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The Transform your Teaching podcast is a service of the Center for Teaching and Learning at Cedarville University in Cedarville, Ohio. Join Dr. Rob McDole and Dr. Jared Pyles as they seek to inspire higher education faculty to adopt innovative teaching and learning practices.
Math is super cool. Like, there's a bunch of art in it. There's creativity. There's all this stuff. But we, like, funnel it down into these, like, really boring chunks and try to say, Isn't this fun?
Terri Bucci:And no, it's not fun when you've already funneled it down for them. They need to be in the funnel.
Narrator:This is the Transform Your Teaching podcast. The Transform Your Teaching podcast is a service of the Center for Teaching and Learning at Cedarville University in Cedarville, Ohio.
Ryan:Hello, and welcome to this episode of Transform Your Teaching. My name is Ryan Lymeing, and today's episode, Dr. Rob McDowell and I interview Dr. Terri Bucci, Associate Professor in the Department of Teaching and Learning at Ohio State University. Thanks for joining us.
Rob:Thank you for joining us, Dr. Bucci. It's an honor to have you on, and today, we're just going to get a different perspective because you're at the Center for Teaching and Learning at Ohio State. We've already spoken to someone who's been teaching math in the k through 12
Ryan:for well, she said thirty plus years.
Rob:Thirty plus years.
Terri Bucci:Mhmm.
Ryan:Down in Southern Ohio.
Rob:Yep. And we want to get your perspective as one who's training math teachers
Terri Bucci:Mhmm.
Rob:And find out where things are in terms of the math shark. So, basically, during the pandemic, there's this gap of math learning, specifically for our elementary and middle school students Mhmm. Seems to be where this terminology has come you know, has arisen. So probably it's been, what, almost two years ago now? We had a professional development all hands day here at Cedarville.
Rob:And one of the things our president mentioned was, this idea of the math shark, which essentially what the he was reading in the literature was that there is a gap now because of the pandemic in math education, specifically to problem solving, math, logic Mhmm. As a whole, and that there was this massive gap. And the the voice at the time was they didn't think it was going to be able to that gap was going to be able to recover and we'd have this massive hole and it would continue on and follow these students. So we're kind of coming back now and I guess maybe that's the thing. You know, what are you seeing in terms of your students that you're training in terms of the pandemic?
Rob:And is there a math gap from your perspective with these students who would probably now be in high school, middle school? What does that look like for the state of Ohio? Maybe you can talk to that a little bit.
Ryan:What are you seeing?
Rob:What are you seeing?
Terri Bucci:I mean, it makes sense that there'd be a math gap, right, because we missed out on a chunk of instructional time depending on when that instructional time was for each individual learner. So, clearly, there was content lost. We can't teach the way we want to teach by jumping onto a computer at like a moment's notice, which is kind of what happened then. So it kind of makes sense that that happened. So what I'm noticing is, once they get to us in academia, I'm noticing some issues with social learning stuff.
Terri Bucci:So being able to have conversations about, and negotiations about processes and structures and contributing to a group decision making, some of those kinds of things, which are like the bigger kind of ideas, not specific to mathematics, but they're the same. They're the ideas that you have to use in mathematics. I mean, we're critical thinkers. We're we're problem solvers, as you mentioned. So so I'm I'm noticing some of that.
Terri Bucci:I don't see it as insurmountable, though, quite frankly. I see it as we just need to figure out a different way to bring experiences with this content to our students. And so one of the things that we kind of do that helps with that at Ohio State on the Mansfield campus is really kind of integrate our content courses with our methods courses. So we work with pre service teachers on their own development of mathematical ideas and structures, and we do that in a way that's participatory, that kinda goes along with our our philosophy, which is this idea of communications and and power sharing in a mathematics classroom. So we do that with them as learners, and then they come into the math methods course, and we talk about why that worked or how it felt and all those kinds of things.
Terri Bucci:Yeah, I mean, clearly we lost out on some instructional time, but experience is going to be the healer of that. And so it's really just what kind of experiences do we want to provide? They've gotten to us, they've gotten past, for the most part, those foundational math courses. So now we're at, okay, we need to give experiences where the content comes through in other ways so that we can hit it. And so when you're talking about K-twelve education, we have to figure out, okay, what kind of experiences, let's say I'm teaching eighth grade mathematics, what kind of experiences can I provide to these students who were in the COVID era when they were developing foundational fractional ideas?
Terri Bucci:So what kinds of things can we provide for them in eighth grade content that also uses foundational fractions, so that they have a utility for that content.
Ryan:Okay. I'm grateful you mentioned that you're educating pre service teachers because there's two potential challenges to that, right? You have to maybe reconcile with the fact that they themselves aren't just having to learn how to teach math to students. They might have to overcome some obstacles in their own math abilities and development as well to be able to train up these students. Besides the pedagogy aspect, there's potential math gap in these college students who perhaps didn't have a great math education coming in.
Ryan:So what are some of those steps that you've taken to overcome that particular hiccup?
Rob:Is she seeing those gaps?
Ryan:Sure. Yeah.
Rob:Mhmm. Are you seeing gaps in students who are coming in from the k through 12, like freshmen, essentially? Are you seeing any any unusual gaps there, or is it something that just you're holistically seeing?
Terri Bucci:I don't know that I'm seeing one that's, like, that much. We always had variances in, like, skill level and, you know, when they came in, when they when they come in from high school. So there's still those variances. I think there was initially, especially coming straight from like students who had, were in the high school years right before they came into university, there was like kind of almost a fear. So it was like they were tentative.
Terri Bucci:They didn't know what to do. They didn't know how to maneuver the academic space in that case. And so that was clear in COVID. Right now, there's always been. I mean, math, longer your years, the longer you are in years, the wider your abilities become between mathematicians and people who are sharing those experiences.
Terri Bucci:That's always kind of been there. And to that point, and I think I've shared with you before, I worked very closely with Bob Moses and he wrote a great op ad that it was basically, you know, we don't want to go back to what it was like before COVID, because the reality is that wasn't a great time for math either. Like, we still had these variances. We still have people who like see themselves as mathematicians and some who see themselves as not a mathematician. And quite frankly, the scary part is the ones who see themselves as not mathematicians are absolutely okay with it.
Terri Bucci:Like, it's culturally okay to to to be not up in mathematics. And and the reality is we live in an in an in a technological world, and you are giving up power in your life if you give up your skills and aptitude in mathematics because a lot of things are being run that way.
Rob:So it's an interesting statement. No question. I don't think I've ever heard anybody say you're giving up your life. You're giving up your power when you give up your aptitude in mathematics. Mhmm.
Rob:Can you speak a little bit more to that?
Terri Bucci:Yeah. People make assumptions that people who throw numbers around and use quantitative jargon automatically know what they're talking about. And so there it comes with this authority that people who believe that they can't understand those things automatically give to the speaker. And so that's a ton of power to give to somebody because you think that you can't learn this thing that everybody in the world tells you is really hard. In reality, that's what people say.
Terri Bucci:Oh, math is really hard. That's why it's excused. Right? You know, people wouldn't say, oh, oh, you don't know how to read? That's okay.
Terri Bucci:That that's super hard. Like, no one would ever in a million years say that. No question. Yeah. It would be embarrassing.
Terri Bucci:So but people say it about math all the time. Yeah. So just imagine those who have, like, a voice and the power to push ideas out. If you have already given up your, like, ability to to quantitatively decipher what someone is saying to you, they can walk all over you, and you're allowing it.
Rob:So so it sounds like you're advocating math as language almost. Mhmm.
Terri Bucci:Oh, for sure. Yeah. I definitely think that math is a language, and I think we need to teach it as a language. That's that's the five sub curricular The process is all about communication. So pictorial communications, written communications, like quantitative, symbolic communications.
Terri Bucci:That's what we need to do is be able to communicate better mathematically. And I know it's been like an aside all the time in mathematics. Like you have to be able to communicate mathematically. You have to be able to talk to other mathematicians. But it's really just like the processes we use in mathematics is a form of communications.
Terri Bucci:Our justification structures are our methods of proof, our methods of using non examples. Those kind of global communication ideas that come from mathematics.
Ryan:Well, yeah, and what's kind of surfaced in that is logic. You know, this idea that wanna be a logical thinker, mathematical skills are foundational to that. Rob mentioned before, creative problem solving. You cannot solve problems if you don't understand math to a certain level or degree. And it's helpful to hear what you're saying there.
Ryan:I'm glad Rob asked that clarifying question, because how can you check your sources or the validity of something if you don't think you can understand it at a fundamental level? You're just gonna trust the sources without going to them and evaluating them. So that's really helpful.
Rob:So you've put forward a a good thesis. Let's just say I don't disagree with you. Mhmm. But, you know, I think the next question that I have for you is, okay. How do you get there?
Terri Bucci:So so first of all, we have to define what the there is. So I'm assuming that the there that you're talking about is like this infusion of communications into mathematics. Is that?
Rob:I would say that there is what you articulated just a moment ago in terms of math as language. And that essentially, it seems to me what you're there is, what your goal would be based on what you said just a moment ago, would be that everyone would be able to analyze mathematical language that is used. Let's say it's an analytics or somebody on the news giving numbers. Mhmm. Right?
Rob:With the ability to say, wait a minute. Is that actually true? And how can I verify that? Mhmm. And taking the time to do that.
Rob:You're you're talking about a process, man, I don't even know how many people would I'm trying to guess how many people would actually think that way. Because I try to get my students in business ethics to have that kind of approach when language is used. Right? Somebody says they have ethics. Well, what do they mean by that?
Rob:What's it based on? So there's this sense in which you start the, you know, coupling and analyzing the words that are used and providing definitions. Very mathematical. Right? You know, from your perspective, what are the next steps to help them to be able to operate in that way that you just provided?
Terri Bucci:So I'll I'll speak from personal experience and and research that's been done, in particular with the algebra project, is Bob Moses's work, but also through work that I've done using the ideas of Paulo Freire, which is community organizing and like I've also done a lot of community organizing work in Haiti. And so taking those experiences together, if we want people to be able to communicate, we have to provide them with opportunities to do so. And so the structures that I've used and that we use at Ohio State in Mansfield is this five step curricular process, which in it doesn't mean every lesson looks like this. It just means there are opportunities. And so let me just talk about what those are.
Terri Bucci:The first one, the first step is some kind of shared experience. This is where the teacher, because of, so we're talking Vygotsky and Hire Knower, like they know the mathematics. So they come together with this experience that can oftentimes be used as a metaphor, some kind
Ryan:of
Terri Bucci:mathematical metaphor, or it could be as simple as just a problem solving situation. But the teacher determines an experience for the class to organize around. And so the class experiences this thing, whatever it might be. There's a very common one in algebra project called the winding game. In the winding game, there's chairs that are sat around in a circle, And depending on the age of the kids, we mark those chairs with symbols, and then the students, like, walk around.
Terri Bucci:There's two teams. They have to figure out what number is being represented on the wind of these chairs, and so they compete against each other. So as an instructor and as mathematicians who know a little bit about this stuff, that that was created for the division algorithm. It was created to give a construct or a context for students to develop an idea about the division algorithm. But if you look at it, it looks like you're doing musical chairs.
Terri Bucci:So the students participate in this. They engage with it this experiential way. And then the second step is to have what's called pictorial representation and people talk. So after they engage with this, they win some games, they guess the number, then they draw pictures about what it was they experienced. So there's a pictorial representation for those learners that see an image.
Terri Bucci:And then there's the narrative piece where students just verbalize what they just experienced, but they use their own language. No mathematical language. It's just, this is what I did today. And then the teacher comes back in in this fourth space, and that's called feature talk. And the teacher then comes back into the space.
Terri Bucci:So the teacher was in the space creating the experience because they have more knowledge. They leave the students alone to play a little bit, to write about it, to draw about it. Then they come back in to facilitate a conversation, knowing well that what they're trying to get kids to share and experience is the rounding of this circle of 12 and is a number of chair and is this number of leftover chairs that doesn't make it round a whole another time. And so those structures come in to create a symbolism then, which is the fifth step of that activity they've just shared. So that is a pretty elaborate example, But basically what it is, is a teacher finds something that's curious, that brings interest, but also is very mathematical.
Terri Bucci:Like it's not just a bunch of fluff stuff. The shared experiences aren't about apples because it's fall. It's they're they're, like, meaty mathematical experiences, but it gets students involved from a space of commonality so they can talk about it. And what the other pieces, this kinda power structure piece that comes through, or the sharing of power that comes through, is that all of this is designed to be consensus making around these ideas. So the students, they talk to each other.
Terri Bucci:They try to justify how they're thinking with each other. And so that's just another communication skill that will be valuable to them even outside of mathematics. They have to prove a point. They have to justify their answer. The teacher has to provide, like, almost a Socratic questioning so that it can keep that that conversation going.
Terri Bucci:And but it's really the students that are holding the water in that experience. And so I think that's one of the most important things that we have to do is give up some of like, holding on to what we know and what we want to give, and instead make it like this open space. That's, like, we need to get away from the front of the room and start walking around and questioning and posing situations. And that's where we're gonna change mathematicians, because right now we're not teaching mathematicians. We're teaching learners of mathematics.
Terri Bucci:We're teaching receivers of mathematical knowledge, and that's much different than teaching mathematicians because mathematicians have, like, characteristics. They have structures that they abide by, and and so every student can be a mathematician. We just need to teach them that way.
Ryan:That's interesting. I'm hearing two things that have been surfaced on our show many times. One is foundational, like a student centered approach. You mentioned you're not teaching mathematicians. You're teaching learners, and they happen to be learning mathematics.
Ryan:And that super fits well with our approach to teaching, servant teaching, this idea that you're teaching students. Are you teaching them content? Yes. But the target is the student, developing them as a person, their skills, etcetera. But then I'm also hearing you kinda talk about this idea of self motivation, right?
Ryan:So the motive in the student comes from the student. It's not just the teacher saying, This is important, so you need to learn it. They're coming to, you know, with your coaching and your mentorship and you walking through that, they're understanding, Oh, I should be motivated to learn this because it's valuable. Does that sound right?
Terri Bucci:Yeah. I think it's also engaging. Like, it it has to be engaging. Like, math is super cool. Like, there there's a bunch of art in it.
Terri Bucci:There's creativity. There's all this stuff. There's investigation. There's experimentation. All of this.
Terri Bucci:But we, like, funnel it down into these, like, really boring chunks and try to say, isn't this fun? And, no, it's not fun when you've already funneled it down for them. They need to be in the funnel.
Rob:I think for our audience, one of the things we set out to do was understand the math shark. Is it still is it real? Is it is it coming in? We've now had two professionals, one thirty plus, who's like, she wasn't really concerned. No.
Rob:She kinda recognized the gap, not too dissimilar from what doctor Bucci has has said. Yep. She's like, yeah, there's that makes sense. But in terms of it being overwhelming and irreconcilable and irreversible, I'm not hearing that.
Ryan:Yeah. No question. You've both been very hopeful.
Rob:So it's it seems, if anything, that there's a renewed we had a renewed sense in our previous guests as well as we're hearing something completely optimistic and pushing the boundaries, if you will.
Ryan:Yep. No question.
Rob:We don't want people just learning math. We want them to be mathematicians. Mhmm. Right? We want them to think and speak mathematically, which is another way of saying logically, I would say.
Rob:Mhmm. You know, math and logic go hand in hand. You you really can't separate the two in terms of their analysis. As you're training teachers, you know, what can you say to those who are currently in the mass system who've been who've been teaching for twenty, thirty plus years? And some of them, I think, have kind of garnered this themselves.
Rob:Sure. And they have a practical approach where in some sense, yeah, they there are certain things that they have them just do repetitionally, you know, repeat, get those foundational pieces, and then maybe they have some projects like what you're talking about. But, you know, what are they supposed to do when the focus for them as their jobs? Because however those children do on those tests also reflect back on their performance. Okay.
Terri Bucci:So so there's a couple of things I want to say. The first is when I talk about a shared experience, the word project doesn't fit there. It's really an instructional strategy. So all that stuff happens in one class period, all of it. So it's a way of engaging with mathematics.
Terri Bucci:So it's not problem based learning, although it could expand into problem or project based learning. It absolutely can. The way that we teach it a it's a way of engaging with mathematics. And so we talk with our students about the initial lesson, and any new concept development is taught using a five step process lesson. It's taught that way intentionally, so it gives the every child an entree into that content because it's starting everybody anew.
Terri Bucci:So everybody's starting with the same experience. Everyone has access then to that new content, whatever it is. And what's cool is when So I also use the five practices for orchestrating mathematical discussion. I don't know if you're familiar with those, but really, really valuable. Talks about how we select students to share their work and how that's an intentional endeavor.
Terri Bucci:And so when they do these five step curricular process, I'm always in the back of the room. Students are always at the front. They're always carrying on the conversation. So that five practices for orchestrating mathematical discussion is also embedded into all of the content. So this is not just a, Here's a fun lesson to do.
Terri Bucci:This is a way of engaging in a mathematics classroom. And so what happens is even when you have those lessons where you're pulling straight out of a book, and you definitely have those days too, or when you have those days when you're doing some kind of rote memory because they just have to know how to do this so that they can complete this higher task, that will always be those days. But my point is that that should not be the majority of the days. Those are the filler days. Those are the ones that you get the stuff solidified.
Terri Bucci:The important days are those initial days where the first engagement with this content, We're doing it wrong right now. We're saying, okay, here's a language. Here's a symbol. Let me show you it. Let me show you what happens to it.
Terri Bucci:And now you figure out what it means to you. And that's completely backwards. Like, it's like starting a language course. Like, it's like complete immersion. Like, let's say you go into a Spanish four class.
Terri Bucci:It's not even starting in Spanish one. It's Spanish four, and and I'm just gonna start spouting off all this stuff to you. You're not gonna get that.
Rob:Mhmm.
Terri Bucci:So we have to really foster the communications part of it.
Rob:This has been extremely enlightening, doctor. I I I appreciate, you know, when we got on here speaking with you, we were headed in a particular direction, at least from our perspective Mhmm. To talk about the math shark. And what I've received is meh shark's math shark.
Ryan:Mhmm.
Rob:It's about, you know, you've taken us back to student centered learning. Yep. They're still students. Creating a desire that's based on a shared experience. And I get where you're coming from there.
Rob:Like, it's like building a bridge, right? You need to build a bridge from where students are to where you want them to be. And so you're helping to scaffold that, create the opportunities for internal ownership
Rob:the learning process. I guess just one final question is, how do you handle those students who and you know you're gonna have them. They were gonna be like, nah. I don't wanna do that. Nah.
Rob:I don't wanna engage.
Terri Bucci:I mean, you're always gonna have kind of those students. I I honestly, I think if the content is engaging, if the activity is engaging, and I think a just purely mathematical question can be engaging. It's how you present it. Like, let's figure this out. Let's see if this works.
Terri Bucci:Like, like, it there's some theatrics, of course, as an instructor. Like, we're all performative. Right? Like, like, even the most introvert is teacher is a performer because they're in front. So So I think we have to use those skills.
Terri Bucci:I think we also have to use the skills of developing a co owned classroom. So if a student comes in and it is their classroom, just as much as it's my classroom, they own it with me, They're gonna be much more likely to respect what happens in that classroom. So I think that's it. That's all the happy cheery. You're still gonna have a kid who's like, this is dumb.
Terri Bucci:Mhmm. Right? Yeah. Yeah. So but you're okay because those are going be few and far between.
Terri Bucci:I mean, let's face the reality. Sometimes you don't get them, but the majority you're gonna, you're gonna get them with this kind of a structure because it's engaging there. It's all based on community. So it's not just you in that case that's trying to get them to involved. It's their it's their peers.
Terri Bucci:Because remember throughout the the learning and the use of this kind of structure, consensus making and coming to agreements, that's part of it. And you can't do that if everyone's not voicing their opinions. So there's some peer stuff that comes into it at that point too. But I think if teachers really kind of embrace this environment of what a math classroom can be, they'll see a lot more engagement from their students.
Ryan:That's really helpful.
Rob:Yep. So I guess to summarize. Mhmm. The math shark doesn't seem to be a math shark. It seems to be a math minnow.
Ryan:Little guppy.
Rob:Little guppy. And there seems to be a good deal of optimism from two now teachers.
Terri Bucci:Mhmm.
Rob:One who trains teachers and the other one who's, you know
Ryan:Actively in the classroom.
Rob:In the classroom. Middle school. 30 in the middle school in Southern Ohio. And I'm I'm hearing hope and I'm hearing passion as well Mhmm. From both that we need to move forward, and we need to create a new normal.
Ryan:No question.
Rob:Well, Doctor. Butchie, this has been excellent. Thank you for your time.
Ryan:It was really helpful.
Terri Bucci:Oh, thank you so much. I've enjoyed this. Always fun talking about mathematics.
Ryan:Thanks for joining this episode of Transform Your Teaching. As always, please feel free to like and subscribe on your favorite podcast platform. Don't forget to connect with us on LinkedIn, and also remember to check out our blog at cedarville.edu/focusblog. Thanks for listening.