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...
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