About Project Z

Making sense of integers is particularly challenging for children and yet is foundational for success with first-year algebra coursework. In this research and development project, we will map developmental trajectories of students’ conceptions of integers. We will analyze 160 interviews across K – 12 students and 30 interviews of specialized adults (those who have revisited their notions of integers by drawing from one of four perspectives: a formal-mathematics perspective, a historical-mathematical perspective, a children’s-mathematical-thinking perspective, or a mathematics-teacher perspective). Collectively, the conceptions identified across these interviews will help us to map the terrain from informal to expert conceptions of integers.

We propose to use findings from the interviews to create a framework to identify problem types as well as problem-solving strategies as related to student thinking about integers and integer operations. Because we will identify increasingly sophisticated conceptions, teachers and researchers can use the developmental trajectories to understand students’ thinking about integers findings, we will use the results from the interviews and subsequent framework to develop a paper-pencil assessment that can be used by teachers and researchers.

This material is based upon work supported by the National Science Foundation under grant number DRL-0918780. Any opinions, findings, conclusions, and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF.