In this episode of Teacher's Corner, we talk to the author of the new book, Joyful Math, Deanna McLennan, and the author of Early Childhood Math Routines, Antonia Cameron about how to nurture a curious and joyful early childhood math community. Listen here or wherever you listen to podcasts.
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Toni: My book is about math routines in early childhood, but the bigger picture is empowering students to think. That's my overall goal, no matter what I'm teaching and no matter who I'm working with. And one of the things that led me to write the book was thinking about what do really rich, deep experiences look like for children in early childhood? And a lot of the teaching I've seen happening is focused on getting kids to do things. It's like they're little performing seals and we get them to do things.
Toni: And some of the activities I've seen don't actually trust children's intelligence. And so for me, thinking about children as these powerhouses of thinking and knowledge and where my job was to really understand how they think and to get them to communicate their ideas. That's why I wrote this book because I think that children know a lot more than they're often given credit for and to try and create routines that help students actually shine and show us what they know and to help teachers think about how to actually do that in their classroom. That's what my book is about.
Deanna: So my book Joyful Math is just really a celebration of what math looks like in early childhood education. The last half of my career, I've been really interested in delving deeply into what beautiful math looks like and becoming a different kind of mathematician myself. And so I think that the book really looks at how math can be a beautiful aesthetic, joyful experience for children and that math really exists everywhere. It's not an isolated subject. It's not something that we teach out of a textbook. It's not worksheets or didactic practices, but it's really just a living, breathing organic subjects that young children are quite capable of engaging within. And I was inspired to write the book because I fell in love with math myself over the last several years. And the children have taught me so much about what beautiful math can be.
Deanna: And I think that so many people have this misconception that math is a cold, dry, dead subject, and they fear math. And so it's my hope that the book will help inspire not just educators and children, but families in the greater community to really rethink what math is and embrace that beautiful math that exists every day and these authentic moments that we experience together with children.
Kassia: A common theme I see in both of your work is a great respect for young children as thinkers and not just as seals. I liked that analogy, but as people with ideas who come to our kindergarten classrooms already as thinkers and competent beings that can do all sorts of interesting things with math. And you explore that in different ways. You both write about play and creating a playful spirit and environment in early childhood classrooms
Toni: Play to me is essential for learning. And I think if you watch children, you observe them through play, doing all kinds of things that mathematicians do and scientists do. And somehow in school we lose that spontaneity. So because of COVID, I've not really been able to see my family and my nieces of... or I'm of an age and they're of an age where they're having children. And so what's fascinating is they've been sending me video of their children. And my niece just sent me this video today that I think encapsulates what I want to see in classrooms and why I think it's so important for us to rethink what we're doing in mathematics. So it was a one minute video of her daughter eating scrambled eggs. Now her daughter is one. And so there's a bowl with eggs, there's a spoon she has in her left hand, and she's sitting at the table in her little seat.
Toni: And this thing of trying to get the eggs on the spoon and the eggs not going on the spoon. And then thinking about, "All right, this is my tool. These are my eggs. I want them to go in my mouth." And taking her spoon and it keeps falling off. And then she puts her hand in it and she takes the eggs with her hand and puts it on the spoon and puts it in her mouth and then celebrates. And I thought, "Wow, isn't that a metaphor for what we want to have happen in our classrooms?" Because if children could realize there are these tools I'm using, and I may not be skilled with them, but I can get better using them. And so it made me think about teaching as the providing of opportunity.
Toni: So the providing of the eggs and the spoon, and you're sitting at the table and all these things. But then the ownership and the completion and the celebration of the completion of whatever it is you're doing is around the play and the playfully engaging with whatever it is you're trying to do. And so I think because we get bogged down in the stuff of math, we often lose that math is play and that when we engage in playful ways, we problem-solve, we may fall down, we may get up, we put our eggs back on the spoon, even though that's not the way we're supposed to do it, but we solve the problem and we eat and we celebrate. And just watching her spirit at the end where she raises her arm like, "I did it." It was just amazing. And I thought, "Yeah, this is what I want to see in classrooms."
Kassia: Giving kids that, like your niece, that time to figure some things out before you're in there with the spoon doing it yourself, it seems critical to give that space to explore and try things and try things in different ways than adults would.
Deanna: You know, as a kindergarten Ontario, I'm really fortunate because play is written directly into our provincial curriculum. So our kindergarten program is a two year program and we welcome children as young as three. And we really try to create a supportive, nurturing environment filled with open-ended materials and time and space so that children can create their own play opportunities.
Deanna: As a responsive teacher, I do a lot of observing. I do a lot of listening, and then I do a lot of playing with children as well. So I find it fascinating to see how they exist as natural researchers. They ask questions, they make observations, they build theories about the world around them. And through that open-ended play environment, I can exist almost as a co-researcher with them and explore the different ideas and questions that they have, while weaving in what I know about the Ontario curriculum and then finding opportunities for assessment as well. So as that play partner, I'm able to scaffold and support those rich learning opportunities without dictating them. I think sometimes we disguise activities as play, but they're very teacher-directed. So I try really hard to have the voices of the children present and leading what we're doing, and I'm the play participant together with them in the classroom.
Kassia: Deanna's getting at idea of teachers being curious, I think is so important and it's such a big part of both of your books and thinking about where's the kid and their thinking and what are they thinking about? What are they wondering about? Toni, do you want to talk a little bit about the importance of teachers being curious and questions you like to ask kids perhaps?
Toni: Sure. I think curiosity is at the heart of teaching and learning. And I think a lot of times, for us as teachers, we get so driven by curriculum and what we're supposed to teach that we lose a little bit of the curiosity and I think the slowing down around, why did the child say that? Or why did the child do that? What does it actually mean? To slow down around that means we have to let go of some of our preconceived notions and our ideas around content.
Toni: I envy what you have. You're talking about the Canadian kindergarten classroom, because it's really not that way necessarily. It is in some places in the US, because we're very driven by content. And so, the curiosity of a child can be very easily diminished by the types of things we're asking them to do, because they don't know why they're doing it. They know they're not being successful doing it. And what greater curiosity is there than, I would really like to know why I'm doing this and what this actually means.
Toni: And so I think curiosity is critical in teaching. I'll give you an example from a classroom I was in. This was years ago and this led me to the mantra of assume nothing. As a teacher, assume nothing. And so looking at a student's response to... It was really kind of an inane problem, but it was the teacher had given him, it was a subtraction problem, and looking at the student's work and analyzing all the work in the class and thinking, "Okay, well what does this actually mean?" And then going into the conference with the child with some preconceived notions.
Toni: As an educator, as someone who's done this for years and starting in a place that wasn't one of curiosity got me into a lot of trouble because he had read the word borrowed as brought. And so it totally changed his solution. And it wasn't until I finally said, "So what was this problem you were working on?" And he told me, and I was like, "Oh, and where do you see the word brought?" And he pointed to the word brought and I'm like, "Oh, you know, Oh." And so then I hear myself being the one saying, "Oh." And I think if I had started with curiosity in the beginning, I would have actually been able to explore his thinking a little bit differently.
Kassia: Yeah. Letting the kids talk and talk to each other and talk to you can illuminate so many things that are unexpected in their thinking. Something that is in both of your books are these great stories and vignettes that are woven into the chapters or at the beginning of the chapters. And Toni's about her wonderful routines and classrooms. And Deanna's about her kindergarten classroom and weaving math into art and outdoor activities.
Kassia: But in both of them, you get to hear the kids' voices a lot and kids talking to each other and teachers taking a little step back and listening to them. And I think that that is something that's hard to do. It's taken me a long time to learn that in my own teaching and I still sometimes have to bite my tongue, but can you give some advice or some thinking about why is that important to let kids talk to each other? And what do you do when you're hearing kids say things that might not be mathematically accurate or it might be a developing understanding? Do you want to start Deanna?
Deanna: Sure. Well for me, it's all about helping make the learning visible, right? Because we don't have those traditional receipts of learning that often people expect. We don't do worksheets. We don't have tests. I do very little checklists or rubrics. Most of my documentation is photos and anecdotal notes. And so when I hear children talking, I want to honor them as learners and I want to become a storyteller and really showcase the beautiful things that happen in the classroom. Not just for their families or my coworkers and administration, but for society in general. I think that so often we underestimate what young children are capable of and when they have these incredibly rich math theories that develop, I really want to honor that and showcase it. So when I hear children talking and working through a problem, often there is a misconception about a math concept or there's something that's not quite working right.
Deanna: But I really believe in that inquiry model of education where children have to go through that natural problem solving process and I like giving kids the time and the space and the freedom to work through things. They know that I'm there to help them. They know that I'm there to offer words of encouragement or help support them in the next step, but I think that the true learning happens when there's that productive struggle with a problem and they build their confidence and perseverance through that task.
Deanna: When I do hear things that are really mathematically incorrect that I think is going to lead them down a very difficult path in the problem, I might offer some observations like, "Oh, I wonder what would happen if you did this." Or, "I see you're struggling with this. Have you considered this?" And those prompts help guide them along the journey, but without giving them the answer. I want them to figure it out themself, but kids know that it's a safe space and if they truly need my help, I'm more than happy to step in and then provide that next level so that they can experience success. I don't want them to become so frustrated with the problem that they abandon the project.
Kassia: How about you, Toni?
Toni: Well, this is a big one, talk in the classroom and how you develop talk, as you well know, Kassia. It's been something I've been studying for a while and I think the best way to study talk in the classroom is to actually notice who's talking. And when you start to really notice who's talking, you notice the power dynamics in the classroom and you notice the children who feel like they're part of the banquet and the children who don't feel like they're part of the banquet.
Toni: And it can be painful to be in classrooms and watch the dynamic. And so for me, it's about how do we develop children's capacity to speak? Part of it goes back to developing and understanding that we care about them deeply, and that they are important, that there's no one more important or less important. And so this idea of equity comes up in terms of your voice matters. So there's any number of things and people have written about this that you can do to help students speak, having them sit in a circle, having them look at each other, using talk moves, all those kinds of things.
Toni: But I think it also comes down to how you listen to children as a teacher. And if they know you care about them, and that comes sometimes by how you're listening to them and how you're looking at them, and they know that you will wait for them to finish whatever it is they have to say or however you encourage them. And then we're talking about math, but this goes across content areas. It's really about giving children, not giving them, but providing experiences where they're empowered to find their voice. And that's something I work on a lot with the teachers I coach, because I think it's essential for learning and I think it's essential for the success of our democracy in the world that children have a voice. I don't know if that was specific enough, but it was kind of vague, but.
Kassia: Absolutely. So transitioning a bit here to we were talking about the challenges of teaching during COVID and both of you were writing your books pre-COVID and then your books are coming out during the pandemic. So you're probably doing lots of learning about what teaching and learning is like during the pandemic. Deanna is teaching Hearst kindergartners in person in Ontario, and Toni is supporting teachers virtually and in person imagine. So what are you learning now and how are you keeping your core beliefs about teaching and learning central while we're in this hard time?
Deanna: Well for me, I think that it's just continuing to have that empowered image of the child. I've learned that the children in my classroom are resilient. They're eager to learn. They're happy to be there. They're excited to be with their friends. And it's continuing to think about the classroom as a safe and supportive space.
Deanna: So we may not have the traditional centers that we normally have. We may have to modify sometimes some of the activities that we're providing, but it's still looking at things through that particular lens. How can I provide an open-ended rich environment and rich activities that support each child, while still adhering to the safety precautions that our local health office is asking? So kids are rising to the challenge and it's forced me to be a little bit creative, think outside the box. We're still offering those open-ended math activities. Some of them have to be a little bit more individualized, so that way it's safe for the children, but unfortunately they're not getting the partnership or the socialization at the math experience. They're not working through things in a group the way I would normally like to see, and we're bringing a lot of our math outside.
Deanna: So we always enjoy the outdoor classroom, but even more so now, especially now that the weather is still very beautiful in Ontario. And I figure anything that we can do inside, we can do outside. So the outdoors gives us not just that big body space and freedom to move, but I think it's very relaxing for children and they're very soothed in that environment. So, we're continuing to learn every day with the children and I just approach every day as just a challenge. And how can we be positive in this and what am I going to take from this and change so that tomorrow is even better?
Kassia: What are you figuring out and learning, Toni?
Toni: Well, I'm not in-person because I'm a person of a certain age, so I wouldn't be going into schools and I think even in New York City, people haven't been necessarily invited to schools and I'm certainly not traveling. So I've been sort of a prisoner in my little apartment, but I have been studying teaching and learning virtually. And I have to tell you at first it was a little terrifying to think about, "Wow, I don't know really much about this." And to go in. And what was fun was given the luxury of time, which we often don't have, I suddenly had this time and working pro bono with teachers, and I have to say, teachers have to be celebrated. They are truly remarkable human beings and watching teachers in their virtual classrooms trying to make the best of what they had and thinking, what can stay, what has to go and watching them and coaching them and being part of conversations around teaching and learning.
Toni: And some of the things I've learned is that good teaching is good teaching even virtually, but you have to adapt. And so some of the adaptions are around, I know as an early childhood teacher, it's the energy being with other human beings that gets you going, gets you excited, the laughter, the play, whatever it is. And being on a screen, you might see a child smile, but you don't actually feel the smile in the same way. Children coming in and out of learning for various reasons, the school I volunteered to do pro bono work, it was in the inner city high L population, poverty, all those things that make such incredible challenges for both teachers and learners. And watching kids come in and out of the learning, a few things that we did learn you'll be happy to hear, is that the routines work really well.
Toni: Not all of them, but many of the routines work really well in early childhood classrooms because 10 to 15 minutes is about the limit. And so what we did was we structured the learning so there was some engagement about math thinking and talk, and I put talk in quotes, but we also built in a lot around social, emotional learning. So finding video to talk to children about habits of mind. And talking to students about how they're feeling and what do you do when you get in that place? Are you feeling happy today? Are you feeling angry or are you feeling quiet? Are you tired?
Toni: And really building that in much more than I ever remember doing it in the in-person classroom and having check-ins, doing little movement breaks or dance breaks. So things that's... What does that have to do with math, but it has a lot to do with learning. And so really focusing on kids' social, emotional wellbeing and using the routines, any number of them work well virtually, and that's been really successful. I think the biggest challenge for the teachers I've been working with is how to stop talking, because there's nothing coming back at you. The children can't write in the chat, and so some of it's really stressful in terms of, I keep filling in the space with chatter. And now I need to maybe pose a question, be silent, give children a moment.
Toni: And that kind of wait time virtually doesn't feel the same as in a classroom where you can read all the students and you get that energy going. It's been a steep learning curve, but I feel like teachers have made remarkable progress, the ones I've been working with, mainly because they've been thinking about what works, what doesn't work, what type of lesson is effective, what type of lesson isn't effective, how do I get students to talk? When do I build in talk prompts and things like that?
Kassia: Yeah. I think that even though both of you wrote your books pre-COVID, they both have parts of them that are really so applicable right now. Toni, you were saying that the shortness and the routineness of the routines in your book make them a perfect bite size amount for a conversation for young learners. And then Deanna, all of your work outdoors makes me think of districts around here talking about how can we use the outside and how can we get kids playing outside, but also thinking about math and literacy outside. And so your book has so much to offer there around that, even though you weren't planning for this time necessarily.
Deanna: And I think too what COVID has done is it's sort of given teachers permission to take that breath and try new things. So maybe teachers who were feeling pressured to get a lot of curriculum done in a normal situation might feel like they have the opportunity to go outside and try something different because it's best practice and also it's the healthiest thing for them. So there've been a lot of positives about COVID helping us just to reflect and rethink things as well. It's given people some permission to try things that they might not normally have done before.
Kassia: I think that's true. I think in Canada, people are more used to going outside with children in kindergarten. And sometimes that, at least around where I am, seems scary to teachers. They're just not used to, or just hasn't been part of what's available to them to spend a lot of time outside with kids. And now they're thinking, "Well, maybe this is going to be the best way to do this." If they're teaching in person is to spend lots of time outside.
Kassia: You can finish this sentence, the best part about teaching math in the early childhood classroom is...
Deanna: That's tough to put in just one sentence. I mean, I think the best thing for me about teaching math in the early childhood classroom is I've become a mathematician again. I have been given a chance to revisit math ideas that I haven't thought about from long ago. I've been given an opportunity to reconcile some of my negative past experiences with math and think of myself as a true mathematician. And that's something that I didn't think. I had some pretty negative experiences with math in my later high school years that influenced the way I thought about math. When I became a teacher, I wasn't thinking about math the way I was thinking about math or I'm thinking about math now. And so I feel really empowered. My daughter is taking grade nine algebra right now, and the old me would have been terrified by that.
Deanna: And then the new empowered mathematician educator that I feel I am now has not been scared to make mistakes, and I've just dove in with her and we've figured it out together. And so that's a long answer to your short question, but I think that I really feel like I'm an empowered mathematician because the children have helped teach me and helped me become more confident in what I've been doing.
Kassia: Yeah. I think that story probably resonates with a lot of teachers that, especially early childhood teachers, that might not have had great math learning experiences themselves, but want something different for the students that they work with. What about you, Toni? How would you finish?
Toni: The cynical me says the best part about teaching math in the early childhood classroom is that there's no testing, because I think that that drives the train of the way many teachers teach in the upper grades, even though they may not want to. It's that we have to cover this content and this idea of covering content is usually, well, it's like driving a bus with no one on it sometimes.
Toni: And so the beauty of the early childhood classroom is that you can actually play more with ideas and you can provide children with a variety of experiences and slow down around those experiences.
Toni: My own experiences in math were things that led me in another direction. It was dry. It was dull. It was memorization. I never had the kind of teacher when I was young that sparked my imagination and it wasn't until I was in my forties and I worked with some Dutch people at Math in the City with Cathy Fosnot at City College, that my understanding of math was transformed and I felt cheated. And one of the reasons I pursue the teaching of math now is that I don't want other children to feel that way. I think something is denied, a door is shut when you have bad math experiences. And so planting the seeds in early childhood where children say, "I can do math. Math is powerful. Math is fun. Math is exciting. Sometimes I struggle, but I can overcome." Under that struggle is having those feelings that take you all the way through. That's what I want for children and I think early childhood was the place to empower children.
Kassia: Yes, you are definitely right. So I'm really excited that Stenhouse has both of your books out at similar times, because I think that sometimes there aren't as many wonderful resources for early childhood math as other grades get or sometimes people just say, "Oh, you can adjust these ideas for kindergarten or for preschool or for first grade." Instead of saying, "This is a resource that is just for the early childhood time." So I'm glad that we have something just for early childhood teachers.
Kassia: What other resources do you love for teaching math to young children that you might recommend, besides your own lovely books, to other early childhood teachers out there that want to read more about math?
Deanna: I am a huge fan of Jo Boaler's work. Jo Boaler's work totally transformed the way I saw myself as a mathematician. It changed the way I thought about myself as a math parent. And it really helped me think about math differently in my classroom. So definitely Mathematical Mindsets by Jo Boaler. I'm also a big fan of Alex Lawson's work. Alex Lawson is a math professor in Ontario and she really goes deeply into exploring the processes behind how children acquire a math knowledge. And that's a gap that I previously felt I had in my training. And so I think that even though we embrace that open-ended play-based program in the classroom, it's important to understand how children develop math skills and math knowledge, right? So that we know those trajectories. We can have an end goal in mind. We can be thinking about the different steps that we need to help children along the way. So a lot of Alex Lawson's work has really inspired my math as well.
Kassia: How about you, Toni? What would you recommend?
Toni: Some of the books I'm really fond of, and this goes back to my own training, would be the Young Mathematician at Work books by Cathy Fosnot and Maarten Dolk and the algebra book with Bill Jacob. I think the Contexts for Learning series and Wonderful Investigations for Children. I love some of the old work like Connie Kamii, I think is a great resource for teachers. I've also been exploring different websites and looking at games and materials on there. I guess I've kind of been thrust into that as I'm thinking about virtual teaching and what's out there and how do you take different resources and use them virtually? Because a lot of the curriculum materials really don't work in this environment and they have to be adapted and teachers doing a lot of thinking about that.
Toni: So, Math for Love. I love a site, I think it's called Math with Bad Drawings. I love that. I love that site. I love the problems the person who created the site puts up to look at. I would say for me, the best thing teachers can look at is whatever you're looking at, think about what does this do for children's thinking. Why am I doing this? And what is it going to do for children? And sometimes it might be something as simple as teaching them a specific idea, or it might be something as simple as opening up a way of thinking.
Toni: I'm also looking at lots of children's literature and thinking about how could I use that and connect it to mathematics. And so for example, with the activity in my book called Who's Hiding? We use the Lizi Boyd called book called Flashlight. There are a lot of good books out there that you can also connect to math. So there's so many resources out there. I can't begin to name all of them, but I keep reading and I keep studying, but I always come back to, how can I use this to improve the lives of children? How can I make them better math thinkers? And that's for me, that's where it all begins and ends.
Kassia: Yeah, I agree. I think that there's elements of in both of your books of storytelling and the teacher telling stories and the children telling stories together about the math. And I'm thinking about how another resource that I've seen early childhood teachers using is just themselves and their own lives and showing pictures of their animals. Or a friend of mine took a little video of herself on a hike and said, "I'm going to cross this stream. How many steps do you think it's going to take me to go across?" And then she sent that off to her kids. So I think that early childhood educators are such good storytellers and good weavers of mathematics and seeing mathematics in the world that their own lives and their students' own lives are good resources too.