Math, Math, and more Math

I hated math for years. I struggled my way through all of my high school courses. I got the only D of my career as a student in high school Geometry. I finally passed college algebra on my third attempt. I was an A student in everything else, but math was the thorn in my side.

Montessori has changed all that. I now adore math and my understanding of it is infinitely better. The materials are brilliant and convey mathematical concepts in a way that just makes them seem perfectly natural. The materials link ideas together and help children (and adults!) connect math to all aspects of life in a concrete way. The curriculum is just absolutely brilliant.

Today, a five year old student who has recently learned the names of all of the polygons in the geometric cabinet and worked with all of the short chains, explored the connections between them.


She started by building a short bead chain stair (above).


Next, she used the chains to build a point, an angle, a triangle, a square, a pentagon, and so on. The 100 chain was in use by another student at the time.
In the background, you can see the arrows on another rug, and the book of polygons she had made earlier in the week and was referencing as she built the shapes.

In the end, she put them all together.

And finally, just when she was about to clean up, the 100 Chain was returned to the shelf, so she was able to add a decagon.

It was a morning full of math work. One 5 year old child took out quite an array of math materials and made some interesting things. I was tempted to ask him to put some of the materials away, as he was using nearly half of the math materials available at once, but he didn't seem to be disturbing anyone, so I opted to stay out of it. He first took out the 100 chain and lined up ten bead bars alongside it. Then, he took the ribbon that we use on the "operations table" to separate addends from sums, or multiplicands from products, etc. and stretched that out beneath the chain. Next, he took all of the unit cards from the large number cards tray and spread them out in order beneath the chains. Then, he took out the number cards that we use for the number rods and cards and the cards and counters and matched those to the large number cards. It was very interesting to observe. I wish I could have heard his thoughts throughout the whole process.

A 4 year old student who has spent all of this week's work time on Beads Practice and Cards Practice continued. I have never seen a child so enjoy the process of composing a numeral with the cards and going to the bank to retrieve the corresponding quantity. His favorite part seemed to be writing the quantity afterward. He has spent a full 8 hours doing this in the past 3 days.

I'm eager to see what these math enthusiasts come up with tomorrow!

Multiplication with the Golden Beads

This is the first year that I have had the freedom to present the math curriculum just as I was trained to teach it. In the past, I have co-taught and had to follow along with the way senior teachers felt things should be presented. That was no problem, of course, but it has been lovely to be able to follow the child - and follow my albums this year.

Today was officially the first time, in 6 years in the classroom, that I was actually able to do multiplication with the golden beads. I think it was even more exciting for me than for the children. Naturally, I took some photos.


Above is the "Operations Table," where each child has brought the quantity 1,321. We always cover it with purple velvet, as that is obviously the only type of material appropriate for use with the golden beads. Unfortunately, I do not have multiple sets of small number cards (or even one set) at my school. So, I used paper to write the multiplicand for each child. Of course, it is paper that the children are familiar with and have used for writing quantities with the golden beads, and it is color-coded. You can't see it terribly clearly here.


Above, the children have put all of their quantities together to find the product, 3,963, and they have brought the appropriate large number cards.


Above, you can scarcely see, but one of the children has written the final problem of the morning and the language "Taking the same number multiple times is called multiplication."

The Color Wheel

After reading Susanne's post over at Beautiful Sun Montessori and filling out all of my conference reports, I was inspired to do some color work. My conference reports include a place to indicate whether a child is working independently with materials that teach awareness of color, and whether they have mastered them for their age and/or level. I really got to wondering what, beyond color boxes 1, 2, and, 3, really helped the children to understand color.

I toyed with some paints and worked a bit with the color boxes and a color mixing work I had available and came up with some extension ideas.

I sat down with one of my second year students today and thought I would give her a simple terminology lesson. She already knows how to mix the primary colors together to produce the secondary colors. So, I thought I would simply teach her the names for these types of colors, and show her how to build them into the shape of the center of a color wheel. This, I thought, would lay the groundwork for a later lesson on how to produce tertiary colors.

So, we sat down at a rug where she had already matched the Colors in Color Box 1. I said, "The Colors in Color Box 1 are..." and before I could continue, she interjected, "Primary Colors!" Well, so much for my imparting of knowledge, huh?

Anyway, we built them into something like a triangle, then added in the secondary colors. Then, we got out the color mixing work and started exploring the concept of tertiary colors. After mixing a primary and a secondary color together, she chose the tablet from Color Box 3 that she thought most closely resembled the color she had produced. The result was the wheel you see below.

I think I will make a paper extension tomorrow if there's time, where children can paint the color wheel with colors they've mixed themselves.






In other news, some traveling musician friends of mine stopped in and played a couple of songs for the group. We recently began a formal music class, so there has been so much interest in music - a perfect opportunity to invite some visitors! Thanks, Leftmore!

Love the Spring!!

Spring is my favorite time of the year for more reasons than I could list, but among them is the beauty of the social life in a Montessori classroom and the exciting work that's going on!

Today was one of those lovely Spring days that completely blew my mind.

All of you teachers (and parents) are familiar, I'm sure, with the little moments that make you realize how far a child has come. Today, two children who can be rather volatile at any invasion of their personal space, or at the slightest conflict of interests, were sitting down in a very tight spot for group time. If I were able to freeze time at the moment that I saw them both head for the spot they chose, I would have guessed that some serious elbow-ing, face-making, and "I was there first!!!" shouting was on its way.

I would have been so wrong!

Oh, me of little faith. Here's how it played out:

G - "Could you please scoot back a little bit?"
J - "Sure." Scoots back. Still doesn't have quite enough space. "Could you please scoot over a little bit?"
G - "Sure."

...and all this with smiles and soft voices.

The children do, indeed, perfect themselves.



All of the excitement of the day inspired me to post some photos I've taken this Spring. It's a rather mixed bag, but here you are.

The Geometric Solids with Bases

A five year old girl is working with the geometric solids and their bases. She has stacked all of the solids with square bases on top of one another and all of the solids with circle bases on top of another.

The first time she worked with the bases, some weeks before this, having lined up the three square-based solids, she remarked, "It's like a square club!"








Birds Eye View aka The 45 Layout.

This is one of my absolute favorite works. I have to take a photo every time it's completed. This is the most recent one.

In my training (MCI), we use a purple mat for all Golden Bead work (though for this work I do eventually hope to make something with a bit of control).

Before giving the first lesson on Golden Bead material, the teacher tells the child that "Gold is what kings and queens used to barter with ..." and therefore we only work with the golden beads on the most luxurious of purple velvet, of course.

Pink Box 1
Objects with the Large Moveable Alphabet

This is a four year old's first completed work with the LMA. He was so very ready!



ai box

This is a six year old's work with one of the green phonogram boxes. She ran out of a and i, so she made some with construction paper. It saddens me that my LMA box does not have red vowels. Oh, what I could do if I had a budget with no limits...
























My lovely assistant made a small sandpaper period, question mark, and exclamation point that I use to give the first lesson on these symbols.

This was an extension of that lesson where a five year old child wrote a sentence for each symbol. This was the first time I had seen this child write full sentences fluently. She was so excited! She didn't stop or hesitate once - she just wrote and wrote. She wrote so much, so quickly, that we had to bring out a second chalkboard for her to complete her sentences on. They were used side by side so she could complete one of her sentences horizontally. When she got to the end, she had to erase what had been on the top line to complete her last sentence. So, it's a bit jumbled, but if you look closely, you can read her sentence, "I laic being a big sister." Next is her exclamation, "My baib bruthr cen screm so lad!" (My baby brother can scream so loud!) And finally, her question, "R we gn do teh tasitg bodls?"(Are we gonna do the tasting bottles?") It was a thrill to behold.

Below is a cultural activity we have been working on for some time now called the Sun Game. I don't know that this lesson is included in any training other than MCI's, but it is absolutely one of my favorite things in the whole of the universe. It is prefaced by a group discussion or two on the sun. These preferably take place outside on a sunny day. You can talk about what the sun is, and what is gives us, etc.

Eventually you involve two identical plants, one of which you place in an area where it gets plenty of sunlight, while the other is placed in a cabinet or some other place with no exposure to the sun. Both are watered and cared for equally. The second, of course, eventually dies. This gives a concrete sense of the importance of the sun to plants.

Later, the actual material is presented, usually in stages. A large felt circle, representative of the sun, is laid out on the floor and cards picturing a variety of different plants are placed around it. These are coded dark orange. Around these are placed dark yellow cards featuring photos of herbivores, and around those light yellow cards with photos of carnivores. Omnivore cards can be added in as well. Half of the result is below - click on the image to see the whole thing.

: )
























Now, off to enjoy the long weekend!

I Think You're Wonderful

One of the many lovely things I learned at Giving Tree Montessori, my internship site and a place where I spent three blissful years teaching was a song called, "I Think You're Wonderful*."


I also took an idea that we used there and have implemented it in my own classroom. We have something called the "Wonderful Necklace," and it hangs on a hook near the reading corner in our room. Anyone is welcome to take it, just as they take a work out, but they take it to a friend and tell them, "I think you're wonderful," and ask permission before putting the necklace around their friend's neck. The recipient can either pass it on when they have finished wearing it, or can return it to its place.

The goal is to facilitate the passing on of kind words and compliments - just because.

If you have tools that you use in your peaceful classrooms, I would love to hear about them!



*From my internet research, it seems that this song is by Red Grammer, from an album called Teaching Peace. You can stream it on youtube here: http://www.youtube.com/watch?v=QPg7i9nIEf0.

Suggestions for beginning work in Montessori

I received an email from a woman asking for suggestions on finding a job in a Montessori classroom. I thought I would post my response here in case it should ever prove helpful for others, and so that any other Montessori teachers can add their thoughts as well. If you have any, please add them in the comments. Let's discuss!

I've never had trouble finding a job in the Montessori world. If you are working toward a degree in education, that shows a real interest in not simply playing with children, but helping along their education and development, so you should be a great candidate and find a position easily. Any lead teacher will be certified by either the American Montessori Society (AMS), Association Montessori International (AMI), Montessori Centre International (MCI), or some other training. These are the three most common, and most respected in the US. If you have not worked in Montessori before, it's probably advisable to seek out a position as an assistant to a teacher at the level you are most interested in. With a resume that shows an interest in Montessori, and work toward a degree in education, this should be easy. If you find that you love the work, you can then consider going on to training yourself (most trainings are full time for a few months, or part time for a year and are followed by an internship that runs one school year. They are incredibly intense, so you will want to take this time off from working on your education degree, or wait until you have finished).

Simply look for Montessori schools in your area, and start sending out your resume! Be careful about the job you choose, however, as the Montessori name is not protected, and anyone can call their business a Montessori program without having been trained, or even read a single page of Montessori's works. This is really the reason for mixed opinions on Montessori. Many people think of Montessori as being incredibly rigid and overly structured, while others think of it as far too loose, with no structure at all. This is because there is no one to say what is a Montessori school and what is not. Make sure the lead teachers in the school you decide on are trained, or you are likely to be turned off without ever gaining a true understanding of how a Montessori classroom should work. In your first year, if you have the option, you may look for a school that has been around for quite some time, and is well-established. Classrooms in newer schools are seldom good samples of what a Montessori classroom is like. In the first two years of a school, it is almost impossible to have a class that covers the range of ages it is supposed to cover equally, and if it does, the older children may be in their first year of Montessori and are not typically able to act as role models for the younger children in quite the same way as children who have been in Montessori since age three. A large part of setting up a classroom that meets the children needs is getting to know the children and observing them as they work to determine what will best meet their needs. A school in its early stages has not had sufficient time to do this, which is perfectly fine, but if you are new to Montessori it will be better for you to see what Montessori is intended to, and can be. However, if you find a great position with a dedicated teacher in a newer classroom, you will be just fine.

Lastly, if there is one thing I have learned about children, it is that they are incredibly perceptive. In environments where the teachers do not get along, or even where they appear on the surface to get along, but harbor unspoken frustrations, the children respond. It is important that you make sure before taking on a position that you can respect and work well with any adults that will be in the classroom with you. In any other job, you may be able to get by with being friendly and civil to people, even if you do not like or respect them, and everything will be perfectly fine. This does not work with young children. My suggestion would be that before accepting any position, you observe the classroom during work time, take note of how the teacher responds to the children, and make sure that you can support her in the way she engages with the children. If there is something you do not like, it will almost certainly be amplified when and if you spend your work days there. Take a few minutes to talk with the teacher or teachers as well, and make certain that you will be comfortable relating to and working with them.

If there is a Montessori training center in your city, they may offer a one or two day workshop for assistants, which would prepare you incredibly well for your first experience in the classroom.

I know I'm long-winded, but hopefully that helps. Let me know if there's anything that doesn't make sense!

Moving

Well, it's the end of my three year cycle and my current school, which I have grown to love a great deal. It's so exciting to see the children who were three when I began there preparing to graduate and move on to kindergarten. They have grown, developed, and changed so much, and it has been a joy to observe.

I've decided that, being the end of a three year cycle for me, it's a perfect time for me to move someplace where I'll have more opportunity, and chance to grow and change myself. So, off to Austin I go. If any of you Montessori teachers are looking for a place to relocate, I must say that Austin seems to be it! I interviewed at six different schools, and all of them seemed to be very true to the philosophy, and to have the best interests of the children at heart. It was amazing. I also got a sense of the reputation of several other schools that I did not have the chance to visit, and all sounded excellent. The Montessori community is vibrant, and the schools seem to be very supportive of one another.

Here in Colorado Springs, I have had the chance to see most every Montessori school, and I know that I could never bring myself to work for any other than the one where I currently am. I have never had to compare schools, and spend a long time thinking about which one was best for me. I just begged for a job, and took what they offered me, because I knew that was the only place where I could be happy. In Austin, I could work at any one of several schools and love my job! I chose the one that suits me the best and I'm thrilled, but had I not been offered a job there, I had several other options to choose from. It's amazing! I am more excited than I can begin to express about this next phase of my work with children.