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Early Numeracy in the Children's Library

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Early Numeracy in the Children's Library

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Math is all around us and is inextricably woven into all of the physical and social worlds we inhabit. Just like literacy, numeracy actually begins at birth. Early numeracy refers to the development of all the mathematical reasoning that children learn during their early childhood years, before formal schooling begins. Early numeracy can be conceptualized into these three main concept areas:

Number sense

Shapes, sizes, spatial awareness

Patterns, sets, sorting and measuring

Similar to early literacy skills, these early numeracy concept areas often overlap and reinforce each other. Let's take a closer look at each one:

We see number sense in early childhood when young children start to understand that numbers refer to specific amounts. This might begin with watching their caregiver's fingers during songs like 5 green and speckled frogs. Children's number sense becomes more sophisticated and eventually leads to simple operations like the ability to add and subtract small amounts. Pausing your storytime to ask the children "how many frogs still need to jump into the pool?" will encourage their number sense in a very fun way.

Understanding the features of different objects' shapes and sizes helps tobuild children's overall spatial awareness and eventually supports the growth of geometric thinking. Block building play, especially with block sets that contain various shapes (squares, rectangles, triangles etc.) supports children's understanding of shapes and spatial awareness. Hands-on experimentation with blocks can help children learn how shapes fit together, how they can be taken apart, rotated, flipped, and how to problem-solve in 3 dimensions.

When you start looking, you will see opportunities for young children to learn about patterns, sets, sorting, and measuring everywhere. Patterns are apparent in children's lives from day one. For example, daily routines are essentially patterns that children learn to expect to unfold in fairly predictable ways. While the sun rises and sets each day, getting dressed and getting fed happen each day, too. Patterning soon extends to noticing visual patterns like stripes of different colours on their clothing, and the parts that make up cumulative stories like The Very Hungry Caterpillar.

Everyday objects like blocks, balls, cars, shoes, etc. offer endless opportunities for sorting objects and children become more and more sophisticated in their abilities to categorize things differently as they grow. For example, rocks, leaves, sticks, keys, and coins can all be sorted into sets by their sizes, colours, shapes, textures, and weights. Homes are full of objects just waiting to be sorted by little hands and kids love sorting stuff!

Measurement concepts begin with the ability to compare the sizes of different things. Before they learn standard measurements like inches or centimetres, children can have fun using their own hands to measure how big something is compared to something else. For example, a toy kitten might be only 2 hand-lengths high while a toy dog might be 10 hand-lengths high. They will love this kind of hands-on math play.

Early Numeracy in Picture Books

Not surprisingly, the books in our libraries offer superb opportunities to play with math and support early numeracy. While counting books are great, you can find rich, specific mathematical concepts in many picture books. I would like to introduce you to three of my favourite early numeracy picture books.

Mouse count written and illustrated by Ellen Stoll Walsh

10 little mice need to work out how to escape the confines of a jar before the snake who captured them wakes up for his mousy meal! You can easily extend this story with a real jar and toys of different sizes. This book supports the early numeracy skills of counting and estimating.

Stack the cats written and illustrated by Susie Ghahremani

Ten cute cats stack themselves in different ways to figure out the best ways to sleep and play. I found it very easy to make flannel version and I can assure you that your storytime kids will enjoy stacking, counting, adding, and subtracting the cats. This book supports the early numeracy skills of counting, adding, and subtracting.

Up to my knees written and illustrated by Grace Lin

In this delightful introduction to relative size and measurement, a small child measures a plant by comparing its changing height with her own toes, knees, & shoulders. Eventually the plant, revealed to be a sunflower, towers over her. Adorable! This book supports the early numeracy skill of measuring.

What YOU can do!

Point out these kinds of math-rich books at storytime and - if possible - demonstrate extension activities with toys, puppets, flannel pieces or other objects and materials, depending on the book. Modelling simple, fun math activities like sorting and measuring stuff may encourage caregivers to try new things at home.

Early numeracy learning opportunities are supported by many of same practices that encourage early literacy such as reading, playing, and talking. Since you already talk about the benefits of these practices, you can easily include some early numeracy tips wherever they fit into your conversations with grown-ups.

If you're attending ALA Annual 2024 in San Diego, we'll be discussing early numeracy at the Preschool Services Discussion that will take place on Sunday, June 30 th 2024 at 10:30am-12:00pm at the Marriott Marquis, Grand Ballroom, Section 5. I hope to see you there!

Additional Resources
Balance in storytime Early Numeracy (PPT presentation by Laurie Danahy, Oregan Head Start) Enhancing Storytime to Build Children's Math Skills (Mother Goose on the Loose Webinar) Erikson Institute Early Math Collaborative Family Math
Finding the Math in Children's Storytimes
Incorporating Math Literacy into Storytime and Other Programs Integrating Technology into Public Library Programs with Bedtime Math Symmetry in Storytime What are your favourite early numeracy resources, activities, and books? Please add them in the comments!
This post intends to address the following Competencies for Librarians Serving Children in Libraries:
I. Commitment to Client Group, III. Programming skills, and IV. Collection Knowledge and Management

Tess Prendergast worked as a children's librarian for 23 years. She has a PhD in early literacy education and now teaches librarianship and children's literature courses at The School of Information, University of British Columbia, in Vancouver, Canada. She currently facilitates the ALSC Preschool Discussion group and has served on both the Geisel (2023) and Caldecott (2016) committees.

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Early Numeracy in the Children's Library - ALSC Blog

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Early numeracy learning opportunities are supported by many of same practices that encourage early literacy such as reading, playing, and talking. Since you are already talking about the benefits of these practices, you can easily include some early numeracy tips wherever they fit into your conversations with grown-ups.

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Incorporating Math Literacy Into Storytime and Other Programs

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Incorporating Math Literacy Into Storytime and Other Programs

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Incorporating math and science into storytime is something I've always tried to do, especially when I was in outreach, but I've realized it's not something everyone thinks of, or knows how to do. Or maybe you are doing some of these things anyway, and just hadn't really connected them to math or science. After seeing an article with a list of children's books to encourage an interest in math, I've been thinking more about ways to incorporate math and encourage a positive attitude about math, and trying to be more purposeful in incorporating math into storytime and other programs.
Now if you're thinking "oh, great, something else I have to worry about doing in storytime...", I get it! First storytime was just about reading stories, then it was about early literacy skills, then we had to add parent education and passing along development and early literacy information, and now we're talking about adding math!
It is challenging to try to include so many different elements in 20-minute storytime, b ut some of these you are likely already doing anyway, and others are easy to incorporate. Plus, I'm a big believer in starting small, and that you don't have to do ALL the things every time. So try them every now and then, and as you get more familiar and comfortable with them, look for ways to incorporate them more often.
First, I'll start with some of the more obvious and work to some that are less obvious:

Counting Books - There are lots of counting books, some better and more interesting than others. Keep the age of the audience in mind. For babies and toddlers, counting up from 1 to 5 or 10 is enough, but for older kids, look for books that count up to 20, and for books that count down. One that comes to mind I really like for older kids is Chicka Chicka 1, 2, 3 by Bill Martin, Jr., Michael Sampson, and Lois Ehlert. This introduces "skip counting", or counting by ten's up to 100. Also keep an eye out for books that have an actual story, as opposed to just counting, like Ellen Stoll Walsh's Mouse Count.

Counting Songs & Rhymes - Again, for preschool and up, be sure to include rhymes and songs than count down as well as up, and try to use more that go up to/down from 10 and not just all the "Five Little..." somethings (though those are still good, too). Whenever I do the "Ten Little..." something song, I always do a second verse counting back down from 10 to 1 (this is also good for fine motor skills, as is repeating the "Five Little" somethings using the non-dominant hand).

Shapes - The obvious connection here is geometry, which is true, but any type of activity that involves categorizing and classifying things involves mathematical thinking and is a pre-science skill as well. There are not a lot of great shape books, but two that I have used a lot are Shape By Shape by Suse McDonald (even though she got the Brachiosaurus' teeth completely wrong) for younger kids and Circle, Square, Moose by Kelly Bingham for older kids. Tangled: A Story About Shapes by Anne Miranda and Eric Comstock is a newer book that looks promising.

Aside from books and simple shape identification activities, other activities that could be incorporated during storytime or as part of a craft or playtime afterward are flannel boards with all different felt shapes kids can play with and put together, crafts using cut-out shapes to make collage pictures ortangrams, magnet board shapes, good old-fashioned wooden building blocks that come in different shapes, and various shape-sorter toys. Encourage parents to point out shapes in real life, like signs, windows, doors, wheels, etc. There are several books that involve identifying shapes in the environment, but City Shapes by Diana Murray is particularly nice, and Bryan Collier's illustrations are lovely.

An example that we frequently use are the counting up and down rhymes with the "Five Little" somethings, where we add or take away things one at a time. Look for stories that have this element as well, and reinforce it. Essentially, all the counting up stories and rhymes are doing addition, and the counting down ones are using subtraction; we just have to be intentional about pointing it out and describing it using those terms.Introduce Addition & Subtraction Concepts -

by Eric Litwin and James Dean, which counts down from four to zero as Pete loses each button and shows the subtraction equations.Introduce Addition & Subtraction Equations - For preschoolers and up, occasionally show them the written equation and talk them through what the symbols mean and how it represents the situation just described. Two books that are great for this are Little Quack by Lauren Thompson and Derek Anderson, which counts up from 0 to 5 and showing the addition equations, and Pete the Cat and His Four Groovy Buttons

Sorting & Matching - There are any number of items you can provide to have children sort and/or match by color, size, shape, or any other characteristics. This can be done with flannel or magnetic boards or with physical objects. A favorite activity of one of my volunteers was leaf-sorting using foam leaf cutouts that could be sorted by color, shape, or whether they were sparkly. This Attribute Apple set is great, too; it has apples in three sizes and colors, some with leaves, and some with worms, so there are many different criteria by which to sort them. This is also a great pre-science activity, and using a pincer grasp to sort small objects makes it a pre-writing activity as well!

Patterns - Just like sorting, you can using various characteristics and activities to explore patterns using flannel pieces, blocks, beads on a string, and more. Seeing patterns is an important skill in mathematical thinking (think statistics, coding, data analysis, etc.). And again, manipulating small objects with a pincer grasp, as with stringing beads, is also great for writing.

Spatial Relationships - Think directional terms and prepositions! Up, down, on the table, in the basket, over the rainbow, beside the chair, under the blanket, over there, etc. Use these to be descriptive, and ask questions that will elicit similar descriptive terms from the children. Also relative size and position, such as bigger than, smaller than, higher, lower, farther, nearer; big, bigger, and biggest, etc. I bet you already do this without realizing it relates to math as well as expressive language! The Berenstain Bears' Inside Outside Upside Down and Jez Alborough's Tall come to mind.

And of course for a hands-on activity, it's hard to beat building with blocks for spatial relationships, but a treasure hunt where they have to follow directional instructions as well as relative descriptions and counting is a really fun way to incorporate several math skills.

Measurement - Have kids measure and estimate things - quantity, length, height, weight, volume. One activity I have used, since we are in the middle of horse country, is tape a row of handprint cutouts up the wall and have the kids guess how many hands high they would be, then measure and see. This is a great science activity as well.

Graphing - This activity is probably best for ages 5 and up, who have started to develop a greater sense of symbolic/representational thinking. This is simple to add onto any of the sorting or counting activities you do by just drawing a simple bar graph to represent your totals, and explaining how each unit of the bar represents 1 whatever you are counting.

Again, don't feel pressured to incorporate math into every single storytime, but just try to be a little more mindful and intentional with some of the activities when you can. Some are a little easier to do than others, and it does depend on the age of the kids. And if you aren't able to fit it into storytime as much as you'd like, then try to sneak it into other programs.

And to help, here are some links to various lists of books that relate to math in a positive way, and most are nicely categorized:

For more ideas for activities:

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Incorporating Math Literacy Into Storytime and Other Programs

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Easy ways to incorporate math literacy into storytime and other programs, with suggested books, activities, and links to more resources.

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If anyone were to go back in time and tell my high school algebra teacher that I was running math programs for preschoolers, I think he would have laughed in your face! I was SO not a math kid. Fast forward quite a few years. As an elementary school teacher, I had the opportunity to earn a post-Master's certificate as a Math Specialist. This program taught me to look at math differently. And different turned out to be very, very good. I'm still not a math whiz, but I love highlighting math content in my storytimes and preschool outreach programs.

In this post on my Preschool Outreach Programs, I'm going to highlight a pre-algebra program I offered to preschoolers. Algebra, to some extent, is about balancing two sides of an equation.

2x + 7 = 35

Think of an equation like a scale or a balance. What does x have to be to make 2x + 7 equal/balance with 35? If I think x is 100, then the left side of the equation is "too heavy." If x is 2, then the left side is too light. But if I think x is 14, then my scale rests balanced comfortably. While preschoolers aren't necessarily going to grasp those complex specifics, they explore the idea of equivalence using their bodies, a book, and a balance.

Program Plan

Bodies: We began by interacting with the concept of balance in a physical sense. First, we stood as we were able and balanced on two feet spread apart and then on one foot. We discussed which was easier and why. Words like "stronger" and "wobbly" were used to describe the two experiences.

Book: Next, we read Balance the Birds by Susie Ghahremani. We followed the reading with a discussion:

Why were the birds able to balance?

What happened when the owl appeared in the story?

The tree needs to have its two sides carry the same weight.

Sometimes the same weight can be represented by different numbers of things (2 birds = 2 birds, but 1 owl = 6 birds)

Balance: Then, we experimented with a balance from Kodo Kids. I distributed weighted teddy bears that were of three different sizes and three different weights.

The students had to figure out how to make the two sides equal. Each group of students had an 11×17″ piece of paper with an image of a balance. They placed their teddy bears onto the two sides of the paper and then tested their hypothesis with a turn at the actual balance. As more tests happened, more information was gathered, and eventually most groups were able to create a balanced "equation."

Lastly, we got more abstract! I shared with them that when we say or write 4 + 1 = 5, that the equal sign is like the middle of the balance. We used hash marks to explore equivalence as well. I drew the following on a whiteboard and asked them to help me "balance" the equation.

| | | + ? = | | | |

The preschoolers loved doing this work, especially when I told them that they were doing Big Kid Math!

Next Steps

On the handout that went home after any of my outreach storytimes or programs, I shared ideas to help adults continue the learning at home. From exploring physical interactions with balance (can you balance a pencil on your fingertip?) to playing with mathematical equations, the ideas hopefully inspired more math explorations at home.

How do you incorporate math into your storytimes? Do you have any favorite math picture books? I'd love to hear from you in the comments!

This post addresses the following ALSC Core Competencies: I. Commitment to Client Group, III. Programming Skills, and V. Outreach and Advocacy.

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Preschool Outreach Programs, Part 3! - ALSC Blog

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If anyone were to go back in time and tell my high school algebra teacher that I was running math programs for preschoolers, I think he would have laughed in your face! I was SO not a math kid. Fast forward quite a few years.

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Finding the Math in Children’s Storytimes 

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Finding the Math in Children’s Storytimes 

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In Massachusetts, the children's librarians at Worcester Public Library (WPL) are weaving math learning into story times. Math, at the library? With toddlers and preschoolers? The answer to both questions is a resounding, YES!

Since 2019, WPL has been our valued partner in Education Development Center's Young Mathematicians (YM) in Worcester project, a Family Math initiative funded by Heising Simons Foundation, Overdeck Family Foundation and the National Science Foundation. Their work to bring math into the children's room is adding up for kids.

Research shows that Early Math Matters! Preschool children's mathematics understanding significantly predicts school achievement over and above reading skills and attention skills. This research has WPL librarians buzzing about ways to tweak their story times to bring out the math.

https://youngmathematicians.edc.org/math-topic/spatial-relations/ " Mathematizing" story books." Co-author Rebecca Raineri hosts a STEM Storytime every Friday morning at WPL's Frances Perkins branch. A former teacher, Rebecca has embraced the notion of mathematizing-noticing, bringing out, and talking about the math around us. She plans story time activities that not only help promote children's literacy skills and love of books, but also bring out the math in what they are reading or doing.
Caleb, Grace, and Ari walk around the small reading room searching for hidden shapes. They have their fingers curled around their eyes as if using binoculars. Caleb shouts, "I found a triangle." When Rebecca asks "Where..." Caleb points and answers, "There," to which Rebecca responds, "You found a triangle inside the basket. And we know it's a triangle because it has three straight sides. Can you find more shapes?"
This shape hunt activity-and reading books about shapes during story time-helps children recognize and describe shapes, an important foundation for later math knowledge.

Other examples of mathematizing storytime include:

Narrated field trip. Librarian Katherine Maher, Children Services Librarian invited children to go on a " Field Trip" to the big window. The children followed Katherine as she headed to the window while narrating her route: We are going past the round table. Now we are walking between the book stacks. We are turning right and walking straight toward the window. Look how close we are. Yay, we made it.

These simple activities help build the children's spatial understanding and spatial awareness - critical early mathematics skills.

After many years of facilitating story times and now bringing in early math, the WPL librarians have learned a lot and offer these five tips:
Be prepared

Pre-read the book and look for ideas to help children notice math vocabulary and math. For example, Small Walt saw a hill ahead- it was a high, high, hill. Can you raise your arms high, high, high?

Have space and materials ready. For example, during a reading of Walter's Wonderful Web , Rebecca held up construction paper shapes she'd gathered earlier to correspond with the shapes in the text.

Include movement
Young children have a tough time staying still for long periods. Adding movement helps keep them engaged. One way to do this is to reference ideas from the story. For example, " Let's turn around two times (hold up two fingers) just like Angelina did."
Take it slow
Slow down while reading. Point to and discuss pictures. For example, the very hungry caterpillar ate through 5 oranges, and there are 5 children who came to story time today- 5 and 5, that's the same! Toddlers may need a long pause to study pictures, process what they hear, and respond to your questions.
Follow a routine
Use a predictable structure or pattern like a welcome song, story, or hands-on activity. Patterns help children predict what comes next, make sense of their world, and feel more secure and confident.
Have fun and show your appreciation
Fun is contagious. If you're having fun, children and families will, too. Cara Young, CSL states that it is important that librarians show their enthusiasm for the book's content and characters. For example, " ...chocolate cake, an ice cream cone, a pickle, a slice of cheese...? That's a lot of food...."

Finally, remember to thank families and remind the kids how awesome they are!

Our guest contributors today are Lori Coletti and Rebecca Raineri.

Lori Coletti is an Early Childhood specialist at EDC. She coordinates, develops, and delivers accessible, research-based professional development opportunities that align with state and national standards. She has expertise in early math development, language and literacy, child assessment, and early childhood programming.

Rebecca Raineri is a Children's Librarian at Worcester Public Library. With over 13 years of experience working with children, Rebecca is passionate about books and learning, and believes that libraries are a fundamental resource for all communities. She can be reached at rraineri@mywpl.org.
Please note that as a guest post, the views expressed here do not represent the official position of ALA or ALSC.

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Finding the Math in Children's Storytimes - ALSC Blog

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Learn how to include math concepts in storytime to significantly increase reading skills and attention skills.

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Integrating Technology into Public Library Programs with Bedtime Math

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Integrating Technology into Public Library Programs with Bedtime Math

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For many public libraries, 2022 saw a slow but gradual return to in-person programming after two years of services altered or disrupted by the pandemic. This past summer was the closest my branch has been to "normal" programming, and we finally hosted our first big school night since 2019 in December.

Read more: Integrating Technology into Public Library Programs with Bedtime Math

Like other libraries, the long pause has forced us to reassess needs and rethink the programming and services we invest in. Finding ways to expand access to out-of-school learning and creating opportunities for families to engage with each other? are both priorities for my team. So, when a librarian on my staff proposed the idea of creating a series of math enrichment programs last summer, I was all in.

The six-week program was very well-received, and we saw high family engagement throughout. Each session featured a math-themed book and a related hands-on activity. One of the most successful elements, however, was the integration of technology. Each program in the series began with a "Math Problem of the Day" from Bedtime Math, a free app ( iOS/ Android) to help families make simple, math-related talk a regular part of their day.

What made Bedtime Math work well in a public library setting?

It was a great way to set the tone. Having the librarian facilitate a conversation around problem-solving and involving the whole group helped build excitement for activities later in the program. There is research showing that "Math Talk" techniques help children see themselves as valued mathematical thinkers and can motivate them to learn.

One of the great features of this app is that it provides a leveled approach. Public library programs tend to draw a range of ages and abilities, so having a variety of challenges was important. Working through all three levels of the "Math Problem of the Day" as a group ensured that all participants felt included.

It was a fantastic way to highlight and demonstrate an accessible resource for parents and caregivers. It's an ideal family math tool - a way to promote math activities within the context of family relationships and everyday life, and empower caregivers with a free tool to start conversations around mathematical concepts.

We wrapped up the series with a sandbox session - a librarian-facilitated free-play program - designed to introduce families to a variety of vetted math apps on our mobile iPad lab. This provided natural opportunities to engage in media mentor conversations around recommended apps, screen time, and other resources like CommonSense Media.

Considerations when choosing technology for programming

As a manager, I try to encourage my team to think about thoughtful ways to integrate technology into program design and delivery, but I know it doesn't always come naturally. Here are some things we consider when bringing technology into a public library program:

Does the technology element add value to the program, or is it likely to be a distraction?

Is it appropriate for the audience?

How will we introduce and model the technology?

How do we envision participants interacting with technology during the program?

Are we building the program around the technology element? If so, think about why:

Are we demonstrating a tool for learning or enrichment?

Are we providing access to something that may not be readily available to all?

Is this a free app or website families can access at home? if it is not free, does the library provide access in some way, either through its spaces or collections?

Will including this element spark conversation with parents and caregivers around children's use of media, and if so is the library prepared for those conversations?

What are some successful ways you have integrated technology into public library programming?

This post addresses the following ALSC Core Competencies: I. Commitment to Client Group, II. Reference and User Services, III. Programming Skills

Additional Resources:

SLJ 10 Podcasts about Math for K-12 Students ( https://www.slj.com/story/10-podcasts-math-students-kidcasts-librarians)

Making Space for Math in the Library ( https://www.slj.com/story/making-space-for-math-in-the-library-stem)

Family Math ( https://nafsce.org/page/familymath)

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Integrating Technology into Public Library Programs with Bedtime Math - ALSC Blog

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For many public libraries, 2022 saw a slow but gradual return to in-person programming after two years of services altered or disrupted by the pandemic. This past summer was the closest my branch has been to "normal" programming, and we finally hosted our first big school night since 2019 in December.

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I love doing traditional preschool outreach storytimes. Sharing great books and fun flannels? Singing and dancing to silly songs? I'm there for it. However, a friend at another library inspired me to expand my repertoire. I added preschool outreach programs to highlight STEM-focused (science, technology, engineering, and math) picture books and offer opportunities for preschoolers to engage in a different way than storytimes. Over the next few months, I'll highlight some success stories and look forward to hearing how YOU shake things up in outreach!

Seeing Double: Program on Symmetry

This symmetry preschool outreach program was so fun for the preschoolers and generated some deep thinking.

Laying the Foundation

I read the first few pages from Loreen Leedy's non-fiction Seeing Symmetry, and I shared a Canva slideshow. With each slide, I asked the children what they saw and then waited. The longer I stayed silent, the more they noticed. Each slide was followed by its duplicate with one or more lines of symmetry added. We talked about how symmetry can be, among other things, matching side-to-side or top-to-bottom.

For one last example of symmetry, I had cut paper letters (B, D, E, and P). I held each cut out and asked the children how I should fold it to match the symmetrical parts. When we got to the letter P, they thought for a moment. Eventually I heard the delighted realization, "There's no symmetry!" I dramatically tossed the letter P to the side, which elicited a few giggles.

Exploration Activities

Then the real fun began! First, we created a symmetrical pattern on the rugs using our bodies. If one child stood on one rug, a second child needed to stand in the same spot on the rug opposite. The kids loved becoming the pattern themselves. Next, I handed out translucent pattern blocks and a sheet of printer paper with one line running down the middle. The preschoolers worked in pairs to create amazing symmetrical designs. When the designs were complete, I had everyone walk around the rug to ooh and ahh about their friends' patterns.

Lastly, I asked the preschoolers to create an elaborate design using pattern blocks on only ONE side of the paper and handed out child-safe mirrors to hold on the line, so they could see a completed, symmetrical design.

Next month, I'll share a preschool outreach program on forces and friction. In the meantime, I look forward to hearing what STEM programs you offer on outreach visits.

This post addresses the following ALSC Core Competencies: I. Commitment to Client Group, III. Programming Skills, and V. Outreach and Advocacy.

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Preschool outreach programs are a great way to shake up traditional outreach visits and introduce STEM concepts in engaging ways.

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Early Math Collaborative Erikson Institute

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Early Math Collaborative Erikson Institute

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Erikson Institute Early Math Collaborative

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Book

Our new book explores the connections between research and early childhood teachers. "Growing Mathematical Minds is a remarkable, lucid, and inviting introduction to early math education."

Read more

Big Ideas

Our set of Big Ideas map the key concepts children ages 3 to 6 need to explore for each foundational math topic. Sift through the resources we have organized by topic.

Learn more

The Erikson Institute Early Math Collaborative is transforming the understanding, teaching and learning of early mathematics from the ground up.

Online Learning

Professional development modules

Our self-guided modules provide materials, strategies, and expert guidance for working with adult learners to explore foundational mathematics. Whether you are working with childcare providers, in-service teachers, or pre-service teachers, modules give you what you need to support professional learning in your local context.

Start a module

"Math skills are increasingly important for getting good jobs these days-so believing you can't learn math is especially self-destructive. We also believe that math is the area where America's 'fallacy of inborn ability' is the most entrenched. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough."

At the 2015 NCTM Research Conference, Mary Hynes-Berry and Rebeca Itzkowich described the importance of relating math to real-life problems, and Jeanine Brownell, Bilge Cerezci, and Erin Reid explained the Collaborative's HIS-EM teacher assessment tool.

Get more when you join. More resources and more ways to connect. Save your favorites so that more is at your fingertips.

Best of all, it's free. Sign-up today.

Early math is big.

Learn why we are so passionate about giving every child a strong foundation in math.

Funding for this initiative is generously provided by:

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Early Math Collaborative Erikson Institute

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The Early Math Collaborative works to improve math instruction for young children in three ways: professional development, research, dissemination.

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‎Looking to add a little math to your daily routine? Bedtime Math's MiniMath will help you and your preschooler explore their world with sizes, shapes, and numbers. Based on the popular Bedtime Math app for elementary kids that's proven to improve math skills, MiniMath is designed for kids ages 3-5....

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Available online at: https://www.olaweb.org/assets/documents/csd_EarlyNumeracy.pdf

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Enhancing Storytime to Build Children’s Math Skills (Mother Goose on the Loose Webinar)

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Enhancing Storytime to Build Children’s Math Skills (Mother Goose on the Loose Webinar)

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Learn to support children's math readiness skills through nursery rhymes, games, and songs through this hands-on 2 hour webinar. The webinar includes: A general overview of math readiness state standards, a research review of math development in early childhood, easy developmental tips regarding children's math development for parents, and hands-on activities that illustrate why and how rhymes, games and songs can support math readiness.
This webinar is jointly presented by Dr. Betsy Diamant-Cohen and Dr. Erica Zippert

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Enhancing Storytime to Build Children's Math Skills

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Enhancing Storytime to Build Children's Math Skills (2 hours)

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Learn to support children's math readiness skills through nursery rhymes, games, and songs through this hands-on 2 hour webinar. The webinar includes: A general overview of math readiness state standards, a research review of math development in early childhood, easy developmental tips regarding children's math development for parents, and hands-on activities that illustrate why and how rhymes, games and songs can support math readiness.

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Problem Solvers: A Free Early Math Curriculum

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Children can learn about math through everyday play. Download our complete preschool and early math curriculum, activity guide and songs.

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Building numeracy skills: Associations between DUPLO® block construction and numeracy in early childhood.  

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Building Numeracy Skills: Associations between DUPLO® Block Construction and Numeracy in Early Childhood

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Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers’ Early Numeracy: A Pilot Intervention Study.

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Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers’ Early Numeracy: A Pilot Intervention Study.

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Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers' Early Numeracy: A Pilot Intervention Study

Abstract

The aim of this pilot study was to examine the immediate and long-term effects of an intervention program that aims to improve preschoolers' ( N = 36, M  = 4.49 years, SD = 0.35) early numeracy skills by combining the learning of numerical relational skills via story reading with fundamental motor skill practice. The intervention program was piloted with two study designs: a within-subject repeated-measures design with 18 children (study I), and a quasi-experimental study design with 18 children (study II). Children's early numeracy, symbolic magnitude processing, and fundamental motor skills were measured. Results demonstrated that children's early numeracy and especially numerical relational skills improved during the intervention, and the intervention had larger effects on children's early numeracy and numerical relational skills compared to the control period (study I) and control group (study II). Furthermore, the results from the delayed post-test demonstrated that the effects were maintained for 4.5-8 weeks after the intervention. These findings provide preliminary evidence that it is possible to support children's early numeracy skills with combined learning of numerical relational skills via story reading and fundamental motor skills despite the socioeconomic or language background, and narrow the gap between low- and average-performing children.

Résumé

Le but de cette étude pilote était d'examiner les effets immédiats et à long terme d'un programme d'intervention qui vise à améliorer les compétences précoces en numératie des enfants d'âge préscolaire (N = 36, M = 4.49 ans, SD = 0.35) en combinant l'apprentissage des compétences par la lecture d'histoires avec la pratique des habiletés motrices fondamentales. Le programme d'intervention a été piloté avec deux plans d'étude : un plan à mesures répétées intra-sujet avec 18 enfants (étude I) et un plan d'étude quasiexpérimental avec 18 enfants (étude II). La numératie précoce des enfants, le traitement de la magnitude symbolique et les habiletés motrices fondamentales ont été mesurés. Les résultats ont démontré que la numératie précoce des enfants et en particulier les compétences relationnelles numériques se sont améliorées au cours de l'intervention, et l'intervention a eu des effets plus importants sur la numératie précoce et les compétences relationnelles numériques des enfants par rapport à la période témoin (étude I) et au groupe témoin (étude II). De plus, les résultats après le test ont démontré que les effets se maintenaient de 4.5 à 8 semaines après l'intervention. Ces résultats fournissent des preuves préliminaires qu'il est possible de soutenir les compétences précoces en numératie des enfants avec l'apprentissage combiné des compétences relationnelles numériques par la lecture d'histoires et les habiletés motrices fondamentales malgré le contexte socio-économique ou linguistique, et de réduire l'écart entre les enfants peu performants et les enfants moyenne.

Resumen

El objetivo de este estudio piloto fue examinar los efectos inmediatos y a largo plazo de un programa de intervención educativa. Dicho programa busca mejorar las habilidades numéricas tempranas de niños en edad prescolares (N = 36, M = 4.49 años, SD = 0.35). Mediante de la combinación del aprendizaje de habilidades de relación numérica a través de la lectura de cuentos con la práctica de habilidades motoras fundamentales. El programa de intervención se ha pilotado con dos diseños de estudio distintos: un estudio de observación y medidas reiteradas de un mismo sujeto, con 18 niños (estudio I); y un estudio cuasiexperimental con otros 18 niños (estudio II). En ellos se midieron las habilidades numéricas tempranas, el procesamiento de magnitudes simbólicas y las habilidades motoras fundamentales. Los resultados han demostrado que durante la intervención, y en comparación con el periodo de control (estudio I) y el grupo de control (estudio II), se han mejorado las habilidades numéricas tempranas de los niños y, en especial, las habilidades de relación numérica. Además, los resultados de la evaluación posterior a la intervención demostraron que los efectos se mantuvieron durante 4.5 - 8 semanas después de la intervención. Estos resultados aportan una evidencia preliminar que defiende la posibilidad de mejorar las habilidades numéricas tempranas de los niños a través del trabajo de las mismas con lectura de cuentos y el desarrollo de funciones motoras fundamentales. Todo ello a pesar del entorno socioeconómico o lingüístico del niño; lo que permite reducir las diferencias entre los niños de bajo y medio rendimiento.

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Introduction

Previous research has shown that individual differences in children's early numeracy (EN) can be observed already before formal schooling begins (Aunio et al., 2015), and the achievement gap between low- and high-performers widens during the preschool years (i.e., from years 3 to 6; Anders et al., 2012). This highlights the necessity for developing effective intervention programs to support low-performing preschoolers, which can prevent them from being at risk of later mathematical learning difficulties (Aunio et al., 2015).

Recommendations for improving EN in the early years include combining EN learning with other curriculum areas and exploring EN through different contexts; for instance, joint story reading offers a valuable opportunity to initiate mathematical discussions with children (Education Endowment Foundation, 2020) and offers meaningful way to learn EN (Van den Heuvel-Panhuizen & Elia, 2011). Positive effects of a story reading intervention on children's numerical relational skills-which are central in the development of EN (Toll & Van Luit, 2014)-have been observed (Hassinger-Das et al., 2015). In addition to story reading, activities which allow children to be physically active may support children's learning (Jylänki et al., 2022). Children learn naturally through play (Whitebread et al., 2009), and can be seen as active players, since their play usually includes bodily movements instead of passive observing (Thompson & Goldstein, 2020). However, due to activities that require sitting (Määttä et al., 2019), children's possibilities to be physically active and use bodily movements are often limited in preschools (Vanderloo et al., 2013).

Bodily movements, operationalized often as fundamental motor skills (FMS), have been associated with EN in preschool-aged children (Gashaj et al., 2019). Intervention studies, which combined EN and FMS practice, have found positive (Fischer et al., 2011; Shoval et al., 2018), and even long-term effects on EN performance (Beck et al., 2016). In addition, interventions which combine FMS with the learning of academic or cognitive skills have been found effective in preschoolers, and combined interventions may even be superior compared to learning academic or cognitive skills alone (Jylänki et al., 2022). One possible explanation for the close association between FMS and the learning of academic and cognitive skills is the fact that especially complex FMS tasks activate the same brain areas as complex cognitive tasks, resulting in a co-activation of these brain areas (Diamond, 2000). Furthermore, these effects may be mediated through an increase in executive functions-inhibition in particular-following FMS practice, which might then be reflected as improved cognitive and academic skills (e.g., ability to inhibit irrelevant information during given tasks; Chan et al., 2022; Pesce et al., 2021). In light of previous research, it is plausible that combining the learning of EN with FMS practice may result in long-term improvements in EN. Our pilot study examined the immediate and long-term effects of a Movement with Early Numeracy (MovEN) intervention program that aims to improve EN by combining the learning of numerical relational skills via story reading with FMS practice.

Preschoolers' Early Numeracy

In 3- to 4 year-old children, relevant EN skills include numerical relational, counting and symbolic magnitude processing skills (SYMP; Clements & Sarama, 2009; Litkowski et al., 2020). The understanding of numerical relational skills in particular has shown to be critical for later numeracy development (Purpura et al., 2011; Toll & Van Luit, 2014). Numerical relational skills consist of concepts that are used to describe quantity relations (e.g., more, half) and spatial relations (e.g., above, between; Toll & Van Luit, 2014) between entities. Studies with preschoolers have demonstrated that the learning of numerical relational skills is important from early on (Purpura et al., 2011) and that children with mathematical learning difficulties in particular benefit from intensified numerical relational skill practice (Hassinger-Das et al., 2015).

EN and language skills have found to be developmentally related (Purpura et. al., 2011), and learning numerical concepts is an important shared area within this relationship (Toll & Van Luit, 2014). In order to learn numerical relational skills, children are required to possess adequate language skills to understand these linguistically expressed concepts (Purpura & Lonigan, 2013), and they need to understand the numerical information embedded in the tasks (Toll & Van Luit, 2014).

Discussion-based approaches that include discussion and instruction following reflection (Gifford, 2005), such as dialogic story reading where the teacher uses questions and prompts children for discussion, have shown to be effective for improving both EN and language skills in preschoolers (Purpura et al., 2017). Indeed, story reading interventions have been found to be an effective way to increase different areas of numerical relational skills knowledge, such as concepts related to counting and number operations (Hassinger-Das et al., 2015), length measurement (Van den Heuvel-Panhuizen & Elia, 2011), and geometry (Casey et al., 2008). Furthermore, Casey and her colleagues ( 2008) demonstrated that story reading intervention was more effective compared to intervention without the story reading component, and Purpura and his colleagues ( 2017) showed that story reading intervention improved not only numerical relational skills, but also children's EN. These findings suggest that the use of story reading is an effective way to increase preschoolers' numerical relational skills as well as EN.

Early Numeracy and Fundamental Motor Skills

In recent decades, studies examining the effects of physical activity (including FMS) on cognitive skills have increased rapidly (Pesce et al., 2021). Previous studies have mainly focused on school-aged children, while children in their early years remain understudied (Pesce et al., 2021). Studies have shown that FMS (balance, manipulative and locomotor movement skills; Donnelly et al., 2017) are associated with EN in preschoolers (Gashaj et al., 2019). Both FMS and EN skills start to develop at the age of two to three years (Clements & Sarama, 2009; Gallahue & Ozmun, 2002), and when children are 4- to 5-year old, their skills are more developed and the gap between the low- and high-performers starts to broaden (Anders et al., 2012; Starkey & Klein, 2008). Thus, 4-to-5-year-olds are a developmentally desirable group to be supported with an intervention. Previous intervention studies that combined FMS with EN learning (Table 1) have demonstrated positive effects on EN (Fischer et al., 2011; Shoval et al., 2018), and the effects have been larger than in EN interventions without an FMS component (Fischer et al., 2011).

Although the previous combined FMS and EN interventions have been found effective, there are some apparent limitations. For instance, some shortcomings were found in the intervention designs: the long-term effects were not assessed (Fischer et al., 2011; Shoval et al., 2018; St. Laurent et al., 2018) or narrow outcome measures were used that only measured one dimension of EN (e.g., number recognition; St. Laurent et al., 2018). The aforementioned limitations, and the fact that there are only a few studies assessing the effects of combined FMS and EN interventions in preschoolers, underline the necessity to investigate the effects of intervention programs that support the development of 4-to-5-year-olds' FMS and EN skills and possibly narrow the gap between the low- and high-performers.

Present Study

Research in school-aged children has shown a correlative relationship between FMS and EN learning (Macdonald et al., 2018), as well as demonstrated the superiority of combined FMS and EN interventions in comparison with EN learning alone (Have et al., 2018). However, the effects in preschoolers remain understudied (Jylänki et al., 2022). This is crucial, since it has been shown that individual differences can be observed already before formal schooling begins, and the importance of early support for low-performers is well demonstrated (Aunio et al., 2015). In addition, while previous EN interventions have been found effective, long-term effects have seldom been found nor reported (Aunio, 2019). Thus, the aim of the present study was to examine the immediate and long-term effects of the MovEN-intervention that aims to improve EN by combining the learning of numerical relational skills via story reading with FMS practice. The effects of the MovEN-intervention on 4 year-old children's EN performance were examined with two study designs. First, a within-subject repeated-measures design (study I) was conducted with two intervention groups, and then, a quasi-experimental design with an intervention and an average performance control group (study II) was carried out to verify the findings from study I.

Methods

Participants

A total of 36 children ( M = 4.49 years, SD = 0.35); 21 girls and 15 boys, from four preschools in the metropolitan area, participated in this pilot study. Of these, 18 children participated in study I, and 18 children (9 in the intervention and 9 in the average performance control group) in study II. Preschools participating in a larger longitudinal project ( N  = 21, Active Early Numeracy) were invited to participate in the MovEN-intervention, of which four preschools volunteered to participate. Children in the intervention groups were, at first, identified as at risk in numerical relational skills learning based on their teachers' experience, and secondly measured with the EN test (i.e., children who were more than one standard deviation below the average in the numerical relational skill measures were regarded as low-performing). Children's parental consent, as well as the university ethics approval (August 28, 2019), was obtained prior to the start of the study. Participation was voluntary, and withdrawal from the study was possible at any time.

Participating children had heterogeneous language and socioeconomic backgrounds, and thus both language skills and socioeconomic status (SES) were used as underlying variables. Children's guardians filled in a questionnaire concerning the family's SES. Participant characteristics and SES are presented in Table 2. Study I participants' guardians displayed a greater representation of higher education and a lower degree of unemployment compared to the SES factor distribution in the respective municipality, while the household net income was in line with the municipality's average. In study II, the education and employment background of the control group followed a similar pattern, apart from demonstrating a greater net income in comparison with the average of the municipality. In the intervention group, the participant's families had an overrepresentation of lower education (i.e., high school) and unemployment, despite having greater average net income compared to the municipality. The first language of the participants in study I and study II control group was Finnish, while in study II intervention group, nearly half of the families reported other than Finnish as their first language, which is an overrepresentation compared to the municipality's average. However, it should be noted that all of the families did not return the questionnaire concerning the family's SES (i.e., 83% of the families returned the questionnaire), possibly influencing the results.

Children's language skills were measured before the intervention with receptive and expressive language items from Lene (Valtonen & Mustonen, 2007; Valtonen et al., 2004). The items varied for age groups and included items assessing the understanding of instructions and receptive questions. The test consisted of eight and eleven items with a maximum score of 12 and 19 for 3-, and 4 year-old children, respectively. In study I, language skills were measured, on average, 7 months before the intervention, while in study II language skills were measured at the same time as outcome measures. The test demonstrated good reliability in the total sample of 4- ( α = 0.81, N = 140) and 3 year-old children ( α = 0.79, N  = 141) in the longitudinal Active Early Numeracy-project.

Children's language skills (receptive and expressive language, Valtonen & Mustonen, 2007) were compared to the corresponding reference group (i.e., children in the longitudinal project; N = 365) prior to the intervention (Table 3). In study I, 4 year-olds' language skills were in line with the reference group, while 3 year-olds' language skills were significantly better compared to the reference group. In study II, the intervention group had significantly lower language skills compared to the reference group, whereas the average performance control group's language skills were in line with the reference group.

In study II, independent samples t test was conducted to reveal differences between the intervention and average performance control group prior to the intervention. There was no statistically significant differences between the intervention and average performance control groups in EN total score t(11.721) = 2.09, p = 0.060, counting tasks t(10.105) =  − 0.45, p = 0.661, SYMP t(10.199) =  − 0.89, p = 0.394, and FMS t(13.737) = 0.27, p = 0.788 prior to the study. However, the average performance control group had significantly greater numerical relational scores compared to the intervention group before the intervention, t(12.447) = 4.19, p = 0.001. In addition, significant differences between the intervention ( M = 14.9, SD = 4.6) and the average performance group ( M = 18.2, SD = 1.0) in language tasks, U = 15.5, z =  − 2.27, p = 0.023, were detected prior to the intervention; favoring the average performance group. There was also a significant correlation between language skills and ENT results at baseline ( r = 0.476, p  = 0.046), suggesting that children with greater language skills also demonstrated superior EN skills.

Study Design

The effects of the MovEN-intervention were examined with two study designs. In study I ( n = 18), a within-subject repeated-measures design was used because the control group was not available due to COVID-pandemic-related restrictions in preschools. Children's EN and FMS were measured twice before and after the intervention (Fig. 1). The first two measurement points (pre 1 and pre 2) formed the baseline (i.e., 5 to 10 months), the third measurement point (post 1) was conducted immediately after the intervention, and the delayed post-test (post 2) eight weeks after the intervention. During the baseline, children followed a regular preschool curriculum (City of Helsinki Education Division, 2019) and the baseline was used as a control period for the intervention (i.e., business-as-usual).

Intervention flow diagram

To verify the findings from study I, we conducted study II ( n = 18), where a quasi-experimental design was used with a MovEN-intervention group ( n = 9) and an average performance control group ( n = 9). Both groups were measured before, immediately after and 4.5-7 weeks after the MovEN-intervention. During the 8 week intervention period, the average performance control group followed a regular preschool curriculum (City of Helsinki & Education Division, 2019).

Outcome Measures

Early Numeracy

EN was measured with the Early Numeracy Test (ENT; Van Luit et al., 2006), which includes 40 items that measure children's numerical relational and counting skills. During the test, children were asked to point out the right answer, count objects or conduct paper-and-pencil tasks. The maximum score for EN was 40 points; numerical relational and counting skills each accounted for 20 points. ENT demonstrated good reliability α = 0.891 ( N  = 175) in the whole sample of 4 year-olds in Active Early Numeracy-project.

Symbolic Magnitude Processing

SYMP was measured with a one-digit subtest from the paper-and-pencil test of Symbolic Magnitude Processing (SYMP Test; Brankaer et al., 2017), which includes 60 one-digit pairs presented randomly in four columns. Digits ranged from 1 to 9. Children were asked to point out the larger number, and the researcher crossed out the number. Children had three minutes to solve as many items as possible. Before starting the test, children had four practice trials to ensure that they understood the task. A maximum of 60 points could be obtained from the SYMP Test. The sum score was used in the analysis. The SYMP test demonstrated good reliability α = 0.898 ( N  = 175) in the whole sample of 4 year-olds in Active Early Numeracy-project.

Fundamental Motor Skills

FMS were measured with a jumping sideways task from the KTK-test battery (Kiphard & Schilling, 2007). Children were asked to jump sideways over a wooden bar (60 × 4 × 2 cm). The jumping area was limited to 100 × 60 cm. Children had 15 s to perform the task, and only correct jumps (i.e., inside the jumping area and toes pointing forward) were counted. Task was repeated twice. Before the actual test, children had five practice jumps to ensure that they understood the task. Sum score of the two performances was used in the analysis.

Intervention

The Movement with Early Numeracy (MovEN)-intervention program was developed based on the current scientific knowledge (Aunio, 2019; Gallahue & Ozmun, 2002; Hassinger-Das et al., 2015). The purpose of the MovEN-intervention was to improve children's numerical relational skills via story reading and discussion about numerical relational concepts, combined with comprehensive FMS practice. The intervention sessions were 45 min in duration, held twice a week for eight weeks. All sessions followed the same structure (Table 4).

The MovEN-intervention program included both numerical relational skills and FMS practice. Numerical relational skill practices were designed based on a previous storybook intervention (Hassinger-Das et al., 2015) and included in the beginning of each session. Over the intervention period, five general children's storybooks with rich mathematical language expressing numerical relational skills (Table 5) were read using a dialogic reading technique (Beck & McKeown, 2001). For example, in the "Who eats first" book, a group of animals are solving who get to eat the peach. Animals are comparing themselves based on the length, weight, size of the mouth, and length of the tail. Finally, the worm gets to eat the peach, as it is the shortest, lightest, has the smallest mouth and shortest tail. During the reading session, children were encouraged to discuss about the measuring options, comparing animals and using the numerical relational concepts based on the questions that were included in the books. A particular storybook was read to completion in three consecutive sessions, before commencing to the next book. During the intervention sessions, children also conducted FMS exercises (i.e., balance, manipulative and locomotor movement skills) that included the same numerical relations as the books (e.g., throw small balls to the nearest target and large balls to the farthest goal, in which goal are more balls at the end?).

Procedure

Twenty-one preschools from the Active Early Numeracy-project were contacted in order to identify volunteering teachers to conduct the intervention in their preschools. Due to Covid-19 restrictions, we were not able to conduct the interventions by ourselves. Five teachers volunteered to conduct the intervention since they had identified children that could benefit from the numerical relational skill practice. In study I, the intervention was carried out in a group of eleven children with two teachers, and a group of seven children with one teacher (two teachers alternated between the sessions). In study II, the intervention was carried out by one teacher and children were divided into two groups (five and four children per group).

Teachers were trained to conduct the intervention via online meetings (two 1 h meetings). Teachers were provided with strict lesson plans, which were reviewed with the research team prior to the start of the intervention. Supporting questions were included in the books in order to guide the discussion during story reading activities. Each lesson was implemented according to the lesson plans. Intervention sessions were held in rooms where children had enough space to conduct the FMS exercises (e.g., a preschool gym). Teachers filled in a logbook for each lesson and participated in meetings with the research team every other week (six 30-60 min meetings in total) to ensure intervention fidelity. Based on the teachers' experiences during study I, some modifications (e.g., one book was changed) were made to MovEN-intervention (Table 4). The first intervention (study I) began in September 2020 and the second (study II) in March 2021.

Children's EN, SYMP, and FMS skills were measured before and after the intervention. Children's language skills and SES were measured only before the intervention and were used as underlying variables. EN, SYMP, and language skills were measured individually in a separate room, and FMS were measured in groups of two to three children. Trained research assistants conducted all of the measurements in preschools. In both studies, children were unaware of the experimental objectives; however, the outcome assessors were not blinded to the intervention.

Dropouts and Intervention Attendance

There were no withdrawals or dropouts during the eight-week intervention either in study I or II. The average attendance to the MovEN-intervention sessions in study I was 14 out of 16 sessions (85%) in one preschool ( n = 11), while the attendance to the intervention sessions could not be defined in the other preschool ( n  = 7) due to inadequate logbook completion. The average attendance in the MovEN-intervention sessions in study II was 12 out of 16 sessions (78%). Missing data occurred in some measurement points due to children not being present during the measurement day or disagreeing to perform the tests.

Statistical Analysis

All statistical analyses were conducted with IBM SPSS Statistics 25. In study II, an independent sample t test, with an alpha level of 0.05, was conducted to examine the differences between the intervention and the average performance control group before the intervention. Paired samples t tests were used to establish the effects of the MovEN-intervention in both studies. Due to small sample sizes, the results were confirmed with a nonparametric Wilcoxon rank sum test. Cohen's d effect sizes were calculated for all outcomes (small 0.2, medium 0.5, and large 0.8; Cohen, 1988). In order to compare the gains during the intervention and the baseline in study I, we calculated gains per month as follows:

$${\text{Gain per month during baseline}} = \frac{{\left( {{\text{pre}} 2{\text{ scores}} - {\text{pre }}1\; {\text{scores}}} \right)}}{{{\text{months between pre}} 1{\text{ and pre}} 2\; {\text{measurements}}}}$$

$${\text{Gain per month during intervention }} = \frac{{\left( {{\text{post}} 1\; {\text{scores }} - {\text{pre}} 2\; {\text{scores}}} \right)}}{{{\text{months}}\; {\text{between}}\; {\text{pre}} 2\; {\text{and}}\; {\text{post}} 1\; {\text{measurements }}}}$$

In study II, gains per month were calculated as follows:

$${\text{Gain per month}} = \frac{{\left( {{\text{post}} 1\; {\text{scores}} - {\text{pre}}\; {\text{scores}}} \right)}}{{{\text{months between pre and post}} 1\; {\text{measurements}}}}$$

The distribution of language skill results was assessed with the Shapiro-Wilk test, revealing a non-normal distribution with a negatively skewed pattern. Thus, the between-group comparisons were carried out with the Mann-Whitney U test. Standardized z-scores were computed for the raw language skill results to allow for the unification of the scores between 3- and 4 year-old children in study I. Pearson's correlation coefficients were calculated between language skills at baseline and ENT.

Results

Results of Study I

Paired samples t test was used to examine the immediate and long-term effects of the MovEN-intervention (Table 6). The results demonstrated that children's EN improved significantly both during the 5 to 10 month baseline t(17) = 4.198, p = 0.001 and the eight-week intervention t(17) = 6.346, p = 0.000. The effects of the intervention were maintained in the delayed post-test 8 weeks after the intervention. The improvement in SYMP or FMS was not significant during the baseline. However, the improvement in FMS was significant during the intervention t(16) = 2.601, p  = 0.019 and the effect was sustained in the delayed post-test.

Table 6 Descriptive statistics and results from study I paired samples t test

To examine whether the gain was greater during the intervention as opposed to the baseline, gains per month were compared (Table 7). The results demonstrated that children had significantly greater monthly gain in EN ( M gain = 2.12, SD = 1.39) and numerical relational skills ( M gain  = 1.39, SD = 0.98) during the intervention than during the baseline period. In terms of counting skills, SYMP or FMS, no significant differences were detected in monthly gain between the baseline period and the intervention.

Results of Study II

Paired samples t test was used to examine the immediate and long-term effects of the MovEN-intervention (Table 8). Children's total EN performance improved in both the intervention ( t(8) = 2.697, p = 0.027) and the average performance control group ( t(8) = 2.329, p = 0.048) during the intervention and control period. However, the effects were larger in the MovEN-intervention group (large; d = 0.899) than in the average performance control group (medium; d = 0.776), and the intervention effects were sustained in the delayed post-measurement. Children's numerical relational and FMS performance improved significantly in the intervention group ( t(8) = 4.031, p = 0.004), while no significant improvements were observed in the average performance control group. The effect of the intervention on EN was sustained in the delayed post-measurement. No significant effects were observed on counting or SYMP performance in either group. At the delayed post-measurement, there were no significant differences in numerical relational performance between the groups t(8.770) = 1.32, p  = 0.056.

Table 8 Descriptive statistics and results from study II paired samples t test

In order to examine the improvements during the intervention period in the intervention and average performance control group, we compared the gains per month (Table 9). While the gains in total EN, numerical relational and FMS performance were greater during the MovEN-intervention compared to the gains in the average performance control group, the effect was statistically significant only in FMS performance.

Discussion

Both FMS and EN skills start to develop in early childhood (Clements & Sarama, 2009; Gallahue & Ozmun, 2002), and the gap between low-, and high-performers widen during the preschool years (Anders et al., 2012; Starkey & Klein, 2008). This highlights the importance of early interventions to support low-performing children, in order to prevent them from being at risk for later mathematical learning difficulties (Aunio et al., 2015). In the present pilot study, we examined the immediate and long-term effects of the MovEN-intervention program, which aims to improve preschoolers' EN skills by combining the learning of numerical relational skills with FMS practice. The MovEN-intervention was first conducted with a within-subject repeated-measures design (study I) and after some modifications with a quasi-experimental design (study II). By conducting the intervention with two intervention designs, it was possible to increase the reliability of the results despite the small sample sizes.

Both studies demonstrated that children's EN skills and especially numerical relational skills improved during the MovEN-intervention. This finding is in line with previous story reading interventions demonstrating positive effects on numerical relational skills (Casey et al., 2008; Hassinger-Das et al., 2015; Purpura et al., 2017; Van den Heuvel-Panhuizen & Elia, 2011) and EN skills (Purpura et al., 2017). When comparing gains per month in study I, EN improved significantly more during the eight-week intervention than during the 5-to-10 month baseline period, which is in line with findings from previous combined EN and FMS interventions (Fischer et al., 2011; Shoval et al., 2018). In study II, the gain per month in numerical relational skills was notably larger ( d = 0.801), albeit statistically nonsignificant ( p = 0.109), in the MovEN-intervention group compared to the average performance control group. While these differences did not reach statistical significance, it is important to note that when analyzing small sample sizes, effects that are large in magnitude, yet statistically nonsignificant should not necessarily be disregarded, as the risk of detecting false-negatives is considerable (Sullivan & Feinn, 2012). Importantly, the improvements were sustained in the delayed measurement in both studies. These findings are in accordance with a recent systematic review demonstrating that combining FMS with the learning of cognitive or academic skills offers notable benefits on preschoolers' cognitive and academic skill development (Jylänki et al., 2022).

In study II, there were significant differences in numerical relational skills between intervention and average performance control group before the intervention. However, the difference between the groups in numerical relational skills was not significant after the intervention, suggesting that the gap between these groups narrowed during the intervention, and the children in the intervention group were able to catch up the average-performing peers during the intervention. According to a review by Mononen et al. ( 2014), previous EN interventions have been found to support at-risk children's EN learning; however only one study has demonstrated that the gap between at-risk in EN learning and average performers narrowed during the intervention (Clarke et al., 2011), highlighting the novelty of our findings. This is also important, as there have been contradictory results from previous studies demonstrating that the low-performers did not benefit from a combined FMS and numeracy intervention while the average performers did (Beck et al., 2016).

It is important to note that the sample used in our study included children from heterogeneous socioeconomic and language backgrounds. Previous studies have reported that children with low-SES and second language learner status tend to have lower language skills (Raviv et al., 2004; Smith & Dixon, 1995). Indeed, the results of study II demonstrated that children with second language learner status had low-SES, as well as lower language skills. This is noteworthy as numerical relational skills can be more challenging for children with lower language skills, since children are required to possess adequate language skills to understand the linguistically expressed concepts (Purpura & Lonigan, 2013). Nonetheless, in our study, we demonstrated that regardless of the SES or language background, children benefited from the MovEN-intervention; especially in terms of their numerical relational skills. As there was a relationship between language and EN skills at the baseline, it is possible that in addition to EN skills, children's language skills improved during the intervention resulting in improvements in the ENT. Thus, in future studies, children's language skills should be measured also after the intervention, in order to find if the numerical relational skill practicing also supports children's language skills.

One potential explanation for the efficacy of the MovEN-intervention on children's EN learning is the comprehensive skill practice via story reading and body movement. Indeed, recommendations for improving EN in the early years include exploring EN through different contexts such as storybooks and combining EN with other curriculum areas (Education Endowment Foundation, 2020). Children can experience EN in a meaningful and informal way via story reading (Van den Heuvel-Panhuizen & Elia, 2011), and it offers children the opportunity to understand and apply the numerical relational concepts (Purpura et al., 2017). Furthermore, in the MovEN-intervention, children are encouraged to extend the numerical relational skills to other daily life contexts (e.g., games in the playground and sport activities). With improved numerical relational skills, children are more likely to be able to engage in EN activities and discussions that further enhance their mathematical knowledge (Purpura et al., 2017), which might explain the sustained effects of the intervention.

MovEN-intervention included features that have been found to be effective in FMS and cognitive skill interventions in children (Pesce et al., 2021). These include face-to-face instruction by trained teachers, a group-based setting in children's respective preschools, and a focus on skill development rather than exercising itself (Pesce et al., 2021). Based on the logbooks and weekly discussions with the teachers, the intervention-in terms of duration and frequency-was considered as feasible to implement into a preschool schedule in both studies. Furthermore, most of the intervention exercises were rated by the teachers as either 'excellent' or 'good', and both the children and teachers reported that they enjoyed participating in the intervention. Indeed, one study that combined physical activity with EN (Mavilidi et al., 2018) reported that children enjoyed combined interventions the most, and this could have a positive impact on the results of the intervention. Finally, some suggestions were made to further improve the MovEN-intervention (e.g., change the order of the books), which will be considered for future studies.

Although both studies demonstrated that the MovEN-intervention program can be effective on four-year-olds' EN and FMS skills, it was not possible to conclude whether practising FMS and EN together is more effective than practising both skills separately. Thus the MovEN-intervention program should be studied further with an intervention-control design including EN only, FMS only and combined EN and FMS intervention groups, as well as a business-as-usual control group. None of the previous combined FMS and EN interventions (Beck et al., 2016; Fischer et al., 2011; Shoval et al., 2018; St. Laurent et al., 2018) have compared the intervention to both EN and FMS learning alone. One study (Fischer et al., 2011) compared a combined FMS and EN intervention to an EN only intervention and one study (Beck et al., 2016) to a FMS only intervention. In both studies, the combined FMS and EN intervention appeared to be more effective than either aspect alone, suggesting the superiority of the combined FMS and EN learning.

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Acknowledgements

We want to acknowledge all the teachers, children, and their caregivers for participating in this study, as well as City of Helsinki for the collaboration while preparing and conducting this study. We also want to thank Eija Väisänen for her help while developing the intervention program.

Funding

Open Access funding provided by University of Helsinki including Helsinki University Central Hospital. This work was supported by the Ministry of Education and Culture [grant number 48825]; and the Finnish Cultural Foundation [Huhtamäen rahasto 2019, no grant number available].

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1. Faculty of Educational Sciences, University of Helsinki, Helsinki, Finland

Pinja Jylänki, Elina Sipinen, Theo Mbay & Pirjo Aunio

2. Faculty of Sport and Health Sciences, University of Jyväskylä, Jyväskylä, Finland

Arja Sääkslahti

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Correspondence to Pinja Jylänki.

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Jylänki, P., Sipinen, E., Mbay, T. et al. Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers' Early Numeracy: A Pilot Intervention Study. IJEC 55, 131-154 (2023). https://doi.org/10.1007/s13158-022-00329-8
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# data[].attributes.attachment_link.title
Combining Numerical Relational and Fundamental Motor Skills to Improve Preschoolers' Early Numeracy: A Pilot Intervention Study - International Journal of Early Childhood

# data[].attributes.attachment_link.description
The aim of this pilot study was to examine the immediate and long-term effects of an intervention program that aims to improve preschoolers' (N = 36, M = 4.49 years, SD = 0.35) early numeracy skills by combining the learning of numerical relational skills via story reading with fundamental motor skill practice.

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The development of early numeracy in deaf and hard of hearing children acquiring spoken language.  

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The development of early numeracy in deaf and hard of hearing children acquiring spoken language.  

# data[].attributes.headline
Early numeracy opportunities through number stories with marginalised families 

# data[].attributes.subject
Early numeracy opportunities through number stories with marginalised families 

# data[].attributes.headline
Math Apps & Games for Preschool & Kindergarten

# data[].attributes.subject
Math Apps & Games for Preschool & Kindergarten

# data[].attributes.attachment_link.title
Math Apps and Games for Preschool and Kindergarten | Common Sense Education

# data[].attributes.attachment_link.description
Math Apps and Games for Preschool and Kindergarten is a list of 30 apps, games, and websites curated by Common Sense Education editors.

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iPad Screenshots

In Birthday Café, children serve up birthday treats to a hungry party! Children seat groups of friends at tables and then distribute trays that have the same number of food items.

Features
* 20 levels of birthday celebration gameplay
* Adaptive pacing to meet each child's math level
* Multiple modes of scaffolding and support
* Aligns with research-based early math learning trajectories
* No in-app purchases
* No advertising

This game is designed for children to subitize. Subitizing is looking at a group of objects and quickly recognizing how many objects are in the group without having to take the time to count. It is an important skill that helps develop number sense and prepare children for mental math.

Learning Goals
This game is designed to help children strengthen their subitizing skills as they:
* Recognize sets of one to five objects without counting
* Learn and reinforce number names and symbols
* Understand that quantity can be represented by a numeral or a set of objects
* Understand that the quantity of a set is not affected by the arrangement of the objects in the set
* Compare sets of one to five objects and identify if the sets are the same or different

Birthday Café is part of the four-game subitizing suite from Early Math with Gracie & Friends™, a first-of-its-kind mobile app brand based in early learning sciences, rigorously researched and developed specifically for preschool classroom use. A randomized control trial demonstrated significant learning gains in children who used the Early Math with Gracie & Friends apps.

Early Math with Gracie & Friends is not just apps! Our research shows the value of hands-on, non-digital play in early learning. In fact, for every Gracie & Friends app, we have created and researched five or more hands-on activities! Check them out at http://first8studios.org

The math-focused curriculum supplement of Early Math with Gracie & Friends is based on the Next Generation Preschool Math research project funded by the National Science Foundation. The research focused on the development of eight learning apps, more than 40 hands-on and traditional preschool activities, and a digital Teacher's Guide-all designed for preschool classroom use.

About First 8 Studios at WGBH
WGBH Educational Foundation has pioneered children's educational media for decades. First 8 Studios at WGBH is dedicated to carrying this pioneering spirit into the digital, mobile world, building and researching new learning experiences for children from birth through age 8, their parents, and their teachers. Gold-standard research, funded by the National Science Foundation, serves as the foundation of our work. So does an ongoing commitment to the teachers and children we have worked with, and continue to work with, to give them a voice in the digital media development process. The countless hours we've spent with them have shaped Early Math with Gracie & Friends™ beyond measure. You'll find evidence of those big hearts and little fingerprints throughout each Gracie & Friends experience.

Privacy Policy
First 8 Studios at WGBH is committed to children's safety and well-being. This app collects only anonymous, aggregated analytics data for the purpose of improving the app experience. No personally identifiable data is collected. For our complete Privacy Policy, please visit: http://first8studios.org/privacypolicy.html

Copyright
Early Math with Gracie & Friends™ and the characters and related indicia are trademarks of First 8 Studios @WGBH. ™/© 2014 WGBH Educational Foundation. All Rights Reserved.

This Early Math with Gracie & Friends™ app was produced by WGBH Digital in Boston.

This material is based upon work supported by the National Science Foundation under Grant No. DRL-1119118. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of NSF.

This app has been updated by Apple to display the Apple Watch app icon.

The developer, First 8 Studios at WGBH, has not provided details about its privacy practices and handling of data to Apple. For more information, see the developer's privacy policy.

No Details Provided

The developer will be required to provide privacy details when they submit their next app update.

# data[].attributes.attachment_link.description
‎In Birthday Café, children serve up birthday treats to a hungry party! Children seat groups of friends at tables and then distribute trays that have the same number of food items. Features * 20 levels of birthday celebration gameplay * Adaptive pacing to meet each child's math level * Multiple mod...

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An adorable story in its own right, this book lends itself to lots of math fun. It is easy to make a set of copy-cats too. Have fun counting, adding, and subtracting cats!

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Dig through your puppet drawers and see if you can find some mice, make a snake out of a green sock and have fun retelling this classic counting tale in real time. You can also use any plastic jar and have kids guess how many mice it will take to fill it. Guessing volume is math y’all!

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One little red fish (Bubble, bubble, pop!) 

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One little red fish (Bubble, bubble, pop!) 

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You can easily make these with scraps of felt and the song is a snap to learn too. This activity would work well with laminate paper and magnets too. Have parents and caregivers make their own sets to take home for counting and color fun too! Here’s a link to the Jbrary video

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An oldie but a goodie for sure, this counting rhyme still delights little kids. Also, since it is kind of timeless, I would guess most parents and caregivers are already familiar with it. Add extra math by having kids do subtraction and addition as you count the frogs from the log into the pool. Why not talk about how many frogs actually fit on the log. Is there space for one more? And don’t forget to compare the sizes of the frogs and flies! Yum, yum! Here’s a link to the Jbrary video

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Probably my favourite new math resource, I think this would be very easy to turn into a measuring game. Grab some measuring tapes from the dollar store and have fun getting the adults and kids measuring along with the little darling in this story. If you are growing plants in the library garden, measure them too!

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Talking to kids about their everyday lives (like taking baths) is a great way to get them interested isn’t it? Pair this simple counting activity with other bath-time fun, blow some bubbles and you’re done. Here’s a link to the Jbrary video

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Numeracy: It adds up to more than counting 

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Numeracy: It adds up to more than counting 

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A free, downloadable pamphlet that is great for sharing with caregivers. You can use this information to come up with simple "early numeracy tips" during storytime too!

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You can download a word document of some of my favourite "5 little" rhymes here then keep adding your own!

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One, Two, Three, Four!

[Chorus]
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Numbers Rumba all day long

[Verse 1]
Number 1, Number 1
Number 1 is straight but fun
Number 1, Number 1
Number 1 all day long

[Chorus]
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Numbers Rumba all day long

[Verse 2]
Number 2, Number 2
Two big feet on a kangaroo
Number 2, Number 2
Number 2 all day long

[Verse 3]
Number 3, Number 3
Three bananas on banana tree
Number 3, Number 3
Number 3 all day long

[Chorus]
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Numbers Rumba all day long

Oh, let's do the Numbers Rumba
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Numbers Rumba all day long

Hey, let's do the Numbers Rumba
Let's do the Numbers Rumba
Let's do the Numbers Rumba
Numbers Rumba all day long

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(Let's Do) the Numbers Rumba Lyrics: One, Two, Three, Four! / Let's do the Numbers Rumba / Let's do the Numbers Rumba / Let's do the Numbers Rumba / Numbers Rumba all day long / Number 1, Number 1 / Number 1 is

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13 Best-Practice Tips for Early Childhood Math Activities

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13 Best-Practice Tips for Early Childhood Math Activities

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Early math skills-such as counting, sorting, making patterns, and sequencing-are an important part of kindergarten readiness and provide a strong foundation for a child's future development in math. In today's post, we're sharing some universal strategies for incorporating math explorations into your early childhood program.

The tips in this post are adapted from Volume 5 of the tiered AEPS®-3 Curriculum-the "Ready" level, which encompasses more complex developmental and early academic skills. The AEPS developers offer these 13 tips for creating fun, open-ended math activities and embedding math into daily routines, which helps build the math interest and skills of all children across a range of skill levels.

Anchor preschool math experiences with multiple collections of small animals, people, vehicles, and colored plastic blocks.

Use number lines, number cards with pictures and numerals, and dice to encourage complex exploration and learning.

Trim down an egg carton so it has 5 sets of 2 egg indentations (10 indentations total) to make a 10 frame that can be used for comparing up to 5 equal sets.

Let children count by using number cards showing 5 pictures (5 tiny cubes, 5 puppets on fingers). This helps children understand that an amount is the same no matter what item is being counted.

Use number lines to teach children how to count forward from a particular number rather than starting at 1 each time. This helps children understand that the "number after" each number equals 1 more.

Place number-rich items in the dramatic play area (ice cube trays of different sizes, telephones, toy clocks, cash registers, play money, menus, calendars).

Provide play pennies for preschoolers to use to buy pretend snacks and bus tickets that cost a specific number of pennies.

Use puzzles, sorting toys, and other manipulatives to support math learning.

Include books in the library center that feature counting, numbers, and other math concepts. Use story extender activities after reading math books to encourage children to take their math learning beyond the story and set the stage for inquiry and discovery. For example, add lots of hats to the dramatic play area after reading a book about hats for sale so children can incorporate math learning into their play. (Refer to the book Cowboys Count, Monkeys Measure, and Princesses Problem Solve for a practical guide to using storybooks to teach math.)

Use recyclables in the classroom as an inexpensive, dynamic way to provide opportunities for children to explore and investigate (let children use different-size cardboard boxes to arrange in order from smallest to largest, sort objects into, and the like).

Make dedicated math activities available each day in a math center, as a table activity, or as embedded parts of the daily schedule. Plan activities that can be intentionally extended to include math skills as estimation, measuring, ordering or sequencing, and numeracy. For example, have children build a fort using recycled boxes, then ask the class to guess how many children will fit into the fort and test the guesses. And for an All About Me week, plan activities that include math, such as having children trace each other's outlines on paper and then use rulers to measure the height of their paper bodies. Have children color or decorate their paper bodies to match themselves and then make graphs to compare their hair color, eye color, or shoe size.

Use math talk throughout the day to capitalize on teachable moments and expand learning. Say during free play time in the blocks center, "Wow, that's a big tower! I bet it's more than 15 blocks tall. Should we count and check?" Comment during snack time, "Look at how fast Matthew is eating his crackers-he only has 2 left. How many are on your plate, Lisa? Is that more than Matthew has? Or fewer?"

Continue to embed increasingly sophisticated math learning into the classroom schedule. Count aloud to 20 while washing hands (the number of seconds children are encouraged to wash with soap). Post a number line on the wall beside the sink to encourage children who can read numbers to count while washing hands. Assign tasks that involve counting to classroom helpers (counting out 15 plates for snack time, helping an adult take attendance in the morning by writing down who is present and who is absent).

Engaging children in daily math explorations in the context of their lives and routines supports stronger connections to math concepts and more meaningful understanding and practice of new skills. Try the tips in this post to give young children lots of opportunities to develop early math skills throughout the day-and be sure to share your strategies with parents to help them continue the learning at home.

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13 Best-Practice Tips for Early Childhood Math Activities - Brookes Blog

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In today's post, we're sharing some universal strategies for incorporating math explorations into your early childhood program.

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A great book about Patterns that invites children's participation.

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This book can emphasize numeracy regarding quantities of objects during storytime. In your story time you can say “When Sal’s mother was putting the blueberries in the pail, there were a lot of berries, but when Sal took them out, there were a little.” And when you talk with children about quantities by pointing asking “Is this a lot or is this a little?” you are actually showing them that the amount of objects can change.  When you add some, you get more, and when you take away, you get fewer. Asking simple questions like this when looking at two groups of objects and talking about them in this way, helps to develop their numeracy skills.

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Math Counts Too! Promoting Family Engagement in Math Activities at Home

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Math Counts Too! Promoting Family Engagement in Math Activities at Home

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This article was published in Children and Libraries Magazine. The online version can be found at: https://www.researchgate.net/publication/317618503_Math_Counts_Too_Promoting_Family_Engagement_in_Math_Activities_at_Home#fullTextFileContent

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After looking at 22 studies, researchers found that the more parents talked about math with their children, the stronger their children's math skills. In these studies, researchers typically observed parents and children interacting in a university lab, a school, a museum or at home and kept track of how often parents mentioned numbers or shapes. Ordinary sentences that included numbers counted. An example could be: "Hand me three potato chips." Researchers also gave children a math test and found that children who scored higher tended to have parents who talked about math more during the observation period.

The link between parents' math talk and a child's math skills was strongest between ages three and five. During these preschool years, parents who talked more about numbers and shapes tended to have children with higher math achievement. Parents who didn't talk as much about numbers and shapes tended to have children with lower math achievement.

With older children, the amount of time that parents spent talking about math was not as closely related to their math achievement. Researchers speculated that this was because once children start school, their math abilities are influenced more by the instruction they receive from their teachers.

None of these studies proves that talking to your preschooler about math causes their math skills to improve. Parents who talk more about math may also have higher incomes and more education. Stronger math skills could be the result of all the other things that wealthier and more educated parents are giving their kids - nutritious meals, a good night's sleep, visits to museums and vacations - and not the math talk per se. So far, studies haven't been able to disentangle math talk from everything else that parents do for their children.

"What the research is showing at this point is that talking more about math tends to be associated with better outcomes for children," said Alex Silver, a psychologist at the University of Pittsburgh who led the meta-analysis. "It's an easy way to bring math concepts into your day to day life that doesn't require buying special equipment, or setting aside time to tutor your child and try to teach them arithmetic."
2. Keep it natural
The strongest link between parent talk about math and a child's math performance was detected when researchers didn't tell parents to do a math activity. Parents who naturally brought up numbers or shapes in a normal conversation had children who scored higher on math assessments. When researchers had parents do a math exercise with children, the amount of math-related words that a parent used wasn't as strongly associated with better math performance for their children.

Silver, a postdoctoral research associate at the University of Pittsburgh's Learning Research & Development Center , recommends bringing math into something that the child is paying attention to, rather than doing flashcards or workbooks. It could be as simple as asking "How many?" Here's an example Silver gave me: "Oh, look, you have a whole lot of cars. How many cars do you have? Let's count them. You have one, two, three. There's three cars there."

When you're doing a puzzle together, turn the shape in a different direction and talk about what it looks like. Setting the dinner table, grocery shopping and keeping track of money are opportunities to talk about numbers or shapes.

"The idea is to make it fun and playful," said Silver. "As you're cooking, say, 'We need to add two eggs. Oh wait, we're doubling the recipe, so we need two more eggs. How many is that all together?' "

I asked Silver about the many early childhood math apps and exercises on the market, and whether parents should be spending time doing them with their children. Silver said they can be helpful for parents who don't know where to start, but she said parents shouldn't feel guilty if they're not doing math drills with their kids. "It's enough to just talk about it naturally, to find ways to bring up numbers and shapes in the context of what you're already doing."
3. Quality may matter more than quantity
In the 22 studies, more math talk was associated with higher math achievement. But researchers are unable to advise parents on exactly how much or how often to talk about math during the day. Silver said 10 utterances a day about math is probably more beneficial than just one mention a day. "Right now the evidence is that more is better, but at some point it's so much math, you need to talk about something else now," she said. The point of diminishing returns is unknown.

Ultimately, the quantity of math talk may not be as important as how parents talk about math, Silver said. Reading a math textbook to your child probably wouldn't be helpful, Silver said. It's not just about saying a bunch of math words. Still, researchers don't know if asking questions or just talking about numbers is what makes a difference. It's also not clear how important it is to tailor the number talk to where a child is in his math development. These are important areas of future research.

Technology may help. The latest studies are using wearable audio recorders, enabling researchers to "listen" to hours of conversations inside homes, and analyzing these conversations with natural language processing algorithms to get a more accurate understanding of parents' math talk. The 22 studies in this meta-analysis captured as little as three minutes and as much as almost 14 hours of parent-child interactions, and these snippets of life, often recorded in a lab setting, may not reflect how parents and children talk about math in a typical week.
4. Low-income kids appear to benefit as much from math talk as high-income kids
Perhaps the most inspiring conclusion from this meta-analysis is that the association between a parent's math talk and a child's math performance was as strong for a low-income child as it was for a high-income child.

"That's a happy thing to see that this transcends other circumstances," said Silver. "Targeting the amount of math input that a child receives is hopefully going to be easier, and more malleable than changing broader, systemic challenges."

While there are many questions left to answer, Silver is already putting her research into practice with her own three-year old son. She's asked counting questions so many times that her little one has begun to tease her. Every time he sees a group of things, he pretends to be Mommy and asks, "How many? Let's count them!"

"It's very funny," Silver said. "I'm like, 'Wow, Mommy really drilled that one into you, huh?' Buddy knows what you're up to."

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Parents Know They Should Read to Their Kids. Daily Math Talk Is Important, Too | KQED

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A new wave of research finds that there's a link between parent math talk and higher math skills.