How To: Teach Math (Concepts)

Before I get into the specifics of teaching your child math I am going to philosophize here for a minute…or perhaps editorialize would be a better word.  In any case, if you do not care to read the upcoming *editorial* feel free to jump down to where I get into the specifics of teaching math.

In the meantime, I feel I have to address a problem that I have encountered with home-schooling parents when it comes to teaching math, and specifically, when it comes to teaching algebra.  I can’t tell you how many times I have been absolutely appalled to hear a parent say either:

a)   Their child doesn’t want to study algebra so they are not going to require it; or
b)   Their child has told them they don’t want to study algebra because they are never going to need it so they have decided they won’t require their child to study it; or
c)   They are intimidated by teaching algebra so they have decided to dupe themselves into believing their child won’t need algebra.

I know that none of my readers would be entertaining such notions, but the fact is: algebra is now considered basic math and something every student should be required to study.  Just because I have a strong math background doesn’t mean that somehow makes it easier for me to require my children to study algebra.  Just because you may not have a strong math background is no excuse for you not to require your child to study algebra.  There are video and computer programs available to teach your child algebra.  You can hire a tutor.  An older home-schooled student (or home-school graduate) would be ideal.  In fact my daughter has been tutoring algebra to teenagers for years.  There is simply no excuse for handicapping your child by not requiring them to study algebra and frankly, the study of algebra should be the minimum requirement of higher math that you assign to your child.  They should also be studying geometry, trigonometry, and pre-calculus.  I will discuss in a few moments some programs you can consider using to give your child a strong background in math that will prepare them for whatever career or educational challenges your child will face in the future.

But before I get to that I would like to address the two excuses listed above where parents actually allow their children to dictate what they will study?  Just where do you go to turn in your parenting card?  I surely know there have been times when I would have liked to turn in my parenting card rather than taking tough stands with my kids and actually acting like, you know, a parent.

It totally boggles my mind when I will hear a home-schooling parent say to me, “We’re sending little Johnny back to public school next year because that’s what he wants.”  You should just hear the bombs going off in my head.  He wants to?  Did you not learn those valuable parenting phrases like, “Because I said so” or “Because I’m the parent that’s why” or “If all your friends were going to jump off a bridge would you jump too?”  I just don’t get it.  I’m guessing these parents had some very well-thought out reasons for home-schooling their child so why would they now allow their child to veto their decision?

I might as well tell you right now my definition of an adult: it is someone who pays all their own bills.  There I said it.  (And by the way, I have told this to my kids many times…no surprise to them.)  What this means is that I don’t even believe an 18- or 19- or 20- year old should get to unilaterally make decisions about their education, religious pursuits, or relationships unless they are completely self-supporting and I don’t know any 18- or 19- or 20-year olds who are.

So you can get what my response would be to my child who told me that he didn’t want to study algebra.  Yeah, I’d be laughing hysterically.  Rolling.  On the floor.  Laughing.  I think you get the picture.


Teaching math actually has two different components.  Both have equal importance.  The first is learning math concepts.  The second is speed and accuracy.  I am going to divide these components into two posts so that I can give each sufficient attention.  Today I am going to address teaching math concepts.

So what do I mean by “math concepts?”  Everything you learn in math whether it is how to add (and the fact that it doesn’t matter which order you put numbers in when you add them) to multiplying fractions to factoring numbers are math concepts.

Generally speaking, math concepts need to be taught in a sequential manner because they build upon other concepts previously learned.  For that reason I suggest you find a math curriculum you like and stick to it.

Now I am not saying that you stick with something no matter what, when it is clearly not working (I discussed how that plan did NOT work for me when teaching one of my son’s to read in my previous post).  BUT, you should try to find something that does work, and then stick with it.  I have talked to too many home-schooling parents who jump around trying to find the “perfect” math curriculum rather than choosing a solid curriculum and making it work.

My point is that, it is likely that your child is going to struggle here and there with math.  That doesn’t mean the curriculum you are using is worthless or just too difficult.  It may mean you need to find another way to teach a concept.  Believe it or not, the internet can definitely be a friend in trying to find ways to make a concept come alive for your child.  Or have an older sibling try explaining the concept.  Or keep a home-schooled teenager on retainer for when you occasionally get stuck! 🙂

One last thing I’d like to share before I move on to specific curriculum recommendations is this:  Do not automatically buy the Teacher’s Manuals.   Actually that was some of the best advice I ever received from a home-schooling friend when I started out home-schooling.  Naturally, every curriculum will try to tell you that you NEED to buy the Teacher’s Manuals.  They make a lot of money off of them.  But the fact is, in general Teacher’s Manuals are designed for the classroom teacher, to help them keep a classroom full of kids busy.  I never started buying Teacher’s Manuals until at least the fourth grade and that was only to get the answer keys.  On the other hand, when your children get into Algebra and other advanced math you will not only want answer keys but also “solution manuals” such as those offered by Saxon Math.  It will make your life (and your child’s schooling) much easier.

Now on to my recommendations for teaching math concepts:

Bob Jones University Press – I use BJUP for kindergarten through 6th grade.  It is a solid program that is easy to use and will prepare your child to study pre-algebra in 7th grade.

Saxon Math – I use Saxon beginning in 7th grade.  My children take Algebra 1/2 (pre-algebra) in 7th grade, Algebra 1 in 8th grade, Algebra 2 in 9th grade and Advanced Math in 10th grade.  Saxon Math is unique in that it incorporates Geometry in it’s Algebra program so there’s no need for a separate Geometry program.  In addition Saxon offers tools (including teaching CD”s and Solutions Manuals) that many find to be a helpful addition to their program.  Using Saxon my children are prepared to take College Algebra in 11th grade, which they take at the community college through the Dual Enrollment program.

I have never used the programs listed below but they are popular among home-schoolers so I felt it was worthwhile to mention them.  You can check them out and determine if they might work for your home-school program:

Horizons Math– According to the Sonlight website, “Horizons Math is designed to help your children understand math from the ground up.”

Key To Math Series You can use the “Key To” programs as preparation for a larger, more intense program of the same subject, as a supplement for a regular hardbound text or the text for an individualized course.

Teaching Textbooks – Teaching Textbooks are strongly recommended by the folks at Sonlight because they (according to Sonlight) virtually guarantee success with minimal knowledge, skill or oversight on the part of mom or dad.

If you have any questions about teaching math concepts please leave them in the comments.  And be sure to check back next week when I will be reviewing math programs that will help your child develop speed and accuracy .

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  • MB

    I highly recommend Math U See especially if you have a special needs kid, like I do. I went and listened to Mr. Demme (the write of this curriculum) at a conference and he knows his stuff. Not only that, this curriculum comes with DVD’s with him teaching each concept. What a breath of fresh air for someone who hates math and hates teaching it!

  • MB

    My last comment wouldn’t let me keep writing. Anyway, I really like Math U See. A great math website for learning math facts is timez attack: My kids loved playing this game and it really taught them all their math facts in a fun way. I don’t get the thrill of Saxon. Maybe its because my kids are weird. LOL

    • Anonymous

      The appeal of Saxon is that it is a solid curriculum that teaches in a method that continually reviews previous material. That doesn’t mean it is perfect and even my kids have had a few complaints…but it has prepared them solidly to take College Algebra by 11th grade (and get “A’s” in it).

      I have heard very good things about Math-U-See and I am glad you brought it up. One of the benefits of having comments is that readers can offer up other suggestions and recommendations, and I am glad you took the time to mention this program.

      I’m sorry about the commenting problem. I have one website I visit that I like to comment on and I often have a problem with it saying my comment is “too long.” 😉 They don’t use Disqus though. However, sometimes even Disqus can be quirky. Thanks for putting up with the aggravation.

  • MB

    The commenting – it gets to a certain point and then it won’t let me see what I’m writing. Yes, I’ve had issues with Disqus too when I had it on my blog. I don’t have an issue with Saxon. I’m sure its great. I’m not using it yet and not sure if I will, but I think overall its a good Math program. I just have others say its the only math program to use. I don’t think that is accurate. There are lots of other programs that I’m sure are fine too.

    • Anonymous

      The one-size-fits-all attitude kind of misses the point of home-schooling, don’t you think? I have found Saxon to be a solid program but I mention other programs because I know others have used these programs with great success. And I am glad you mentioned Math-U-See for that very reason.

      Where I have a problem, and this has nothing to do with your comment, is when parents make excuses for not challenging their kids…which is what I deal with in my “editorial.” It may be that you haven’t run into this but having home-schooled for over 20 years I have had interaction with many home-schooling parents and families, and I will never understand why parents seem to be afraid to expect more from their kids…and in some cases it’s almost like they think it is “unspiritual” to want, and expect, their kids to excel academically. But there I go editorializing again!

  • MB

    On one hand, I think striving for academics alone is not really scriptural. Where does it say you must be an A student to enter God’s kingdom. Nowhere. However, it does say do all things unto the Lord and not unto men. I do find it appalling at times that homeschoolers care so much, almost in a snobby way, how much of a geniues their kid is. I’m not saying that in reply to what you said. Just a general statement. I think parents need balance. Yes, we should set the bar high, but not just for academics. Spiritually too. Like you were stating earlier about the child that no longer wants to be homeschooled. When did it become the opinion of the child? I totally agree with you there. And yes, I do know someone who made excuses that their kids wouldn’t need math and now their kid is a drop out of college. I can’t say whether that had to do with math, but it was the total outlook she had. Everything was laid back. Everything was easy going. Hard work? Nah. Just do what you want. I find that approach disturbing. I personally HATE math. However, I don’t let my kids be limited by my poor math skills. No one took the time to teach me Math. No one sat down and tutored me so I could understand it. In fact, I taught my kids Math using curriculum and I learned! I never understood what borrowing meant. I just did it. I didn’t understand the groundwork for the concepts being taught. Now I do because as I have been teaching, I learned it too . It wasn’t that I was dumb. I just needed to understand it. I’ll never be a math genius. My husband is and I have him teach my kids Math. I use the public schools. If I can’t do that, there is online stuff. There are videos. Like you said, we are not limited in teaching. There is no excuse. I think my main point here is that we are all given gifts to be used by God and I think when we align ourselves with what man and culture say, everything we do is in vain. Academics is great if we actually teach our kids that God uses us for His purposes, not to attain some kind of self worth or notorioty about ourselves, but because we want to serve Him in all things. Does that make sense? So I’m not at all coming down on what you are saying. Just adding my two cents to it or maybe restating it differently. I do think we should hold our kids up to a standard and not let them just be lazy and uneducated.

    • Anonymous

      I have personally seen less of people bragging on their home-schooled kids than perhaps you have. Sometimes I think it’s the circles we run in…or perhaps the type of people we end up reading about. Frankly, read ANY family’s Christmas letter and you’ll find that mom is heading up ten committees while the kids are being recruited by half a dozen colleges for their particular sport… 😉

      In some ways, home-schoolers may emphasize their children’s academic achievements because, you have to admit, we continue to be accused of failing our children in every possible way. Just read some of the recent panels on home-schooling in the New York Times online (and the comments people leave) to find how hated home-schoolers still are – not to mention the distortions if not outright lies that are expressed concerning home-schooler’s academic and social achievements.

      By the way, I think that the vast majority of home-schoolers – like 99% – are doing a bang-up job and are certainly giving their children a better education than the government schools while at the same time protecting them from the moral vacuum that those schools invariably are. I just don’t countenance parents letting kids set the agenda, nor do I think that we should allow children to choose to not tackle an academic subject because they don’t feel like it or it’s “too hard.”

      I’m with you when it comes to learning things with my kids. I have a strong math background but the public schools never taught history in a coherent way, in my opinion. I have loved learning history with my kids using Greenleaf Press.

      To get a little more of my view and what I have worked to accomplish with my kids you could read my post on goals:

      And thanks again for the conversation!

  • MB

    On an unrelated (sort of) note: Aleks is offering homeschoolers 3 months free of online Math for children. Check it out:

  • bluejava

    Totally agree that algebra is too important not to teach. I’m no math genius either, but as you mentioned there are so many resources available to us now. We have always used Saxon Math and last year (4th grade) we started using the Saxon DIVE into math DVD teacher. We like it since we can rewind the teacher as many times as we need to in order to understand each new concept. I still go through each lesson with my child as well. Well, that’s my two sense worth, haha. Thanks for this post!

    • Anonymous

      Thank you so much for leaving your comment! The DIVE DVD’s sound like a fantastic resource. My guess is my kids might have appreciated if I had purchased the DVD’s for them (of course they didn’t have them when my oldest was taking Saxon Algebra). One thing I didn’t mention in my post is that I actually require my children to teach themselves math starting in 7th grade, if not before. The reason I do that is to get them used to learning independently.

      Of course, I’m available if they have questions. And my sons had their older sister to help them (as a matter of fact my 17-year old son is taking chemistry at the community college now and my daughter’s science background is helping him a lot!)

      I appreciate you stopping by and offering your two cents!

  • Loved the editorial, and the helpful math tips! We use A Beka and love it. Not sure what we will use for Algebra and beyond, but I will keep your suggestions in mind.

    • Anonymous

      Thanks for the encouragement! ABeka is also a solid math curriculum. As for the advanced math, we are fortunate to have so many choices!

      Glad you stopped by!

  • Michael

    Math is one of the section in the SAT test so it is important that you have a solid knowledge about it. offers online SAT Math preparation courses.

    • Anonymous

      Thanks for stopping by Michael!  As you point out, a solid math background is essential for the SAT.  I sometimes get frustrated with home-school parents who don’t ensure their children take the higher math courses because they say, “My child isn’t going to college.”  Since there is no way to know if their child may want to attend college one day (and I for one require my kids to go to college) – parents should prepare their children for every possible eventuality which should include a solid foundation in Algebra as well as other courses such as Trigonometry which are covered in a solid Math program like Saxon. 

      Thank you for sharing this information.  My 17-year old is already in an online SAT prep course but I appreciate you offering this information to my readers.