Montessori Sunday: Golden Beads Part 2

Last week I introduced the Golden Bead material, one of the key Montessori materials for teaching math. This work allows young children to work with numbers in the thousands while only needing to be able to count up to 10. Pretty neat.

When Dr. Maria Montessori first came up with the idea of the golden beads she thought they would be used at the elementary level, that the younger students in the Children's House would not be interested or able to understand the idea of them. What she found though was that it was children around 4 or 5 years old who were truly interested in using these beads to convey the idea of numbers, not the older elementary children! It's pretty amazing what children can comprehend if given the right context to experience something with.

Once the child has become comfortable with identifying all the beads and cards by their names (1, 10, 100 & 1000), they can begin learning the change game. Learning this as adult even made an impression on me. I remember needing to carry over numbers in school, but didn't really have a good understanding of why. Learning to do so with the golden beads finally made it click exactly why and what was happening. Now I wish I would have just learned it this way in the first place!

The directress will have the child bring a large tray over to the supply of golden beads on the shelf and begin loading it up in a haphazard manner. Handfuls of 10's, fistfuls of units and piles of hundreds are added to the tray without much thought as to their order. At a mat the directress informs the child that they are going to count ALL these beads, usually sparking a shocked response since the messy pile looks unconquerable. To make it a little less intimidating the beads are sorted into categories.

"Let's start with the units. 1, 2, 3..." The directress shows how to count the beads one by one into a small cup. "10! Wait, 10 units? That's the same as 1 ten bar. Let's go back and exchange these." Together child and adult go and exchange the units for one of the bars of 10. And so the counting goes until there aren't enough unit beads to make into a ten bar. The ten bars are counted and exchanged in to hundreds, then the hundreds counted and made in to thousands. Finally there's only a small piles of beads left and the child is sent to fetch the matching cards to form the written number.

"That's our answer, we counted all the beads we had on this tray. Want to do it again?"

The act of simplifying this messy mountain down is a favorite with children. It seems so intimidating until they begin to actually do the process and find out how simple it is. It's also extremely important that they fully understand this concept because they will need to be able to exchange beads freely using the four basic math operations.

Late Start!

What do you do when the roads are icy and the school district calls a late start?

Well you smile warmly at your students, watch them work happily for about 20 minutes, then call them to the circle to end the day.

After all, it takes nearly half an hour to get that bead on and get all dressed to go home. Plus if it's warmed up enough that now everything is melting in rivers off the roof you don't want to miss having some extra play time outside in the sunshine!

(Minnesota weather is just crazy sometimes!)

What we do all day

Thought you might like to see what sorts of things we do all day. I have to say there's quite the variety!

Looking up and coloring flags

Getting really good at that tricky trinomial cube

Practicing a puzzle map of the world

Cutting and pasting to make snowflakes

Learning how to pin fabrics together

Fetching different flags (they wanted to have ALL of them)

Cutting and arranging flowers in vases with our new stand

Cracking the code of the decanomial square

Practicing colors and learning how to use a screwdriver

Building tippy towers with the knobless cylidners

Keeping our new bird feeder full

Washing and drying dishes

Peeling and cutting carrots

Mixing colors to see what they make

Learning the different categories of numbers up the 1000!

Taming tricky botany puzzles (left: parts of a flower, right: parts of a tree)

Peeling and slicing hardboiled eggs

Ok, so we still need some work with getting just the peel off!

Language is ridiculous

What's harder than learning to read?

Learning to read when the book you want to read is about pirates...pirates who speak piratese.

While practicing reading with a first year elementary students today I had to pronouce and explain the following words:

-Aye!
-Lubber
-doth
-thy

And a mix of more that I can't remember. Then we got to the part that stumped her cold. She sounded it out, hesitated, looked at it again and looked up at me.

"Um..."

"Yep, that's what it says.It's in the book. Go ahead."

"Shut up," she read again, hurriedly skipping away from the bad words and racing onward. Oh the perils of reading, the world opens!

Making decisions isn't always easy

The children are in charge of so many decisions over the course of the morning work cycle. They get to choose what to do, when to do it, who to work with (or not), and even how long to work with something. It may not seem like a lot, but to children who are so used to having adults be in charge of them it's a novel idea that they are in control.

Some children settle right in to the idea, like M. I have to admit that she is my star decision maker. I watch her go from activity to activity all morning, it's rare to see her  wandering the room; there's always something she wants to do next. Sometimes I can even hear her decision making as she chats with the other children. Like when she wanted to have snack today and the table was already full so she said to another student how they could go and choose a work to do and then when they were done it would be their turn to have snack.

M is also really flexible with her decisions. She and C were going to do some fetching with cards today, but another child was using the Solar Sytem set that they wanted and as soon as she realized it she paused for a moment, then turned back to C and said "Oh, we can't do that, someone's using it. But we can do the flags instead!" Wow, that's an extremely mature response from a 3 1/2 year old. Not only did she not get upset about someone else using what she wanted, she also got herself on track to do something else.

Now that skill is going to serve her really well at some future job!

But making decisions isn't always easy, and even being able to do so is something that you need to learn. W is on the opposite end of the spectrum from M. He's more than happy to work with the classroom materials, but when he finishes with something it's very obvious that he has no clue what he wants to do next and wanders about the room instead. He gets distracted by what the other children are doing, pausing to watch them for a little bit then wandering off again.

He'll choose some of his standard favorites like watering plants or washing windows, but as these aren't a real challenge for him they're over quickly and he's once again wandering the classroom. He'll often imitate what the other children choose (like this morning when he took out a puzzle after S and C began working on some) but again most of these things that are simpler exercises that don't engage him for long.

For a while I had thought that W really wasn't interested in any of the materials and that's why he wasn't choosing work--nothing appealed to him! But the last few weeks I've been specifically asking him if there is something new I could teach him. Oh he chose a few things, namely work he'd just seen other children working on. So it seemed like he just didn't know what was interesting to HIM and was just following the crowd.

So this week we're starting a new regime to help him learn some choice making skills. I have a box on my desk with pictures of the materials. When I see him wandering we're going to get that box out and choose 5 different materials that he wants to work on. These go in the cover of the box and he chooses one to start with immediately. Then whenever I see him wandering later in the morning I can direct him to go choose one of the other pictures to take out next.

I'm hoping this will help keep him focused because he does seem to want to work, but just isn't sure what to do. He gets to choose the initial materials based on his interest (though currently he seems to mainly choose what is on top of the pile) and so when he's directed to those materials latter it's still  his choice of what to do, rather than mine as adult.

So that's our experiment in decision making this week. Here's hoping that it goes well!

Montessori Sunday: Golden Beads (Part 1)

The Golden beads...I'm not sure if there is a more versatile material in the classroom. This lovely material introduces the child to the decimal system (including numbers up to the thousands), the idea of carrying over from one category to another (such as 10 tens turn in to a hundred), and also gives the child a concrete way to preform the four basic math operation (addition, subtraction, multiplication and division).

Wow, that's a lot to get from one material, so to make this a more complete post I'm splitting it into two parts. Needless to say learning this material is a long process; children may end up using the golden beads for both their second and third year of children's house. A classroom that I student taught in did a great job as building a solid foundation with the golden beads and it was very apparent that the children had a good understanding when they progressed to later materials.

The initial presentation to the child is simply naming each of the different categories (units, tens, hundreds and thousands). Ideally the beads for this material are made out of glass, so when the child is introduced to the thousand cube there is a very distinct impression of how heavy and large a number this is. It is also convey to the children that there are 10 units in one of the ten bars, and 10 ten bars in a hundred square, and then 10 hundred squares in a thousand cube. This idea will be reinforced later with a special activity with the beads.

 From there the children begin fetching certain quantities of the numbers. For example: "Bring me 5 10's.No that's not a typo, I said "5 10's." The child may not have mastered the formal names of numbers yet (such as twenty, fifteen, etc.) but they can count to 10, so why should we hold them back? Yet another reason why the English language makes education so much harder!

As the child get competent they are asked to get more and more numbers until finally they are fetching from all four categories (ex. Get me 3 thousands, 4 hundreds, 5 tens, and 6 units). How's your memory feeling? I know that I sometimes forget what number I've sent them for!

Around this same time the child is introduced to the decimal cards, which are introduced the exact same way as the beads. The children also learned to recognize the cards by fetching them, and eventually work up to getting four cards at once.

Finally the beads and cards are combined and the child's memory exercised as they are asked to get numbers such as 6,592 with both the cards and beads. This can take children weeks to months to master, but it's a vital step to make sure they understand and can remember these large numbers because the next step is doing math problems with them. 

Yep, we teach children how to add, subtract, multiply and divide using numbers in the thousands. None of this silly single or double digit stuff for Montessori children....ok, ok so it sounds like bragging, but is it really all that tricky when all you need to do is be able to count to 10 and remember the names of the categories?

A geography day

W and C started it by working on the world map today. I think W just really wanted to use the clay, but they also had fun putting the puzzle pieces in the frame. While they were doing that S took out the new little flag book I had made for them and was heading to the library to look at it when M caught her.

"I wanted to read that!"

"Ok," said S, who's always up for some socializing. So together they got out the reading mat and crowed around, flipping the pages to look at the different flags.

"That's South America," S said matter of factly as they flipped to one page. Now I know "South America' doesn't have a flag but hey, at least she was using geography terms! Then S got in trouble with the next page.

"What's that one?" M asked.

"I don't know." S replied after a short pause, quickly flipping away from it.

"How about this one?" M asked again. S just looked at it for a minute, struggling to figure out what to say. Finally she came up with,

"You have to read it silly!" and turned the page again and stated "That's South America." I couldn't help but giggle a bit as she kept trying to convince herself that she knew the names of those flags. After a few pages she did come and ask me to read a few of the names, but S was definitely determined to know them by herself. I have a feeling that girl's going to learn to read by sheer determination some day when she gets it into her head.

Afterwards C recruited M to do fetching with him using the flags. She happily pointed out the pictures in the book and sent him to bring them over from the stand. Unfortunately there were so many flags there that it was hard to pick out specific ones so I helped them spread all the flags out on one mat and work at a second with the ones they had already found. They were so in to their little game that when we noticed that some flags in the book were not out they asked me to check in the closet for them.

Soon they had ALL the flags for North and South America out on the mat or in the stand. They were bound and determined to find all the matches. M was having a great time directing C, who couldn't have been more pleased than when he brought back a matching flag. They made it through nearly all the flags before they finally got tired and went on to new work. I checked it later and that's about 35 flags....They went back and forth nearly 30 times matching the flags and pictures. Without any prompting or real help.

Now that's a great example of the kind of repetition we want happening in the classroom!

An individual presentatioin?

So I finally got tired of waiting for our world map to arrive in the mail. Though I only mentioned it yesterday I do have more than 24 hours of patience, I promise. This material has been on order since early August...I think I've been quite patient.

Anyways today I dug up in the attic of the school to drag out an old one. A large chunk of central america is missing and there are only 3 knobs on the entire puzzle but I decided it was better than nothing. W takes out the globes in our classroom almost daily and I have really been waiting to introduce him to more aspects of geography. I've talked about the puzzle maps before in this post: Montessori Sunday: Puzzle Maps, but today was the first time I've actually presented it to a child using all the steps.

My favorite part is using clay to demonstrate how a round sphere (like the globe) can be cut in half and then flattened to make the two flat circles of the map. I started the presentation with S and as soon as she started bringing materials to the mat the other two little girls in the class had also wandered over to watch. By the time we had discovered that the colored continents were the same on both the globe and map the boys had all joined us.

So I presented how a globe can be turned in to a mat to the entire class. Now in my album this presentation is written up for an individual, and I did insure that S was the one who actually got to do the squishing down of the clay, but who am I to tell a group of quiet and attentive 3 & 4 year olds to go away. I just figure I saved myself having to repeat the exercise 4 more times!

The puzzle itself was no problem for S, and I hadn't thought it would be but it's a doorway to other things for her later down the road. What I hoped would happen is that the other children would be eager to try the giant map out for themselves, seeing how fun and easy it was for S. We'll find out tomorrow when there's more time. I'm quite curious to see how W especially does with it....he's still in a bit of a wandering mood and needs some work to engage with. Hopefully geography is it.

Onward to the New Year!

The children came back today for their first day of 2015 and it went so well! It was a great morning with a lot of self-directed work. Several children helped me put away the small mountain of laundry we had washed before break, while the rest quickly settled back in to some of their favorite work activities.

C tagged along with me for a little bit before asking, "Eggs, teacher Alex." Lucky him he got the very last hardboilded egg and proceeded to spend the next half-hour peeling and cutting it, happily engaged in getting himself a snack.

W went through is usual repertoire of washing the windows, sweeping off the tables, trying to sweep the carpet, watering the plants; all the usual classroom maintenance stuff that he likes to do. Then it was back to the tried and true globes. I'm really hoping to get the world puzzle map soon so I can introduce it to him since he seems so interested in the globe. Then I'll be able to judge whether he actually likes the globe itself, or is just taking it out because it's easy ;)

Our lovely new flower arranging stand
(thanks dad!)

C and S did fetching with the new solar system cards, I helped them out with learning the names and spawned interest in some other children to learn some new vocabulary as well.

Meanwhile M went from work to work to work, I couldn't even keep track of what she was doing other than to note that whatever she took out she put back properly and seemed to be concentrating on while she had it out. My friends, those are the types of children you dream about having in your classroom. I need to remember to mention how great she is at keeping engaged during the next parent teacher conference.

At the end of the day they were all tickled silly by the amount of beads we had to put on our string to catch up for all the days we had been gone. That was it, the end of our day. It was like they'd never left...please tell me that tomorrow's going to go off just as well...please?