Friday, April 13, 2012

Why are there no numbers?

As the toddler teacher at Dynamite, one of the questions I answer most often is, "do you teach counting and numbers? I don't see any materials for that..." The last part of the question shows that they already know what my answer will be, but are hoping I will reply, "well, actually, we DO teach..." But we don't.
So why don't we have math materials in our class?
There are a few reasons. The first reason is that children in the toddler community are still developing an understanding of how to control their bodies, concentrate for longer periods of time, and manage frustration. These skills may not be necessary to repeat a rote memorization of counting, but they are extremely crucial to using the math materials and doing work with any level of understanding. Even when counting one-to-one (where the child matches each number with an object while counting and does so correctly) the child must be able to  keep track of each object, remembering which he has already counted and which he hasn't. If the child isn't ready and able to do that, it seems silly to teach him to repeat something he can't use and that doesn't have any meaning to him.
The second reason is that the materials we use for math are initially quite large, and then quite small. Even if we had a child in our class who was able to manipulate them effective and understand their use, there would be many others who would not. The children in the toddler class have very little, if any, ability to wait for something they want. This ability is augmented by another person already having that something, and this is usually enough to stop a toddler from taking it. Math materials would necessarily only be used by the oldest and most advanced students, leaving them available for a longer portion of the day than materials that all the children can use. This gives children who are not ready more of an opportunity to misuse them and see them being misused. We don't want their absorbent minds picking up incorrect use of the materials over a long period of time.
Finally, the third and most important reason - there is a progression of materials in the primary class environment that lead to the math area, and toddlers haven't mastered them. They don't have the control of movement or the logical sequencing to even use them.
Children first learn to use the cylinder blocks, which have elements of the later materials but are more easily manipulable by small hands. Next, they work with the pink tower. The pink tower increases incrementally in all dimensions, making it easy to discern the difference in size. The child builds the tower from largest to smallest. Children working with this material are indirectly prepared for the idea of 10, and see how three dimensions changing in unison make a more of a hyperbola than a straight line. They develop their ability to visually discriminate dimension. After working with the pink tower for a while, they are introduced to the brown stair. It is slightly more challenging than the pink tower because it changes in only two dimensions. Instead of evaluating size, the children evaluate thickness. This helps them to discriminate in more detail, and see how the shape changes when only two dimensions vary. Following the brown stair, children work with the red rods. The red rods are slightly more challenging than the brown stair because (I'm betting you've already guessed this) only one dimension changes. Now the children are evaluating length. The first rod is one decimeter in length, the second is two decimeters in length, the third is three, and so on.
In the use of every one of these materials, children are using highly mathematical concepts and evaluative skills. What I have described is merely the first lesson with each material - the barest introduction. After they've practiced with that, they take the measure of difference between each piece, they build from a distance, and match the pieces to things in the environment that are the same size/thickness/length. But these are all indirect uses of mathematics. I'm guessing you're wondering where the direct use comes into play?
Well, after the red rods, there is a material called the number rods. The shortest rod is identical to the shortest red rod, but then they start to alternate colors on each rod while remaining otherwise the same. The second rod is red-blue. The third is red-blue-red, and so on. Each rod is the physical embodiment of a number, with the units differentiated but not separate. Thus the child understand the concept of seven as a discrete quantity, while still seeing and feeling through the use of the material that it is made up of individual units. It's the perfect introduction to what a number actually means.
Why would I skip over all that beautiful preparation, that leads so perfectly into the concept of quantity, just to be able to say they know their numbers at two? Besides, they wouldn't really know them, not in the same way that a child who has followed this progression will.
The rest of the math materials follow in the same kind of logical progression so that by the time a child works with a material, he is really ready to understand it. In depth. And this deep understanding helps him be ready to understand the next material in the same way. It seems contradictory, but by not rushing things, the child is able to actually move through the concepts faster. He doesn't have to struggle to understand each one; the lessons are just challenging enough to be intriguing, and not so challenging that the child finds the work frustrating. Everything in a Montessori environment is like that. We call it "isolation of difficulty". Genius, right?
So when someone asks me why we don't do number work in the toddler class, I know they think I should. But I'm glad we have this beautiful progression, because it shows a profound respect for the child's learning process. Knowing the Montessori way, I would never do anything else.

Welcome to Montessori Moments, a blog written for Dynamite Montessori School in Cave Creek, Arizona. If you'd like to check out our school, please visit Dynamite's website.

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