The project Mapping Developmental Trajectories of Students' Conceptions of Integers, led by faculty from San Diego State University, is using data from 160 interviews with K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Two questions frame and guide the proposed research:

* What are students' conceptions of integers and operations on integers?

* What are possible developmental trajectories of students' understandings?

The investigators are seeking answers to those questions through structured interviews with students in elementary grades prior to instruction about negative numbers (Grades 2 and 4), students in middle grades whose formal learning experiences have already included explicit instruction about integers (Grade 7), high school students who are expected to use prior knowledge about integers in more advanced mathematics (Grade 11 PreCalculus and Calculus students), and adults who use integers in their work.

In addition to providing an empirically-based picture of ways that students reason about negative numbers, the project is producing useful interview protocols and a reliable and valid assessment instrument for describing the understanding and skill of students at various stages on such a progression.

Both the characterization of common learning progressions and the assessment instruments will be broadly useful to curriculum and test developers and teachers in K-12 mathematics classrooms.