“When will my son stop playing with the blocks in the classroom and start to do some real work?” This is a question I’ve heard many times from concerned parents. Parents are anxious to see some tangible results of their child’s time in the classroom. I can think of no better learning pastime than “playing” with the blocks in a Montessori classroom. Let me show you the Pink Tower.
In the Montessori primary class, for three to six-year-olds, we introduce the Pink Tower to the three-year-old as part of the sensorial work to help develop the sense of visual discrimination. The Pink Tower stands prominently in the classroom, ten pink colored cubes, the largest being 10 centimeters on each side, and the smallest being a one-centimeter cube. Dr. Montessori took the butcher’s wooden weighing blocks and painted them pink to make the tower enticing to the child.
To work with the Pink Tower, the child works on a rug and carries one block at a time with both hands. Ten trips over and ten trips back to get all the blocks to the rug, so this activity builds concentration and memory. The work with the Pink Tower also is a lesson in physics, with the child’s inner teacher asking some of these questions:
What combinations of blocks can I stack and the tower will continue to stand?
What other building combinations can I make besides a tower?
What relationships does the Pink Tower have with other materials in the classroom?
The physics of the work is the child’s exploration. The Montessori teacher doesn’t pose these questions to the child. It is the child’s mind that poses the questions, consciously or unconsciously, as the child explores and discovers the answers on his or her own by manipulation of the materials over a period of time in the primary classroom.
As the child works with the Pink Tower, the child’s body and mind are absorbing information that will help in future math work. At the simplest level the Pink Tower is a set of pink building blocks. As the child explores the other materials of the Montessori classroom, the child begins to see relationships within this material and among other materials.
For example, the child will discover that the ten-cube is much heavier than the one-cube. Perhaps in counting the 1,000 chain or working with the decimal system with the golden bead materials, the child will notice that the 10 cube is 1000 times heavier than the one cube; that its numerical value is 1000 times greater than the unit cube; and that its volume is 1000 times greater. Numerical value is not an abstract concept in the Montessori classroom. Working with the Pink Tower the child knows by sight and weight the difference between one and a thousand.
Many children enjoy drawing the Pink Tower. The Pink Tower lends itself to artwork and challenges the child to figure out how to draw a cube, how to maintain the proportion of the tower, how to shade, and more.
For the elementary student, we “borrow” the Pink Tower from primary to make the initial presentation for the cubing material. We introduce the idea that each cube of the Pink Tower has a mathematical name and numerical value. The one cube is expressed as 13 andthe ten cube is written 103.
Using the Cubing Material we use the algebraic binomial, (a+b)3, and trinomial, (a+b+c)3 , formulas in a concrete way, to build the cube of one number to the next larger cube. Our explorations lead us to analyze and name the parts of the new cube and derive the algebraic formula for the binomial and trinomial. The eight pieces of the binomial cube are each given a mathematical name, as well as the 27 parts of the trinomial cube.
Binomial Formula:
(a+b)3 = a3 + 3(a2b) + 3(ab2) +b3
Trinomial Formula:
(a+b+c)3 = a3 + 3(a2b) + 3(a2c) + b3 + 3(b2c) + 3(ab2)+ 6(abc) + c3 + 3(bc2) + 3(ac2 )
We allow children to use their imagination (usually in their 6th elementary year if they are interested) to use these keys and derive the quadranomial formula, (a+b+c+d)3, on their own.
For the older child that has a desire for more mathematics, we will revisit the Pink Tower in the form of the cubing materials to derive the cube root of numbers to 10,000,000.
For geometry work in the elementary, the child can derive the formulas for volume and surface area from the cubes of the Pink Tower. Geometric progression is an inherent concept within the Pink Tower. In primary and in elementary, we can further explore the Pink Tower by rolling and moving the cubes through a tub of sand or flour, thus creating a footprint of a solid moving through space, and a concrete hands-on experience with calculus.
The beauty of the Pink Tower, and all the other Montessori materials, is that there are multiple physical concepts embedded in the materials, whether we are cognizant of them or not. Children and adults, and amazingly even Montessori teachers, do not need to be aware of the concepts of numerical value, weight, geometry, art, engineering, or calculus to enjoy working with and learning from the materials.
As in the Zen proverb, “When the student is ready the teacher will appear”, the Montessori proverb could be, “When the student is ready, the concept in the materials will appear”.
When your child tells you he or she worked with the Pink Tower today, you can say with sincerity “I’m glad to hear you are doing such important work.”
–Excerpted from Understanding Montessori: A Guide For Parents by Maren Schmidt, M. Ed.
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