Material Spotlight: Bead Work
If you have ever been in a Montessori classroom, you have probably noticed the bead material. It is an indispensable part of Montessori mathematics curriculum, and it is so striking and beautiful that it’s hard to miss. (Also, it's pretty large). Here’s a picture of the cabinet:
A specific number of beads is strung on a wire, and the color of the beads corresponds to the number. One bead is red; two beads on a bar are green; three are pink; four are yellow; and so on. These are called bead bars. Next, there are chains made out of the bars. Two bars of two (green) are put together to make a chain; three bars of pink; four bars of yellow; all the way up to ten bars of orange, making a chain of ten ten bars, or one hundred chain. Next, each color of beads is presented in a square: four green beads, nine pink beads, sixteen yellow beads, all the way up to 100 orange beads. Finally, the beads are presented in a cube: eight green, 27 pink; 64 yellow, 1000 orange.
There are also two beaded counting frames, where each wire is labeled for ones, tens, hundreds, and thousands.
Here’s how it works - and guys, this is genius.
On the most basic level, children can use the bead bars to learn to count, and then to learn to add. If your child went to a Montessori preschool, you probably have seen reams of paper with little beads colored in and the number of beads written beneath it. My own daughters were also thrilled to bring home their addition books, where they showed, for example, how a two bar placed next to a five bar added up to seven beads. Children can master their simple addition and subtraction in this way, by combining different bead bars and counting them.
After this is mastered, children can move to the counting frames and learn to build very large numbers - the larger counting frame includes millions. They learn about place value and are set up to understand decimals. They learn to combine large numbers through the manipulation of the beads on the frame. 317 + 482, for example, is solved by having three beads on the hundred wire, one on the tens wire, seven on the ones wire, and then moving over four more on the hundreds wire, eight on the tens wire, and two on the ones wire. The child can then see that the sum is 799 by counting the beads on the wires and understanding their place value.
The beads also brilliantly show children how squaring and cubing works. When you look at the the orange square, you are literally seeing ten ten bars - ten squared - as a square. It makes the concept obvious. The cubes present the same way: 10³ = 1000 beads literally in a cube, where each side = 10. Presented like this, squaring and cubing makes sense. We are not just attaching a random word to the idea of multiplying a number by itself, because the child sees that when you multiply a number by itself it makes an actual square.
The bead material makes mathematics visual as well as manipulative - children can see what is happening as they move the beads, and that makes remembering it easier. It is not just rote memorization. Mathematics in traditional elementary schools has moved towards trying to present the concepts and theory of math alongside - or even instead of - the memorization (if you have a child in elementary school now you have probably heard about math mountains and ten partners), but Montessori math has been teaching the concepts and presenting the theory of math for generations already. The beads make it even more concrete, and more attractive, for children. It is difficult to resist the draw of a lovely and organized cabinet of colorful beads, especially when presented alongside the colored pencils and small pieces of paper used for drawing the work you’ve laid out, and when you're figuring out the sums and equations you’ve created.