Where's the Math?

Books, Games, and Routines to Spark Children's Thinking

Mary Hynes-Berry,Laura Grandau

• Editorial: The National Association for the Education of Young Children
• Año: 2019
• ISBN:
  9781938113529
• Categoría: Pedagogía
• Categoría: Enseñanza de matemáticas

Make math learning both meaningful and fun by building on children's natural curiosity to help them grow into confident problem solvers and investigators of math concepts.

Using five math-related questions children wonder about as a framework, this book helps you go deeper into everyday math with children by offering:

• A basic overview of math ideas behind matching and sorting, patterns, number sense, measuring, and spatial relationships
• 20 activities appropriate for children in preschool and kindergarten based on new and classic children's books, games, and classroom routines
• Suggestions for individualizing activities for diverse learners
• Recommendations for more than 75 children's books that encourage math-rich thinking and investigation
• Examples of intentional questions, comments, and conversations that stretch and focus children's understanding of math concepts

Empower yourself with the guidance and ideas in this practical resource to use play and storytelling to challenge children to think more complexly about the math in everything they see, hear, and do.

Chapter One

MATCHING & SORTING

HOW ARE THESE THE SAME? HOW ARE THESE DIFFERENT?

Math Concepts Explored in this Chapter

• Attribute

• Binary sorting

• Comparing

• Comparing and ordering sets

• Exact matching

• Matching

• Multiple set sorting

• Open sort

• Set

• Single attribute sorting

• Sorting

Almost from the moment they are born, babies can sense in a very general way that the things they feel and the world around them can be the same or different—warm or cold; full tummy or empty; sleepy or wide awake (Gopnik, Meltzoff, & Kuhl 2001). As they grow into toddlers, they begin to compare and contrast various qualities, or attributes, that people, places, or objects may share. At this age, children are especially aware of attributes that they can discover through their senses, like size, color, smell, taste, sound, and texture. They also use more and more specific words to explain what they like and what they don’t, but they still depend on making sounds, facial expressions, and gestures to communicate that while red is their favorite color, they don’t like red tomato juice or that scratchy red sweater. By the time they enter preschool, many young children begin to think logically about the ways attributes can be used to organize objects.

Exploring Matching and Sorting

The preschool class at Rocky Glen School returns from an excursion with their first grade buddies. They collected pinecones, seeds, twigs, and other natural treasures outdoors, and now they are sorting their finds into bins.

Six-year-old Tina is helping 3-year-old Aza use the word and picture labels on the bins to match the objects she has picked up. “This is the same!” Aza announces as she holds a pinecone up to the photo on one of the bins and then drops it into the bin. “We can’t put the seeds here ’cause they don’t match,” she tells Tina, who nods and helps Aza find the bin labeled seeds.

Another pair of buddies, 4-year-old Timon and 7-year-old Jaz, had decided to collect only rocks while they were outside. The rocks in their basket range from small, smooth pebbles to large, chunky stones. Jaz grabs a few containers that do not have labels and says, “We have to figure out how to sort our rocks. There are lots of ways they are the same and different.” Timon takes one container and says, “Can I do just my favorites, the little shiny ones we found in the creek?” “Go for it,” Jaz laughs. He works on the other rocks, clustering the medium-size rocks into a pile together and tossing the biggest rocks into a pail. As he works, Jaz examines the rocks more carefully and exclaims, “Timon, our rocks are same and different in some really cool ways. Some are just brown or black, but I’m seeing some that are kind of striped and others like this one, all speckled black and gray.” Timon looks over and then finds one of his smaller ones, declaring, “This is speckledy too!”

Ms. Priti, the preschool teacher, comes over to see what is so exciting. As both boys pull out more examples, she smiles and says, “What superstar observers you two are! You could put the ones that are speckled in one container and then decide what other categories you want to use. What do you think?” The boys enthusiastically agree and set to work. Because Jaz is so intrigued by the many different types of rocks he is seeing, Ms. Priti makes sure to point out the rock books she put on display in the science learning center in preparation for this activity.

Young children’s understanding of the rules that guide matching and sorting, or dividing and organizing a group of objects into sets by shared characteristics, follows an established developmental trajectory (Early Math Collaborative 2014).

Exact matching, or recognizing and identifying objects that are completely alike, is the earliest stage. In the vignette above, when Aza sees that the pinecone she is holding looks the same as the one on the photo label on the bin, she understands that items with the same exact attributes can be matched.

Single attribute sorting expands on matching. Timon and Jaz begin sorting their rock collection by focusing on size. Jaz, who is older, can see that it makes sense to break the large collection into three categories of size: small, medium, and large. Very often, younger children will do single attribute sorting using color because determining the difference between red, blue, and green objects is much more straightforward than judging differences in size, which can be more relative.

Binary sorting is closely related to single attribute sorting—a collection of objects is divided into two distinct sets, one set with a specific attribute and one set without that specific attribute. Essentially, this is what Timon does when he takes all the small, shiny rocks from the collection and leaves the others for Jaz to deal with.

Multiple set sorting calls for focusing on several different attributes and creating increasingly complex categories based on those attributes. Timon is happy to follow Jaz’s lead in deciding which rocks are a solid color, speckled, or striped, but Jaz sees that he could make one set of rocks that are large and have different colors in them and another set of rocks that are large, are a single color, and have a rough texture.

Comparing and ordering sets means observing and analyzing different sets of objects to compare them using specifically mathematical attributes: amount (quantity) or size (magnitude). By the time children are a year old, they have a strong natural instinct to look at groups of objects and wonder “Which has the most?” or “Which is the biggest?” (Sarnecka 2016).

You can turn just about any classroom activity into a mathematical experience through conversations. For example, ask the child who enjoys playing with toy vehicles to tell you how rescue vehicles are the same as and different from delivery vans. Not only will she enjoy sharing her expertise, explaining these similarities and differences will help consolidate her understanding and lead to new discoveries and learning.

Using Open Sorts to Promote Mathematical Thinking

As children have more and more experiences with sorting objects as well as gathering and interpreting information, they develop a more complex understanding of the various ways they can organize collections. Eventually, they discover that a collection of objects can be sorted in many different ways based on the attribute or attributes they choose to look at. It is important to provide children with a lot of opportunities to do open sorts, where they can sort a random group of items any way they want. This encourages logical thinking. When children are organizing and sorting objects, encourage them to explain the rule they used. You will be surprised and delighted with how deep and flexible children’s thinking can get when they are engaged.

When sorting experiences are linked to children’s everyday lives, they make meaningful connections and grasp the math concepts more readily than when they work with commercial objects that have specific, limited ways to be sorted. They are...