My youngest daughter is 2 ½ years old and she has yet to discover just how much her mother loves mathematics. The other day, as she worked on a puzzle of shapes, she held up one of the shapes and said, “diamond.” I wrinkled my nose as I corrected her with the correct term, “rhombus.” To my surprise, she turned to me and in a slower, louder voice she said, “ NO rhombus, D-I-A-M-O-N-D.” I quietly laughed, but later it really made me ponder the work my team and I at The AIMS Center do and what we have learned about how young children come to know mathematics.
The brains of young children literally make thousands of connections a day. When a connection is then revisited with a similar experience that connection becomes stronger. In the case of my daughter, when I introduced a new sound image for the same shape, she entered into what we call disequilibrium. She then had to make a choice – would she accommodate this new information and reorganize her connections or would she resist the disequilibrium she was experiencing? This is something that may happen to each of us everyday. Life is full of unexpected experiences and these become opportunities to construct new knowledge and connections.
The children we worked with throughout this year seemed to experience this kind of disequilibrium and accommodation. One of our goals was to learn as much as we could about the types of experiences that would benefit their mathematical knowledge constructions. Etched in my mind is an interview that is linked below. Here, my colleague and I decided to investigate which children could recognize their numerals. Many of the children we worked with showed confusion about the concept of “before.” We were curious if we could use this connection to numerals to further expand their understanding of “before” and “after.”
You probably noticed that my young friend seemed so much more enthused once I made it a game and included myself. In just the three minute clip, you will see the student doing a variety of mathematics, including counting down, recognizing numerals, and starting his count from a number other than 1. You will also notice me questioning his numeral recognition, asking him for an example if the 5 is a 15. I also tried to use the words “before” and “after” as much as possible. As this interview progressed, so did his confidence. He felt accomplished, perhaps in part for “winning” the game, but also because he completed a task that was both challenging and achievable.
The children we worked with never ceased to both challenge and inspire me. As I improved in the ability to put aside my own mathematics, this allowed for their math knowledge to shine through. We tend to think of children as sponges ready to soak up what we pour in, but in reality they are stars ready to show us just how brightly they can shine.