Montessori Sunday: Spindle Boxes

It's been so long since I did a post on a specific Montessori Material that I had to go back and check what I haven't already posted about. So today's post is going to be about the Spindle Boxes because A) I haven't done them before and B) because I just recently showed them to a child in my class.

The spindle boxes are one of the earliest math materials children are exposed to in the classroom and are supposed to convey the idea that numbers mean a specific quantity of something. They are shown after the child has had practice counting the number rods (which are units that are bound together so that 5 is always 5 and you can't accidentally drop any parts to make is 4) and is comfortable identifying written numbers. The material is made up of a shallow box divided into 10 separate compartments. The numbers 0 to 9 are written in the space above each compartment. There is also a container with exactly 45 spindles in it.

The adult double checks that the child is familiar with the printed numbers and then begins demonstrating how to count out the desired number of spindles, beginning with 1. Each time the spindles are counted into the hand first and when the correct number is reached then the spindles are counted again in to the correct compartment. 

When the compartment for 9 is filled all the spindles will have been used, creating a built in control of error for the child. If they haven't counted correctly their will either not have enough spindles for the last box, or there may be some extras left over. 

Once all the spindles have been counted the teacher introduces the 0 compartment. "This is zero, zero is nothing so we don't put any spindles in here." The teacher then demonstrates how to bind the groups of spindles together and place them back in their compartments. This binding is done to show that the number is the whole quantity grouped together.

That's it. A fairly straightforward activity that introduces the child to the idea of 0, careful counting of objects, and double checking of work (by counting the spindles twice). I really miss the spindles from my training class, they were like old fashioned sewing spindles, smaller and smoother than the current type and just felt so much nicer in the hand. They were also smaller, I found that when showing my classroom set to C that he had trouble grasping the spindles in one hand as soon at the quantity was any higher than 7. This makes binding the spindles together even more difficult; how are you suppose to bind something that you can't even hold in one hand, what hand do you have to use then? So I'm currently brainstorming ideas on how to complete this part of the lesson. I'll let you know how that turns out.

Presentations, presentations and more presentations!

A presentation is what a Montessori directress calls the process of showing a new material to a child. Most children love getting presentations, even if they're not particularly excited about what the activity is they love the one on one time with the adult. I normally don't do a lot of new presentations in our classroom because we want to limit how many new things the child is introduced to at a time so they go back and practice what they have already been shown. So my fellow teacher and I have decided that it's best if she does the majority of the presenting and I focus more on showing the children extensions and reinforcing what they learned the first time. Today though it just worked out that I had a lot of opportunities to give new presentations.

I caught L right when she came in and said that magic words "I haven't worked with you in a while, what would you like to do?" The first thing she blurted out was the color wheel. I grinned and reminded her that she already knew that work so well that she didn't need me to help her. Instead I offered to show her the leaf cards and had her set out the mat. She laid out one set of the cards and I read off the names of the leaves before handing her the card to match.

Unfortunately I was interrupted a few times during the presentation. Ideally this should be a time where the teacher is completely focused on the one child, but with one of the other teachers busy greeting children at the door I had to step away from L to remind other children to stay in the classroom. Luckily L was patient and I did try to leave her with a card to match when I stepped away. Overall I think L enjoyed matching the cards and she was really quick even though there are a lot of different leaves to look through, and since they're real leaves they aren't truly identical.

My next presentation actually started before I even finished doing leaves with L. A came in and the first thing she asked me was if I was going to give her the presentation I had given her friend M the day before. I told her sure, surprised she had remembered that I wanted to show her subtraction and seemed pretty excited about it. So I had her start setting up the cards for the golden beads. That's one of the really nice things about working with the older children, they can really take direction, and set up even new works independently.

A and I flashed through the process of doing subtraction. She knew exactly how to count the beads, remembered the numbers she needed to get and eagerly followed the steps. In fact she had such a good time that as soon as we finished reciting the problem she asked if we could do it again! I apologized that I needed to work with some other children and suggested a few other friends who knew subtraction that she could ask to work with her. Unfortunately they all declined and she just cleaned it up instead.

Next I reviewed a counting work with one of the four year old boys, helping him recognize his numbers and double check his work. I got another boy started on the sound book he was supposed to be making, helping him find a table where he wouldn't get distracted. I also tried to engage one of the four year old girls in to doing a fetching work since she wasn't working, but rather being silly and distracting her friends. She didn't like that idea though and turned me down. Ouch. Though she was polite about it. Just asking though had desired affect of getting her to buckle down and choose a work to do.

As the day was drawing to a close I saw N running around the classroom, trying to play chase with some other children. I got him to stop running, asked if he had a work out and then told him to come with me and choose one of the chains. This was the first presentation I gave today that wasn't optional. Usually it should be optional if the child wants to come to the presentation, but occasionally, like in this situation, it's necessary to divert them to something more productive.

So N chose the short 7 chain and I introduced him to the arrows that went with it. He quickly caught on to the idea of counting and placing the arrows. Since it was so easy for him I also introduced him to writing the numbers down on special graph paper. Why hold him back when he's obviously ready for more challenging work? It took right up until the end of the work cycle, but N finished writing his number for the chain and I'm sure he's excited to bring that paper home.

Whew, a lot of new materials today. Now hopefully they all liked the work enough to try it again tomorrow.

Sometimes work really is just a lot of work

"276, 277, 278, 279....."
"What comes after 79?"
"70, 10?"
"Sort of. Do you remember what we call it when we have 7 tens and add 1 more 10?"
"80!"

This was my afternoon conversation with one of the older students in the class. He was counting one of the long bead chains which are the cubes of a number in physical form. Still with me? Yeah, I wasn't there the first time either, and we actually don't tell the children this fact until the elementary years. I'll put some more pictures at the bottom of the post if you're interested in just how they work.

But on with the story.

In the ideal world the boy counting the chain would have immediately started counting "281, 282, 283..." etc. etc. Instead this happened-

"280, 290, 300..." Hmm...doesn't sound quite right does it? Obviously he has the concept of the numbers 1 to 10, and knows that these numbers repeat, but he hasn't fully understood it yet. The head teacher and I were discussing the matter and think that one of the preparatory materials for this work was actually making it harder for him to count linearly. Oops.

Especially in the math area of the classroom, early activities lay the basis for later ones. In this case the child had done a lot of work with the thousand chain. This chain has a thousand beads on it, bound together in sections of 10. The children are supposed to count the beads, and place the correctly numbered arrow at the end of each section of 10. This student had quickly realized that all the arrows he needed to place ended in 0 and that he just needed to put the first number in order. A pretty good shortcut, and one we wanted him to figure out eventually but it's making it really hard for him to do the 9 chain as the sections now each have 9 beads in them instead of 10 and the pattern of arrows is much harder to recognize. This means that he now needs to actually count each individual bead, an exercise he skipped earlier when learning how to do the thousand chain.

Now an activity that was super simple for him, has suddenly become a lot more work. And not work in the Montessori sense of the word. In a Montessori environment the activities of the child are generally refereed to as work. This is because the job of the child is to build up themselves into the adult they will become. The term work is used as a sign of respect for what the child is doing and is not meant to seem as though we are submitting them to drudgery as a adult might think when we say the child is doing work. To the child work is purposeful and fulfilling; they enjoy it.

Unfortunately, nothing ever works flawlessly, and even with all the preparation materials in a Montessori classroom you run into stumbling blocks like this one. So I spent about half an hour gently coaching him on how to count linearly. Together we made it up to 250 and will tackle the chain again tomorrow. Hopefully the work will make the shift from drudgery to purposeful.

Some more explanation of the bead chains for anyone interested-

The chains come in two different types, short and long, and there is one of each type for the numbers 1 to 10.  Below is an example of the short 5 chain-

The short chain shows the number squared. So since this is the 5 chain there are 25 beads total, separated into sets of 5. The square in the upper right is bound together and helps to subtly introduce the idea that this chain is the square of a number. The long chains on the other hand show the cube of a number (125 in the case of the 5 chain) and instead of a square the end of the chain is symbolized by a cube, such as in the photo below.

So yeah, there's a lot going on in these chains. However, when the children take them out in the environment they are simply counting the beads and placing the arrow with the correct number next to it. The idea of squares and cubes are supposed to be passively absorbed and pulled out again later when the child is introduced to this concepts in their elementary years.