The main focus of the study was to describe how students of various ages established the truth of their ideas in school geometry. Thirty-two students in grades 2, 5, 7, and in a high school geometry class were interviewed. Formal proof was used in less than 1% of the student arguments. Second and 5th graders were most likely to convince themselves or others by using a basic image process or by drawing pictures. High school students and 7th graders were more likely to convince themselves and others using an Intuitive Affirmation. In addition, their arguments were more elaborate and propositional in nature than arguments given by 2nd and 5th graders. (Author/MKR)