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The Spiral Philosophy for Teaching Math

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Elementary school math concepts are taught over and over again.


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Most math curricula use a "spiral" philosophy of teaching. This means they cover the same topics several years in a row, advancing them slightly on each pass. Thus a child practices basic math facts, telling time, working with money, fractions, and other topics in 1st grade, then again in 2nd grade, then again in 3rd grade, and so on up to 5th or 6th grade.

Some children don't learn the concepts the first time, and of those who do, many will not retain them. The expectation is that after being exposed to the same topics for five or more years running, most children will have mastered them.

Don't Expect Mastery on the First Pass

For most topics you shouldn't become upset if your child does not master the material the first time through. There will be another chance next year. You can practice any topics the child has difficulty with (e.g. telling time) around the house so that he is better prepared next year.

Math Facts Meet the Spiral

Although the spiral approach works well enough for learning shapes, time, and other topics, it can present a problem for learning the math facts. Without continuing practice, young children tend to forget their math facts very quickly. When the spiral progresses to the next topic (identifying shapes, for example), the child has a break from the math facts and starts to lose them. School vacations and especially summer vacation present further opportunities for backsliding. Some math books/curricula provide a degree of practice for maintenance, but many don't provide enough.

What should you do if the spiral approach to math facts isn't working for your child? One solution is to provide a math maintenance program of your own. This is done by printing practice sheets at the child's level for use on vacations and on days when the book provides no practice. This way the child doesn't lose ground during the many breaks.

Another solution is to jump off the spiral and practice the math facts to mastery independently of the book. After all, you don't have to use the spiral for everything. You can blend the two approaches by having the child continue with the spiral in the book for the other math topics while practicing math facts independently. We did this for my son, as described in the page on systematic practice.

See the help screens under Strategy for more details on maintenance and on systematic practice.

Advancing the Spiral

I see no reason why homeschooled children should not progress beyond grade level in math if they have the aptitude. Too often I hear a mother say that her Johnny finished his math book in April, so now they are done with math for the year. Sounds like Johnny has some math aptitude. Why not have him continue into next year's material at a comfortable pace? This could put him one or two grade- levels ahead in high school, which offers two advantages:

  1. The lead provides a cushion. If he has trouble with Algebra II or Trigonometry in high school he can then proceed at a slower pace rather than being rushed.

  2. If he doesn't have trouble then he has the option of taking calculus and even some calculus-based advanced placement courses if desired.
There are two ways to progress beyond grade level. The first was mentioned above--if the child is progressing faster than normal, then you can give him the next book in sequence as he finishes the current one. This way he can end up a year or more ahead going into high school.

The second way of progressing is to simply skip a year. For example, suppose at the beginning of 4th grade you realize that your daughter has mastered the material and is bored with the exercises. You can skip to the 5th grade book. This will cover the same topics as the 4th grade book, but in a little more depth.

I don't advise rushing children, but in a homeschooling environment it is relatively easy for a child's math program to progress faster than in the public schools.


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