Homeschool Math

Fear not! You CAN do it!

When you think of math education, the first things that comes to mind are probably fundamental skills. (addition, subtraction, multiplication and division) If you have an older child, you probably think of geometry, algebra or maybe even calculus. Within these specific disciplines, there are three different aspects that should all be included in your teaching. Make sure your homeschool math program covers each of these. You can think of them as the “what to teach."


MEMORIZATION of arithmetic and geometric facts, rules, formulas, and procedures. For example, you learn how to multiply fractions. Children must memorize the basics before advancing to higher level skills. You don't want them spending time figuring out simple operations when they should be focusing on the higher level analysis. Make sure your homeschool math program provides plenty of practice on "the facts." Find out why educational math games are a great way to provide extra practice on the facts.



UNDERSTANDING of facts, rules, formulas, and procedures. For example, you learn why you invert and multiply when dividing fractions. This should be taught as the student is ready. Manipulatives (blocks, Cheerios, poker chips) are often effective in explaining the “whys” of fundamental skills. They provide a concrete model for an abstract idea which is great especially for young learners.



APPLICATION of facts, rules, formulas, and procedures in practical ways, sometimes this is called problem solving. A homeschool math program should provide plenty of opportunites for application. For example, you learn that to figure out how much sugar to use in a halved recipe that originally calls for 3/4 cup of sugar. Problems should be challenging and level appropriate.

For some "real life math" ideas, click here.

There are two schools of thought on how to teach math. Homeschool math programs usually follow one of these two philosphies.

First, is the spiral approach. This approach presents a wide assortment of topics to students each year, never in much detail, with the hope that they will “get it” a little better each time they are exposed. The argument for this is that children are capable of learning more difficult concepts at a younger age than we expect. For example, instead of waiting until 8th grade to introduce geometry, a spiral curriculum will cover it in first grade, then again in second, and so on with the expectation that by the time they reach 8th grade, they’ll have a good grasp on it.

Personally, I think this approach is counterproductive for math education, especially in the early grades. This subject in particular is built “block by block”. It’s confusing for a child to finally start to figure out a new and difficult concept then instead of getting more practice and having more success (thus building confidence), he is quickly introduced to a new concept that is often totally unrelated to the one he JUST started ot undertstand. My oldest child was subjected to a spiral curriculum like this in kindergarten and 1st grade. She was great at identifying fractions and geometric shapes, but couldn’t add 2+2 without counting on her fingers. The elementary years must provide a firm foundation of skills to ease the transition to advanced math.

The other approach is mastery learning. This approach is based on the belief that all student can learn if given the appropriate amount of time and instructional opportunities. The standards are clear and defined and objectives are organized into small, sequentially organized units. Basically, you don’t move on to the next level until you have mastered the prerequisite.

When beginning formal arithmetic instruction (usually addition) children memorize the facts, use blocks to show addition concepts, and apply it to everyday life. Once they’ve mastered that and have built confidence through success – they move to subtraction. Small sequentially ordered units may be easy to find, but if you teach with the mastery approach, you need to make sure the concept is MASTERED and not just COVERED.

Confidence building in math education is CRUCIAL. This is why the mastery approach makes the most sense to me when it comes to teaching math.

It is easy to see how to fit in memorization, understanding and application in a homeschool math program for the younger grades, but what if you have older students studying algebra, geometry, calculus? Do you have to be able to prove theorems or solve complicated equations to be an effective teacher? No. By the time students are working at this level they are much more self sufficient and should for the most part be able to “learn on their own.” There are many companies that provide video lectures and online/telephone help for students using their programs. If higher math isn’t one of your strong subjects, these will be an answer to prayer.

In summary, make sure your child understands and can apply math concepts. Memorizing the facts won't provide a complete education.

Grades K-5
Grades 6-8
High School
Programs with a K-12 Sequence

Make sure to check out my Check out the Homeschool Math Curriculum Reviews page. I've only done a few reviews so far, but they are thorough, honest, and hopefully helpful. I'm working on more!

Grades K-5

CalcuLadder 1, Classic Edition
By The Providence Project - Six levels available

Grocery Cart Math
By Jaye Hansen / Common Sense Press

Grades 6-8

Teaching Textbooks - Programs for grades 6, 7 and Pre-Algebra are available.

High School

All Levels - Curriculum that serves K-12

Switched on Schoolhouse Math
**Grades 3-12

Horizons Math

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