This week, we asked two of our Upper Elementary teachers, Monica Curley and Ned DiGregorio, to share some of their favorite stories that illustrate those moments of joyful discovery when an idea really clicks for a student and the “aha!” epiphany brings new life to learning.
Huge leaps take place at this level in math as the students make strides in the move from concrete to abstract, so it will come as no surprise to find that this week’s stories are about breakthroughs in this subject.
Monica’s Racks and Tubes Story
When I was asked to write this article I realized that I witness “Aha” moments on a daily basis at Inly—whether it is someone realizing that the 3sq is actually in the shape of a square to someone finding out that Africa is not a country but a continent that consists of 53 countries.
I had my first Aha moment some years ago, when I worked in a large urban school in Chicago. I had a child in my Lower Elementary class who really wanted to learn division with the racks and tubes. She was in 3rd grade and I decided that it was absolutely the right time for her to be introduced to the materials. I showed her what to do, but no matter how hard she tried she could not understand the concept. At the end of the year she still struggled with the concept.
After the summer she came to visit my class from her upper elementary classroom. I asked what was she working on in math. She sighed and said the she would be working on division with the racks and tubes and would probably be using them for the rest of her life. About four weeks later I could hear commotion in the hallway outside my classroom and went to see what was wrong. And there she was, bounding down the stairs, yelling at the top of her lungs, “I get it! I finally get it!!” She was overjoyed and wanted to come to my class to teach it to the younger children. It was an “Aha” moment for her, and for me as well.
That was the day I really understood that no two children are alike and they all develop at their own rate. I realized that no matter how much you want them to learn a particular lesson or what the educational system decides is the time to learn a particular lesson, a child must be developmentally ready to internalize the information—and that is when they have their Aha moments. I am in the fortunate position to see the joy on their faces when they do.
Ned’s Math Facts Story
Being a new teacher, I have quite a few of my own aha moments in the classroom every day. Many times over the past few years, I have been completely amazed at the work the children do at Inly School. I believe this is what brought me here. I have been lucky enough to witness some aha moments with my own students and this really hits home for me. These are the moments that keep me going. The story below is about a student who has worked hard to make some great progress.
Math facts, multiplication facts, times tables—whatever you called them, we all had to learn them. It is a tedious task, which takes more time than a 6- to 12-year-old child wants to spend. All of us know now how important it is to learn them and how useful they are in our everyday lives. Try telling this to a child in your math group or your own child. You will receive a blank stare from her as if you told her she needed to learn quantum physics to go grocery shopping. She will resist with all her might. In a Montessori classroom, we help the children learn the concepts with materials, but at some point they need to do some memorization.
This year, I had a student who was working on mastering her math facts. She resisted all the way through but she did it with the help of her parents and teachers. In the past, she did struggle a bit with math, and she lost confidence in her own abilities over time. Once she mastered her math facts, she was still hesitant. I encouraged her, and her work became noticeably better. She also started to gain her confidence. We began to tackle some long division, and I could see her become resistant. After a few lessons, she was off and running with her long division with little trouble. When we started working with equivalent fractions, she really caught on right from the start. One day, she came to me and said, “Ned, why couldn’t I do this before? It’s not so bad.” I asked her why she thought she could all of a sudden do the work. She thought for a while, gave me a sheepish grin, and said, “Because I know my math facts now.” At that moment, it all came together for her. This student truly realized how important it was to learn her math facts. The best part is that she is more confident now and really proud of the work she is doing.
[This post originally appeared in Rhythm & News, the Inly School newsletter, on April 24, 2009.]