Which Math Curriculum Should You Choose?

People often ask about math curriculum -- which one is best, which one do I use, which would I recommend, which would be a good change from "x".

Mathematics can be learned without a textbook

When it comes to boys and math, I think there are three things to keep in mind: first, young boys especially are spatial learners, so a curriculum using manipulatives will probably be better; second, boys will probably prefer math to other subjects because there's not as much writing, so a curriculum that they could sometimes do independently will be useful so they can spend a lot of time doing it as and when they feel like it; finally, boys are not all the same, so what suits one, may not suit another.

And likewise, girls.  But that's another story ....

Probably the biggest surprise, however, is that research has shown that it's not so much which curriculum you choose and use, but whether or not you, the teacher, are excited by it.

Homeschoolers in the US and UK tend to choose different programs from each other: partly, it's availability; partly, it's price (it almost always costs more in the UK); and partly, it's measurements and money which Brits, rightly, want to focus on metric and pounds stirling, and not imperial and dollars.  (As a dual citizen, I'm quite happy either way.)

While the UK has access to programs like Singapore maths, Miquon maths, Galore Park, and even the free program known as MEP (Mathematics Enhancement Programme from the Centre for Innovations in Mathematics Teaching at the University of Plymouth, UK), all these options are text-based, or even workbook-based.

Another option open to both markets -- and gaining in popularity lately -- is the literary based concept of Living Math.  This is basically a good dose of reading books with mathematical concepts to explore.  My own children have dabbled in it since discovering the Murderous Maths series, but there's much more to it than I can do justice to here.  So, check out the website by Julie Brennan here.

But back to the US and curriculum choices with manipulatives.  Below, I list the four main competitors when it comes to manipulative-based math (if I forgot another major one, just give me a nudge and I'll add it in).  I think they're probably listed in order of popularity, but as you will see, certainly not in order of preference!

• Math-U-See: 

K-12 program using colorful rods, also comes with video instruction.  Primary school levels are called by Greek alphabet names (Alpha, Beta, etc.). Plus side seems to be how it explains concepts and ensures a child understands it rather than just memorizing it. One downside of this program is that, by using colored rods, a child has to make a symbolic leap that one size rod is more or less than another size rod -- autistic children apparently struggle with this.  As do children with color-differentiation issues. Cost per year: $40 instruction kit, $25 students kit, plus one-off purchase of manipulative blocks $35.

• RightStart Mathematics: 

K-5 program using an "AL abacus" (where colored beads are grouped in 5s and 10s).  It is unique by not starting with counting, but with visualizing quantities as children are taught in Japan.  People who use it note that it is teacher-dependent, and though it isn't onerous or difficult, it does require teacher input rather than a child working independently.  Finally, because its scope and sequence is different from most other curricula, some people say it's important to stick with it for at least two years -- by then, the child will have grasped the important basics of conceptual maths (rather than memorization), because otherwise, the transition to a more traditional program will be difficult.  Cost per year: many options to choose from, but roughly $150 initial outlay, then about $100 per year afterwards.

• Making Math Meaningful: 

K-6, plus algebra and geometry. Manipulatives include colored links, counting chips, and unifix cubes. This program, from a Christian publisher, sets out to ensure a child has full, logical understanding of concepts, and not just a skill in parroting or memorizing. As an example, it teaches that a thorough understanding of mulitiplication up to 5 will allow a child to understand that 8 x 7 is the same as 8 x 2 plus 8 x 5.  Re-arranging computation like this is an effective skill. Cost: $45 for both teacher's and student's book, plus a one-off purchase of manipulatives for $15.

• ShillerMath: 

K-3 (Kit 1) and 4-6 (Kit 2).  This Montessori-based curriculum uses a spiral approach, scripted lesson plans (where the teacher reads the script, or as children get more independent, they read it for themselves), and a stable full of manipulatives, much like RightStart.  However, one of its unique selling points is its dedication to the four different learning styles of children, and each concept will be approached using all four styles (including CDs with songs), to ensure complete understanding.  Cost: $399.95 per kit, plus free consumables downloads for 5 years. (See Cathy Duffy's review for a more thorough description).

Now here's where I show my hand.  I moved from Singapore math to ShillerMath two years ago, and am thoroughly astounded by the clarity, the depth, the explanations, and everything covered in it.  Apparently, there's a junior high kit in the making, and I just can't wait!

Teaching with Thomas the Tank Engine

He's only a little blue wooden train with a number 1 on his side and a fairly jolly looking expression on his front, but Thomas the Tank Engine seems to be one of the few toys amongst our mountain of plastic that is a perennial favourite.  I mean, my kids really do play for hours with their trains.

Did I say "play"?  I meant to say "work", because that's what a child's focussed attention is with any object or in any activity.  It's their work, and should be respected as such.  In fact, if you look at this article here about child development and Montessori theory, you will see a list of bullet points about learning through play, all of which a good session with Thomas and friends will satisfy.

Let's take for example the second point in the list, "creativity expanded using problem-solving skills".  If you've ever tried to make anything more than a simple figure-8 or circular track with the Thomas railway, then you know that this activity is all about problem-solving skills.  Just how can I get one more bridge into the scheme, how can I make this bit of track match up to that bit of track, and how can I make that shed hook up when I've run out of little pieces with two sticky-out ends?

Then there's the point about building muscle control and strength.  This article here lists how delicate an operation it is to push along an engine and its trucks without losing the back cars, but even the youngest of children will enjoy passing the tactile pieces from one hand to another, turning their wheels, tapping them (bashing them) against the floor.

Rocky and Killer pose with their collection
(notice how they've grouped all the square faces together)

Perhaps most interesting of all is the connection to Thomas and a child's emotional education.  Countless articles are written about children on the autistic spectrum and how Thomas makes an important developmental connection for them.  In conjunction with watching the short little films, an autistic child benefits from a relationship with Thomas, ranging from language skills to facial expressions.  A very helpful article about this can be found here.

I can personally vouch for the way that Thomas the Tank Engine served a purpose in emotional intelligence for Killer when he was about 2.  He's not on the autistic spectrum at all, but we both derived great pleasure from his learning to imitate the different facial expressions used by the engines on the show: angry, happy, surprised, snooty, sad.

I'd like to hear from other readers about how they've perhaps used Thomas or other wooden trains in a "work" capacity.  We have done all kinds of things mathematical, like sorting and grouping.  I made copies of all the engines with numbers, from 1 to 12, and pasted them into a file to be part of a "math mini office", and I also trawled old Thomas magazines to cut and paste pictures from A to Z as a sort of alphabet primer (hint: go for a kite for "k" and a queen for "q").

Above all these suggestions, however, are those which emphasize the enjoyable, the sociable, the imaginative work which is more than child's play -- it's just plain purposeful fun!