I thought it would be relatively easy for me, with my six-year background of high school teaching and tutoring of math and physics, to co-op in the OC classroom with my first-grade son. I was both right and wrong. Indeed, my teaching experience and professional knowledge as a graduate student in child psychology helped me design activities suitable for first- and second-grade children. However, in terms of philosophy of teaching and organization of learning activities, my experience with traditional schooling was more harmful than helpful. My previous experience prepared me for delivering a lesson to a whole class or an individual. I was used to controlling children’s talk, which was supposed to be addressed only to me, and my students had learned early on in their schooling that they could talk legitimately only to the teacher and only when it was allowed by the teacher. The teacher was supposed to be the director, conductor, and main participant in classroom interaction. In the OC, I was shocked to discover that this traditional format of instruction was actively discouraged by teachers, co-opers, and children. This kind of teaching was not supported by the children in their interactions or by the classroom structure, with its small-group organization, children’s choice of groups, and nonsimultaneous rotation of the children from group to group. However, I did not know how to teach any other way. At the beginning of the school year I planned an activity that I called Magic Computer. It was designed to teach the reversibility of addition and subtraction as well as reading and computational skills, and it had worked beautifully with first- and second-graders in the past. The activity involved moving a paper strip that carried “computer commands” (“Think of a number. Add five to it. Take two away from it,” and so on) through an envelope with a window, to see one command at a time. The commands were designed so that addition and subtraction compensated for each other; therefore, the last message was “You have got your initial number!” The children’s job was to discover addition and subtraction combinations that cancel each other out and write them down on the paper strip, line by line.
The Degree of Abstraction in Solving Addition and Subtraction Problems
