Logo Homeschool World ® Official Web Site of Practical Homeschooling Magazine Practical Homeschooling Magazine
Practical Homeschooling® :

Teaching Arithmetic

By Sam Blumenfeld
Printed in Practical Homeschooling #42, 2001.

Find out what counts about how to teach arithmetic.

   Pin It

Sam Blumenfeld

In my last column I discussed the genius of our place-value arithmetic system, how it consists of only ten abstract symbols - we call them numerals - with which we can perform any arithmetic function.


Arithmetic is a counting system, used to keep track of quantity. Thus, the first task is to teach your child to count. You can use pennies, for in the future your child, like everyone else, will be using arithmetic mainly for keeping track of money. Show your child that the numeral 2 stands for two units, or pennies; 3 for three pennies; etc. Show how a nickel stands for five pennies. Thus the child sees the numerals and the quantities they stand for and can articulate this information. One uses all the senses in learning to count. And let your child count anything that can be counted: days, weeks, years, birthday candles, marbles, pages in a book.

Show the child the number at the bottom of each page so that he or she learns the convenience of using numbers. Incidentally, numerals are merely quantity names. The word five, for example, means the sum of five units and position five in a sequence.

The Four Operations

Once your child has learned to count at least up to 50 or 100, you can begin to teach the four basic arithmetic functions: addition, subtraction, multiplication, and division, starting with simple addition facts. Each fact should be demonstrated with concrete items, so that the child sees the truth of the fact. Again, using pennies, demonstrate the truth of 5 + 6 = 11 by having the child count the five pennies at the left plus the six pennies at the right so that he sees that they add up to eleven. Do this with all the arithmetic facts, making a table of these facts, which the child will be required to memorize. Teach the facts in each column from top to bottom. Once they are learned you can mix them up to see how well the child has memorized them.

As we have pointed out, arithmetic is a counting system. In addition we count forward. In subtraction we count backward. In multiplication we count forward in multiples. In division we count backward in multiples.

Place Value

In order to demonstrate place value, you might construct a Hindu counting board with its columns denoting ones, tens, hundreds, thousands, etc. You might place pebbles, or pennies, or peanuts in each column so that the student can see how place value is derived from the counting board. Have the student write the quantities in each column on a piece of paper starting from the far right and proceeding to the left. Doing enough of these exercises will leave an indelible idea in the student's mind of what place value is and where it came from.

Memorization Works!

Rote memorization is the easiest and fastest way to master the arithmetic facts. You can make your own arithmetic tables, starting of course with the addition table. Have your child read each column in the table with the answers visible. Thus your child sees the fact and says it at the same time. To test how well your child is memorizing the facts, cover the answers with a slip of paper. Whenever the child hesitates indicating that he or she doesn't know the answer, don't tell the child to "figure it out," but quickly show the answer. And keep showing the answer until the child tells you not to show it because he or she has memorized it.

If we tell a child to "figure it out," he will merely resort to counting by ones. If that becomes a habit, it becomes an obstacle to developing a good arithmetic memory. The reason why you should show the answer is because that is the only way to create permanent memorized knowledge. For example, supposing you were in a play and had to memorize many lines. Supposing you forgot some of the lines. Would the director tell you to "figure it out?" No, you would see and reread the written lines so that by repetition you would remember them.

The simple fact is that our place-value, ten-symbol arithmetic system is a memory system. It requires memorization in order to be able to use arithmetic with efficiency.

How about calculators? Why have your child labor over memorization when the calculator can provide the answers? The trouble with using calculators instead of memorization is that the student won't know when he or she has made an error. The student will simply accept whatever number comes up on the calculator.

Thus, memorization must come first. Can memorization be made easy and enjoyable? Yes, if you tell your child of the powerful benefits of memorization. Besides, some of the facts involving ones, twos, fives, and tens are easy to memorize. Concentrate on those that are not as easy: threes, fours, sixes, sevens, eights, and nines. What could be easier than seeing the answer when one has forgotten a fact? In short, rote memorization is a technique, which makes best use of the mind's remarkable ability to remember what it sees and hears.

Was this article helpful to you?
Subscribe to Practical Homeschooling today, and you'll get this quality of information and encouragement five times per year, delivered to your door. To start, click on the link below that describes you:

USA Individual
USA Librarian (purchasing for a library)
Outside USA Individual
Outside USA Library

University of Nebraska High School University of Nebraska High School
Free Email Newsletter!
Sign up to receive our free email newsletter, and up to three special offers from homeschool providers every week.

Articles by Sam Blumenfeld

The Whole-Language Boondoggle

High School for Freedom!

Dyslexia: The Man-Made Disease

Teach Reading to the “Learning Disabled”

Uncle Sam Wants Your Child on his National Database

Why the Internet will Never Replace Books

Teach Reading to the "Learning Disabled"

Homeschooling and Charter Schools

Homeschoolers and Vouchers

The History of Public Education

College At Home

Learning from The "Old Dead Guys"

The Meaning of Educational Freedom

The Importance of Rote Learning

The Exodus Continues

A World Without Public School

The Benefits of Teaching History at Home

How to Tell Real from Phony Phonics?

Getting Started in Arithmetic

Teaching Arithmetic

Teaching the Alphabet

Teaching the Alphabet Sounds

Teaching Blends

Teaching Long Vowels

The History of Geometry Education

Never Bored Again

Learning Greek

How and Why to Teach Shakespeare

How to Get the Most Out of Homeschool Conventions

Forgotten American History: The Barbary Wars

Forgotten American History: God's Providence in the American Revolution

Forgotten American History: The Spanish-American War

Forgotten American History: The Great Awakening

Forgotten American History: Puritan Education

Colonial Education: The Free Market in Action

America Started with Educational Freedom

How Harvard Became Liberal

The Glory of the Alphabet

19th Century Communists & the Origin of American Public Education

The Benefits of Cursive Writing

It Pays to Know Your Legislator

Intelligent by Design

Teaching Kids to Enjoy Classical Music

Before Compulsory Education: The Private Academies

What Schools Teach: Then and Now

The Real Meaning of Easter

The Truth About Independence Day

The Benefits of Reading Biographies

Why We Celebrate Veterans Day

The Purposes of Education

Why Homeschoolers Should be Book Collectors

How History Was Taught Back Then

The American Almanac: A Great Learning Tool

The Fun of Going to an Antiques Auction

Politics and Homeschoolers: A Primer

A Novel Suggestion

Who Wrote Shakespeare?

Why Homeschoolers Should Learn Public Speaking

The Presidency

Party Politics in the United States

The Road to an American Independent Nation

George Washington: Our First President's First Term

George Washington: Our First President's Second Term

Celebrating Flag Day

Going to School Back in the Great Depression

Middle School During the Great Depression

High School During the Depression

Inventions and Progress

On Falling in Love

A Taste of the Old Days

The True Root of American Freedom

Classical Gems on YouTube

Curing Dyslexia

How to Increase Your Vocabulary

The Joy of Journaling

Popular Articles

The Charlotte Mason Method

The Benefits of Debate

The Benefits of Cursive Writing

Myth of the Teenager

Patriarchy, Meet Matriarchy

Start a Nature Notebook

How to "Bee" a Spelling Success

Saxon Math: Facts vs. Rumors

Discover Your Child's Learning Style

The Charlotte Mason Approach to Poetry

How to Win the Geography Bee

The History of Public Education

Shakespeare Camp

Whole-Language Boondoggle

Getting Organized Part 3

Why the Internet will Never Replace Books

Getting Organized Part 1 - Tips & Tricks

Top Tips for Teaching Toddlers

Phonics the Montessori Way

Teach Your Children to Work

What Does My Preschooler Need to Know?

Art Appreciation the Charlotte Mason Way

Montessori Math

Classical Education

Montessori Language Arts at Home, Part 1

A Reason for Reading

Advanced Math: Trig, PreCalc, and more!

AP Courses At Home

Give Yourself a "CLEP Scholarship"

Can Homeschoolers Participate In Public School Programs?

The Gift of a Mentor

The Equal Sign - Symbol, Name, Meaning

Interview with John Taylor Gatto

Combining Work and Homeschool

Laptop Homeschool

Don't Give Up on Your Late Bloomers

Who Needs the Prom?

Getting Started in Homeschooling: The First Ten Steps

University Model Schools

Teaching Blends

Joyce Swann's Homeschool Tips

Columbus and the Flat Earth...

Bears in the House

Character Matters for Kids

Narration Beats Tests

A Homeschooler Wins the Heisman

I Was an Accelerated Child

What We Can Learn from the Homeschooled 2002 National Geography Bee Winners

Critical Thinking and Logic

Top Jobs for the College Graduate

Terms of Use   Privacy Policy
Copyright ©1993-2021 Home Life, Inc.