Choosing a Math Curriculum

"Country Schoolhouse" by Morgan Weistling

1857 edition of Ray's Primary Arithmetic
About a mile from our home sits a cute little house that was formerly a one room school. I like to imagine that something like the picture above took place there, though I know this nostalgic painting gives a rosy view of a job that had to be very taxing. Hard as it must have been to instruct a classroom with more than a dozen children of a wide variety of ages and abilities, one part of the job must have been simpler than today: curriculum choices. Educational publishing houses were few and therefore teachers (or parents or school boards) didn't have to wade through the seemingly endless stream of options that homechooling parents today face. McGuffey Readers were standard fare in little schools around the country from the mid-19th century through the mid-20th century while  Ray's Arithmetic series was a popular math curriculum for perhaps fifty years or so.

When we began homeschooling in the late 1980's, homeschoolers had far fewer choices than they do today, but new possibilities appeared rapidly. While I tried to find the "perfect" program, we switched math programs so frequently when my oldest children were in elementary school, I sometimes wondered if I was ruining them for life. Here's a peek into our travels on the road to finding quality math products for our children, in the hope that it might be helpful as you seek out the best fit for your students. At the end I list some questions that can help you think through the important qualities in a math program.

Andrew and Kara began with Miquon Math, a program which developed in Montessori classrooms back in the '60s. I loved Miquon then, and I love it still, though we've used it more as a supplemental resource than our primary one for the youngest children. Miquon excels in encouraging creative, logical math thinking skills, and rewards children for coming up with different ways to solve problems. Cuisinaire rods, those most versatile of all manipulatives, play an essential part in this program. We also used other supplementary Cuisinaire rod books such as the Alphabet Book; Hidden Rods, Hidden Numbers; and Picture Puzzles. (Miquon - is designed  for K/1st -3rd grade.)

The question of what to do next arose after Andrew finished the Miquon books in second grade. Being a novice homeschooler, I turned to that standby, Saxon. Andrew, whose native language seemed to be math, had no difficulty with the problem sets in Saxon 54, but the repetition of concepts threatened to erase all the love he naturally had for mathematics. Ugh! He was bored, and so was I! Something had to change! So the next years were a flurry of trying various products: Moving with Math, Math-U-See, Making Math Meaningful, Scott Foresman, the Keys to Series, and maybe a few more that I can't remember. Sometimes I required the children to complete two programs simultaneously. (Yes, I was a curriculum junky in those days, something I've repented of since.) The frequent changes didn't seem to phase Andrew, though I wondered what they were doing for child #2, not a natural math head. She generally seemed to take it in stride, though probably more consistency might have been helpful for her. (On the flip side, working in multiple programs requires kids to learn how to approach problems in different ways, and can actually strengthen their math muscles, if they are game.)

A few years later when Singapore Math (Primary Mathematics) was introduced to this country, we began using it for the elementary students, and I breathed a deep sigh. Finally! The program I'd been looking for! This curriculum teaches math thinking along with math skills, just like Miquon does. It goes deeper than simply showing children a standard method for solving a particular type of problem, and encourages logical, orderly, and creative math skills while teaching math concepts. The word problems are particularly challenging, and a method is taught to solve problems that would otherwise require algebra. Singapore also excels in teaching mental math strategies. Excellent!

By the time my oldest two hit Algebra and Geometry, we again found a program that scored top ratings:  Harold Jacob's Elementary Algebra, and then his Geometry text.  Both courses teach logical thinking, though that's particularly evident in the geometry text with an introductory chapter on logic and a great emphasis on proofs. Mr. Jacob's strong content with a large dose of wit make these two books a great choice for 8th-9th grades, especially for abstract thinkers.

After that, our curricula of choice is the University of Chicago School Mathematics Project series. Because I'm hooked on the Jacob's books, we don't begin UCSMP until Advanced Algebra, but the series has upper level courses for grades 6-12. This excellent program, though, is not a designed for self-teaching, and I don't have the time it requires, so at this point I prefer to get some help by using either a tutor or online class. For two of my seven so far to hit upper level math, we've not followed this approach, but actually taken the Saxon route for reasons specific to those students and/or our life at the time. My current Saxon student also uses the DIVE CDs to give a bit of personal instruction before he hits the problem sets. Saxon is not my favorite, and I would not recommend it for any child who might be heading toward a math or science field, but it has its utility as times.

So, that's our particular patchwork of curricula. In addition, there are several supplements that we routinely use at each stage. I'll save that for a later post.

But more to the point - how does one go about choosing a math program? What are the important factors to consider? Of course no program is entirely one way or the other (conceptual instead of computational in orientation, for example), but these generalities still give some framework for you to think about.

1. Is it primarily computational or conceptual?
Some programs focus more on teaching the basic facts (A Beka, for example), while others emphasis teaching mathematical ideas and concepts (Singapore or Math-U-See).

2. Does is primarily take a mastery or spiral approach?
Spiral programs (Saxon, Horizons, A Beka) teach little bits of new information, but give lots of review of old problem types. Mastery programs Singapore, Math-U-See, UCSMP, etc.) are organized by chapters on a particular topic, and review is done separately.

3. Does is have a rule orientation or is it more manipulative or hands-on?
Saxon54 and up and A Beka tend to stress memorization of rules and facts. Math-U-See and Moving With Math use manipulatives heavily to introduce topics. Singapore takes a three step approach from concrete (real objects) to pictorial to abstract.

4. Does it teach or encourage mathematical thought or focus more on memorizing step-by-step algorithms to solve problems? Singapore and Miquon excel at the first, while Saxon stresses the second. For some students one approach is best, while for others the opposite can be more effective.

5. Is the content comprehensive? Are there missing elements? Check out scope and sequences or reviews that you trust. If you otherwise love a particular curriculum, but it is thin in a particular topic, you might be able to supplement.

6. Is it designed for independent learning or is it teacher-based? If the latter, will you have the time needed to implement it? If the former, is it "easy" to use because it is a "math lite" program or because it uses an excellent self-teaching method?

7. Is it pricey? Consumable or reusable? Budget issues always play a role in curriculum choice as well.

There's no one-size fits all math curriculum. We need to consider the individual needs of each of our children plus the peculiar dynamics going on in our home and school. Here's a good article on choosing a homeschool math curriculum. Make sure to check out trusted reviews. Cathy Duffy's are absolutely terrific, and then it often helps to read opinions from folks who have been working with a particular curriculum for some time.

Topics I hope to cover in future math installments: Super supplements; Making and using triangle flash cards; Drill websites; Khan Academy; Time tested manipulatives.

Let me know if something else interests you, though.


Lisa said…
Anne....I am really enjoying your blog. I feel so nourished after reading a post...especially on homeschool. Thank you so much for taking the time to share from this journey you are on. Hope we can get together sometime.

Much Love - Lisa
Jessica said…
Hello Anne,

Could you please send me an email:

We are in need of a consultation from a Christian contractor and I noticed on your blog that your husband is in that field.

Thank you,

Anne said…
Hi Jessica,

I sent you an email, but if it went awry, here's how you can reach my husband, Tim:
cell: 325-3768

I was so thrilled to read on your blog about your new son, Joseph! His story is so beautiful and such a testimony to God's sweet mercies!
SarahD said…
We have been very happy with Math-U-See so far. I love this curriculum because I am TERRIBLE at math, and it helps me teach them a subject I never learned well. In fact, I'm learning my math facts right along with my children. Sad, but true! We do have to make sure we keep up with flashcards, since it doesn't review as much as a spiral approach would. But that's easy enough to schedule in.

By the way, Anne, I was extolling your blog to my husband the other day, and he said, "Well get on the computer and leave a comment telling her so! Don't be a lurker!" So here I am, praising you in the gates. Thanks for the time you take to bless the rest of us.
Anne said…
Sarah - We used Math-U-See a VERY long time ago when it was in its first incarnation. It was a real help watching Mr. Demme present math concepts, and I still use some of his tips, not to mention the fraction overlays, which I pull out quite regularly.

Thanks for taking the time to comment! I am one of the worst about "lurking" and not commenting. I even find it hard to get back and comment on my own blog! But I have been greatly enjoying your Wifely Wednesday posts on Andrew's blog! I tried to comment a few weeks ago on your Chesterton post (love that quote!), but something happened and I had to suddenly leave the computer.
Anonymous said…
Hi Anne,
I am getting ready to start my first grader in Singapore Math and wondered if you found the Home Instructor's Guide necessary or helpful.
Thanks for all you have written to provide newbies like me with some wisdom in getting started!
Erin Polderman
Anonymous said…
Hi Anne,
I am getting ready to start my first grader in Singapore Math and wondered if the Home Educator's Guide was necessary or useful, especially since the material is very basic.

Thanks for all you have written. It has been such a help for me to sort through a much smaller selection of curricula as a newbie!

Erin Polderman
Anne said…
Hi Erin,

No, I don't think the Home Educator's Guides are really necessary for the first several years. By about 4th grade, they do become more helpful, as some of the problem solving strategies with SP are a bit different, and the HE Guides show worked solutions to some problems instead of answers alone. (They also have enrichment ideas for further explaining concepts.)

I just looked at my collection, and I guess I don't own the 1st grade HEG's, so I must never have felt they were necessary. :)
Anonymous said…
Hi Anne,
Do you have any familiarity with the Math Mammoth curriculum? It seems to be very popular down here in Texas (along with Math U See and Teaching Textbooks), although I decided to start my kindergartener with Singapore Math Essentials, and a checklist for what a child should know before 1st grade (includes things to master like telling time, counting coins, etc.).
Thank you,
Jessica Woods

Anne said…

I have not used Math Mammoth. When I'm thinking about something new, I tend to check out Cathy Duffy's reviews, as hers are some of the best out there. She has chosen Mammoth Math as one of her "Top 101 Picks," and she has very good things to say about it. Here's her review:

Both Math-U-See and Teaching Textbooks are also among Cathy Duffy's "Top 101 Picks" so they get good reviews. I have some concerns about the rigor of these programs over the long run. (Esp. Math-U-See, which we used long ago, though only in the first edition.) Particularly for kids heading in a math, science, or engineering direction, you want to give them a strong background not just in solving problems but also in thinking mathematically.

Here are some interesting thoughts on teaching conceptual math from The Potter's School. (We use them for several of our junior and senior high classes.) The discussion here mostly applies to older students, but maybe you'll find it interesting:

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