4-Digit Multiplication -- the proof is in the Montessori pudding!

Rocky is just now 8, and though she should be in the 2nd grade (year 3) if she went to school, she's in the 3rd grade (Year 4) Shillermath book.

Rocky, the (not always) model student!

Some of you may be thinking: "Oh, that's all right for you!  She obviously has the genes/the talent/the instruction/(insert explanation here", but let me tell you, this is the most free-wheeling, doll-playing, coloring-book-addicted child I've ever seen.

Yet, somehow, she picks things up.

(I've just deleted the phrase "just by listening", because I'm not sure she even does it by listening -- when we do our read-alouds, she can rarely muster up a decent narration beyond "There was this guy ... and he rode his chariot to this other guy ... and he shot him in the head or something" -- Rocky's version of 2 Kings 9 where Jehu shoots Joram in the back with an arrow. Kudos to her -- there WERE two guys, and there WAS a chariot, and someone did some shooting.)

Maybe she picks things up because she's a thinker behind all that cloud-cuckoo-land exterior.  I mean, usually, she's the kind of child who does things like choosing the alias "Yellow Rocket Ship Plane" when the other kids chose Phoenix, Killer, and Timmy.

Last year, though, she surprised me by saying, "Your grandma must have been pretty young when she had Grandma."  And I said, "Why do you say that?" She replied, "Because Great-Grandma has just had her 90th birthday, and Grandma is going to be 70, so she must have been 20 when she had her."

At that time, her maths books were still only doing addition up to 5. Yet, we were working with the decimal materials like 1000s cubes, 100s "flats", etc, so I'm guessing she just had a really good visual picture of what it means to subtract one number from another regardless the place-number it is.

Anyway, two days ago I introduced simple multiplication to her a la Lesson 3 of Shillermath's Book 3.  We had out the 1000s cubes and the 100s "flats" and the 10s "bars" and unit cubes. We practised multiplying 3 of the 1000s cubes and got 3000. We practised 4 of the 10s bars twice, and got 8 10s bars, or 80.

Then today, she did this:

4-digit multiplication with exchange

I'm flabbergasted. I'm astounded.  And it's not Rocky so much I'm amazed by (though maybe I should be), it's just this Montessori-based maths curriculum that teaches everything SOOOO carefully, SOOOO visually/aurally/kinesthetically, and SOOOO well!

So if anyone asks me what's the best purchase I've ever made in all my 8+-years of home educating, Shillermath would be at the top of my list. (Ambleside Online is also brilliant, but I haven't had to purchase it!)

I wish Mr Shiller had continued his math adventure beyond primary school (there are rumors that middle- and high-school version are on the cards), but that discussion will lead me into a review of Life of Fred, so I will just sign off instead.

In the meantime, you might want to look at my review from a few years ago when the curriculum was still new to us.  It gives a bit more detail, and compares it to other hands-on math options.

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!