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Math is one of my favorite subjects, so I’m not afraid to teach it at home up through high-school, although I’m sure I’ve forgotten some concepts over the years. (Math is the one serious subject not taught at our co-op, and this is for the best. There are too many differences of opinion when it comes to math, and it’s too important to compromise on. And even more importantly, I believe there is less flexibility when it comes to teaching math concepts. If a child is learning one method on Monday, he really should be taught Tuesday through Friday with the same method. And finally, I choose each of my children’s homeschool math curriculum based on the individual child’s educational needs and preferences.)

How I Choose a Math Curriculum for My Children

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When I decide on which math books to use with my children (I did make that plural on purpose), I consider each child’s learning style. I start off with two or three books during the early grades and go back and forth between them. I like each homeschool math curriculum for a different reason. I happen to like Horizons Math because of the drill and review it provides, as well as its incremental approach to teaching concepts. I like Singapore’s Primary Mathematics because it teaches to mastery, and I love the way they teach number sense.  Spectrum Math workbooks are a favorite as well. They are a little different than the other math books in that they don’t teach a lot in the way of concepts. They do, however, provide excellent review and remediation for difficult concepts, stripping the math of all the extraneous stuff in the other textbooks. (That extraneous stuff is actually necessary most of the time, but when a student is haven’t difficulty, sometimes they just need more practice and the Spectrum books offer that practice.)

I don’t teach all of these books at the same time; we alternate back and forth between them. It probably sounds weird, but I look for natural transitions to alternate. It seems to work for us.

I like the Singapore method because it teaches to mastery. Same thing with Spectrum Math. And I like Horizons because it teaches with review.

Once my students get to about fifth grade, I stick to one to finish out all elementary math material. Prior to fifth grade, even though the books have grade levels, I ignore them. I use them based on content, going up and down the grade levels as needed to master and review concepts.

This probably sounds crazy, but I like variety. It keeps us from being bored, and to me it ensures that my children really understand their math. If a child can only do math in one textbook by one method, then I question whether they really and truly understand the math concepts they are supposed to be learning. Think about it this way: Do standardized tests base their math questions on the Saxon method of teaching math, or the Singapore method of word problems? No. Kids must be able to really understand fundamental math concepts regardless of how the textbooks present the material.

This is not in contradiction to the statement I made earlier about consistency when teaching math. I think it is too confusing to switch in the middle of teaching concepts. When I start teaching a particular topic to one of my children, I finish it with that topic. If one of my kids has a problem with comprehension, I will switch to a different text or a video lesson if I have to, but before I do that, I try to work with them one on one until they understand the concept. When we switch math textbooks, it is usually at the end of a semester or the end of a school year.

When a Child Has Math Trouble

Like most children, my students do sometimes have difficulty with math. In fact my current fifth grader is having difficulty with Singapore word problems. So to alleviate the problem, we are working a set of word problems together on the wall (a white board). When we are finished working them together, he will rework the same problems by himself until he can do them. If we have to, we’ll rework the problems together before he attempts to rework them on his own a second time.

When my oldest student has difficulty with upper level math, she goes through a similar process. Mid-year through Algebra 2, she had to complete a mid-year final. She did horribly, which came as a complete surprise to her. To remediate, she went back over every single problem she missed and reviewed the textbook for that material, after which she redid the math problem.

Going through this process has been helpful in identifying any missing gaps that she has in her understanding of math concepts.

As I related to her, I really don’t care what grade she earned on the first test. More important than grades is understanding.  And if necessary, we are going to review, redo, and repeat until they get it.

When we finish the fundamental concepts—addition, subtraction, multiplication, division, fractions, decimals, percents, ratios, and word problems via Singapore math, we move on to pre-algebra for a year. Because we do skip around so much and often teach to mastery of a concept with little review, I use pre-algebra to ensure we have no gaps.  (I hear ya’, but it’s working. My daughter who is going into the tenth grade has finished up Algebra 1, Geometry, and will finish Algebra 2 shortly.)

Math Facts

For the dreaded math facts, we use Horizons because of the constant review and drill it provides for basic addition and subtraction. For multiplication facts we use the Schoolhouse Rock videos along with whatever math book my child is currently working in.

If and when one of my children forgets their math facts, usually because he only memorized them and didn’t really learn them, we do math facts copywork. Sometimes that means straight up copywork, other times that has meant drill sheets with a multiplication table next to them. Then we play beat the clock. Beating the clock is great because they eventually learn that it is faster to know the math facts than it is to look them up. Basically, children are just really smart and efficient. They are going to find the easiest and laziest way to get the job done. And sometimes it’s easier to just know stuff than it is to have to look up stuff.

And by the way, just because one of my children doesn’t know his math facts, I find that it is not a sufficient reason to suspend moving forward on math concepts. My hope has been that the memorization will eventually catch up with the understanding. So far, my two oldest children have proven me right. One is going to the tenth, and the other the eighth. They have not always known their math facts well, but when they didn’t, we drilled via the beat the clock method and, at the same time, kept moving along with the concepts. Now they know their math facts extremely well, and their grasp of basic and more advanced math concepts is also great.

As you have probably picked up on, we follow the traditional math sequence for high school. What we do different is school all year from about pre-algebra on. My kids do math during the summer. For pre-algebra, we use Chalkdust. (I purchased this used because it was so expensive.)

Our Favorite Homeschool Math Curricula

For algebra, we use  Paul Foerster’s Algebra 1: Expressions, Equations, and Applications (affiliate link) along with the Math without Borders supplementary lessons on DVD Rom.

For geometry, we use Chalkdust—again purchased used.

For algebra 2, we use Foerster’s Algebra and Trigonometry (affiliate link) again with the Math without Borders video lessons.

For my daughters geometry review, we used the Life of Fred: Geometry textbook. When my daughter initially completed Geometry, she received a low A, so she asked if she could redo the geometry course. So while she was working on Algebra 2 in the summer, she reviewed Geometry with the Fred books. She was uncomfortable with her grasp of the concepts taught in Geometry. I attribute her desire to voluntarily review Geometry to the fact that she is internally motivated. This conscientious behavior is, I believe, the result of child owning their education. They know when they are on rocky ground in a subject, and they want to fix it because it is their education.

If you haven’t heard of the Fred books, they are quite fun and actually good enough to be used as solo textbooks. The Fred books teach math in the context of stories. With these books, children can see the real world application of the math they are studying. Fred is, I believe, a five year old genius teaching at Kittens University. The author, Dr. Schmidt, teaches math concepts as they are used by Fred as he tries to get himself out of various predicaments.

Note: At the high school level, we don’t switch a lot between books. I don’t want them to miss any concepts at this point. Different books have a different scope and sequence, and I have to make sure that we completely cover each subject thoroughly, so while we made add a supplemental book or two, we do not switch unless absolutely necessary.

Another note: I know many people don’t like math. The more you dislike it, the more important it is to do it first and get it over with. I tell my kids doing things we are afraid of or don’t like doing is like taking medicine. You either swallow it fast and get past the nasty part, or you hold it in your mouth and savor the disgusting mess. Same thing with hard work that we don’t like. Better to swallow than savor.