Building Blocks Math From Pre-K to Grade 2

Monday, September 8, 2008

Last week, The Washington Post explored key issues in math education.

This week, staff writer Michael Alison Chandler reports on the

development of math sense and skills among the youngest learners.

Outside a kindergarten classroom at Lakewood Elementary School in Rockville, students used a bar graph to show how they felt about returning to school. Students placed green stickers on the graph to indicate whether they felt scared, nervous, okay, happy or thrilled. Across the hall, first-graders traced numerals and updated a tally chart of "The Number of Students Absent."

These students will be steeped in numbers and shapes for the next nine months, as teachers set out to instill in them basic principles of mathematics.

With math skills at a premium in a technology-driven economy, children are expected to learn more math, and sooner. Algebra is taught in middle school to help prepare students for advanced math in high school. High-stakes standardized tests add to the pressure. The first years are considered crucial for laying a solid math foundation.

Kindergarten: A Readiness Gap

In the first week of school at Cool Spring Elementary in Prince George's County, kindergartners counted little rubber trains or cars at their desks as the teacher called out different numbers. Some students tallied the right number of objects each time, said teacher Laurie Walker. Others understood the exercise in Spanish but not in English. Still others were unsure of how the word "eight" translated into the colorful toys at their fingertips.

Kindergarten traditionally has been the starting place for formal math education. Earlier lessons in math concepts are often informal or sporadic. As a result, students arrive in kindergarten with significant variations in what they can understand and do.

To raise the level of math readiness for all students, there is a growing push among policymakers and educators to start teaching math to younger children through universal pre-kindergarten programs or other preschool instruction.

The National Council of Teachers of Mathematics introduced standards for pre-K math in 2000. The standards emphasized these concepts as important for children to begin to understand: numbers; shapes and sizes; and measurement. Many states are drafting similar standards to focus math education in pre-K programs. There are also efforts to train child-care providers and parents to be more effective math teachers.

A First-Grade Math Snapshot

The first-graders at Lakewood Elementary School sat cross-legged on the floor on the first week of school. Each was equipped with a lap-size dry erase board, a marker and a white sock for erasing.

In response to the first question -- "How old are you?" -- students put a wobbly 5, 6, or 7 on their white boards and then displayed them proudly. One boy wrote "6 +."

"Why did you do that?" Lisa Adkins asked. "I'm six and a half," he told his teacher. He did not know how to write one-half, he said, so he wrote the symbol for plus, because he knows that means more.

This is the kind of conversation that Adkins likes to have in class. Rather than asking students only to memorize and record facts, she wants them to explain how they come up with answers.

"There is more of an emphasis on the thinking about the math," she said.

In some classrooms, students use journals to record math thoughts.

What Second-Graders Should Know

Virginia second-graders are expected to master 22 standards in the math curriculum. Here are a few examples provided by the Virginia Department of Education ( http://www.doe.virginia.gov/go/Sols/home.shtml):

Number and Number Sense

The student will compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words (greater than, less than, or equal to).

Computation and Estimation

The student, given a simple addition or subtraction fact, will recognize and describe the related facts which represent and describe the inverse relationship between addition and subtraction (e.g., 3 + __ = 7, ___ + 3 = 7; 7 -- 3 = __, and 7 -- __ = 3).

Measurement

The student will:

a) Count and compare a collection of pennies, nickels, dimes and quarters whose total value is $2.00 or less; and

b) Identify the correct usage of the cent symbol (¢), dollar symbol ($) and decimal point (.).

Geometry

The student will identify, describe and sort three-dimensional (solid) concrete figures, including a cube, rectangular solid (prism), square pyramid, sphere, cylinder and cone, according to the number and shape of the solid's faces, edges and corners.

Probability and Statistics

The student will record data from experiments, using spinners and colored tiles/cubes, and use the data to predict which of two events is more likely to occur if the experiment is repeated.

Patterns, Functions and Algebra

The student will identify, create and extend a wide variety of patterns, using numbers, concrete objects and pictures.

Helping Teachers

The Post interviewed Maria Gallagher, a child-care specialist for Fairfax County's Office for Children, about how she trains child-care providers to teach math.

Q: How has early math education changed?

A: It used to be rote memorization and lots of practice -- worksheets and drills. The new theory is that mathematical experiences need to be more hands-on. They are more of a part of everyday life. . . . Rote memorization is abstract. . . . Young children need to learn in concrete ways. We used to never be able to count on your fingers; now we encourage it.

What are some ways you train child-care providers to teach math?

Look for natural ways that children can engage in math. If they are playing at a sand and water table, put out pots and pans and cups. . . . Ask children to predict how many cups it will take to fill up that pot. When it's time to set the table for snack time, ask children to count the number of people there, and then put out a plate for each one. . . . Don't set a preschooler down and say, "Now we are going to work on math concepts."

What are some other tools you can use?

Just the language you use helps bring math reasoning into your day. Talk about "fewer," "less than," "more than," "adding to." . . . You also want to have the right materials in the classroom. For example, have things that children can sort and classify by shape and size -- buttons and keys and shells. Math is all about learning about comparisons and putting things into sets and being able to differentiate and classify. These are tools you use later in geometry and algebra.

Math Thinking Emerges

"Most math started by trying to describe the world around us in one way or another," said Henry Kepner, president of the National Council of Teachers of Mathematics. "What is shorter or taller? How does this compare to that? Is that bigger or longer?"

Children encounter math when building a tower of blocks, sharing jelly beans with a friend or measuring their height on the kitchen door frame.

But it takes a teacher or a guide to help "mathematize" the lesson, said Douglas Clements, an expert on early math education at the University of Buffalo. That often means giving children a vocabulary for what they are doing or helping them analyze the activity.

Many approaches to early math education center on capturing children's natural interest in observing, measuring and comparing.

Math at Home

Here are tips for parents or child-care providers who want to introduce math concepts. They are adapted from guidelines promoted by Fairfax Futures, an organization that promotes early childhood education.

With an infant or toddler:

· Count buttons as you dress your child; count the number of cookies on a plate.

· Use toys that allow your child to sort shapes.

· Show your child how to recognize patterns; arrange toys or food by whether they are the same or different.

· Use a few number words, such as "one" and "two."

With a 2- or 3-year-old:

· Make counting a part of daily routines. Count steps as you walk.

· Ask your child to help you sort socks by color and size.

· Teach your child common shapes, such as circle, square and triangle.

· Make comparisons based on size (big or little) or position (under or over).

With a 4- or 5-year-old:

· Ask your child to help you use measuring cups and spoons when following recipes.

· Talk about time with your child. For example: a long time, a short time, before you go to school, after dinner.

· Help your child trace the shapes of household items onto pieces of paper.

· Ask your child to guess how many grapes will fill a cup; then fill the cup with grapes and raisins to see the difference in number.