When I first unveiled the felt numbers I made for K, I asked everyone why they thought I’d only made numbers 1-9. A few people guessed, but nobody got it right. It has to do with the way Montessori teaches numeracy.

At first, the kids seem to learn how to count objects. Then they begin learning the numerals, which is when they break out the sandpaper numbers (or in our case, the felt numbers). This activity teaches children to recognize the numerals and prepares them for writing numbers as well. The sandpaper numbers only include the numerals 1 to 9.

The next math activity teaches the student that the numerals represent a number of objects. It is called the spindle box, and looks like this:

As you can see, the spindle box introduces the concept of zero. Zero is not part of the set of “natural numbers” (a term which, if I recall correctly, translates roughly as “the way people counted sheep thousands of years ago”) and no child would reply “zero” if you asked them to count something that wasn’t there. They would say, “There aren’t any”. So in this activity the children learn, both visually and kinesthetically, that zero is a placeholder that means “this slot is empty”.

Okay, so now we know why zero isn’t represented in our sandpaper (or felt) numbers. What about 10?

It seems odd to us not to end a child’s number activity with ten. Isn’t that the first big milestone in counting? The truth is, though, that by detaching “10” from everything before it, Montessori sets the kids up well for future math concepts.

You see, the thing I (and possibly most people) overlook is that 10 isn’t just another number. 10 means “we can’t count anymore digits until we move them all over to another column”. 10 means that our cup of ones runneth over. It’s not the end of the first set of numbers – it’s the beginning of the second. 10 opens the door to 2-digit operations. 10 teaches the kids the basics of “making change”. 10 enables us to use an abacus to make quick calculations (well, it does once you really understand what 10 means).

If this isn’t a bit of a revelation to you, it’s either because I’m not expressing it well, or more likely, you’re not as math-impaired as I am. I’m probably the farthest thing from a “mathlete” – I freeze up when math is involved. I panic. I don’t understand, and I feel this impairment keenly. If I can spot connections between words (both in English and between languages) and play with them to make them do magical things, there must be people who have such an understanding of numbers.

I am not one of those people. But seeing K learn math the Montessori way has taken me back to the beginning. If I can uncover the simple but amazing things that “10” means, maybe there’s hope that one day I’ll be half as numerate as I am literate. A girl can hope, can’t she?

Cuisenaire rods are both similar and different. Similar because zero is represented literally – with NO rod. But then – totally different – there IS a rod for ten. It’s an important one, too, because learning how the numbers “team up” to make tens (I call them “partners of ten” with Naomi) is very foundational to later arithmetic.

I agree, though, that knowing ten (and the lower teens) well before understanding place value can lead to confusion. If TEN doesn’t mess them up, the words ELEVEN and TWELVE will for sure. I read about a math system that introduces the number-names as “ten-one” “ten-two” “ten-three” like in Japanese (?) just to avoid a bit of the confusion.

However, in my experience, with rods, and probably with any tactile system, like Montessori, kids learn quickly that when a TEN has a TWO on top, we call it TWELVE. Sorry, English-speaking child, that’s just the way it is.

Postscript: want to REALLY mess up a little kid and his number sense??? I just turned around because GZ brought me a racecar and announced that it was “number forty.” Ha ha ha… the number was “04.” Thanks a lot, Hot Wheels!