it?"
So in my class, when kids come in for their first time, that's not exactly how we start. It's like a progression, it's like baby steps a little bit along the way. We do small, little tidbits of work and then show the teacher, and work in groups and show the group, and have small interactions. Like this is where my... Or not mine, but where resources from the internet have worked great to get your class into that. Like small steps, like start class with an open middle problem at the wall. It's like you're not saying, "We're going to spend 15 minutes at the wall on this problem." It's like 10 minutes, 5 minutes, working together, sharing an idea from open middle. Or maybe you're starting class with which one doesn't belong or would you rather at math.com. And kids are discussing and collaborating, but they're sharing together. And then, they're like just small chunks and because they're doing small chunks, they're getting used to sharing ideas, they're getting used to... engaged with each other, more so than waiting for you to do the math. And then when you're ready, then it's like, okay, now you can start to ease into or start a problem based task.
And then, you could also chunk that problem based task early in the year. So it's like not like, "Hey, go ahead!" It could be smaller steps into it, whereas you take up a little bit and then keep them plugging along. Like put a spin on that question or give them an extension question. So I feel like in your multiplication lesson, you progressed along the way in that lesson. I want you to think more long-term about your style of lessons that you're going to progress your students into a problem solving kind of atmosphere, but it can't be done all at once. And so it's like I think that's... Sometimes we think we got to jump right in with two feet, I think, but the kids aren't ready for that. We got to show them, we got to teach them how the class will progress and it's going to take time to do that. And I think we just have to be ready for that. But I'm going to stop talking here, George and see what you have to say about that tip.
George Garza: A lot of that kind of reinforces just observations that I've already made. I almost always start class with a which one doesn't belong because I knew from the get-go, I wanted them sharing their ideas. And like I said, I use Desmos for that rectangle lesson is because when we got to... when I threw in an X for the first time, they had different thoughts on it and I used the little snapshot tool in Desmos to... okay, so which of these is right? And we had a little conversation about this one's right or what do you think. And so, I've got the student's used to sharing ideas and a lot of them are okay with being wrong, which I know is the huge thing. That's for them and for me. They've told me that, "Yeah, this is the first class like I felt like I could be wrong in and I'm not going to be judged."
So I think what it is is... I'm looking back. The kids that are struggling... the feedback I'm getting from the kids is telling me that I'm not giving them work that's appropriate for where they're at. So the kids that are really struggling, they want me to spend more time explaining stuff. And then I've got a group of kids that they're just... they're ready to go. The kids that are fast, that's something I've built into my Desmos is I'll put a whole bunch of escalating problems and maybe six or seven problems and I'll have the kids work through. And I'll stop them once the bulk of the kids get through like problem four and then the faster kids have already gotten through like problem seven or eight. And we'll consolidate because all I really wanted them to get through was problem four. And so the kids that were a little bit faster, they got to explain around with these deeper ideas and not be as bored. So I feel like I'm getting that honed down, but it's... I'm wanting to know how I can... best help the kids that are just falling behind. That they're trying and I can't spend 20 minutes talking about one idea.
Kyle Pearce: Right, right. I'm wondering, George, something that popped into my mind when you had mentioned about those students, like that feedback that you were getting. That it sort of sounds like some students feel like you're teaching maybe a little bit above them. And I'm wondering did you get any feedback, or maybe you didn't get any feedback and maybe that's a positive thing, when you did your binomial lesson? Starting all the way down at three groups of five. Because I'm going to take a guess that you probably... that 3x5 is probably a much lower floor than the students sort of need in your classroom. I'm wondering was the feedback the same or different? Or maybe there was no feedback? And like I said, maybe no feedback means no complaints. Did you notice a difference with that particular lesson? Or did you feel like they still felt this as the floor slowly was raised as you worked your way to binomials? Did they still feel this feeling of not being at that level?
George Garza: No. You're right. And that's what I said. I think that's what encouraged me when I saw the engagement was much higher because I've noticed the engagement drops down when I start losing them. So the engagement being higher told me that they were able to keep up. They might've been wrong with some of their answers, but, yeah, a short discussion with everybody, with the group, gets that straightened out. So... I guess what you're saying is just making sure I start with those low floors.
Kyle Pearce: And it kind of... for me, it felt like there was a... sort of like a lightbulb went off for me as soon as I heard that because I was thinking earlier on with that particular lesson and what's great because you had brought it up as a win, right? So like that lesson was a win. And when Jon and I were... We spend multiple years kind of working through and trying to come up with some sort of way that we could better determine how... or at least better prepare ourselves so that we would have more lessons that would go off without a hitch versus the alternative, which was what we were dealing with where it felt like a high probability of our lessons didn't work and it was like we were just super excited when one did. And that's what sort of got us thinking about that three part framework, our Make Math Moments three part framework and, in particular, the curiosity path.
And I'm sensing that that pebble in your shoe right now kind of has a little bit to do with this curiosity piece because you had mentioned the engagement piece. And then, I feel like... in tandem, at the same time, in order for students to be truly curious, that floor has to be low enough as well. And the challenge there is lowering the floor, I think lowering the floor even more so than you need to. Sometimes, students can maybe roll their eyes or say like, "Oh, why are we doing..." Like maybe with 3x5, they may have even done that, right? Where they're like, "3x5? Like come on! We can do better than that." But sometimes just getting those couple quick wins and we think about even video games, right? Those first few levels when you try a video game usually, they're very easy. You're out of the first level very quickly and you're like, "Oh!" You feel pretty good about yourself. And doing both of those things at the same time, trying to keep the curious... And when we say curious, it doesn't always mean it has to be a video or an image. Although, we tend to enjoy those, personally, because we enjoy creating them. But oftentimes, too, there's some topics out there that aren't that interesting, but the way we question our students can sometimes provoke that curiosity.
And I was just in a class yesterday, it was a grade 12 teacher working with students that were going into more of like a trades field. So the math that they were doing was not university level math where they were going into a university math program. And one of the topics they were looking at was exponent laws and if you want to talk about a pretty dry concept, well, exponent laws is kind of where it's at. You're like, "Oh my gosh, what are we going to do with this?" But how she started it was kind of like your 3x5. She began with this idea of... she was using three to exponent 2 and three to the exponent 3. And she had the kids sort of calculate that and just giving them some questions like how many different ways could you calculate that and how many different ways could you represent that, what does it look like. It was almost like a number talk. So there wasn't really like a context there, although if we could, if a context comes to us, great. It's awesome if we can, but just in how she was questioning, it was like posing purposeful questions. The floor was low enough and the questions she was asking them had the kids thinking about the math.
So for example, one student was like, "Well, since three to the two is... 3x3 and three to the three is 3x3x3." Another student said, "Well then, it's the same as three to the five." And she was like, "Oh, okay." She didn't confirm it, she just kind of let it go and then all of a sudden, gave another problem and someone noticed the same. And then it was like when won't it work? And now kids were off trying to find... like trying to break it. Like how can I break this? And sometimes math, just doing some of those sorts of things can be enough to get them interested. And then, of course she's going to have to get to variables and even rational... having fractions involving exponents and all kinds of chaos going on. But it's like beginning with that low, low floor and then thinking about those purposeful questions that we can ask that are intriguing, that make you go, "Huh." Or just kind of almost make a head go sideways, right? Like when you ask the question where they go like, "Oh." Like I took something that's easy or obvious, and now, suddenly, the question I'm asking has you thinking a little more deeply than you maybe even thought you could've.
So, I'm wondering if we've maybe honed in a little bit on one of those challenges and what your thoughts on based on what we've shared about the curiosity path and those low floors.
George Garza: That makes really good sense. That definitely the component of that lesson that worked really well, keeping at that low floor. I had some kids that didn't remember how to find area, they found the perimeter instead. So that, real quick, took a minute or 30 seconds or so for them to do that. And then it's, okay, they found the area and so they were able to go. So... sorry. A little off-topic there. Sidetracked. But I think you're right and that is... I'm seeing now how that low floor enables that curiosity. And so we need to break it down to a level where they can engage with it.
Jon Orr: George, it sounds like you are... which is want we want, like you're thinking of your next steps. You've got your like, "Oh, I think I know what do to now." And now you're like, "Okay." I can hear it in your voice, that you're like, "I'm now thinking of my next steps-"
Kyle Pearce: The wheels are turning.
Jon Orr: Yeah. And as you kind of think about that, George, I feel like we've nailed your big takeaway. We've nailed it, but you've said it, your big takeaway, I think, which was like making sure that you're going to lower the floor, I think it's important for curiosity, those are some of the words you've used there. How are you feeling right now going into, say, tomorrow and thinking about these ideas?
George Garza: Oh, I'm kind of excited. Because again, I've been just doing, this... whole year has been hit or miss, hit or miss. And now I've got a design parameter, right? I need to make sure that any kid, the lowest kid in the class, can look at this and they can understand where we're starting from. And that makes me feel good about raising the quality of instruction and helping those students learn it better.
Kyle Pearce: I'm feeling really good. I feel like I could sense those wheels turning, which is great. And of course, math instruction. Once we fix one thing, we're going to find something new. It's like an old car, right? It's like you fix the squeak over here and then something else, you go, "Ah!" And I think that's one of the reasons why I love education so much and, in particular, in math education because there's so many things we can do to learn and to... Essentially, it's like a math class. We're investigating and we're tinkering and we're trying and we think we've got something and then we see if we can break it. And I'm really excited for you to be able to take that and start maybe even using that in framing.
Like sometimes it comes down to this... call it a provocation, call it a context, call it a... Again, we say curiosity all the time and curiosity comes in so many different forms. And as long as we ensure that floor is low and we think about almost like it doesn't matter who you are, you will be able to hop on this, we'll call it the elevator, with us and we'll slowly push this elevator up. I love how you had mentioned so some students confused area with perimeter and was like... almost like highlighting something that now you got to roll back to that and quickly address that misconception and keep on going. So you stop at the second floor and you do a little bit of work there and then you keep on rolling along. And I think in the long run, while it might seem like things are going to go maybe a little bit slower, I think in the long run, things are going to be moving faster.
And what I mean by that is if students can truly conceptualize what it is they're doing, then going all the way back to earlier in this episode where Jon's talking about the box method. If students just think this is another procedure to use, which is a lot of students do, right? They're like, "Oh, I take the binomial, I put one term here, one term there. And then I match the rows and the columns." Like if they don't even get a sense that that's actually an array that is more abstract or showing it as area. If they don't know those things, then it just becomes something to memorize, an additional thing to memorize, which is really, really tough for those students that you're referencing, those students that are having some struggles in math class because to them, math is all rules and procedures anyway.
So to help them with connections, I think, is really key and if we can start that thought process about how do I ensure that everybody's getting on this elevator, and then thinking about that trajectory, those questions that are kind of... breadcrumb your lesson along and those prompts that you might have. And you're, of course, going to think of some on the fly as well, but the more we can do that leaves us doing less ad-libbing on the fly, I think, the better of we are. And then it allows us to pivot more when we need to and kind of focus that attention versus the entire lesson being a bunch of pivots, where you're not really sure where you're going. So, I'm loving this conversation. And I'm wondering, if it's okay with you, are we able to maybe check in with you, George? In, say, 9 to 12 months and see how things are progressing? And see what quick wins you have for us at that point?
George Garza: Totally. I'd be totally down with that.
Jon Orr: Awesome stuff. Awesome stuff. Would love to-
Kyle Pearce: Beautiful.
Jon Orr: ... keep chatting with you about what's going on in your classroom and seeing that progression that you're making, George. We want to thank you for your time here to chat with us and look forward to, as I said, chatting with you, but hope you enjoy the rest of your evening.
George Garza: Will do. Thank you.
Kyle Pearce: As always, both Jon and I learned so much from all of our Make Math Moments That Matter Podcast episodes, but in particular, we love these Math Mentoring Moment episodes because we really get to think with three of us. Three brains are way better than one and we get to hash out all kinds of ideas around struggles. And remember, you've got to do some reflecting on your own so that anything that you've learned here or any epiphanies that you've had don't wash away like footprints in the sand. So make sure you're doing that reflection, whether it's writing it down, whether it's talking into your phone using like the voice record feature, or whether it's having a chat with a colleague, either online if you're teaching online or face-to-face in the staff room. So definitely do that work so that you can benefit and really invest this time wisely so that it sticks and you can make some shifts in your own teaching.
Jon Orr: Remember that we are on all social media, so you can find us at Make Math Moments on Facebook or Twitter or Instagram. And be sure to get yourself in the private Facebook group for all of our Math Moment Makers. We've got so much, such a great community in there. Teachers helping each other, posting questions, posting wonders, and getting the support from the Math Moment Maker community. So definitely be checking us out over on Facebook.
Kyle Pearce: Awesome stuff. And if you want to join us for an upcoming Math Mentoring Moment episode where you share a big math class struggle because, remember, you're not alone. These are struggles that we're all dealing with and all Math Moment Makers can benefit from. Go over to MakeMathMoments.com/Mentor. You'll fill in a very short, little form and you might be hearing from us soon to hop onto a call and to hash out how we can remove that pebble from you shoe.
Jon Orr: In order to ensure you don't miss out on new episodes as they come out each Monday morning, be sure to subscribe on your favorite podcast platform.
Kyle Pearce: Jon, I don't know if I can recover after you've kind of sang that last line, but I love it. Show notes links to resources and complete transcripts, which you can read online or download and take with you. Can be found at MakeMathMoments.com/episode126. That's MakeMathMoments.com/episode126.
All right there, 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 high fives for you!
Kyle Pearce: Oh, he's in a singing mood!
Speaker 4: (Singing)
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