In my learning of constructivism and the theories of Piaget, I often think of this quote: “No one but you can make your associations, and no one but you can isolate your sound-image and whatever you conceptualize in your experiential field.” (Von Glaserfield, 1995) This quote is from a chapter on language and meaning, but it is a profound reminder of just how individual we all are. Each of us is constructing knowledge from our unique daily experiences and it is upon these constructions that new constructions are built. Just this week I read a great example of this from Seymour Papert, a former student and colleague of Piaget. He describes his love of gears that began at just 2 years old. It was from this interest in gears that he later made associations in other fields like mathematics, science, logic, and eventually computer programming. Papert points out that some might hear his story and think that every child should have a gear set. “But to hope for this would be to miss the essence of the story. I fell in love with the gears. This is something that cannot be reduced to purely “cognitive” terms. Something very personal happened, and one cannot assume that it would be repeated for other children in exactly the same way.” (Papert, 1980)
As the Early Math Team works with young children, we see this same story unfold before us. Children who in one-on-one interviews showed us little in terms of their number sequence and counting ability, seem to blossom in our center activities. We saw them extend their number sequence and count with more accuracy all in the context of play. This seemed to be very evident in one of our recent center activities – Tubes and Cubes.
At first we just put the objects out to see what the children would do. Some were hesitant and asked, “ What are we supposed to do?” Our response, “ What are you curious about? What can you do with these things?” It didn’t take long for one of the children to figure out that the cubes could fit inside the tubes. Then we began to ask questions. “ How many cubes will it take to fill the tube? How many more do you need?” Their curiosity was heightened, but nothing was more enjoyable than to see their faces as they carefully lifted the tubes to reveal a tower within.
Many of our most inhibited students were engaged by this activity and created tower after tower. Our goal was that they would embrace counting opportunities, but we found they did much more. During the engagement with Tubes and Cubes students also estimated, compared, sharpened motor skills, engineered new ways to stack tubes using the plastic sleeves and simply had fun. It was a spark of what we dream will spread to many more classrooms as our work continues.
As my colleague and I looked on, we often exchanged glances of surprise and smiles of accomplishment. We know that we just didn’t give a child a moment of happiness, we may have just helped them discover their own “gears.”
As summer approaches, we encourage caregivers of our youngest learners to embrace opportunities to count, explore, and play. Share your experiences as a comment below!