Number Concepts and Operations in the Middle Grades

For many students, learning mathematics in the middle grades represents a watershed activity. If they fall behind or fail at this point, they are unlikely to recover and to pursue a career in the sciences or other mathematics-dependent occupations. The authors reveal at least two of the reasons for this watershed experience. First, the content itself is much more complex than that at the primary grades, a complexity that is only now being fully appreciated. Second, conventional instruction often is based on faulty assumptions about the way in which the content is learned. The chapters present the latest understanding of the nature of the mathematics content in the middle grades and the processes by which it is learned.