Montessori and The Spiral Curriculum

In a Spiral curriculum, students revisit the same topics throughout their education. Learners benefit from a spiral curriculum because each repetition reinforces previous learning and builds complexity.

As complexity builds so too does the level of abstraction. Though not exclusively found in Montessori schools, Montessori students experience a spiraling curriculum with the added benefit of using similar or even the exact same materials they used while mastering previous concepts. A spiral curriculum is most easily seen in mathematics because most topics in math build off of each other with increasing complexity. This is even more dramatically demonstrated in the Montessori Math materials.

Let us take, for example, the simple, beautiful bead stair.

The bead stair is certainly not the first math material children have experience with. Early concrete experiences with math are everywhere, but arguably, the first structured, purposeful math concepts start with sensorial materials like the iconic Pink Tower: ten cubes, placed from largest to smallest. This is the first work that illustrates the concept of bigger and smaller; a very concrete lesson, where the child experiences biggest and smallest and then the associated vocabulary.

But let’s get back to the Bead Stair. A child in children’s house has spent months or years working with intro to number materials; counting the long and short number rods, tracing sandpaper numbers; they can identify 1-9; they have been counting each spindle, one at time; and they can place the numbers in order and lay out the correct number of red counters. They have mastered numbers 1-9.

Up until this point, all the numerals and all the objects to count have been the same color. The only differences are the shapes of the numerals and the corresponding quantities. This is by design; Montessori materials highlight one concept at a time. The bead stair, in its simplest presentation is reminiscent of the first lessons with the number rods. The child places the beads in order from 1 to 9. The bead stair is an opportunity to revisit and reinforce what the child has learned.

The bead stair is both a culmination of 1-9 work and a bridge to more abstract and complex number concepts. The bead stair does not teach the 1-9, the child works with and memorizes the bead stair because it will become a tool. Like the Pink Tower, the Bead Stair is a deceptively simple work that lays the ground work for amazing conceptual leaps.

Now the color of each quantity is different. Now 3 is pink and 4 is yellow and the idea of three, ●●●, and 3 are held together and remembered and the child can move 3 and add 3 without need to count 1,2,3. The student no longer needs to count 1-9.

The child uses the same bead stair to build teen numbers. The child lays a ten bar next to three bead bar and counts to 13.
The bead stair is used for addition, and again, when children start counting the square chains and cubed chains.
Multiplication bead boxes are full of the same bead bars. The student will use bead bars in the Subtraction snake game.
When elementary children use the Golden Mat or when they finally get to use the checker board to multiply large numbers, guess what they use to represent each amount? The bead bars. The student has combined his/her thorough understanding of place value and operations and now the humble three bead bar becomes 3,000.

Children continue to use these bead bars through Upper Elementary, when they create the decanomial. (for a great step by step photo demonstration of the deconimal click HERE).
Once they lay out the grid they exchange the bead bars until they create a diagonal line down the middle made of cubes. The child stacks the 9 cube onto the 1000 cube and continues to stack the next smallest until the one bead sits atop a tower.

The child who started the mathematical journey back in Children’s House many years ago, takes a trip to a 3-6 classroom in search of something that looks just like their Cube Tower. And they find this…

From a conceptually complex work all the way back to the very beginning of mathmatical work.