Montessori Sunday: Golden Beads (Part 3)

Ok, so I'm a day late but the Golden Beads are just so darn useful that I can't short them now. Trust me, they do justify having 3 separate posts for themselves.

After the child finally has a solid foundation and understanding of the beads themselves, and how they relate to on another it's time to begin the basic math operations. This same material will be used to teacher addition. It'll be used to show how subtraction works. The children will multiply, they'll divide--all with the same golden beads. Now that is a multipurpose activity.

I do want to point out that the golden bead material includes both the physical beads and their matching cards. The beads are present to give the children a concrete material to manipulate, while the cards are there to show the abstract symbols that society uses. Both parts are important to help prepare the children for further mathematics work at the Elementary level. While doing the operations with the golden beads we're not focusing on whether the children are getting the right answers or not. The process of how things are done is what matters in the children's house. Having the children physically experience adding the beads together to make a larger pile matters more than what 8,932 + 6,247 equals. They can see that putting two smaller quantities together makes a larger one, so they can really understand what the process of addition is.

The idea of subtraction is similar. The children get to be a part of actually taking away a certain number of beads from a larger quantity. They can see that this process results in a smaller number then they started with.

Multiplication usually puts a grin on their faces because they have a 'secret' when they go to collect their beads and cards. (Hint: The secret is that they're all getting the same number). The children who have done multiplication before think it's hilarious and the new ones are properly shocked when the secret is revealed. It's definitely a more fun way to show that multiplication is really just the adding of the same number a certain amount of times.

Finally the children learn the process of division, which usually ends up becoming their favorite way to use the golden beads. I think it's because everything ends up 'fair' and these older children are just beginning to build up a strong sense of right and wrong. The beads are handed out from largest to smallest, with each person getting the same amount and any extras 'remaining' with the teacher.

That's what a remainder means! I remember thinking during my Montessori training. Somehow I made it all the way through high school calculus and all of college without having a real understanding what was happening with division. And I could have learned it at 5 years old.....I kind of feel like I missed out...

Montessori Sunday: Number Rods

Introducing, the number rods. These pretty red and blue rods are the child's first formal introduction to numbers and counting. By the time most children get to this work they may already know how count by rote, maybe learned from songs, stories or just parental repetition. The number rods help them to associate the name of the number with an actual quantity.

The idea of quantity is reinforced by the fact that the sections of the rod are bound together. Rather than introducing the child to counting with say, shells, whose number name with fluctuate based on how many they grab, the number rod of 9 is always going to be 9 (barring the introduction of a power saw into the environment, but I think we can say that most likely will not happen). 

The child brings the rods to the mat and the Directress has him or her build them in order of length. This process should be relatively easy because the child has already had experience with building the red rods, which are identical (except for color). After arranging the number rods the teacher takes down the shortest rod and introduces it in the form of a three period lesson.

"This is the rod of 1." She demonstrates counting it, placing a finger on the rod while saying, "1." Next she brings down the rod of two and repeats the process, moving her finger from the red section to the blue when counting each new number. This is repeated for the rod of three and then the teacher begins to give fun little commands that have the child interact with the rods. Things like, "Tap the rod of one," "Give me the rod of 3," and so on. The child is introduced to all the rods this way, until they can identify them all through counting.

And this is just the initial presentation, there are lots of activities and extensions that help solidify the child's concept of quantity and their ability to count to ten. There are also small cards with the numbers 1 to 10 on them for the child to match to the rods when they can identify the written symbol for the numbers. 

One of the things that I think is coolest about the number rods though is that there is an actual activity with them is the introduction of the idea of addition and subtraction. Yes, that's right. In preschool we are not just teaching how to count, but introducing children to the operations of math. I know there's a lot of other toys/games/activities for young children that are supposed to teach counting and math, but most don't even attempt to claim to teach the operations, thinking young children aren't capable of it. However, thus far I've shown this to at least four different children and all of them have been fascinated by the idea of adding two numbers together and easily picked up on the idea of how to do it. Score one for well designed learning equipment!