The Benefits of Everyday Math for Kids

APS’s Özge Gürcanlı Fischer Baum chats with Melissa Libertus from University of Pittsburgh about her new article about interventions to increase math learning in children. They discuss various strategies parents can use to reinforce the development of math skills in everyday life like at the grocery store or using board games. 

Send us your thoughts and questions at  [email protected].

Unedited transcript

[00:00:00.000] – APS’s Özge Gürcanlı Fischer Baum

Having numerical skills is important in life. Before children start school, there is significant variability in their mathematical skills. What can be done at home to support children? What type of parental activities can make a difference in their math proficiency? What are the learning opportunities out there? This is under Under the Cortex, I am Özge Gürcanlı Fischer Baum, with the Association for Psychological Science. To speak about activities designed to facilitate math learning at home for young children, I have with me Melissa Libertus from University of Pittsburgh. She is the author of an article published in Current Directions in Psychological Science, examining the Relationship between foundational numeracy skills and parental Interventions. Melissa, thank you for joining me today. Welcome to Under the Cortex.

[00:01:00.520] – Melissa Libertus

Thank you. Great to be here.

[00:01:02.900] – APS’s Özge Gürcanlı Fischer Baum

Yeah, we are very happy to have you, too. I want to start asking, what got you interested in studying children and how they learn?

[00:01:11.830] – Melissa Libertus

This is a really good question, and it started I did it a long time ago. I first started tutoring when I was in middle school. At first, it was just other students in my class who came over to my house after school to get help with homework. Over time, the teachers asked me to help students in other classes and who were struggling. And by the time I finished high school, I probably had about 10 to 12 students who regularly saw me for extra lessons, and most of them needed help in math. And what fascinated me about this was that for some students, It was just some extra practice that they needed. And other students, they really struggled understanding concepts. And so I came up with ways to explain the same concepts in different ways to them until it finally clicked. I got really interested in how it is that children sometimes struggle understanding different concepts, especially in math, and how we can best support them to learn what they need to succeed in the long run. I really wanted to know more about what these foundations are that set up children for success in math.

[00:02:26.960] – APS’s Özge Gürcanlı Fischer Baum

Right. First, I want to say it’s an impressive number of students that you held when you were younger, and it feels like it was like a natural experimental setting for you to observe differences in your friends at the time. Yeah, thank you for sharing that story with us. I want to continue with a very generic question, but I think it is important for us to have these conversations. Why is early math literacy for children important? What is the early stage, according to developmental researchers?

[00:03:02.040] – Melissa Libertus

Yes. Ample research has shown that early math skills are predictive of a host of later life outcomes. For example, Richie and Bates showed that early math abilities at age seven predict socioeconomic status at age 42, even when you control for socioeconomic status at birth. And similarly, Pamela Davis-Keen and colleagues showed that math skills at four and a half years of age predict later high school math class and ultimately college enrollment. And importantly, math skills in this study were measured before children start formal schooling, which emphasizes the importance of fostering math skills long before children start learning in a formal setting. So what do these math skills prior to elementary school look like? Math concepts for very young children start from birth. So research by Fais Hsu and Laspalki and others in the early 2000s showed that even young infants possess a basic understanding of quantities already. For example, if you repeatedly show a young infant images that have the same number of objects and they get habituated to seeing, say, images that have eight dots on them over and over, and then you show them a picture that contains 16 dots, they tend to look longer at those.

[00:04:27.540] – Melissa Libertus

What we know is that these A basic understanding of quantities is something that children have long before they acquire the verbal skills and the language to really describe what these quantities are and to count them, obviously. And so 10 years ago, Ariel Star, Liz Bryant and I, showed that individual differences in infants’ early approximate number abilities is predictive of children’s math abilities at the age of three and a half. And then as children acquire language, they slowly learn the meaning of a number of words. And most of the documented evidence for this development currently comes from toddlers who learn English. And for example, in her seminal work, Karen Wyn showed that around 30 months of age, many children are able to correctly give one object when you ask them for exactly one. But they are unable to give two or three objects when you’re asking them for two or three, and instead, they might just grab a handful. And it takes a couple of months after learning the meaning of this number one, that children are then actually able to also correctly give two objects when they asked for two, and then it takes several more months until they can correctly give three objects when they asked for three.

[00:05:48.040] – Melissa Libertus

It takes a really long time for children to get this exact understanding of these number words. It’s around four years of age that many English-speaking children are then finally able to create sets of specific numbers of objects when given a specific number word. Those are the early stages of math learning, but there are other things to it, too. Young kids do learn to understand what more and less means, and they learn to see patterns in shapes and numbers around them.

[00:06:26.480] – APS’s Özge Gürcanlı Fischer Baum

You gave us a list of very important pieces of information. Let me repeat them for our audience. We are clearly born with some skills for quantitative knowledge. But from research, we know that the challenge lies in tying it to our language. When children do nonverbal tasks, they are quite skilled at these numerical skills. But when we see them using language with maths, it is a slower process and slow progress, in fact, for them to get to regular counting or using numbers in the ways that we do. What I hear is that everything is interconnected. Even though we come to this world with some quantitative skills, there are challenges ahead of us, which brings us back to your interventions, I guess. Let’s I’ll talk about them a little bit. So your paper is very comprehensive. I really enjoyed reading it. You go over two different theories that scientists use. Can you go over what they are?

[00:07:44.670] – Melissa Libertus

So there are two main theories that play a role in thinking about math interventions, especially in the context of early childhood and the home setting. The first one is the Opportunity Propensity Model, and the second one is the Sociocultural Theory of Development. The Opportunity Propensity Model was originally put forth by James Burns and colleagues, and it suggests that academic achievement is a product of opportunities to acquire content knowledge and practice this knowledge, as well as a learner’s propensity to benefit from these opportunities. In the context of math learning, this means that children need opportunities to learn math concepts. We might be born with a very basic, rudimentary understanding of quantities, but we really need opportunities to sharpen and really arrive at an exact understanding of numbers. This can happen in a classroom where a teacher introduces the concept, But also it can happen in the home when a parent guides a child. For example, you might be counting how many blocks they each have and who has more and who has less. It can happen during everyday situations, like when a child finds a penny on a street and the parent points out that this is a penny and it’s worth less than a dime, for example.

[00:09:08.360] – Melissa Libertus

But at the same time, this opportunity propensity model also highlights that children have to bring some propensity some skills to the table. They need domain general cognitive skills. Obviously, they need to have language skills. They need to be attentive to remember what was said. So attention and working memory are key. But they also need to have some basic understanding of numbers than to build concepts like more and less. Then on the other hand, we have the sociocultural theory of development championed by Barbara Róhoff and others that It’s that children learn through participation in everyday activities that are embedded in their communities. Children grow up in communities where people use math for different purposes. Children might participate in meal preparation in their family, which requires to set the table and count if there are enough plates and utensils for everyone. They might help with cooking and measuring ingredients. They might go shopping or maybe even sell family’s goods and thereby learn about the value of currency. Children’s opportunities to learn math are tightly coupled to the cultural context in which they grew up and how math may be embedded into that setting.

[00:10:26.350] – APS’s Özge Gürcanlı Fischer Baum

When I think about these cultural opportunities, in a way, I’m always thinking about Halloween or other holidays in Turkey during Eid. I used to receive candy, and my brother, he’s older, tried to take them away from me, and I had to be really good at math, knowing how many candy pieces I had. So yeah, great theories, and you explained them really, very nicely for us. In your paper, you talk about different types of interventions that parents could use at home to help their children to think more about math, to use math more? Which would you say is your favorite and why?

[00:11:14.250] – Melissa Libertus

My favorite and why? My personal favorite is to integrate math into grocery shopping. I think there are so many opportunities, and they can also easily scale with the child’s math abilities. Initially, with a young child, grocery grocery shopping provides an opportunity to count the number of tomatoes you want to buy or the number of apples in a bag, or to identify Arabic numerals on prices and to point them out. One can use this also as an opportunity to compare weights of items and to weigh the bag of apples to see, is this really three pounds in the bag? Or to take different-size tomatoes and see how much each Then as children get older, shopping provides a great opportunity to learn about money, which is a really complicated concept for kids initially, because why is it that one green bill is only worth $1 because there’s a one printed on it, but then I can have another bill that has a two and a zero printed on it, and that’s now $20. It’s also just one piece of paper, so to speak. Teaching children these abstract values and obviously being able to do arithmetic in the context of money.

[00:12:38.590] – Melissa Libertus

Then as children become even older, there are decimals in prices. You can figure out how much something What does something cost if there is a 10% discount on it. I think there are just a whole host of opportunities for children to practice math skills in this context and to really also see how important it to know math and to be able to do it exactly. It’s not helpful if you can do it, but you actually should know if the change that you got back is correct or not.

[00:13:13.080] – APS’s Özge Gürcanlı Fischer Baum

If you want food, you need to know your numbers, basically. Yeah, that’s a great example. There are other examples, options of interventions in your paper. One option was a numbers-based board game. What games are those and How do they learn and practice numbers using this particular game?

[00:13:35.220] – Melissa Libertus

Yes, most of the board games that have been used in research studies are actually very similar to shoots and letters and other commercially available board games like this, where you have a player roll a die or spin a spinner and advance across the board, and whoever reaches the goal first wins. But what’s key here is that along the way, children can practice counting number of steps they are allowed to advance. In one of our own studies, my postdocs, Andy Ripner and Leon Elliott, as well as my graduate student, Alex Silver, asked parents to play a number board game twice a week for eight weeks. On this board game that we used, we had 65 fields, and parents were instructed to label the numbers that were on these spots as they and their children were moving their tokens across the board. If you had your token on the spot number 23, for example, and you spun a three, you would say 24, 25, 26. Children not only counted and learned the small numbers that were on the spinner, but children also read and heard the labels of these double-digit numbers that were printed on the board.

[00:14:47.990] – Melissa Libertus

We think that those are natural ways where kids can practice age-appropriate counting and numeral literacy skills, where they just get to repeatedly read and count and say out these number words in the context of playing a fun game with a parent.

[00:15:07.310] – APS’s Özge Gürcanlı Fischer Baum

You said they did this intervention twice a week for a long time, and the outcome was helping children, right?

[00:15:18.510] – Melissa Libertus

Yes, exactly. In the study, we found that children who played this board game with their parents repeatedly for these eight weeks had greater math skills after this intervention compared to children who played a board game that didn’t include this number P. They had different shapes on the board instead, and they spun a spinner that told them which shape to advance to next. A very similar game, yet it did not have the number-based focus.

[00:15:53.660] – APS’s Özge Gürcanlı Fischer Baum

Yeah, that’s impressive because two months is not a long time. The The game sounds like fun and it is quality family time. They get to hear numbers and it helps with their math skills. That is what is not to like about this intervention. Yes. There’s another one. Another strategy was reading number-based books, but for this one, benefits didn’t last at the two-month follow-up, right? Why do you think that is? Do you think the children didn’t retain knowledge or that the control group caught up? Or why do you think this is different from the board game that we just talked about?

[00:16:37.870] – Melissa Libertus

The specific study that you were referring to here was done by David Purpura and his group at Purdue University. They asked parents to read picture books with their children four times for four weeks. Half of them received books with math content, and the other half read similar books without the math content. What they found is that children in the a math book group showed significant improvements in comprehension of math language, so words like more and less, least, and enough, immediately after the intervention compared to those children who read the other books that didn’t have math content. However, then this effect was no longer present eight weeks later. But when they did detailed follow-up analysis, they found that there were still improvements, even two months later, when they looked at the specific math language that was covered in the picture books. And so there are some benefits that do get retained. Importantly, I should point out that children in the math book group also showed significant improvements on a standardized math assessment compared to the control group, and that effect was present immediately after the intervention and also still eight weeks later. So I think in some of these findings suggest that children do indeed benefit from reading such math picture books and that these effects can last beyond the immediate intervention period.

[00:18:12.000] – APS’s Özge Gürcanlı Fischer Baum

The benefits can vary, right? Depending on what the activity is. There are multiple ways to test the benefit after these interventions. Exactly. Yeah, thank you. Thank you for your explanation for that. Let’s talk about parents’ attitudes towards math a little bit because not everybody loves math. This is, I think, something true across cultures. How do parents’ attitudes towards math impact their children’s math learning?

[00:18:42.660] – Melissa Libertus

Yes, this is an excellent and somewhat understudied topic because there are a number of different aspects that need to be considered, too. For example, as you rightly point out, parents’ own affect toward math plays a role. Some people experience math anxiety, for example. They get really nervous or show negative physical responses when they have to solve math problems. And there’s been some really interesting research by Susan Labine and colleagues at the University of Chicago that show that parents with greater math anxiety tend to have children who perform worse in math. And importantly, they found that parents’ math anxiety is particularly detrimental if math-anxious parents help their children with math homework. But on the other side, they also found found that when parents who were math-anxious were given explicit guidance on how to engage with their children by using a math story app, that those children’s math performance then increased as much as the math performance of children of low math-anxious parents. Parents’ attitudes can impact children’s math learning, but that can be offset by giving parents the right guidance and tools to overcome that anxiety, at least at these young ages that we’re talking about today.

[00:20:06.940] – Melissa Libertus

But then I think math anxiety is also just one part of the story, because I think the other part is really that parents’ beliefs about the importance of math and other related beliefs. How about who’s responsible to teach a child math or what role the school plays versus the home? That’s important, too. For example, my graduate student, Alex Silver, and my postdoc, Leon Elliott, and I found that parents’ beliefs about the importance of math interacts with their math anxiety. We found that parents with high math anxiety who believed that math was particularly important, had preschoolers with above average math performance, whereas parents who rated math as less important had children with lower than average math performance. And in contrast, if you looked at parents with low math anxiety, the beliefs were not associated with children’s math outcome. So what I think is key here is that when parents have really strong beliefs about the importance of math, then they are trying to seek out opportunities for their child to learn math, even if they themselves don’t feel comfortable, or especially if they themselves have math anxiety because they might not want to transmit that anxiety to their children.

[00:21:28.290] – APS’s Özge Gürcanlı Fischer Baum

What I hear from I guess the first part of your answer is that parents themselves sometimes need an intervention about their anxiety about this. If it is addressed well, it benefits both the parents and also children. It is something important to know for our listeners.

[00:21:48.030] – Melissa Libertus

Yes.

[00:21:49.030] – APS’s Özge Gürcanlı Fischer Baum

I would like to ask you a little bit more about what science says in general about these interventions. Is there a consensus about what How does early interventions work? Should we be trying some different approaches? What are your thoughts about that?

[00:22:07.630] – Melissa Libertus

I think that research demonstrates that parents are indeed capable of providing children with opportunities to learn math, and especially increase that when given appropriate instructions or materials, and that those interventions often lead to improvements in children’s math. I think it’s really important to highlight that parents don’t need a lot of training or extra time or resources to provide their children with opportunities to learn math. I think that’s the beauty that math is everywhere and can easily be integrated into all sorts of different activities. My Bachelor of Philosophy student, Erin Hannah, for example, showed that simply putting up signs in grocery stores that provided adults with simple prompts for math conversations with young kids, such as saying, How many eggs are in a carton? Or, How How many would be left if we each ate two? Are sufficient to get more adults to talk about math with their children while they are shopping. And importantly, Sue Hasposs and I replicated these findings in a food pantry, showing that this can be done anywhere and everywhere. So I think this is really key that we just need to nudge adults and parents just a little bit to see the opportunities to integrate math into the everyday activities that they are already doing with children.

[00:23:30.960] – Melissa Libertus

I think that failures to sometimes find improvements in children’s math abilities in some of those rigorous research studies are no reason to abandon these interventions or these ideas. Instead, I think that future research should carefully consider how children’s skills align with the intervention activities and which families in which contexts may benefit the most from the interventions. I think making the interventions meaningful for families’ lives and something that they see value in, that they can integrate into things that they are already doing, are key to really giving kids the opportunities and in the long run, benefiting from it. I think The other piece that’s tricky with some of these intervention studies is that oftentimes, durations and dosages may not be aligned with what’s best to find the effects. Then obviously, it also takes time to consolidate the skills and for children to integrate the skills that they may have learned through these interventions. Different children may take different amounts of time to do so. Oftentimes, these intervention studies have a one-size-fits-all. You’re doing this four times a week for four weeks. You’re doing this for eight weeks. That might not work for everybody.

[00:24:53.560] – APS’s Özge Gürcanlı Fischer Baum

I want to just repeat what you said because it is very important. There is no one-size-fits-all solution solution to this. We should pay attention to what families, in what context we should address. All these different interventions and approaches you have been talking about, focus on making this part of everyday conversation. It doesn’t have to be a separate math time that needs to happen in already busy schedule lives of parents.

[00:25:26.730] – Melissa Libertus

Exactly. Absolutely, yes.

[00:25:29.250] – APS’s Özge Gürcanlı Fischer Baum

Yeah. I would like to ask if you have anything else to add to share with our listeners about these parental interventions.

[00:25:41.160] – Melissa Libertus

Yes, absolutely. I think if you have young children yourself or regularly interact with them, find ways to point out math, see the opportunities to make comparisons like more and less of finding patterns, identifying shapes, counting forwards and backwards, we’re skip counting, we’re making up arithmetic problems. I think we also need to raise people’s awareness that it’s important to integrate math concepts in these conversations, that it’s not too early to start exposing young children to math, that we don’t have to wait for them to start kindergarten or first grade. Because these days, more than ever, we need people with problem solving skills and STEM skills, and those are the people who ultimately get the jobs that are out there. We need to prepare our children today to be ready to join the workforce tomorrow.

[00:26:43.210] – APS’s Özge Gürcanlı Fischer Baum

Yeah, let’s make Matt part of everyday conversation to support children and to support their quantitative skills. Absolutely. Melissa, thank you very much. This was a pleasure. All these questions you answered, I would like to thank on behalf of our listeners.

[00:27:03.960] – Melissa Libertus

My pleasure. Thank you so much.

[00:27:06.640] – APS’s Özge Gürcanlı Fischer Baum

This is Özge Gürcanlı Fischer Baum with APS, and I have been speaking to Melissa Libertus from University of Pittsburgh. If you want to know more about this research, visit psychologicalscience.org. Would you like to reach us? Send us your thoughts and questions at [email protected].