Mathematical tasks designed to foster a reconceptualized view of early arithmetic

We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8 world for up to six weeks. A key aspect is that we develop base 8 vocabulary. We use base 8 analogs of instructional sequences developed in classroom teaching experiments in the elementary grades that have been proven successful to promote deep conceptual understandings of basic arithmetic and place-value numeration in young children. As a result, our students have unique opportunities to develop a reconceptualized view of early arithmetic and learn how it can be advanced.