Knowledge implies interaction, and we cannot step out of our domain of interactions, which is closed. We live, therefore, in a domain of subject-dependent knowledge and subject-dependent reality… We literally create the world in which we live by living in it. (Maturana, 1978)
One of the most exciting experiences for me is watching someone else discover something. It is so cute to watch a baby discover their toes and eventually their toys. It is invigorating to watch young children solve problems for themselves; perhaps they figure out how to assemble a toy structure that they have shown interest in, or build a ladder system so that they can get to the cookie jar that has been put beyond their reach. I even find it fascinating when young children find ways to tell lies in order to mitigate uncomfortable circumstances. Generally, we don’t see this as a positive behavior. However, it does demonstrate that the child is exploring the understanding of truth, the power of their words, and the consequences of their actions. Initially, it is almost always followed by a questionable look on the face of the child. They look to us to see how we are reacting.
All of the above are examples of knowledge that has come from the child’s interaction with his environment. What makes each of those so exciting is that it is not the environment that “tells” the child what to do. The environment does not give directions or lay out a set of steps to follow. The joy on the child’s face is because he discovered something that met a need or satisfied a curiosity.
We, adults, are not so different. We find satisfaction in solving a problem, coming up with a solution, or creating something by ourselves. I want to explain the phrase “by ourselves.” It does not mean that I was alone. It does not mean that my ideas were not originally rooted in someone else’s actions or ideas. It means that I was the driving force behind the activity. It means that the “new” idea was mine because it was new to me. Perhaps I had seen the activity done by others or heard others describe the idea, but previously I had never taken ownership and had the “a-ha” myself.
It is in this vein that the teams with which I work are looking at research around children’s mathematics. We have the opportunity to read to understand something about the way in which children make sense of mathematical ideas based on what psychologists and mathematicians, and in some case neuroscientists, have observed and studied. We then get to take what we learn from the research out to classrooms to work with children right here in our central San Joaquin Valley and watch their faces light up as they discover something for themselves. It is our goal that we will be able to share this experience with teachers around the Valley so that they too understand how children make sense of mathematics. We want to work with teachers to create experiences that children will be excited to engage in and will then be delighted by the discoveries that they make. We want to engage teachers in conversations with their students, and have students engaging each other in conversations that challenge them to express what it is that they already understand and pushing them to build stronger, and deeper and, possibly, new understandings.