Embracing Math

Cultivating a Mindset for Exploring and Learning

Deanna Pecaski McLennan

• Publisher: The National Association for the Education of Young Children
• Year: 2020
• Print ISBN: 9781938113659
• eBook ISBN: 9781938113666
• Topic: Education
• Subtopic: Early Childhood Education

Nurture Creative, Exploratory Math Learning

Discover what math teaching and learning looks like in the playful, emergent environment of the early childhood classroom. Every day, children explore math concepts in their conversations and interactions. You can build on that natural curiosity by engaging children in meaningful, complex math learning opportunities that are grounded in their observations and questions.

Based on the experiences in her own classroom, author Deanna Pecaski McLennan helps you reflect on your curriculum through a mathematical lens and see the potential for math teaching and learning everywhere. Each chapter of this engaging, easy-to-read book is packed with practical strategies and ideas for fostering hands-on, collaborative, integrated math explorations and inquiries with preschoolers and kindergartners.

With the information and guidance in this resource, you will develop a math-rich classroom while increasing children’s interest, confidence, and success in mathematics.

PART 1
Exploring Math with Open-Ended Materials and Strategies

Val and Emerett, both 5 years old, search through a basket full of shells, studying and picking out their favorites as they describe what they notice.

“Oh, this one is pretty!” says Val. “Look at how the colors look like a pattern.”

Emerett holds up a scallop. “I like the dark purple on this one. Purple is my favorite color. I wonder why the purple ones aren’t all this dark.”

After sorting through more shells, Val points out, “This one has long ridges in it. It feels bumpy.”

“This one is smooth on one side,” replies Emerett, “I like the way it feels soft, but it’s hard.”

“Hey,” Val says excitedly, “we should start a collection!”

“How many shells do you need to have a collection?” asks Emerett.

“I think we have enough, but let’s see. One, two, three …”

Val counts. “Okay, we have 20 shells.”

“That’s a lot! We can use our collection to start a store.”

“Yeah,” Val agrees, “but I don’t want to sell them. Let’s use them for money. The purple ones can be worth one dollar and the white ones worth two dollars.” She pushes the shells into two separate piles.

Emerett wrinkles his nose. “The purple ones are prettier. They should be worth more. Let’s make them two dollars and the white ones one dollar. I’m going to get a tray to put them in.”

Open-ended materials—or materials that can be explored, played with, and used in many different ways—have the potential to draw children deeply into an experience, enhancing their engagement, development, and learning (Daly & Beloglovsky 2015). These materials are transformed into whatever vision a child has in a particular moment of play—feathers are added as spices to a delicious stew, a scarf is suddenly an invisibility cloak, and tree cookies become stepping stones in a pond. Take the time to thoughtfully consider the materials in your classroom and ask yourself questions like the following:

▶ What potential does this object have for sparking children’s interest and sustaining their learning?

▶ Are there real objects? Found, recycled, and natural materials? Unconventional materials?

▶ Does the material appeal to the children’s senses?

▶ Will children be motivated to use the material innovatively in their explorations?

▶ Are there materials that are specific to the community, city, and/or geography where your program is located?

▶ Do the materials reflect the diverse backgrounds and cultures of the children in your class?

In addition to supporting play, open-ended materials can serve as supports in children’s exploratory and organized math learning experiences. Sometimes the mathematical potential for certain materials is not immediately obvious, but when children are provided with opportunities to explore them in depth and incorporate them in their play—pretending, combining, and thinking—objects often naturally become mathematized (that is, framed and explored using math terms and concepts). Just as Val and Emerett pretended the shells were money for a store in the opening vignette, open-ended materials can inspire, provoke, and extend children’s play, shaping the setting and story line for themes of exploration. For example, children might spontaneously notice and wonder about the many colors, shapes, and sizes of buttons in a collection and decide to sort them accordingly. Other times, math learning experiences with open-ended materials are planned and purposeful, like when children used wooden dowels to measure the length of the room.

Open-ended materials are a map that children can use to navigate the complex, abstract world of math through tangible, hands-on experiences. They create opportunities for children to test their own mathematical theories through authentic exploration in a real-world context, which in turn helps to build their confidence, interests, and abilities.

Using Math Tools

A few 4-year-olds are grouping toys in baskets, and I ask if they know the total amount of toys. Tamin begins to quietly mouth numbers as he counts, using his fingers as an aid. However, as soon as Tamin sees me notice what he’s doing, he quickly hides his hands behind his back and looks away.

I want the children to recognize that it’s okay to use tools to help us in math explorations, but I also don’t want to call Tamin out specifically. He is shy and already seems embarrassed about being “caught” using his fingers. Instead, I announce to the group, “I think I might know how many there are. If I want to add three to five, I can use my fingers to help.” I hold both my hands up in front of me and model how I can use my fingers to count. “Five,” I say, waving my left hand. Then, wiggling each of the three fingers raised on my right hand, I continue, “Six, seven, eight.” Sending a smile toward Tamin, I explain, “Fingers are a great math tool because we always have them with us.”

Using imaginative, innovative materials in the classroom helped me rethink what a math tool might be. While they can take many forms, standard and nonstandard, they can be grouped into a few broad categories. Flynn (2017) identifies five categories, including the following two, which are the primary focus of this book:

▶ Manipulatives, or physical objects—including open-ended materials—that help children tangibly explore math ideas (blocks, geoboards, connecting cubes, even your own fingers!)

▶ Representational tools, or resources that help children organize, explore, and represent numbers (five and ten frames, number lines, hundreds charts)

These math tools invite children to become immersed in math experiences that engage their senses, helping to connect concrete actions to abstract math concepts. Take the time to introduce and model using standard math tools before having children use them. Provide children with the time and space to practice using a tool in teacher-guided small group work like a planned activity. Once children are familiar with the tool, make it available for children to access and use independently. You can continue to support and scaffold children’s use of these tools while engaging in playful situations together, helping children to notice and name math learning opportunities as they arise naturally. Eventually, children will incorporate the math tool in meaningful ways in the context of their future play and explorations.

Some Terms and Tools to Know

Using and understanding math terminology can empower teachers and children. Throughout this book, specific math vocabulary and learning tools are mentioned. Here are a few brief definitions for those terms and tools.

code: a set of instructions for a computer

coding: the process of creating step-by-step instructions a computer understands and needs in order for its programs to work

five frame: a graphic organizer made up of five equal-sized boxes (each large enough to hold a counter) arranged in a row

hundreds grid: a graphic organizer made up of 100 equal-sized boxes usually arranged in rows of ten

number line: a straight line with numbers placed at equal intervals along its length

precoding activities: developmentally appropriate games and activities in which children explore some of the concepts involved in coding in ways that are meaningful to them

ten frame: a graphic organizer made up of 10 equal-sized boxes (each large enough to hold a counter) arranged in two rows of five

CHAPTER 1

Unexpected Treasure

How Real and Recycled Objects Inspire Thinking and Learning

To a young child, the world is full of materials to touch, discover, and explore. To find, collect, sort, and use materials is to embark on a special kind of adventure. For adults, gathering materials means rediscovering the richness and beauty in natural, unexpected, and recyclable objects that are all around us, but not often noticed.

—Cathy Weisman Topal and Lella Gandini,
Beautiful Stuff! Learning with Found Materials

One of my favorite things to do is grab a...

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• Introduction
• About the Book
• Part 1: Exploring Math with Open-Ended Materials and Strategies
• Part 2: Embedding Math in All Areas of the Classroom
• Part 3: Scaffolding Mathematical Inquiry
• Appendix: Reproducible Resources for Families
• References
• Resources
• Acknowledgments
• About the Author