The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…

Presents a covariation approach to learning exponential and logarithmic functions based on a primitive multiplicative operation labeled splitting that is not repeated addition. Suggests that students need the opportunity to build a number system from splitting structures and their geometric forms. (30 references) (MKR)

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)