Visitors in our Long-View math classes often inquire about the ages of the children, because it is surprising to see such young children engaged in high-level content. How is it that an 8-year-old can do that?
The answer begins with letting go of developmental constraints previously imposed on young learners. Because our classrooms are multi-age and our instructional planning does not start from an assumption that children can only do as much as a generic textbook says their grade level can accomplish, we move much further and much deeper, traversing some very interesting mathematical terrain. We know well-designed and well-implemented learning experiences, in combination with the cognitive capacities young children bring to their work, can unveil levels of reasoning not typically seen in the early grades.
Additionally, the culture in our mathematics block is very different. Ours is not a culture focused on maintaining order (think worksheets and the teacher as the only voice of correctness); rather, you'll see that we foster a learning community in which children have agency and recognize that mathematics is about making meaning. We work to establish classroom cultural norms and practices that place reasoning, debating, conjecturing, discussing, and providing proof at the center of student work.