| This was a qualitative study focused on the fourth grade students in a rural southeastern school where approximately 96 percent of the students are from traditionally underserved populations, primarily black students, and where 90 percent of the students receive free or reduced lunch. The purpose of the study was to describe the problem solving strategies of these students as reflected in the representations used to solve counting problems and to investigate the external and internal influences from which these representations emerge, including dispositions of teachers, delivered curriculum, and past experiences with problem solving.; Data were collected through teacher surveys, observations in classrooms, review of artifacts from student problem solving sessions, and interviews with students.; Interviews with students were central to this study. Based on the work of Maher (2003), counting problems were posed to fourteen fourth grade students in individual interview sessions. Each student was interviewed two times using a format in which students were encouraged to discover methods for solving these nonroutine problems. Interviews were audiotaped and artifacts from student problem solving were collected. These artifacts were reviewed, and the representations and problem solving strategies exhibited during the interviews were documented.; The strategies exhibited in the interview sessions contrasted sharply with students' everyday experiences in the classroom, where the curriculum was most often delivered in a traditional approach centered on teacher instructions followed by student practice.; Review of teacher responses to surveys and observations in classrooms revealed that, with few exceptions, teachers did not highly value a problem solving approach to mathematics education and that their own mathematical backgrounds had not prepared them to plan and implement lessons that would engage students in the study of significant and meaningful mathematics. This situation, combined with an incoherent curriculum and excessive emphasis on preparing for state testing and on discipline, served to limit students' opportunities to learn the mathematics they need.; Other than lack of experience, this study revealed no significant evidence that students lacked the ability to learn mathematics or to engage in problems solving if they had opportunities to engage in these kinds of activities. |
