In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for supporting students' further learning. While the findings showed that the PSTs noticed a wide range of aspects of mathematical learning, their analyses of students' thinking and their ideas for supporting students' learning lacked sophistication. Also, there was considerable divergence between the students' thinking as evidenced in the hypothetical problem solutions and the PSTs' suggested support. Based on these findings, we provide some suggestions for teacher education.