Math Through the Eyes of an Artist

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Susan

All right, Ruth, thank you so much for coming on to the podcast today. It’s great to have you here. 

Ruth

Oh, it’s great to be here. 

Susan

Awesome. Awesome. So tell us a little bit about yourself and your work. 

Ruth

Um, you know, I am just a teacher quotes. I’m on this sort of journey to understand how kids brains really work and really support them in whatever their brains are doing at this moment. Um, you know, Big listener of podcasts, big explorer. I’m currently looking a lot at Frobel’s Gifts and math in my art class, both with Frobel’s Gifts and other materials. So tell us a little bit about Frobel’s Gifts, because I’m sure lots of people are not aware of them. Yeah, they might have had like a page in their pedagogy class that they had in college. But it is one of those things that… if I hadn’t heard it on the podcast, I would have no clue what I was listening to here. So yeah, Froebel’s Gifts is a series of tangible items and works. So activities that children can do that were invented in the 1800s. And Friedrich Froebel is credited as having invented kindergarten by inventing these tangible blocks and toys and things, the first educational toys. So those… Those gifts that he created allowed very, very young children to understand concepts of whole and parts of a whole, counting. It brought them really slowly but creatively through the idea of the world as a place that you could make sense of and tell stories about and understand through real observation. So Friedrich Froebel, 1800s, invented these cool toys, basically, that kids could play with and then structured a kindergarten around it. He kind of made a whole list of, you know, this is what you’re supposed to do and how you’re supposed to introduce these gifts as well to keep it really conversational. It was kind of cool recently. We were talking about how relationships are at the fore right now. Everybody’s talking about how relationships with your students are the most important thing in your classroom. 

In these early manuals for kindergarten, it’s all about, yes, really structured exploration of these gifts, but constantly conversing with the kids, talking to the kids, saying, kids, what do you see here? What are we talking about? Tell me a story. And really understanding them through the gifts. 

Susan

Wow. So what’s the difference between Froebel’s gifts and something, an approach like Montessori, for example? Because I know a lot of people know about Montessori. 

Ruth

Right. So they’re very similar. Froebel’s gifts are hyper-focused and specifically about these sort of math concepts, although they do get into ideas about community and physical space as well. But it is quite math-oriented, whereas Montessori, of course, has programs to get you into the language and the social studies and world studies as well. They have… 

In Montessori, all of your, what do you call them? The life works, right? Works of life, right? Where you’re pouring from one cup to another. Those sort of practical life, there it is. Those practical life works are this beautiful extension. Whereas Froebel’s is almost like if you were just in the math room of a Montessori classroom, it’s a lot like being there. 

Susan 

Gotcha. Gotcha. So much more hands-on and play-based, but done so within the math lens, right? So here’s a question that I know we’re going to get because we’re going to hear from some educators who are like, well, it sounds like this is just for kindergarten or just for the littles. So how can we maybe modify some of Froebel’s gifts into older students for teaching older students? 

Ruth

Yeah, you’re right. A lot of this, I’ve had my great successes with the little kids because it was a kindergarten program. And so that’s what I went ahead and was like, oh, well, I’ll do it with the kindergartners. Then, you know, I started it last few years. And when we had to close down the schools, we didn’t get through the whole program. So we went to the first graders with the same objects and got just more out of it. Even when we started sewing with our first graders, now we’re still in the little ages, aren’t we? So when we came back and we had our our sixth graders exploring things as well, I knew they didn’t have the full breadth of their math curriculum from fifth grade. So when we went to make angles or in our mandalas or reflect things in our mandalas that we were creating, we were able to pull these toys out, right? And because they’ve never gotten this in kindergarten, those activities, those concrete activities where you have the object in your hands  were equally valuable to the older kids as they would have been for the younger kids. 

So if you’ve got a group of eighth graders or 10th graders that never got to take two sticks and move them from acute to obtuse angles, they’re going to benefit from the exact same activity that you had your kindergartners do if you were using Froebel’s gifts and examining angles. But you can get more fidelity, right? So instead of just perpendicular and parallel, those kids could be examining the whole breadth of angles that you can accomplished with two sticks next to each other. 360 degrees, right? They also were really cool with the works of beauty are really quite complex. So each of these gifts has works of life that you can make. So you can make things look like, oh, a train from real life, or you can make things that are abstract, beautiful designs. And the works of beauty are tricky because my older kids really connected with those because it was more like building a mosaic if you were using cubes, or it was more like creating the outline of perimeter of a building and finding its area when they were using the rectangular prisms. And it was more like constructing these very complex shapes when they were using their triangles, not just a trapezoid or a square, but going beyond that and getting stars and formations like that. So the older kids can just go further with these gifts and they can also get some of those concepts in their hands rather than just, you know, getting them first off with numbers. So the angles were a huge one. The complex shapes was a big one and fractions was a big one. When you are working fractions with big kids, they, 

benefit just as much from a fraction wheel as a little kid does. And so definitely starting with something in their hands and then you can give them numbers and then they can start thinking in their brains. 

Susan 

Yeah. Well, and, and I think for anybody who’s been intimidated by math, you know, even adults, I mean, you ask the adults in a room, how many of you loved math as a kid? And I think you might get a spattering of hands, but not too many. And so, and where did, where did Is it where people begin to get frustrated with math? It’s fractions, right? It’s in that aspect at grade three, when we start to really look at fractions and understanding numerators and denominators. And if you can have something concrete to put in their hands, I think even adults can benefit from that in order to visualize and interpret and understand the process behind the fractions, right? So truly- You know, everything we needed to learn, we learned in kindergarten. 

Ruth 

And when you have the foundation early on, that can help, but it doesn’t hurt to revisit, right? So if you learned your fractions with your Frobel’s gifts in kindergarten, third grade, you’re starting to put a number to it. It’s like, ah, I got to get my toys out again so I can break them in two and in four and then really understand what your numerator, denominator is and all that. Yeah, it was funny. I was thinking of kind of just the math that we have through history. And our first math is just the counting numbers or our whole numbers or whatever. And those all are so conversational. Even when you get into like fractions a little bit, that’s all something that you can tell a story about because those were all numbers that we made to tell people how much of something we had or how much we owed somebody else or how much got taken away. 

Like that’s just so naturally conversational. It comes up so easily for the kindergartens and for the older kids as well, even just more complicated. But yeah, once you get to fractions, it’s like, well, why would I cut my sheep in half or whatever? When you have your toys, when you have your toys out, you can really figure out, you know, well, why would I ever need to know how many parts of a hole I had? Well, what if I had a toy that broke into eight parts? I would need to know, right? So, yeah, it’s really more conversational, like all their first learning is, like all our first initial math is. Yeah. And I think you bring up a great point about storytelling because, you know, it’s the oldest art form, I think, with people just being able to we learn through story. Right. And we don’t often think about storytelling and math. 

Susan

So talk to me a little bit how you use storytelling and math as a natural pairing with visual art. 

Ruth

Absolutely with the kids involved in play, you know, involved in construction and building things, they’re talking to themselves, absolutely, in their own brains, or they’re talking to their neighbor. And when the teacher can come around and drop in on that conversation, as they’re building, they’re using a lot of those you know, both there’s telling a story like my little princess is climbing the tower, but also like this tower is much bigger than the other tower, which is only two blocks high. Well, the teacher can say, well, how much higher is the tall tower from the small tower and build up their math concepts as they’re just telling a story. So stories, like you said, that’s how you learn. It’s how you kind of express why math matters. It’s how you express 

the differences between things and the similarities and that kind of comparison with these tangible building tools in a kid’s hand, it just is math. It couldn’t not be math. 

I mean, it’s amazing. So when you’re working with them in visual art now, is this happening in their classroom? Is it happening in the art room or is it both? How does that work for you? We currently have it just in the art room. I’m piloting how this works in the art room. And just so everybody knows, it works awesome. It’s the best. And we’re starting to kind of lend in. As this year, I’ve been on a cart and been in other people’s classrooms using the gifts in other people’s classrooms. They’re starting to see that’s cool. oh, can I borrow those or you’re doing sewing with the kids, let’s do a sewing craft and now I know how to get them in order where we perforate first and then we sew. We are naturally now that border is being blurred and we’re able to pass those materials back and forth. This is something that absolutely, formally, we ought to bring those eight cubes over to the kindergarten teachers in their very first days of school. 

And we absolutely should bring those eight rectangles and teach them how to kind of curate those materials they either already have or the ones that I can bring them so that they are already in a set that allows the kids to do that kind of comparison in a controlled environment that they’re getting those comparisons. Instead, if you give a kid a thousand blocks, they’re going to play. But are they really, you know, working within a whole environment? Maybe not, unless they can count to a thousand. But if you give them a set of, and then they’re fine. But if you can give them a set of eight, can they work within that whole and understand it as a whole? Much easier. So curation is a huge part of this, that we’re definitely going to work a lot in the next few years with our kindergarten groups. Yeah. 

Susan 

Well, and I think you’re doing organically what we share with educators all the time is best practice when it comes to arts integration and with STEAM in that you’re not telling, you’re showing, you’re kind of organically inviting classroom teachers in to see, like, here’s what’s happening. And, you know, I’m a big believer that if people can come into a classroom and see or watch another teacher and what they’re doing, you know, the ideas start to fire in your brain and you start to make connections on, oh, I could use that here and, oh, I can use that there. And that’s really the power of of integration, no matter what you’re using is being able to make those connections and then facilitate that with your kids. So I think the process that you’re using is so wonderful because it is, it’s inviting them in. You’re not telling them, here’s one more thing you got to do. It’s exciting for them to see that, right?

Ruth

Totally. I mean, it couldn’t have been, I’m just thrilled to be in their classroom, which you wouldn’t normally hear, you know, oh, I love being on a card with my art stuff everywhere. I’m falling off in the hallways, but it has been absolutely thrilling. 

to go into their classrooms and both see what they’re up to and be like, oh my gosh, like this really does fit. I read the standards and they fit, but now I can see they have their counting cubes out and they’re counting to eight. It’s the perfect day for this. It’s been amazing to go in there. It’s really a weirdly awesome experience this year with all the constraints that there have been and all the weirdness that there’s been. It has been the best practice pressure cooker for creativity in my curriculum and I think for a lot of other teachers’ curriculum as well. 

Susan

Wow, that’s so powerful. I love that, the best pressure cooker for creativity. Because you’re right, creativity happens when we are constrained. Oftentimes, that’s when we have the biggest creative leaps, right? So what a wonderful experience for your teachers and for your kids this year. That’s amazing. 

Ruth

And isn’t it just a beautiful, like a beautiful mirror of the gifts, right? We’re constraining them to eight blocks. That seems mean, but it makes them creative. So yeah, I’m constrained to like staying in this one spot or going to the classrooms, but it really helps. Yeah. 

Susan

So I’m curious, your background, how did your background in math and digital storytelling and visual art lead you to… this kind of an approach? 

Ruth

Absolutely. So the, um, the maths background, I am one of those people who would be like, I loved math. And I recently started studying to, um, get a certification in math education as well. So then I can just kind of get out there and see what’s, um, what’s happening in the upper grades classrooms, what’s happening with higher level math as well. Um, and when I started getting into that education, really wonderful program at NJCTL, New Jersey Center for Teaching and Learning, they really focus a lot on having something concrete, even for older grades. They’re doing algebra class, right? With these concrete manipulatives, then giving them some sort of representational stuff, their numbers or whatever it is, or pictures, get it 2D. And then they really get them into their abstract thinking. They really talk about supporting the kids where they’re at through their peer circle. Another thing that was like, oh, well, they’re doing that in Frobel’s Gifts. When I heard about that, that’s how it worked out there. The kids can tell each other, well, this is how I made my locomotive or this is how I made my house and model it for them right there in front of them. They don’t need a teacher to dive in and show them how to make the house. Their peers can do it. So a lot of peer teaching was in that same program. And that really made me recognize Froebel’s Gifts as something  the opportunity that it was, where I would have been like, oh, that sounds really cool. Let me just log that one in the back. Knowing that it was going to bring out the storytelling in kids, which is something art can tell a story. We always teach that one. Knowing that it was bringing out storytelling in kids provoked me to make my first set of cubes. And even I started with those foam cubes that you can buy as math manipulatives as well. Started with those, said, let’s see where it goes, you know? And then it was like, well, this actually is quite successful. This is getting new stories out of the kids. It doesn’t require them to have fine motor skills, so they don’t have to be good drawers, quote unquote. But you can still access those imaginations and the stories that they want to tell. So having done a lot of digital storytelling with my older groups as well, and having constantly done storytelling with my younger groups in a traditional art classroom, knowing that I could add one 

beautiful object that would extract stories from kids who didn’t have success on the computer, didn’t have success with drawing. They had another mode that they could use, another tool they could use to find success.

Susan

Wow. I think that’s key. And also, I’m struck by the fact that it sounds like your passion point was right at the intersection of these components. And you just kind of found the niche that you needed to unlock everything for your students, but also for you as a teacher, which I think is really empowering, right? Because you all can’t see this, but I’m watching her face and she is smiling the entire time because she’s just, you’re filled with joy. I’m so psyched about this. I am so, so excited to share this. 

Ruth

Absolutely. It’s thrilling to get this kind of inspiration and to be able to share it with people. And it’s absolutely thrilling to have this gift to make a little Froebel’s joke there. This gift, you know, just placed on your, you hear it on the radio. Podcasts are wonderful. Shout out to podcasts. We’re on one, right? So it’s thrilling to just hear something and say, this could work. Give it a shot. You never know. Yeah, absolutely. Absolutely. So I always end with one last question for everybody. What do you think is the most important thing that educators could walk away with from this year? Awesome question. I think it’s what we just referred to earlier, right? We talked about how this is such a high pressure environment this year. Maybe not from our normal pressures like testing or the state or your administration, everybody’s kind of like, oh, you know, we’ll give you a little bit of a pass this year. But the pressure of like, I have to do things completely differently this year gave us an opportunity to really be creative about how we taught our curriculum and give ourselves kind of the opportunity, kind of this sort of free pass to say, well, it’s not going to be like it always was. So how can I still give the kids a chance to express themselves the way they always did in this brand new way, in a way that works with going into classrooms, having minimal supplies, not having your cleanup sink, whatever it is. This is so accessible and so easy to clean up that it was, you know, what I wanted to take away from this year and what I got from this year was that, you know, being creative is your ticket to success in any environment. high pressure or low pressure and being flexible and being able to make those creative choices on the fly is really what I got out of this year. 

Susan

Wow. Wow. And with that, thank you so much, Ruth. This was an amazing interview. Thank you so much for being on the show. 

Ruth

Gosh, it was a pleasure. Thanks so much for having me on. 

Ruth’s Twitter account: @ruthcbyrne

Learn more about Froebel’s Gifts