This is the Montessori golden bead material. It is composed of thousand cubes, 100 squares, 10 bars and units. The age for this work is 3-6 years.
We have already learned, how to exchange quantities, addition and subtraction. Here we are learning about multiplication. This is a visual representation of adding a number 3 times. This work gives the child a visual and hands on understanding of what multiplication looks like.
Multiplication is adding a number a series of times.
The picture you are seeing is pretty much the end of the work. In the beginning he had 3 horizontal rows of 1,232 laid out with the corresponding bead material. In the photo above, he has already combined all three 1,232 and is now calculating the answer, by counting the units first, then the tens, the hundreds, and the thousands. He will make the answer with the number cards and place it under the white bar.
The Montessori method to teach math is wonderful. Math is such an abstract thought. Much of the time when I was in school, I really did not have a visual understanding of many of the mathematical concepts I was taught. I memorized formulas and plugged in the numbers, but what did it really mean? What was I actually doing? This did not give me a solid foundation in mathematical concepts and hindered my progression in higher mathematics. Montessori math gives children a visual understanding early. They can really internalize mathematical concepts and in turn gain a great foundation in mathematical concepts.
The journey of Mathematics starts with concrete materials that lead to abstract understandings. Montessori Math materials provide many opportunities to experience number as quantity and measurement. Counting shells, objects and rods of graduating lengths gives the child a sensorial "feel' for numerical properties. Sandpaper numerals are presented for the child to trace and form a "muscle memory" for later writing of that numeral. When the child has mastered the concepts of `1-9, the decimal system can be introduced concretely by use of the golden bead material. Beautiful, hand made glass beads represent units, tens , hundreds and thousands. The child can construct 4 digit numbers using these materials in the Bank Game. They build quantities and match the symbols (numerals) to them. We do not expect children of this age to be proficient in 4 digit numbers, that is not the goal of these exercises. It is to form a foundation for future learning. Anything experienced concretely at this age will stay with your child. When they are in third or fourth grade and these concepts are presented in a abstract way, this early contact will be recollected and lead to mastery.
Addition, Subtraction, Multiplication and Division are also introduced in a concrete manner. The child can experience the action of these processes e.g. addition is putting things together, subtraction, taking things away. In like manner, fractions are handled and understood. Long and short bead chains are counted introducing skip counting, preparation for multiplication. These chains are based on the square and cube of numbers, indirectly preparing them for future learning. Math in a Montessori classroom is dynamic and enjoyable, a first choice of many of the students.
Montessori students use hands-on learning materials that make abstract concepts clear and concrete. This approach to learning offers a clear and logical strategy for helping students understand and develop a solid foundation in mathematics.
Resource: Gettman, D., 1987. Basic Montessori: Learning Activities for Under-Fives. St. Martin's Press, New York, 159.
Here is a article on Montessori Math ages 3 to 6 - http://www.michaelolaf.net/1CW36math.html