Apple Montessori Blog
Apple Montessori Math: Simply Incredible!
Building a strong math foundation from the beginning!
If I had to pick a favorite area of the Montessori curriculum it would have to be the math area – and this from a lackluster student who hated Algebra and Calculus! I’m not the only teacher who has proclaimed, “If only I had had these materials when I was a student…”
The genius of the Montessori math materials is hidden by their simplicity. A set of golden beads, a few boards for addition and subtraction, counting by 5’s or 6’s on short or long chains, pegboards that look like mere toys; the list goes on and on. But with these mundane looking objects your children can SEE, and come to understand, all of the mathematical principles inherent in a subject that far too many of us grew up dreading!
Most of the materials were actually invented by Mario Montessori who was the son of Maria Montessori. Taking his cues from his mother’s insight into how young children learn by doing he created materials that allow children to move tangible objects in such a way that the underlying concepts become crystal clear in their minds.
Each builds upon the concepts shown in earlier presentations. Each has a whole series of lessons that move the child from mastery of the simplest tasks such as adding 3 + 4, to memorization and generalization of very complex equations which set the foundation for work in algebra and geometry.
One fabulous material is the elementary checkerboard which is used for large multiplication problems such as 213,458 X 3,659. Using such big numbers is, in itself, an incentive to the child. It seems so much more interesting than 37 X 24!
The child uses multiplication beads, which have been introduced in earlier activities, and begins by placing tiles around the edges of the board to represent the multiplicand and the multiplier. Just knowing and using these terms is impressive.
Next the child begins to “decompose” the equation. In this process the child takes the numbers apart and multiplies them step-by-step on the board. Reciting the “checkerboard chant” the child multiplies units times units, units times tens, units times hundreds, and so on, placing beads to represent the products in the correct, color-coded square on the checkerboard. When I first learned this game, in my Montessori training class, one of my first “Aha” moments came when I realized that I was multiplying 9 units times 5 tens, or 4 hundreds, or 3 thousands. Growing up, I had merely been told to multiply 9 X 8, 9 X 5, 9 X 4, etc. No wonder the answer is so huge!
As the children progress through the various lessons that accompany the checkerboard they review all of their basic multiplication facts over and over, which helps in memorization, they “exchange” tens for hundreds and hundreds for thousands, reviewing basic addition facts along the way, and finally arrive at a very large answer which they then must record and read. It’s really hard to place the commas in the correct place, let alone read 781,042,822! But children return to this game over and over creating the biggest numbers they can think of to challenge themselves – is there a better way to learn math?
When I was a student I had to simply memorize the steps: multiply n X n, write the answer here, oh yes, don’t forget to move in one space on the second line and two spaces on the third (no one ever explained why…) then add all the numbers up. If I made a mistake along the way it was nearly impossible to find the error and I had to start all over again – I hated it – I never would have chosen to do that over and over again!
When a child records the “partial products” with the checkerboard it is self-evident why the second line in the answer has to move in one space and the third line moves in two: units times tens equals tens. There are no units when you multiply 50 X 50. There are no units or tens on the third line because I am multiplying 600 X 8 and 600 X 50.
Just the terminology “partial product” is helpful. I knew I had to add all those rows of answers to get the final product but I never really realized that they were “partial” pieces of the final product.
I accept that by now you are probably confused by this explanation of the game – you really have to SEE it with the material to understand the process – but isn’t that the whole point? Your children do get to see it, every day in their classroom. They get to choose this work over and over again until they truly understand how it works. In my school days we worked on multiplication problems for perhaps a few weeks and then moved on to division or fractions or some other incredibly confusing operation whether I really understood what I was doing or not. That is the genius of Montessori!
The materials are always available and someone is always using them. If a child is uncertain of the process he or she will find a partner to help them until they are as competent as the lead child. Then they will, in turn, help another child master the work, clarifying the concepts in their own mind as they assume the role of “teacher.”
While using the checkerboard, or any of the Montessori math materials, your child is practicing simple multiplication and addition, exchanging into ever higher place values, keeping track of just where in the work one is, recording and reading large numbers, moving, which all by itself was never allowed in my fifth grade classroom, socializing with a partner, and free to go to the bathroom if the need arises without any adverse consequences. The beads are still in their place when the child returns and he or she can pick up where they left off.
I could go on and on. I’d love to explain the racks and tubes for long division. But you grew up in the same kind of math classes as I did and perhaps you get a head ache just thinking about learning long division. “If only we had these materials when we were children…”