I was excited to capture this video of a preschool friend doing the 9 Layout recently. The 9 Layout is a Montessori math activity that presents the ideas of place value and increments. Beads representing ones, tens, hundreds, and thousands are counted and matched with the numerals. Here, my friend has completed the ones place and has started the tens. She is adding bars of ten until she makes ninety. (You might turn down your volume. The background is a bit noisy.)
What I noticed when I reviewed the video is how she stops to reflect after each increment. She moves the bars up, adds one, then sits back to review or reflect on the work. This is one of the beautiful aspects of Montessori - or really, just scientific pedagogy in general - the child doesn't need a teacher to step in and say, "Great! That makes 60!" All she needs is to see how to do the work then be allowed to do it. When she is all finished with the tens, then she looks up at me. My mentor, Don Czerwinskyj, made sure I understood the importance of offering a child a reflection when they were finished with work. He told me to wait for the child to finish and watch her face when she looks up. Is she pleased? surprised? excited? confused? Wait for her to assess her own work before offering any feedback. In this child's case, when she looked up at me and seemed satisfied, I said, "Ok. You did it! You completed the tens. Are you ready to count the hundreds?" She said she was and she continued.
A friend of mine told me recently about visiting a preschool where every child's work was praised lavishly. Every painting or block structure was met with, "Oh my! That's the most beautiful picture/castle/birthday cake I've ever seen!!" Montessori educators try to avoid empty praise because it causes children to look outside themselves - rather than inside - for affirmation. Just like adults, kids have opinions about their work and their performance. If a child is happy with her work then we can be happy for her. If she is unsatisfied with her work or feels she doesn't understand it, we can offer empathy, advice, or suggestions - depending on what's needed.
When this student was finished with the work, I snapped this photo just as she added the last thousand cube. She was pleased with herself, as the photo shows.
Now, because my job is to observe and assess her understanding of the concepts she was learning, I noticed that she had only stacked 8 cubes, instead of 9. This was no time for criticism - look at that beaming face! So I commented on how pleased she was with her work. I asked her if we could count all of those cubes. When she got to 8 thousands she realized that she needed one more. She added one more cube, we counted them again together, and I said, "There are 9 thousands and this says 9000. Is that correct?" She said it was, and together we determined that her work was complete. She then put all of the materials away.
Sometimes we think our grown-up words are essential to motivate children to learn and to keep them on track. But most of the time, we could get by with a few words and more time simply observing and offering reflections. Rather than saying, "That's a beautiful painting," we could say, "Wow! You used 5 different colors in this painting. Do you have a favorite?" It requires more work for us to look so carefully before commenting, but it shows the child that we are truly interested in her work. And, we are interested in the process and not just the product.
If words fail us, we can always try those three little words everyone loves to hear, "You did it!"
I had the great pleasure of working in my former classroom today and it reminded me of why the three-year cycle in Montessori classrooms is so beneficial, not least of all, to the teachers.
Our Montessori preschool classrooms are composed of a mixed-age group of children who remain, ideally, in one classroom for three years. A child starts at age three and stays through her Kindergarten year. This is called the three year cycle. Each of those years brings new and unique learning opportunities for the child. As a three-year-old, the child observes her older peers and benefits from their experience. As a four-year-old, she starts to see herself as one of the “big kids” and expands her social circle. In her Kindergarten year she is recognized as a leader and takes pride in helping others.
When I took a sabbatical at the end of the school year in May, I left behind children who had been in my classroom for one or two years. I was able to catch up with many of those students today when I visited the classroom. I observed that two of “my” third-year students, I’ll call them S and K, were part of what Montessorian John Chattin-McNichols calls a “roving pack of 5-year-olds.” They were wandering around with some other boys and mixing it up a little. I knew these two boys when they were just barely three years old. I knew them before they could consciously control their bodies at group time and even before they could dress themselves successfully. Now, here they were - big, bold 5-year-olds and I was curious to see who they had become eight months after we last worked together.
Angie, my dear friend and the lead teacher of my former class, shared with me that S and K had been working on the squaring and cubing chains in the math area, so I asked them about those activities. They were eager to show me what they had already done and tell me what came next. Within a few minutes, they broke off from the pack and were ready to master the 10 cubing chain.
The 10 cubing chain - or 1000 chain - is a concrete representation of 10 cubed. It’s made up of one thousand pea-sized beads organized into bars of ten. The bars of ten are attached at the ends to make a chain. Children are ready for this work after they have mastered the 1 - 10 squaring chains and the 1 - 9 cubing chains. This video from the DuPage Montessori School in Naperville, Illinois provides a good overview of how the squaring and cubing chains are presented in the Montessori classroom.
The 10 cubing chain is nearly 30 feet long so it must be laid out in the hallway outside the classroom. So, off to the hallway we went.
S and K divided up the tasks between themselves. One carried the rolled-up mat and the other carried the chain. We established the space we would use in the hallway and K unrolled the mat while S went back into the classroom for the number tabs. We discussed how they would sort the tabs on the tray and move it down the mat as they worked.
S found the 1000 tab. He knew it went at the very end of the chain but he left it on the tray. There was a pause before they started and I asked what number they would start with. S said, “We have to count them all.”
That is certainly one way to do it. But when a child is ready for the 1000 chain, he is generally ready to complete it without counting every number because he can now count by tens and hundreds. Once you trust that 10 is ten, you don’t have to count it again.
I asked if they thought they could first put tabs on the hundreds. Yes! They were sure they could. Together, we counted the bars as 10, 20, 30 and so on until we got to 100. S got the 100 tab and marked that spot. K quickly grasped the system and immediately went to work sorting out all of the hundreds tabs in a separate group so that S could place them. This was my cue to find something else to do. I went back inside the classroom to assist Miss Angie while the boys marked off every 100th bead on the chain with the appropriate tab.
They repeated the process, stopping after each bar of ten. K was the sorter, S was the placer. “150! I need 150,” S said. K had it ready. There was never any disagreement, that I heard, over who would do which task. They just got started and they each found their niche as they went. And they were really digging their work.
They started the cubing chain work at 9:45 and I checked in with them every few minutes. They finished at 11:00. One of them stopped to use the bathroom then went straight back to his work. Other children would step into the hall to see what was happening and then go back inside to their work.
Sometimes I checked on S and K without speaking and other times I acknowledged their progress. Once, I said I would be back to check on them in a bit unless they needed some help. “We need some help,” S said. They could not find the tab for 590. I suggested they leave a space for that number and they could put it there when they found it. They never found it, but they were able to move on without hesitation.
As they got to the very end, S picked up the 1000 tab and started to place it under the 1000th bead. K said, “Hey! We decided we would put that one on together!” And so they did. That’s when this photo was snapped.
If you had asked me three years ago if these children were developing normally and if they were going to learn to read and write and grow up to be compassionate humans I would have responded, “Of course they will!” But in the back of my head there would have been a tiny voice saying, “What if they aren’t? What if they are never able to sit in a chair for more than 8 seconds? What if they never learn to put their shoes on by themselves? What if they show no interest in reading? What if they always write six as 9?”
That doubtful voice is a familiar one to parents because most of us only get to experience the development of one or two children. We fear we will do something wrong and our children will not achieve their potential. Preschool teachers should know better because we get to observe hundreds of children over the course of our careers, right? But sometimes, even with years of experience, we forget that our job is simply to prepare a nourishing environment. It is the child who must do the work of building the man.
In 1949, Maria Montessori offered us some guidance in our quest to relax and trust that each child will reveal himself as a competent and confident being in his own time. In The Absorbent Mind she wrote, “...for while, in the traditional schools, the teacher sees the immediate behavior of her pupils, knowing that she must look after them and what she has to teach, the Montessori teacher is constantly looking for a child who is not yet there.”
Dr. Montessori also implemented the three-year cycle in our classrooms to give us enough time to look for that child and see him before he moves on to primary school.
I am not at all surprised that S and K can count to 1000 by tens and hundreds. I am not surprised that they can recognize 3-digit numerals or that they can prepare, complete, and put away their work. I am not even surprised that two 5-year-old boys willingly work together on a math material for 1 hour and and 15 minutes with only a bathroom break and very limited guidance. I’ve seen it before.
I am surprised at the sense of joyous relief I feel each time children reveal themselves in this way. It's an experience that never gets old. I suppose that’s the ultimate reward of being a teacher.