The Collaborative joins more than 150 organizations — including school districts, universities, federal agencies, corporations, nonprofits, and others — committed to help recruit, prepare, and retain 100,000 STEM teachers in 10 years.

To become a 100Kin10 partner, the Collaborative underwent a rigorous vetting process conducted by the University of Chicago that reviewed the boldness and innovative nature of Erikson’s commitment to STEM and capacity to contribute to the movement.

The Collaborative recently held an open lab at Erikson for 100Kin10 participants from around the country to showcase its work to build early childhood teachers’ foundational math knowledge.

Participants were introduced to the Whole Teacher Approach to teacher development. Led by instructors Mary Hynes-Berry and Jeanine Brownell, participants got a taste of all the components of a learning lab for teachers. The components included an adult learning activity and analysis of videos of children’s thinking and classroom practice. The learning lab was designed to address all domains of teacher development: mathematical content knowledge, attitudes and beliefs about mathematics, and effective teaching practices.

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The Growing Story by Ruth Krauss, illustrated by Helen Oxenbury, was first published in 1947 but the story is timeless. From early spring through fall, a little boy easily can see how baby chicks, puppies, and plants in the garden grow—but his own growth isn’t nearly as easy to measure—until he finds he has outgrown the warm clothes his mother put away in the spring.

Helen Oxenbury’s warm pastel illustrations will help young readers track precisely how the chicks change in appearance and size; how the rolly-polly puppy becomes a dog; and how the apple tree goes from barren, to bud, to apples ripe for picking. The story links beautifully with an inquiry unit looking at farm animals; it invites rich discussions of how different creatures grow at different rates—a baby chick’s childhood is a matter of months while a human’s lasts for years.

Michael Rosen’s Three Feet Small, illustrated by Valeri Gorbachev, takes a different tack but one that is equally important to little ones. The concern about getting bigger is not just a question of physical growth—it has just as much to do with how getting both older and bigger means we can do more things. The little bear who is the center of this book is just not sure that he is growing—especially when he sees all the things his older sister and his adult relatives can do that he is still too little for. However by the end of the book, he also finds that he needs new clothes and that he is beginning to do some of those things that seemed out of his reach earlier.

These books could be used alone or together to open up a wonderful exploration of the benchmarks children can identify concerning what it means to “get bigger”—either in terms of size or abilities. Rosen’s book includes at least one picture showing a measuring chart—if you don’t already have one in the classroom to mark the growth over several months, you could start one now. However, be sure to emphasize that height isn’t the only attribute that shows growth. Include discussion of other physical attributes such as weight. The most emphasis should be put on how we can measure how much we are growing our brains as well as increasing physical abilities. What are things the children know now and can do now that they couldn’t when they were one year old? How about things they couldn’t do at the beginning of the school year?

We have exciting news to share: the Early Mathematics Education Project at Erikson Institute is now the Early Math Collaborative. Our new name illustrates Erikson’s ongoing commitment to supporting high-quality math education for young children—math education that is practical, rigorous, inclusive, culturally-aware, and developmentally appropriate.

And of course, we have a new website! The goal of this growing site is to become a thoughtful archive of all things early math… from video of children explaining their math thinking, to our own articles about best practices, to links to external resources. And when possible, everything is categorized according to our own foundational math concepts and Big Ideas, as well as the Common Core State Standards; so if you want to, you can search by “shape” or “number composition” to see what we have. On the site, we always strive to give things context and explain why we think they are important.

What do you think? We would love to hear your thoughts about the site in the comments section below. It’s still in testing and we hope to add additional features over the coming weeks, so we are eager for feedback as we continue this journey online.

And please come back soon. Not only do we intend to add additional content and resources often, we also hope to create ongoing discussions around the subject we care about: improving math education in the early years.

Thanks for visiting!

Jennifer McCray, Director
Early Math Collaborative

You can go on to ask the children if they can act out the story so that the number of monkeys in the book will match the number of children playing the monkeys. Be sure to enlist their help figuring out this problem. In doing so, you will be able to assess the children’s ability to estimate as well as their understanding and skill in using 1-to-1 correspondance.

Refer the children to the double spread picture of the monkeys in the tree. Remind them of how many children there are in the class. Then ask them to estimate if there are:

• More monkeys than children in the class,
• Less (not as many) monkeys than children in the class,
• About the same number of children and monkeys.

Record the children’s estimates and some comments about estimations. Depending on the level of the children, either have them count along with you or have them count how many monkeys are in the tree.

It is likely that children will find it hard to keep track of which monkeys they counted and which they didn’t. Ask if the children have any ideas of how they can keep track of the monkeys so each is counted only once. Some may suggest using a post-it or some other kind of marker on the page. However, you can also turn to the picture of the salesman settling under the tree with all the caps stacked in groups of 4 on his head. Ask if this picture would make it easier to see how many monkeys there are. Some children should be able to explain that since each monkey gets a cap, if you count the number of caps, you will know the number of monkeys. Children who have difficulty understanding this point have not yet mastered the principle of 1-to-1 correspondence.

If there are more or less children in the class than the monkeys, involve the children in further mathematical thinking. Discuss alternative ways to do the acting out.

• If there are more children than monkeys in the book, do all the children want to be included? If so, how many caps will be needed? (You can have the children make their own using paper plates.) If you only use the number in the story, what can the children who are not the monkeys do?
• If there are fewer children than monkeys in the book, how many caps will be needed? How many less than the number of monkeys in the book?

All of this rich mathematical thinking is likely to deeply engage the children in a way that a worksheet never could—that’s what happens when we mathematize using authentic playful situations.

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One of our research lessons on number arrangements gives children opportunities to develop visual number sense of quantity and to build subitizing skills (the ability to rapidly and accurately quantify a set of items without counting). The children find many different ways to arrange three popsicle sticks. As they look at their own and other children’s creations, they develop a sense of “three-ness” and the different ways it can be constructed (composed and decomposed).

In turn, teachers themselves have found many ways to give children the repeated experiences they need to solidify their understanding of number.

Program participant David Newman at Chappell Elementary finds it easy to give his preschool children plenty of experience with comparing the value of numbers by having them play a simplified version of the classic card game “War.” The pack of cards he uses only have two suits, stars and dots. While a few cards use the number symbols, most arrange the dots and stars in configurations similar to those found on dice so that the game reinforces subitizing and visual number sense. Appropriately for prekindergarten, the numbers only go up to 6.

Mr. Newman finds it important to introduce the game by modeling. Playing a few rounds with a child while others watch is all that is needed. All cards are distributed face down between the two players. Each player turns up one and the higher number takes both cards. If the same number is turned up, the one marked with a star wins. Otherwise, the winner of the next round takes the cards. Mr. Newman notes that this game is a great way to introduce children to playing a game with rules without adult supervision. He noticed that the game also helps with fine motor skills as the children learn to handle cards and keep them in piles.

Another program participant, Melinda Chum, and her kindergarteners at Bridge School enjoyed creating a Three Museum after doing number arrangements with craft sticks. Later after reading 10 Black Dots by Donald Crews one child suggested, “We could use the dots to make the ‘three museum’ like we did with the sticks.” Ms. Chum put this idea into action.

She invited small groups of children to join her as she brought out a basket of black dots and 3” x 5” index cards. She then modeled how many different ways she could arrange the dots. She labeled one card with a 1-1-1 pattern as she said, “I put one here, one here, and one here.” She went on to demonstrate 1-2 and 2-1 patterns that put two closer together and one further away. The children went on to create their own patterns by sticking their three black dots on the white index cards.

Ms. Chum really understands how important it is for children to think and talk about what they are doing in order to deepen their understanding. So once they completed their patterns, she asked them to place their cards under the labeled number pattern cards and explain why it fit where they put it.

She reports, “It was wonderful to see how they think and decide that their card could belong just about anywhere on the number pattern graph depending on how you turn the card and how you are looking at it. During center time, they continued to think and rearrange their cards, commenting on things like ‘My card looks like one, two and if I turn it this way it looks like two, one. So it could go here or there.”

That rich conversation gave Ms. Chum clear evidence that her children really understood the Big Idea that pictures and objects can be arranged in different ways and that no matter which way they arrange their three-dots-card, there would still be three dots.

Parts of this video are in response to certain points that Dr. Charles Payne made in his presentation earlier that day.  A video of Dr. Payne’s presentation is available here.

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Since a recent session addressed important ideas of geometry, the discussion of data analysis didn’t get much attention—in the workshop, that is. However, the Idea Book includes a variety of great ways to make surveys and analyzing data meaningful, engaging activities.

Heather Duncan did a particularly striking job of explaining how she and her kindergartners at South Shore Elementary have made collecting data from surveys and discussing them a regular part of their classroom life.

Heather prefaced her description of their process by pointing out how important it is to take time to really explore the ideas and emphasize the children’s work and thinking. She typically does a process that stretches from three to five days and always ends up with a product everyone can see.

• Day One, they collected results of a survey, usually related to a topic they were already studying. For example, while studying the human body, Ms. Duncan had them compare each student’s height to a cut-out of an average kindergartener hung up in the class.
• Day Two, they synthesized the results. “We used the chart,” she wrote, “to count and determine totals for each designation (taller, shorter, same size) and whether any groups have more/less or the same amount as any others. We also compare totals from the a.m. class with the p.m. class and discuss any similarities or differences in results.”
• Day Three, they further discussed the results and talked about the best way to show them on a graph. In this case, they decided on a bar graph.
• Day Four, they used the resulting graphs to make some conclusions. She wrote, “Which group had more or the most? Which had less, the least, or the fewest? What do we know about the question or our class as the result of our survey?”

They turned the results into a poster, a bulletin board display, or part of a “trivia book” at the end of the school year. Ms. Duncan comments, “[The activity] has since become practice, because we have found it to be a very rich experience. It’s been invaluable using math in context to study things we care about and to answer questions generated from our own interests.”

The difference between “through” and “between,” for example, could be a difficult distinction for ELLs. Teachers can help students learn these distinctions by amplifying language.

Here is an idea. With small groups of children, create an obstacle course in your classroom where children would need to do the following: walk between two chairs, go under a table, skip around the water table, climb over a cardboard box, and crawl through a tunnel. As you model each movement, use language to describe what you are actually doing: “What am I doing? I am walking between two chairs,” putting an added stress on the positional word “between” and the word “two.” When it is their turn to go through the obstacle course, you can continue to ask all the students what each child is doing.

Then you can invite the students to verbally repeat the sentences, describing their movement as they go through each obstacle in the course. When everyone has completed the entire obstacle course, you can ask, “What did we do in this obstacle course?” They would say: “First we went between two chairs, then under the table, then we went around the water table, then over a cardboard box.” On another day, you can ask the children to create a different obstacle course and once again intentionally amplify language to help them learn the labels for the positional words.

Using the above activity enables ELLs to learn not only the labels for the positional words but gives them the linguistic context they need to use them. Doing the language activity with children answering all together provides differentiation in terms of levels of English proficiency. For children who are in the very early stages of English language development, techniques that combine language with action provide repeated exposure to conventional models of English. For children who are more fluent, the verbal component gives them the opportunity to use English in a conventional fashion without fear of being singled out.

Once children have experienced the action and been exposed repeatedly to the label for each prepositional word, you can continue to amplify the language by matching those words with drawings that illustrate the concept they represent. You can make these drawings into cards that can be used for games or to give students directions for lining up or during other transitions throughout the day.

These strategies to make content comprehensible and promote language development are beneficial to all students, but they are essential to DLL students in order to learn foundational concepts and the language we use to describe them.

In the same way, Ann Morris’s Shoes, Shoes, Shoes and Bread, Bread, Bread can jumpstart a survey of the different kinds of shoes the children are wearing or the kind of bread they like, as well as encourage some serious thinking about good ways to categorize them. Make sure you have them show the results. Once again, the best thinking comes as the children and teacher converse together about what questions they have and how they see the data making sense.

Ms. Beza comments, “I was surprised by the popularity of the bulletin board. Parents and students alike stop to find and count all the objects. I change the objects occasionally to make it more interesting. This has been very beneficial in motivating children to count objects independently.”

Laura Carbajal of Armour Elementary and her kindergarteners also used the book to develop a deeper understanding of number sense and number recognition using dice. Laura had each of her students roll a die and then count and identify the number of dots. Then they found the number on the number chart and wrote the numeral. Ms. Carbajal gave her students many opportunities to practice by moving the activity into the centers. The children in the classroom have a heightened awareness of numbers as they discover them in books and see their use in everyday routines. The students are enjoying counting using manipulatives in class and real-life objects at home.

Ms. Carbajal commented, “I have a different perspective and understanding about mathematical thinking at my student’s level.”

Adaora doesn’t want to eat her paw-paw fruit because she loves the shape inside – a star. The conversation with her cousin that ensues sets the stage for an exploration of shape and the search for one shape in particular – a triangle. As Adaora sees that her world is full of shapes and learns the names of these shapes, we also learn about life in a Nigerian village.

As we journey with Adaora and her cousin, we see the rectangle of Uncle Eze’s robe, the circular tops of the elephant drums, and many other beautiful shapes in her world. We see the shapes, but we also see the culture and hear the life of the village. We are drawn in with Adaora on the search for the elusive triangle, and when she finds it, we are able to celebrate with her. Her exploration invites the reader to search their own world for shapes and to see that geometry is all around us.

This book is a wonderful way to connect mathematics with children’s lives. Teachers can explore the culture of the children in their classrooms from a geometric perspective by encouraging the children to identify different shapes unique to their family and discuss the shapes that they have in common. Having collected all this data, don’t forget to graph it to answer the question, “Which shape is most common in everyone’s family?” The results will be both fun and enlightening. Children may eventually be able to come up with additional questions this data can answer.

Program participant Leandra Gonzalez at Lara Elementary Academy found she could extend the book to do an authentic assessment of how well children understood numerosity. After reading the book to her prekindergarten class, she invited small groups of children to decide how many dots they wanted to use to create their own picture and to dictate something about what they had created. Ms. Gonzalez had each group share their pictures to continue the good conversations.

She says, “When students were given the opportunity to create something and decide on their own how many dots they needed for their creation, I feel I got a true idea of their comprehension of the concept. I had the opportunity to hear them count, use number words, and apply quantity.”

Crews is not the only author to use the simple dot to bring numbers to life. Herve Tullet’s Press Here is an amusing commentary on how many young children have become proficient at pressing on computer screens to bring about some kind of change. The book uses instructions on one page such as “Five quick taps on the yellow dot” and so when the child turns the page, they see a line of 5 yellow dots! It’s the magic of the imagination. Here again, all kinds of learning fun can happen as children count taps, give shakes, and find the patterns. Inviting them to do their own variations on the book will extend the delight and the understanding even further.

Beyond counting and growing patterns, there are many more math-related ideas and activities that can be drawn from the book. Building and decorating a real snowman outdoors provides opportunities for children to talk together about spatial relations, size, quantity, symmetry, and shape as they plan and problem solve. Indoors, children can create their own paper snowman collages with art materials such as ribbons, pom-poms, stickers, yarn, and so on. Children can dictate a story about their finished snowmen, using math language to describe the number, location, and attributes of all the trimmings they selected.

One Mitten by Kristine O’Connell George, The Mitten Tree by Candace Christiansen, and Missing Mittens by Stuart J. Murphy play with the idea that mittens come in pairs in other ways.

All these mitten stories inspired a lot of mitten math! The activities began with the children doing a binary sort. They divided their handwear into two groups: mittens and gloves. They then compared the two sets of handwear by making a bar graph to see which set was larger.

The next day the children found the same collection could be sorted in many other ways. All they had to do was to change the attributes they used. Children sorted both mittens and gloves by size, then re-sorted them based on whether or not they had stripes.

The children also used their mittens and gloves to make repeating patterns on the rug. Later, the children used paper mittens to create patterns that they could glue down.

“Starting with interesting stories and using the mittens and gloves they wear every day really engaged the students,” reflects Trevino.

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Sort It Out! by Barbara Mariconda provides a great model for incorporating math into everyday activities. This brightly colored picture book shows Packy the Pack Rat trying to obey his mother’s order to put away all the treasures he has collected.

The Button Box by Margarette S. Reid could launch another exploration of a collection many teachers may have in their sewing closet. In this story, a little boy finds all kinds of stories in his grandmother’s collection of buttons. Grandma’s Button Box by Linda Williams Aber uses another approach. In this book, Kelly and her cousins help Grandma sort the buttons that spilled when Kelly accidentally knocked over the box.

They also got lots of practice using directional language such as “down the stairs” or “through the opening” and relative words like “near to.” Sharon knew that both first- and second-language learners need many repetitions of these terms. These words can describe a relationship between two objects that shift. For example, one person pointing left looks like they are pointing right to someone facing them, or just as a bush that might have been in front of you at one point soon is behind you as you continue along a path.