I like to judge my work by student response. I pay close attention to how students respond to learning experiences.
Today there were a number of memorable, positive events.
First, one boy bounded into the classroom this morning telling me that I had solved the problem to the right of this page incorrectly. "Gee," I said, "I think I solved it right as I checked my answer, but let's solve it together so we can see. I'm glad you're letting me know about this because I do make mistakes." A small group of students gathered around the child as they found the problem on the class website.
Then he said, "If you didn't put the parentheses in, you would have found another answer."
We copied the problem onto a piece of paper and then I solved it again in front of the child. As I solved it, he said, "Try it without putting parenthesis in."
"Okay, "and then I wrote PEMDAS and solved the problem talking aloud, "P-parenthesis, there are no parenthesis so I skip that. E-exponents, no exponents. MD, from left to right solve the multiplication and division and I did that. AS-I then solved the addition and subtraction and solved the problem.
"Oh," he said, "I understand."
"Thanks for challenging me," I replied, "If you hadn't spoken up I wouldn't have realized that yesterday's explanation of order of operations and PEMDAS was confusing. I hope you'll speak up again if you think I've made an error. Everyone was satisfied.
This question came up during number talk. We wondered and I wrote the question on the board. Then as students were headed out to recess, a student came up to me and said, "I'm proving that square numbers are the only numbers with an odd number of factors; see I'm writing down the square numbers and then I'm writing their factors. It's because one factor pair of every square number has the same number."
"I'm so proud of the way you've demonstrated this; I want you to share that with the class tomorrow," I replied.
Rule Posters
Our class is making posters about school rules to help the whole school understand the rules. One child has the topic of bus rules. He read the rules, and then he came up to me and said, "When I was little I didn't follow any of these rules."
"Not one?"
"No, and no one follows this one: speak quietly on the bus," he added.
"Well maybe if you write the the rules on your poster in a different way, the little children will understand better and follow them, and remember they are young--it's hard for young children to speak quietly," I replied. He gave me that knowing smile of a fifth grader who is a bit wiser than his years and returned to his poster creation.
These kinds of student responses, simple, but direct, were a positive assessment for me today--they feel comfortable honestly sharing their ideas, challenging the teacher, and persevering to prove a point. We're off to a good start.
