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Teaching Early Arithmetic Skills Effectively

By Michael Maloney, MA



Teaching beginning arithmetic can be fun and rewarding for most homeschoolers and their children. One of the secrets of success is to decide what skills must be taught and the order in which they should be taught. A good instructional program will list the objectives and their order of presentation. Several different objectives may provide tasks for any one lesson.


Scope and Sequence

The list should look something like this for kindergarten students:

1. Identifying and writing numerals from 1 to 100.

2. Rote counting in which the student memorizes the numbers from 0 to 100 in consecutive order starting with the number 0.

3. Rational counting, which involves counting objects as you touch them.

4. Counting forward beginning with a number other than one.

5. Counting backward from 100 to 0.

6. Ordinal counting where students are taught to say first, second, third, etc., instead of one, two, three.

7. Counting backward from a number other than 1.

8. Skip counting by 5s, 10s, 2s, and other numbers.

9. Drawing lines or marks to represent a number (e.g., //// = 4)

10. Learning signs and symbols for arithmetic operations (+, -, x, =, etc.)


Determining Excellence

Each skill needs to be measured so that the parent knows the child has learned the skill to a stated degree of excellence. Children can count at 200 counts per minute when they are skillful. A simple timing where the parent listens to the child count for a period of 15 or 30 seconds provides a quick and easy measure of how well the skill is being learned and remembered. Any pauses or errors indicate the points at which the child needs more instruction or more practice. The learning objective for rote counting can be stated as: "The child sees and says numbers from 0 to 100 at 200 counts per minute with no more than 2 errors."


Learning Channels

Generally, learning new skills is easier if the child can see the numbers as he counts. Once the child can see and say the numbers fluently without pauses and errors, you can change the learning channel to a harder task like "think and say numbers 0 to 100."


As with see/say numbers, children can easily think and say 200 counts per minute when they are well versed with counting.

Writing Numerals

Children are often slow at learning to write numerals. This could be a result of how they hold a pencil, of not knowing where to start, or not knowing which direction to draw the line. The task becomes easier if we teach them the easiest numbers first. Numerals that require one consistent stroke are the easiest to make. The numeral 4, which requires the child to lift the pencil and start again in a different place, is more difficult. Teach the child to write numerals by drawing a ball where the student begins and a small arrow to show the direction to go.


Tracing Numerals

It is easier to trace numerals than to create them literally from scratch. Make up practice sheets of random numbers that the child can trace with a pencil, marker, or crayon. When the child can see and trace 60 numerals per minute, you can change the task to "think and write numerals."


A Timed Task for Writing Numerals

Once children have learned to write the digits from 0 to 9, you can do 30 second practices with them until they are completely fluent number writers. You simply have them write the digits from 0 to 9 over and over again as quickly as they can for 30 seconds. Any numeral that you could not read if it were on a price tag is considered an error. The task looks like this:







Initially children will write larger, more widely spaced numerals. As they become more proficient, they reduce both the size and the spacing and increase in speed.


Children with fluent number writing skills are able to think of and create numerals quickly, which means that assignments get done much faster and seem less arduous. Children with poor number writing skills often spend a long time finishing a worksheet and do not feel well rewarded when they are done. Children can write 150 digits per minute when they are fluent. Try the task outlined above. Because people do not normally think of this task in terms of output per minute, you will be surprised as your results.

Counting Skills

With the exception of rational counting, all counting skills can be learned at 200 counts per minute. Generally these are first done with a sheet filled with numbers for that particular task. These worksheets can be created by the parent or downloaded free of charge from the "freebies" section of our website homepage Specific formats for all of the learning objectives listed here are available as well as other formats for skip counting.


Rational counting is slower because children have to touch or point to objects as they count. Fluent levels of rational counting are at 100 per minute or better with no more than 2 errors.



Counting skills are a necessary basic skill for all other arithmetic activities. Children who cannot count forward, backward, from a number to a number, and skip count wind up counting on their fingers. When children are trying to subtract, counting backward on their fingers or writing digits very slowly is an invitation to disaster. They sometimes get so focused on the counting process or the writing process that they completely forget what they were doing. Children who can count and write numbers fluently are able to pay less attention to these basic skills and more attention to the arithmetic operation they are working with. Which child do you want your child to be?


Michael Maloney, MA, is a former public school teacher, principal, and educational psychologist. He is the best-selling, award-winning author of Teach Your Children Well, creator of the award-winning software series Scholastic's Math Tutor, and creator of the Teach Your Children Arithmetic Well software series. He was a winner of the National Literacy Educator Award in 2001.


Copyright 2003.
Originally appeared in Spring 2003. Used with permission.
The Old Schoolhouse Magazine.


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