Beyond Numbers: Transformative Math Teaching with Tiffany Goettle
4 Tiffany Goettle
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[00:00:00] Hi, and welcome to another edition of 20 minutes of teaching brilliance on the road with trust based observations. Today I have with me Tiffany Gettle, and I watched Tiffany in early December, I think, when I was out doing the Crookston Diocese in rural northern Minnesota. And so, Tiffany, how about you give us a little background on you and we'll take it from there.
, I'm, I am married and have four kids. , this is my 13th year teaching. I started out in a private school in Fargo and taught fourth grade for two years. And then I to public school and taught eight years in second grade there, and then one year and fourth, and then moved back to private school. And taught Fifth grade there last year and then, uh, moved back to second grade this year. So, which I love. [00:01:00] Yes, I am back to my stomping grounds.
And all the other experiences are great though too, right? I mean, you learn a little
they were. I've, I've loved.
all the other levels, right?
Yep, I've loved all the grades. I can just tell that second's kind of where, where my jam is.
I hear you. We all have our one that we when we like the most. I totally get it. Well, listen, the day we were in there, we were watching math class and it was it was so like for me, the ultimate measure is what 20 minutes are up. How did that happen? And it was definitely one of those days. And and so when we started, they were doing the century game.
So why don't you just start talking a little bit about that lesson and that and then we'll We'll move on to the stick flash and all the other good stuff that we saw going on.
The century game is a game that is from the Bridges math curriculum, and they count by tens and get to, it starts out to 100 when we're at the 10th day of school, because that's the first century. And then we just continue moving [00:02:00] on. So the 20th day of school is the 200th century, or the second century day.
And so we continue. Moving on, and so now we've hit the 10th century day so we're up to a thousand now. But it's counting by tens in a circle, one at a time, just kind of a whip around. And then as the year goes on, we kind of move, now we're counting forward and backwards by tens. That's a little added thing that I've added to it a little bit, and Counting on and off the decapole, off the 10.
So, starting at 12 instead of 10 and things like that. Just
another version of it.
you mean? Do you mean like 12, 22, 32, like
Yes. Yep.
And yeah, you're just pushing your, your scaffolding and making it tougher and more challenging for them and, and definitely on the carpet and the circles and they all know what's going on and it's a little, I mean, I know there's some pairing that you're doing on purpose, but there's some randomness to where you start.
So [00:03:00] everybody's, you can't just count on knowing the same thing every day. They've got to, you know, Yeah, for sure. Well, that was the, that was the start. It was fun to watch the kids get into that at first, but I think if we dig into it even more, why don't you talk about the, the stick flash and what you're doing in that and, and the use of the whiteboards and all that, because the kids were so into it.
And it's, it's always such a tell, telltale sign to me. It's when they're into it.
Yep. Stick Flash is also a was a lesson from the Bridges Curriculum. And we have, so you start out with popsicle sticks. And showing them, like, two bundles and three ones. And have them share what it
Bundles of 10, right? Just
10. Yes, sorry. Bundles of 10.
people know.
And then they share what it is. And then as we move forward a little bit, we start to cover it up. So we cover the, the sticks and bundles up, and I flash it. So I take a piece of felt, and I cover it up. And then I show it to them, and then I cover it up again. Uh, so [00:04:00] then they're just briefly seeing it, have to remember, and can try and hold that number. After we get familiar with that a little bit, we
add in another.
just for the audience, just a little bit. So what we're talking about is you've got popsicle sticks, rubber banded, if I'm, or if I remember right, or something, in groups of 10s, and you've got singles. And so they're on the pile, and they're not even necessarily neatly placed in order of each other.
They can be kind of, if I remember right, even kind of disorganized in the way, am I right on that?
Yes, so I will start with having them organized into tens and ones and then as we move forward a little bit I do move them around so they can't Have that that structure
predict
Balance them.
in the moment, right? Okay.
Yep
Yeah, okay. Keep going with that. Sorry, I just wanted to make sure everybody listening knew what we're talking about.
So after we move to or have done just one number then we start to move to [00:05:00] two numbers So I might cover up Have the sticks and bundles and then cover them up with felt and then show another number and then but keep that shown so show show another set of sticks and bundles, so
(ad here) Tiffany, I'm going to back this up just a hair. So, you show them just for, I just want to make, because we know what we're seeing, but they didn't see it, right? So, so, every kid in the class has a whiteboard, right? And you're all on the carpet, and so, the first round, you show the numbers real quickly, and then they've, They write the numbers on the whiteboard?
Is that what it was? Or do they talk about Remind me, I
Yeah, so the first round when I'm just showing the Sticks and bundles I have them Write it on their whiteboard so that way they're still engaged with it and I can quickly glance around who's got it
and Once I see that Everybody is kind of has it and is understanding. Okay. Yeah, they can see the sticks They know how many it is.
Then we cover it up [00:06:00] and then Flash them and show okay So here's the sticks cover it up show them and then I have them write it on their whiteboards again So then I can see okay who's ready To add in that next number. And then we had been previously working on addition strategies and hopping by tens and counting by tens.
Uh, like so if it's 23, adding 20, we talked about going 23. 3343. So then when we bring the sticks and bundles into it, it gives them a visual. So now we're them, okay, so we have 23 hidden underneath the piece of felt and I'm going to add in 20 more to, to show them the two, the two bundles, and they can then see, okay, 23, I have to hold it because it's covered up. I can't count those again. So now I have 23 and I know, okay, 33, 43 with those bundles [00:07:00] and then putting it together and showing, okay. What addition sentence did we just do? So then I might have them write down, okay, 23 plus 20 equals 43. And then that can show me that they're seeing the addition piece of it. And they're not just counting sticks. Uh, and then we continue to move forward where I might then show
36.
you, Tiffany? Just, uh, just to get So, holding it, you mean remember it, just for people listening at home. And then, so, basically, they write the number down, but then afterwards, You ask them to basically show their work for how they solve it, for the strategy that works best for them on their whiteboards as well.
And then I think it's a combination. If remind, remind me, remind me if I'm wrong. A combination of them showing the whiteboards, but then also having some kids volunteer or you, you pick out to, everyone gets a chance to share out their strategies as well. Was that right? And,
[00:08:00] so, when they put it on their whiteboards instead of me just having one person call out and share what their answer was, I'll do a turn and talk. So I'll say, okay, turn and tell your partner what what your, what the answer is, or what numbers did you see, and then they'll tell them, and then it's, Also, how did you figure that out? Not just the answer is 43. It's 43 because 23 plus 10 is 33 plus 10 more is 43 and then on their boards, um, with what we've been doing in the past, they would then show it on an open number line. So they're starting at 23, and then they have a hop of 10, and then show their land at 33, and then another hop of 10, and show their land at 43.
and just to be clear on that, it's like, sometimes a turn and talk, one kid can do all the talking, but the way you've got it set up in there, it's really more than a turn and talk, it's more like a, a Kagan structure to me, where [00:09:00] every kid's getting an equal opportunity to talk and making sure that both kids are having a chance to talk and share their work, not just one kid, so they're both learning from each other.
Would you say that's accurate?
Yes, we practice turn and talks from day one. So, we don't just do them in math, but we do them across the board. So, we have learned that You, you share and then your partner shares and then sometimes because there's always kids that like to share first I'll say okay, if you shared first last time you have to wait and the next person shares To make sure to challenge those Kids who are a little bit more nervous to share or maybe don't get it super quick that they now have to share And they have to listen to each other.
And if someone doesn't get it, it's the opportunity for that uh, student who does understand it to teach them. I have them paired strategically [00:10:00] where I have usually a higher student with like a middle student and then a middle student with maybe a, a lower student that struggles a little bit more. So that way they're still close in ability, but they can teach each other. Okay. Because sometimes a really high student might just say, well, it's 43 because it is. And, and then it's the, the student who's still trying to figure it out is going, I have no idea how you got that, but I believe you because you're good at math. So it's
Tiffany, can I jump in again? Cause I just, I just, I know you guys haven't had that cooperative learning training yet, but you're already doing it because you've, you know, just intuitively or experientially, you know, that if I pair that high student with the low student, that's where you're going to get the most frustration.
And we want teaching others by design because that's the most powerful form of retention of learning. But. If that gap is too big, the frustration from either party, the high or the low, can get in the way of that [00:11:00] learning. So because of the way you strategically group them, that learning, that teaching others can still happen, but not in a way where that frustration happens.
Am I right?
yes, very much so.
No, that's, that's, I mean, it's just so important when that happens because it is giving that. And the other thing is like, if you think about it, like if you had to get through all 20 some kids that you had in the class and then they're getting corrected. So they're getting the right answer so much quicker.
Yes.
you can get to them, right? So I just love that about that. I
Well, and I just love that they all are sharing then, because if you just have someone raise your hand, you get the same kids that raise their hand, and they share out, and the rest of the kids tune out. So, if you
do that, then,
attention because, because I didn't get called on. You had to tell me because you're
And so then I've even done where they share and then I will say, okay, you two tell me about it. And so they're not [00:12:00] necessarily raising their hand, but it's also not a cold call because they, they've already talked about the answer together and it's not this one person has to share. It's what did you two come up with together? And when I do that, I usually know If they have the right answer or not, because I kind of go around, I listen in when they're doing the turn in talks, I try to walk around and listen, okay, who's got it? Who's still struggling with it? Are we ready to move on? What needs to be scaffold for, um, as I continue the lesson?
you're checking for understanding on every single problem. So you're setting kids up for success when you know they've got the right answer, right, or teams up for success. And especially if you know, there's that struggling team, it's like, Oh, they've got it this time. Like I'm going to call on them. Right.
Yep. Yep.
that success for them totally. Spencer Kagan, who's the Kagan guy. My favorite, favorite quote of his is why ask a question and have one student give an answer when you can ask a question and have every student give [00:13:00] an answer, right? That just the engagement is so much different.
And when you've got the whiteboards, one, every kid's getting the answer by themselves. They might get it right or wrong, but then you've got a pair too, so afterwards, they're doing it together. There's a four person activity called Numbered Heads Together, and really you're doing a two person version of that.
But it's ensuring that every time they're getting it right. It's just, it would, and they're having so much fun while they're doing it, right? They're so, they're so animated, and then you're watching every single time, and you've taught them how to socially interact with each other, so.
Yep. And I've got a really good group this year and they just. They, they love school. And so the, the passion there for when they are working together and they're getting along with each other and they kind of challenge each other. And so that's, It's been really fun to see how they work together in those pairs.
(ad here) Tiffany, let's be honest. I mean, sure, we can say some classes are more [00:14:00] naturally stronger than others in terms of the way they get along, but that never just happens by itself, right? I mean, you still have to do things at the beginning of the year. Like you said, you started turning talks in all your subjects at the beginning of the year, and you're socializing them to the right way to do it, right?
Yes, it does have to be taught, because otherwise it's mass gas.
Right, what? Do you want to go into maybe like what you do at the beginning of the year? Because I think that matters.
Yeah, so at the beginning of the year depending on, I mean it can be anything. It can just be sharing something. It can
Oftentimes it's better when it's non content
Yes, and it doesn't doesn't have to be something difficult. It can just be turn and tell your partner your favorite color and then
What I did over the weekend or whatever.
Um, so yeah, we just start out with that and sometimes I, I bring it a little bit more specific where I say, like, teach and that brings in a little bit of the whole brain classroom when there's more signals with that,
um,
more about that.
[00:15:00] what was
more about that.
So whole brain is just kind of, it's a management piece that I've taken the class on and it's just kind of has that. Interaction back and forth. So there's a lot of hand signals. There's a lot of just the responses back and forth with the students. I do pieces of it. I don't do It's fully like some teachers do and they do it very well, and it's great but I just use some pieces of it and then the turn and talks I've learned through trainings that I got at a past school that I was at the Steve Dunn writing program is based off of a lot of the Turn and talks and all of those things writing and reading program.
So That's where I've kind of learned how to do it, um, and it's, yeah, you just, you have to start out day one right away when you're teaching all your routines and everything like that, how to, you know, walk from one end of the classroom to the other, it's, everything has to be taught because [00:16:00] if they haven't done it before, it's, They're just going to think it's time to talk, have, have, you know, socialization hour during the middle of a lesson. So yeah, we start small and like I said, I have different partners for different subjects too. We kind of start out with the same spots, but like now as you move through the classroom or move through this school year, it's, we have very like specific reading, they have specific partners, writing, they have specific partners.
Um,
it's not universal. That grouping doesn't stick with us because we're kids. We have one subject and we can get sometimes caught in that loop of thinking it's the same for everything.
yeah,
so
mix them up periodically too? Because after a while it's good just to,
yes, I try to switch them up. Sometimes I forget and then they're with them longer than others. But it helps when their reading partner is different from their writing partner. That's different from their math partner because then it's not always the same one. [00:17:00] And so that does help with it, but I do try to switch it up, too, because sometimes there are groups that you find somebody's getting frustrated, because one is having a harder time focusing, or one is higher, or one is lower, and they just, you know, they just have, maybe don't click as well, and so then, or they click really well, and they talk about everything, and so then we have to Switched because of the distraction level.
which is also just saying I have to differentiate. I can do my best to arrange it, but sometimes I'm not going to get it right. And then I have to make an adjustment. Even if that's separating a group that's functioning well together. But to get two groups that work better together than one that doesn't, one that doesn't, that's what you do for successful teaching, right?
Why don't we go back a little bit more, because I know we got a little bit off topic talking on all these other things, but talk more about the stick flash and then how that builds and how this, because the strategy piece is really interesting as they're talking that out and sharing that out because you had multiple, [00:18:00] So, there's a lot of strategies, at least two if not three, that the kids have developed over time and so why don't you go just continue a little bit more with the sticks as that's building because I think that especially the speed thing with the covering the numbers up and then having to remember the one and then just like the scaffolding of that and the focus that it requires for seven year olds, right?
Seven turning into eight year olds to remember that, like, I just think it was so impressive. So, you know, I cut you off to go on a little detour but let's come back to that more
Yeah, so once we get to what the goal of the lesson is the two digit by two digit addition. So instead of just showing kids numbers, bare numbers, what we would call them, 25 plus 17 and then having them solve that, they won't use a mental strategy. They might go to an algorithm or something like that. So we're trying to teach them to add. without using an algorithm and using a mental strategy. So when we, I have the sticks and bundles and you start by showing them one [00:19:00] number and then you add in another number then you have to scaffold it because. They're not always going to have popsicle sticks in front of them to add. So, you, when you cover it up, it's start, starting to get them to that bare number, to just kind of understanding what that 25 is. And so, they can visualize it, two tens and five ones. and hold it. So, when they cover it up, they have to hold it. And then, you add in, you know, and you might even start with. seven, 25 plus seven. So you show seven sticks and if they can then kind of think, okay, 25, if I take five more of those sticks where I can't see the 25 anymore, but she's showing me the seven. So I think, okay, five more is going to make another 10. So then I'm at 30 and then I have two left. Now I'm at 32. So they're doing that mentally, but then when on their whiteboards, the purpose of those is to show it on an open number line or to show that strategy of [00:20:00] Okay, so I started at 25, I added 5 to get to 30, now I'm adding 2 more to get to 32, and they show it with their hops on a number line.
They're basically showing you their mental math that they do.
This all I came from training when I, that it's part of the Bridges Math Program, but it also is Math Recovery Training, the Math Recovery Council that I've had to help me understand more the why, and why this is so important for kids. Um, and so then once you get to covering them both up, now they're having to hold So, maybe I did 25 plus 7 where they could see it, and then I do 25 and I add and I do 17. So, now they figured out before 25 plus 7 was 32. Now it's 17. Well, that's just one more 10. So then I hop 10 more and so that kind of helps the [00:21:00] progression of Some of those numbers as you're covering them up and then when When they're both covered up and you start to add in more numbers, you can also some kids won't make those jumps like that.
Sometimes they'll split the strategy. So they might see, okay, I had 32 underneath the first one. I saw it. Okay, I covered it up. I know there's 32. Now I'm going to show 25 and cover that up. And then they might go, okay, well, there was three 10s, there was two 10s, now there's five 10s, five 1s and two 1s, and they split it into 10s and into 1s. And then they can show that on the open number line too, or if there's another way that they want to show it on their whiteboard, but it's two different strategies that these sticks and bundles kind of present with them. It, it guides them to a strategy without, Making them, [00:22:00] telling them how to do it, because if they figure it out on their own, they're going to remember how to do it. So that's kind of the, the goal of that. And then as you're doing that, where you cover them up, like if you're covering up the second number too, some kids don't, can't always hold both numbers. And so I try to glance around and see, okay, she needed to see that longer. So then some kids have moved on to showing their work, but I can tell some aren't ready.
So then I'll say, okay, I'm going to show it again. Because when I cover them, the sticks and bundles up, I don't show it to them for five minutes and then
cover it up. They do it like 30 seconds or less sometimes. It's a
very brief.
it's way less. It's very quick. I thought it was like a flash.
So, I mean, it's quick. It's really
quick because I don't want them counting them by ones.
I don't want, the whole goal is that [00:23:00] they can go, Oh, there were three 10s and two 1s, that's 32. Where if they see it too long, they're going to go 10, 32,
every time.
Right,
Just because it's in front of them. Where if they have to hold it, then they can, And it is really hard for some kids, so then, you know, you have to pull it back and you have to, those kids, they need to see it more before it's covered up.
But I think that's, but I think a couple of things you're doing really help with that. One, every kid has a whiteboard, but two, they're all on the carpet really close to you. And so, because like if you're in a classroom and they're sitting at their desks, whether they're in groupings or whatever your grouping is, like for you to work your way around and see that, that takes way more time because you're right there and the kids are on the floor and they've all got their whiteboards and you're doing those constant checks for understanding.
You like instantly know. Oh, I need to give a second showing for those that need it right where in a different setting that wouldn't work nearly as [00:24:00] well
Yeah, it's, and that was one of the we haven't, hadn't done a lot of the math circle and, but when we were
doing the center thing, and it, but I was trying to think, how am I going to show them these sticks and bundles? So they can see them because I
knew it wasn't going to work on the board on a document camera
because it just doesn't work as well.
I've done it before. It doesn't work as well. So,
But when they're all literally peering in because it's like two feet in front of them
yeah,
pulls them into it way more doesn't it?
yes. And I have found like they love when we go to the mass circle spots. So you can just tell that like they must be able to see a lot better and they must just feel more unity or something because. They love it when I
say they're like my circle spots like instead of facing me or whatever because we're always at the carpet Usually [00:25:00] for lessons, but it's you know, it's different.
I think they just like
the circle
an energy there that that pulls in. And I think when they're all deciding together and doing those turn and talks and explaining there's, they have so much passion behind sharing their strategy. Like you, somehow you've built that in where they're super excited to share their strategy. So you can see how then that energy builds upon itself.
So now it's a new one. We all get to look and that's, that's what they're like. I mean, it's, it's, it's. It's joyful to watch, for sure.
Yeah,
Uh, I was gonna say, why don't we, let's do one more thing. I think we got a pretty good idea on, on the, the math. One of the things I know, cause we, we had a pre chat, and one of the things that we talked about that I think is really, really important is you talked about your mentor math teacher along the way, and your, uh, and your, I forget what job it was, one of your previous jobs you had though, that person that was like, that really, really influenced what you've become and done with math, and just, do you want to talk about that a little bit, and the influence of that, and for anybody else out there, especially [00:26:00] if it's a younger teacher, the importance of, you know, finding those people,
it was our math coordinator at my at the public school that I was at previously, and I was on the math committee, and it was every time we had a math committee meeting, which I'm sure lots of teachers are like, oh, another committee meeting. It was like we all got a lesson on how to teach math every single time we had a math committee meeting because she always started out with something like that and her passion for math just totally set tone with me because she she loved it and it just was like this is why kids don't understand math or this is how you can get them to love it or how you can really break it down for them and why. Why we don't just do the algorithm, you know, there's a lot with that right now is why don't we just go back to how we learned it when we were kids and everything [00:27:00] and there's, there's very good reasoning for it because I, this isn't how I learned how to do math. It's how I learned how to teach math and
the way they,
share a little secret. I was at the school last week, no one knows, we filmed this so I can say it, and I saw a class, it was a math class, and it was, it was like when I went to high school, and I stopped liking math, because you just started doing problems on the board, okay, everybody got it, next problem, never really checking in with us, and we're copying the problems, but there was no sense of why, and I just like, I was really good at math and I was just like, I just lost all my passion for it because it wasn't fun and nobody explained it anymore.
So you're talking about the why and the passion and all that and it makes a difference. Yeah.
and she trained for, so I had, I have my math recovery, recovery training, and she was actually our trainer for it, like, she got trained to be a trainer and it was phenomenal. What I learned from those, [00:28:00] you know, I'm sure every trainer is amazing, but I can't imagine there being a better one because he just made it make so much sense. And, I think that just, yeah, I mean, I loved being on the math committee and I think people thought I was crazy because I was the one who
was like, I moved to fourth grade and was like, but I still get to be on math committee, right? And they were like, sure, you can be on math committee. Yes, I mean, I think they did.
Like, you're crazy. So people always laugh. Like, if they get me talking about math, they're going to be there all day when it comes to
this.
Tiffany, have you, with, with that, the Math Recovery Program and that mentor, like, have you, do you feel like you're, you're playing it forward, like, at your new school? It's not your brand new school, but they're, like, are you working and showing and sharing? Because we haven't really had a chance to talk about that with, with your peers.
Yeah, I mean, I try, you know, a little bit here when we, we have a new math curriculum [00:29:00] and So I've tried to, uh, build it up a little bit because it is based off of a lot of that kind of those pieces on the why, the conceptual why we do this, and it's a hard transition when you've taught a different curriculum for, you know, a long time to know, okay, well, this seems like a lot more work in a way because it, it
is.
And if you don't know why you're doing it then, then it's kind of like, it doesn't make sense. And so, my hope is that we'll be able to get that, like, AVMR training for everyone in our school, because I think the curriculum itself would just make more sense. Oh, this is why, this is why we're doing it and I know that teachers who have started this new program are seeing like, whoa, the kids really, they get it, they enjoy it it's a transition.
So [00:30:00] I was really excited when I heard our school was going to be doing this math program because they, I piloted it in the public school that I was at previously and so, um, I was super excited when I heard that they were doing it. What they were gonna adopt it here. So
Well, Tiffany we're nearing the end. One of the things that I always ask our guests if they're willing to do it is, uh, in case anybody that's listening in has any questions and want to reach out and learn a little bit more about what you're doing with math, and we'll have the names of the programs in the show notes that you were talking about, but would you mind sharing, uh, contact information for anybody that might want to reach out?
yeah, I'd be more than Yeah, that's totally fine.
Sure. It's
you can email me, I don't know if I can use my school email.
been okay in the past.
Okay. So T GLE, G-O-E-T-T-L-E at St. Joes, [00:31:00] uh, morehead school.com.
G-O-E-T-T-L-E at j st joes morehead school.com.
Yes, and sorry, Moorhead is just MHD.
Oh, so St. Joes, MHD Yeah, sorry. Sorry about that. mhd com. Okay, good. That's good. Okay, Tiffany, thanks so much for spending time with me today and, and sharing your 20 minutes of teaching Brilliance with everybody that's out there.
You're welcome. Thank you