The Silent Way – What I Learn When I Shut-Up
Caleb Gattegno is the reason most people know about Cuisenaire Rods. He is also the father of 'The Silent Way' of teaching. The Silent Way stresses the learners' autonomy and participation in the learning process and, as the name suggests, uses silence as a teaching method. The teacher is not pouring information into a student, rather the teacher facilitates and directs while helping the student develop their natural capacity for learning and capitalizes on the desire to learn with which all of us were born. The Silent Way is a method to help the student learn for himself, with little verbal interference from the teacher. I'm pretty much a convert - at least philosophically.
The Silent Way - Learning to Monitor The Teacher
I have been attempting to do some work with P. (my 6-year-old son) that covers the next post in my blog series on Gattegno Mathematics Textbook 1. He has different ideas about what he wants to do with math. I'm fairly lenient with his exploration at math time as long as it is going somewhere and he's not just knocking rods all over my dining room table. Our scheduled work had to do with multiplication and fractions inside 5.
He got derailed when we tried to cut 5 in half. That can't be done with the rods; it needs a white end cap. That led us to a conversation about odd and even, and he decided he wanted to find odd and even numbers using rods. We know odd and even but I let it go because we haven't touched on the subject for months.
He placed all the rods out to find trains with two cars of a single color. Those rods that can be made with an equivalent two car train of a single color are even; those that need a white caboose are odd.
We gave the rods names based on white as our unit. That means 1, 3, 5, 7, and 9 are odd and 2, 4, 6, 8, 10 are even. We knew that already so I tried to extend this activity. The pattern for the trains is a single white, a pair of white, a pair of white and a white, a pair of reds, a pair of reds and a white, a pair of light green, a pair of light green and a white and so on. My idea was to have P. read the equivalent train pattern for the rods and then he would extend the pattern without having to make the numbers 11-20 and place the equivalent trains underneath. Now I wish I would have recorded our conversation because I was genuinely perplexed by what happened next.
I said the first four patterns while I pointed to each train. Then I asked P. to read the following patterns in the same way. He did it. Then I asked, "What will be the equivalent train for the number i1?"
He said something like, "A blue and an orange."
I thought he was joking so I said something like, "Oh come on...what comes next in the pattern?"
To which he replied, "Oh, is it a black and purple?" Black and purple make 11, we were getting closer - still not the next rods in the pattern. It's possible he didn't get what we were doing so I pointed to the rods and asked him to tell me if the equivalent trains contained a pair or a pair and an extra white. We went through each rod in order and read 'a white, a pair, a pair and an extra white, a pair, a pair and an extra white' and so on.
After we had reached the orange rod I asked, "What comes next: a pair or a pair and an extra white?"
"Oh, a pair and an extra white!" Ok, we are getting there I think.
"What color pair?" We are looking at the rods, and you can see that the orange rod contains a pair of yellow rods. So this should be easy for him.
"Blue?" Completely baffled, I decide to stop talking since it is clear that he doesn't understand the pattern and he isn't sure about this. So I decided to let him explore. I left to make a pot of coffee. Obviously, he understands odd and even, but we either have a problem with pattern recognition, or we have an auditory problem. P. has trouble with hearing a pattern and creating it. He also has difficulty with math compositions when the rods aren't in front of him. So, maybe it was a combination of the two.
Back to the table I go and he still hasn't figured out which rod fits the pattern.
I have him make a staircase; he then reads the rods. I point to the corresponding rods in the staircase while he reads each train, "A white, a pair of whites, a pair of whites and a white, a red, a pair of reds and a white..." He still has a glazed look in his eye. And then I get up again.
We are about 30 minutes into the exercise, and I noticed I was getting very frustrated. There were thoughts going through my head, "he is dragging this out on purpose, he is just being lazy, he knows what you want and is just being defiant, what it so hard about this, I have stuff to do." Dad walked in as I was getting up from the table.
The first thing P. says is, "Dad, we are having a rough go with math this morning."
I was startled he said that so I asked, "Why do you think we are having a rough time?"
"You have irritation in your voice."
The Silent Way - When I Actually Shut-Up
This is not how I want math time to go, and I certainly don't want my child to feel the weight of my impatience over his math performance like a shadow. I didn't realize I was irritated until I stopped talking. But it was true; I was annoyed that what should have taken 30 seconds had evolved into a 30-minute ordeal. I had things to do that were evidently more important that his education. My underwear was in a bunch over it, and P. knew it.
Mother took a deep breath. I had an idea. Why not try The Silent Way? Without saying a word, I lined all the trains up side by side in a staircase and then ignored the child in front of me while I talked to his father.
The child, miraculously, found the rods that made the next line of the pattern and then, by himself, extended it to 21. He made several observations on his own. When I quit crowding his space with questions and irritation, he was able to think. He knew that 30 and 31 could be made with 3 oranges and 3 oranges and a white. It could also be made with 2 oranges and 2 yellows, and 2 oranges and 2 yellows and a white. 36 and 37 could be made with 3 oranges and 2 light green and 3 oranges and 2 light green and a white. When I pointed out that there were 3 oranges and 3 is odd, he told me that the orange could be made with 2 yellow.
What I should have done differently:
- Pose the task, "What rod comes next in the pattern?" and then ask him to figure out how he will solve it.
- Shut my mouth until he asked for help.
- If he asked for help, instead of having him read the rods over and over, I could have asked what he noticed about the pattern.
Obviously, I don't always have a good handle on The Silent Way of Teaching, but I am getting better about checking myself. Much of my time teaching is spent gauging my attitude and need for adjustment. Denise Gaskins, from Let's Play Math, shared this video with some friends today. What I love about it is that it distils a lot of Gattegno's teaching into two questions/ideas: notice and wonder. You find these two ideas all over Gattegno and Goutard. However, I haven't seen anything this concise before. Anyone can keep this at the back of their mind. Did you run out of questions? Notice and wonder.