Learning from Self-Study: Gaining Knowledge about How Fourth Graders Move from Relational Description to Algebraic Generalization

Abstract

In this article, Laura Grandau traces a self-study research project focused on teaching algebra to fourth-grade students. Facing a new curriculum and a new grade level, Grandau considers what good instruction and "good habits of practice" may be. Through journaling, videos, observations, analysis of students' verbal and written responses, and consultations with her "critical friend" Sean (also a teacher), Grandau develops a "critical distance" from her teaching. While doing this reflective work, she negotiates the ambiguities of teaching and learning. Although Grandau's work is of interest to teachers of mathematics, those in critical friend or peer mentoring relationships, and teacher researchers, it also serves as a model of how inquiry teaches, fostering growth in teachers, students, and communities of practice.