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Teaching Math Every Day
By Nancy P. Alexander

"Derrick will not be returning next fall," Mrs. Williams told Mr. Hernedez the director of the preschool Derrick attended.

"I'm sorry to hear that," Mr. Hernedez replied. "Is there any problem? Has anything happened that I'm not aware of?" We'll really miss Derrick. He's progressed so much in the year he's been with us."

"That's just it," commented Mrs. Williams. "I don't think he has progressed nearly as much as my sister's child who attends another preschool. They visited last month, and my niece could count to 100, name all the shapes, including trapezoids. I'm afraid Derrick won't be ready for first grade. He's really had a good time here, but my niece is only two weeks older, and Derrick can't do nearly all the things that she can do."

"Why don't you have a seat, and let me show you Derrick's records. Maybe we haven't kept you as well informed as we should have," Mr. Hernedez said.

Mike Hernedez opened his file drawer and removed Derrick's portfolio. One by one, he reviewed the contents with Derrick's mother, especially the ones related to mathematics.

"Here's a photo of him using the blocks taken just last week. The teacher's note shows that he estimated the number of blocks that it would take to make a road as long as the shelf. Then he got the yardstick and a ruler and figured out that they were four feet long together. She goes on to describe how he continued to build sections of the road using that measurement as a reference. You, know, that's pretty amazing for a child his age."

"I remember that day," responded Mrs. Williams. "When I picked him up, he was all excited about the long road he had made. He said he made it as long as the shelf, then two times as long, and then three times as long. I really didn't think about it being math, but I guess it is. I thought he just had a good time with the blocks."

"When children learn through play, the learning is relevant and meaningful. They don't tell you exactly what they are learning because they may not realize themselves that they are learning math skills. The children simply have an idea and need to figure out how to follow through on their idea with the teacher's help. And estimating and measurement are very important math skills. It is clear from his teacher's notes that he really understands the concept of estimating and linear measurement."

"Here's a checklist of some of his other accomplishments," continued Mike bringing out a checklist of skills that Derrick's teacher had completed for his portfolio. "According to this, he is certainly within the expected range for skills in math. All of these are checked off, which means that his teacher had observed him using the skills during some of the many activities they do during a typical day."

"Did you know that he was especially good at recognizing and making patterns? His teacher saw evidence of that according to this anecdotal record. It describes a very complex pattern he made with the parquetry blocks. Patterning is another important concept that he's mastered. He could easily copy the patterns that were made with the cube blocks. The anecdotal records show that he understands the concept very well. Since mathematics is based on patterns, understanding patterns is important in having a solid foundation for math."

"Here's a record about a conversation the teacher had with him about time. His teacher notes that Derrick was able to show her when school begins and ends. He could also explain about minutes and hours," Mr. Hernedez explained.

"I've noticed that he does look at the clock when we're in the car. The other day, he told me that we only had 10 minutes to get to school! I was surprised that he realized that," responded Mrs. Williams.

"Some people don't realize that math is a lot more than counting. Children need to learn about sequence, measurement, patterns, and much more. Many times children can count to thirty or more, but they don't understand the one-to-one relationship. When they don't understand that each number stands for an item, then they may count really high, but it's just repeating words without understanding-sort of like saying words in a foreign language without knowing or understanding what the words mean," explained Mr. Hernedez.

"Let's look at some more," he continued. "Here's a copy of his story about a graphing project Derrick did with a group of children. After several of the children started talking about what foods they liked most with peanut butter, the teacher helped them make a graph, and here's a copy of it. Seems three of them liked peanut butter with banana best, and four of them liked it with jelly more! Here, Derrick even wrote his name-at least his first three letters-beside the jelly jar picture that represented his preference. Graphs like this are an excellent way for children to begin to understand abstract concepts in a useful way. The children learn that each picture represents one child who liked that item most. And they begin to see how graphs work."

"He told me about making a picture of who liked peanut butter best, but I didn't realize they were making a graph. I thought it was some sort of art project," Mrs. Williams contributed.

"Let's take a look, while you're here at the screening Derrick's teacher just completed. Here's the math section. Actually, he's right on target for his age, and even above in some skills. I don't see anything that would make me concerned that he would not be ready for first grade. Why don't we make an appointment for you to come back, and I'll ask Derrick's teacher to meet with us and talk to you more about his progress."

"Why, yes, that would be great. I would like to hear more about what he's done. You've already reassured me a lot. Thank you for your time. This has been very enlightening and helpful."

The Importance of Frequent Communication Between Teachers and Parents
Mrs. Williams judged Derrick's preschool on what she saw and compared it to what her niece was doing. This anecdote illustrates the importance of regular and frequent communication between teachers and parents and the variety of math skills children learn beyond counting and shapes. There are many opportunities for teaching important math skills each and every day. Two concepts that are particularly important are: informal measurement and classifying. Evaluate the chances you have to incorporate these two math skills into the experiences you provide for children.

Informal Measurement
Consider the words below as they represent informal measurement experiences. Identify ways that the children in your classroom become aware of informal measurement and opposites. Make a point of using the words as you talk to children and note when you see examples of children understanding and using these words and concepts.

1.big-little

9.long-short

2.cold-hot

10.loud-soft (sound)

3.fast-slow

11.more-less/fewer

4.fat-skinny

12.near-far

5.heavy-light

13.older-younger (newer)

6.higher-lower

14.tall-short

7.large-small

15.thick-thin

8.later-sooner (earlier)

16.wide-narrow

Classifying
Classifying is another important math skill for young children. Many opportunities to classify materials occur in the daily activities of a classroom. Here are a few to watch for and incorporate as you work with children. Communicate to parents the examples of classifying that you see. Let parents know how the activities develop math skills in young children:

Association
Class name
Color
Common features
Function
Material
Number
Pattern
Shape
Size
Texture

Mathematic Opportunities Throughout the Day
Below are some examples of the various types of mathematical opportunities that occur in a child's daily routine. How many have you seen?

Texture

Ming Li says, "I found all the rough paper."


Order

The teacher asks, "Do you want the story now or would you rather finish your collage?"

 

Comparison

Clayton looks for the largest cookie.

 

Function
Madison says, "I'm going to find all the things I can use to draw."

 

Sequence
Quentin looks at the schedule to see what comes after group time.

 

Fractions
Sudi and Rachal divide the counting bears equally. Sudi gets half and Rachal gets half.

 

Color
The children make a train, using only the yellow chairs.

 

Class name
The teacher says, "Let's put our snacks over here."

 

Parts of the Whole
Shadonna breaks the play dough in two pieces and gives part to Daren

 

Pattern
Taylor puts cube blocks on his construction: red, blue, yellow, red, blue, yellow, red…

 

Material
Latonia sorts out the wooden and the plastic blocks.

 

Time
"Can we have just five more minutes?" asks Michelle.

 

Numbers
Jose says, "I need four more bears."

 

Size
A child says, "These cars are bigger than those."

 

Pattern
Kristen says, "I have a new striped shirt and striped pants, too."

 

Temperature
"Look how cold it is!" exclaims Jerod, pointing to the thermometer.

 

Number words
"That says four," states Haley, pointing to the word on the cover of a book. "That's the story about the four fish."

 

Association
Brad says, "I'm going to find a spoon to mix the paint."

 

Common features
Mario tells another child, "Look, all the trucks have big wheels!"

 

Shape
Sheri uses all of the triangle blocks and looks for more.

Seriation

Lois lines up the blocks from shortest to longest.

Nancy P. Alexanderis Executive Director of the Northwestern State University Child and Family Network in Shreveport, Louisiana. She is the author of many articles that appear in early childhood publications and the book, Early Childhood Workshops That Work: The Essential Guide to Successful Training and Workshops published by Gryphon House, www.gryphonhouse.com