In this episode, we talk with Dr. Jennifer McCray from the Early Math Collaborative at the Erikson Institute about mixing early math and social studies in preschool classrooms.
More About Our Guest
Dr. Jennifer McCray is an Associate Research Professor and the Principal Investigator of the Early Math Collaborative at the Erikson Institute. The Collaborative conducts research on the teaching and learning of early math and disseminates information through its books, journal publications, newsletter, and website. Jennifer has run several federally funded development projects, is the first author of Growing Math Minds, published by Routledge in 2018, and is the Lead Developer of a toolkit on teaching math to young children for the Institute for Education Sciences.
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Transcript
Intro: Thanks for joining us for a podcast from the Illinois Early Learning Project. Our project is part of the Department of Special Education at the University of Illinois at Urbana-Champaign and funded by the Illinois State Board of Education. On this podcast, we share information about how young children grow and learn as well as strategies adults can use to help them thrive. My name is Natalie Danner.
Natalie Danner: Okay, welcome to the Illinois Early Learning Podcast. Today, we’re talking about mixing early math and social studies in early childhood education. We are joined today by Dr. Jennifer McCray. Welcome, Jennifer.
Dr. Jennifer McCray: Thank you so much, Natalie. It’s great to be here.
Natalie Danner: Jennifer McCray is an associate research professor and the principal investigator of the Early Math Collaborative at the Erikson Institute. The collaborative conducts research on the teaching and learning of early math and disseminates information through its books, journal publications, newsletter, and website. Jennifer has run several federally funded development projects and is the first author of Growing Math Minds, published by Routledge in 2018. And is the lead developer of a toolkit on teaching math to young children for the Institute for Education Sciences. Well, let’s begin. Dr. McCray, you lead the Early Math Collaborative at the Erikson Institute. Tell our audience a little bit about the Early Math Collaborative and what it offers to teachers.
Dr. Jennifer McCray: Excellent. So, the Early Math Collaborative has been around for about seventeen, maybe eighteen years. Now, we’re getting old, and I was there when it got started. Essentially, my dissertation was about how children develop their understanding of mathematics, and what teachers – preschool teachers – need to know in order to help them do that. Right? Because as a preschool teacher, you know, you want to be in there responding to what kids are doing and saying, and you can’t respond in the right ways if you don’t know what the developmental process is for understanding that four is always one more than three, and three is always one less than four for example, right? So there’s a lot of really good research, cognitive developmental research that’s been done since Piaget. Really, since like the 1970s that bears on helping us understand how children construct their mathematical thinking. And 20 years ago not much of it had been translated into teaching at all. There are other people who’ve done this work, you know, more thoroughly than I have, and preceded me at it, but the collaborative has as its mission to take this understanding of math, this beautiful understanding of how kids develop their math minds and help teachers understand it and think about ways that they can help, you know, foster it. So we try to do that in a lot of different ways.
Natalie Danner: So, what kind of early math concepts should young children be learning and practicing in the preschool years?
Dr. Jennifer McCray: So, preschool can mean different things to different people. And a lot happens in these early years. Right? So what a typical three-year-old is ready to do is really different from what a typical five-year-old, you know. So it’s a big range. However, I tend to think of it, as you know. Of course, there’s numbers and the most important thing about numbers, it’s probably getting that cardinal meaning. So I’m going to explain why, and we’ll see if it’s interesting enough to make the podcast, ha. So, when we think about children counting. You know, in our lives, as a little kid, “she can count to five!” Well, what we often mean is that she can say the numbers one to five in order, which is a huge accomplishment and an important accomplishment, and a beginning one for learning to count with understanding. But the key is, can she actually count a set of objects? So take the words and pair them one to one with each object, because counting only works if you count each object once and only once, right? Otherwise it doesn’t work. So you have to get that tagging thing going, and then you have to know that the last word you say means the amount. And just because a kid can count to ten, it doesn’t mean that they understand that five is the number of fingers they have on their hand. So, as a teacher, you want to, you know, see the counting process. See what kids are capable of doing. Do they know the words? Can they do the one-to-one tagging? And do they know that if they count one, two, three, four, five, six, then there are six apples. And so, after they count, you have to say, so how many is that? And there’s a stage at which kids, they say, you say, count these blocks. And they say “one, two, three”. And you say, “how many is that?” And they say “one, two, three” because they’ve learned that when an adult says how many, they’re supposed to count. That’s the appropriate response to the “how many” question and it may mean that they really don’t understand the tricky thing that we use the word three to tag an object, and then we use it to describe the whole amount. It’s a very confusing thing that we don’t do with other parts of language. So that’s a huge one. Okay, but there’s also all other kinds of math. I mean, shape, obviously, is a category that is mathematical. And it’s because it’s about the relationships between spaces and those are all measurable attributes, and so on. When we talk about, you know something being curved or straight, it’s the attributes of shapes, and the fact that they’re defined by rules. Like a square always has equal sides that makes them truly mathematical. But there’s a lot of other math, too. You know, small children can think a little bit about data analysis, which I think is something we might circle back to. Since we’re talking about social studies. They can do patterns. And one of the things at Erikson that we like to make sure doesn’t get skipped over is sets and sorting because it’s such an important experience in terms of the development of logical thinking to be able to categorize and to know what the rules are. You can’t count the apples until you know which ones are the apples and which ones are the oranges? Right? And that’s what a set is. It’s membership in a group that we decide, right? You know, you can count the apples that are red and the apples that are green if you want, or you can count the apples. It’s up to you. So set, and basically, I was just reading about set theory, which is a really high level math field. I think it connects pretty directly to why we want children to experience taking a collection, organizing it into smaller groups and realizing that gosh! That same collection can be sorted another way. Those are powerful experiences. And one thing I will say, too, we tend sometimes to go to numeral writing early.
Natalie Danner: Right hmm.
Dr. Jennifer McCray: I would recommend, there’s just no need. Okay, to help preschoolers learn to write a numeral. Kindergarten is a good place for that, and by that time the fine motor is coming in, and by that time they’ll probably be more familiar with what the numerals kind of look like. A little bit. What you want is the meaning of quantities. You want high levels of familiarity with small amounts: one, two, three, four, and five. The fact that four can be made with three and one. Or it can be made with two and two. Just to see and experience that. Not to be able to turn it into an addition problem, but understanding that there are smaller amounts within larger amounts. This is why the work with the small sets is so important because the ideas are so abstract.
Natalie Danner: That’s great. There’s so many different math concepts there to explore with young children. It’s an exciting field to get into.
Dr. Jennifer McCray: Really, it’s really cool. It’s really exciting. And it’s really fun. And it’s super important that we try to make math fun. That we try not to make people math anxious, right? Because math anxiety is a big problem. So keeping the math joyful, keeping it meaningful and connected to things that children do understand. That’s a big deal.
Natalie Danner: So, speaking of math anxiety, some teachers really shy away from teaching math, due to their own struggles with, or anxiety around, that subject. So what can these teachers do to ensure that future generations of students feel excited rather than anxious about math?
Dr. Jennifer McCray: Right, right, isn’t it? It’s just so unfortunate. But we, you know, if you poll a room about how many people experience math anxiety. You get really high numbers. Some reports over 90% of Americans report some level of perhaps mild or moderate math anxiety. And if you ask people, sometimes I hear this, I heard this from another speaker recently. If you ask people to remember an early experience of shame? And then you say, how many of you did that happen in a classroom? How many of you did it happen with math? You’d be shocked. So unfortunately, right? You know, we in our country and other countries have the problem, too, but I would say, ours is pretty bad. Our math anxiety problems. You know, we learn to not like math, and we learn to avoid it because it’s stressful. So our terrific, wonderful early childhood teachers do not want to pass that on, and I know that because I’ve talked with many of them. But they’re the walking wounded from these horrible experiences they’ve had, right? So first of all, I guess a thing that one can do is commit to never saying “I’m just not a math person”. Just take that phrase, whether it’s true to you or not, and just put it over here on the side. Because when you say you’re not a math person, you’re sort of giving up on the whole field. It’s like, well, you know, I’m not a redhead, so I can’t pretend to pretend to be one. Like no, we are all math people of some kind. Everyone can understand quantity to some extent, and participate in math, and we all do a lot of math in our daily lives, all the time. I think the key for the math-anxious and math-avoidant teacher is to have fun with it, and to emphasize joy. Not to play into that idea that some of us are just going to swim. We can just throw them in the water, and the math water is going to be warm, and they’re going to love it. And some people can’t. No, no, no, no, no. That’s us giving up on a whole lot of students, okay? And everyone in your classroom can learn some math and is a math person. We’re all people, and we all use math just to judge the size of a space, you know, to describe where something is. That’s all mathematical. So those are overly simple. I would also say that the content is actually interesting and a little complex, right? And if you really want to understand it. Professional development in early mathematics specifically can be a life changer. And early mathematics is really different from elementary math, because it doesn’t involve the writing down of things. It’s not about the numerals yet, you know, all the math that happens for preschoolers should be in their words and their actions, and what they see. And you know it’s all very tactile and perceivable in those ways. And it shouldn’t be symbols. We’re not ready for symbol systems for math until a little later.
Natalie Danner: Yeah, great ideas to share with teachers. Now, when we’re talking about lessons and activities, as you mentioned in the end of that question, how might teachers combine math and social studies in preschool lessons and activities?
Dr. Jennifer McCray: Yeah, I really love this question. You guys came up with it. You know, how can we bridge these two fields? It’s great, and of course, I know, and I’m sure you do, too. How many demands are put on preschool teachers these days? The expectations have grown. They continue to grow. It can be assessment, it can be literacy, it can be “here’s a new curriculum,” you know. Please achieve these standards, right? All that stuff is pressure. So having lessons that do help you learn things about what kids know and understand from different content areas can be super helpful. So I started thinking about this question by looking at the Early Learning Standards for social studies and thinking about what is social studies for preschool? Because, of course, that’s not my area of expertise. And what I discovered didn’t surprise me too much. You know, you can’t teach preschoolers about world geography in a way that’s going to make sense to them. Nor is it going to be easy to talk about culture and getting what a definition of culture really is. But there are all kinds of things about being a person in the world, and understanding that people live together and then have to compromise. You know, what it’s like when there’s enough of something or not enough of something. Those are meaningful experiences to young children, and that’s the key right? Is to keep the content something that is within their realm of understanding. So there are some ways that the math can really speak to these meaningful social studies questions, like voting on something. So let’s say there are a couple of different books we could read today, and we decide to vote. And a way to vote with preschoolers that helps is to make the voting really visible. So you give everybody a post-it note or something and each child comes up and puts their post-it note. You know, yes, for this book, or for that book. You could even put them right on the books right? So you’ve got the books sitting up there. My post-it goes here. Yours goes there. When you finish, you’ve got two countable data sets that you can compare. And if you line the post-its up one on top of another, you would actually get a visual representation of the difference between the amounts. Which is bigger? Which is more? Which is less? So, in this instance, you use that sense of magnitude and the comparisons of magnitude to make a choice for your classroom community. Right? So that’s, I think, one nice way that they can dovetail. Another way that I was thinking about, and this goes back to the idea of geography. The beginnings of that are just locating everything in space and being able to talk about it. So up, down, on top of, behind, through and around, you know, one of the things we recommend teachers do is use obstacle courses and talk about what is happening during the obstacle course. Oh, now we’re going through. How could we do something where we go between things? What does that mean? How would we set things up in the classroom so that there’s a place for us to go between the chairs? Again, this is all about relative thinking. It’s about relationships and just getting that spatial language into the thinking of kids. It’s going to be foundational to understanding that, you know, I live in a town, and the town is part of a state, you know, or that the world is round, and you know all these things, right? So I was thinking about that one and I do have one more. I was thinking about the dramatic play area. If you have a dramatic play area where kids are imagining themselves as probably as grownups, right, is what they usually do. So I’m the mom, you’re the dad, or I’m the policeman, whatever it is. A dramatic play area can be a terrific place for counting. Because sometimes you want to set the table, and you have to see if you have enough. Enough is a profound idea. Right? There are three people, and that means we need three plates. And it’s an idea that has everything to do with social studies. Right? Is there enough for everyone? And if there’s not enough for everyone, what should we do? I mean, you know, that’s a terrific question that hopefully classrooms find different ways to engage that all the time. It doesn’t have to be in the dramatic play area right? As a teacher, you know, you’re distributing snacks, or you’re setting up the new art table, and you know you want six kids there. So how many pieces of construction paper do we need? Just making those thoughts and those connections sort of a public property, by describing them to children in a really slow and clear way, and making the connection that if we know that there are going to be six kids, then we need six, and we want one for each one. We need six of whatever it is. Just making that clear makes numbers useful. Right? The kids get to see that it’s not just sort of arbitrary, memorized stuff. It’s something that helps us to function in the world.
Natalie Danner: Those examples were great for preschool teachers that are coming up with ways to teach in their classroom, as well as set out activities that really lend themselves to learning about math and other curricular areas like social studies. So, the first one that you were talking about with the example of voting. I thought that one combines really well with the area of math called data analysis. Now, that sounds kind of complicated. But what does data analysis look like for young children, and you gave an example there of how data analysis could be used as a jumping off point to also integrate social studies, but do you have another potential example for teachers to use data analysis in the classroom?
Dr. Jennifer McCray: Yeah, I sure do. I think the best thing, data means that you’re taking. When we use data as adults, right? We take information, and we sort of mold it, we categorize it, and we summarize it a bit so that we can see a broader picture. Right? That’s what we do, we set the information up so that we can make a comparison of some kind. And so that’s central to the data analysis experience of young children. So the key before it gets too complex is to keep it meaningful to the kids right? You know, so that they don’t lose track of what’s happening because they’re not gonna- they don’t have enough working memory for these new ideas. They can’t keep all of that in their heads. So they need, you know, some handholds. One of the things that we’ve had teachers do. And you can actually find a video of this on our website I think, is a shoe sort. And so you have each of the kids put one of their shoes in a big pile in the middle of the room. And you say, I wonder what kind of, you know, how could we describe the kinds of shoes that we have in our class? There’s so many. How would we say anything if someone said, “What kind of shoes are in your class today?” How would we tell them? I mean, it’s clearly an academic question, but kids will get into it. They love it, I mean, I’ve taken one shoe off and put it in a pile. Great. So then it becomes a process of determining with the children what the categories are going to be. What are we interested in? Do we want to see how many boots, you know? And what does that have to do with the weather? Again, social studies, right? So you develop the categories. And I guess that’s all I’m going to say, because I’ve already talked about the books and the fact that you can use the post-its, right? But there are a couple things, thinking about how many categories you’re going to track is useful with really young threes, I love yes or no questions, or either/or questions, right? Like this book or that book, because then you’re comparing two numbers. That’s all you’re comparing. Just how many for this book, and how many for that book. So a single comparison between numbers is something that the younger kids can do. As kids get older, the shoe sort stuff makes a little more sense, and they can think about how many shoes have laces? How many have Velcro? How many have buckles? Or you know, whatever. You can have three categories or four, and you can have discussions with those kids about how we’re going to categorize our shoes. So there are judgments to make there. But making it meaningful is absolutely central. Right? If the kids don’t, if they look at the data display and a data display is important, right? If they look at it and don’t understand it, then you haven’t accomplished much. And you need to remember, after you put your data together, to talk about what it means you know. Show that you have answered the question that you set out for. Right? Data analysis isn’t just a process with no purpose, you know, it’s purposeful. And having children see that is helpful to them.
Natalie Danner: I love how you described how this particular activity of shoe sorting can be a very different type of activity, depending on what age or developmental level you have in your classroom, and how you can make it a little bit more complex or a little easier, depending on the level and the age group of the students you have, and I think it makes it such a fun activity. Even if you have a multi-age class, you could be asking some of those same questions and getting different points of analysis from the different children that you have in your class. So I think it’s such a great activity.
Dr. Jennifer McCray: Absolutely thanks for that. I think so too. And I think to me it makes clear why it’s important that preschool teachers do understand the math a little more than most of us do. I mean, the understanding of math that I’ve been describing here today are not the layperson understanding of math. It’s not the way, you know, just growing up in the world and living and being an adult, you would think about it, right? It’s particular knowledge that is relevant for the preschool teacher. And there is a world of that. And sometimes I think we think early math is easy, because it’s early. But it’s not. It’s really interesting as heck. And you know, as a preschool teacher, you’re constantly adjusting curriculum. Well, you can do that with math too. But in order to do it, you have to understand what are the challenges for children when they’re trying to learn to count and understand that it means how many, or you know all of those things.
Natalie Danner: Well, as we end this podcast, are there any resources that you would recommend to preschool teachers who want to grow in their ability to teach these math concepts?
Dr. Jennifer McCray: For sure, for sure. First of all, you know, there are a couple of good early math curricula out there. “Building Blocks” has some good evidence that it’s a good math curriculum. “Big Math for Little Kids” also, that’s Ginsberg. That’s a nice curriculum. And a thing with curriculum. I mean, a curriculum really helps. It sort of gets at your own learning through the activities. I think they’re well designed enough that you just sort of implement those activities, and you start getting it. You start being like, Oh, yeah, that’s why we’re doing this. That makes so much sense. However, you can also sort of directly try to address your own knowledge and understanding. Right? We have a book and I’m not about selling it. Okay? In fact, all the money for the book just goes to Erikson, and it’s not, you know, it’s to help further more research about math. It just all feeds back into the cycle. It’s a book called The Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know. It’s a paperback, and it’s not thick, and it has some pictures, and it’s, you know, it’s friendly. And it’s written to help the preschool teacher just have those key concepts in mind. Right? And know some of the tricks and have a lot of ideas. So a book that we’re very proud of. And then we also have a very robust website. It’s earlymath.erikson.edu. And there is no C in Erikson, because it’s Eric Erikson, the developmental psychologist. earlymath.erikson.edu and that website has, you’ll see, there’s a little cloud. This was before the cloud became something else, but it’s a little cloud symbol, and it says “Idea Library.” And if you click there you can find a whole lot of resources that you can, you can use it like an index. You can sort and find something on shapes or something on number, and maybe it’ll be an article that we published in our newsletter. Or maybe it’ll be a video that we’ve used in training, and you can watch it. There’s a lot of really fun videos there, because the kids are so darn cute and because it’s fun to watch really great early childhood teaching. I think. So, I encourage people to go to the site and see if there’s something there that can be useful to them.
Natalie Danner: Great. Well, we will share all of those resources at the bottom of our webpage. If you’re listening to this on the Illinois Early Learning web page, you’ll be able to scroll down and find these resources.
Dr. Jennifer McCray: Yay, that’s so good.
Natalie Danner: I know, and I’m excited about it, too, because these books I’ve heard of some of them, but not of all of them. So I want to do some research on my own to read more about early math.
Dr. Jennifer McCray: Excellent.
Natalie Danner: I just wanted to thank you. So many helpful tips have been shared here about early math and I just wanted to thank you, Dr. McCray for being our guest on the Illinois Early Learning Podcast.
Dr. Jennifer McCray: Well, thank you. You know I now know a lot more about what you’re doing at Illinois Early Learning, and I’m impressed. I think you’re doing important work, and I love your website, and I really appreciate you taking an interest in the topic.
Natalie Danner: Thank you.
Dr. Jennifer McCray: Yeah.
Natalie Danner: And I know all of our listeners will be very excited to learn more about early math as well. So until next time, thank you and keep early learning at the forefront.
You have just heard a podcast by the Illinois Early Learning Project. For more information, please visit us at illinoisearlylearning.org where you can find evidence-based, reliable information on early care and education for parents, caregivers, and teachers of young children. Thanks for listening and for helping the children in your home, classroom, and community have a strong start in their early learning.
IEL Resources
Resource List: Math for Preschoolers