Teachers' Beliefs About Mathematical Problem Solving in the Elementary School

This study focused on 5th‐grade teachers' and students' beliefs about mathematical problem solving; attributions for the causes of performance in problem solving; and beliefs about the teaching and learning of problem solving in mathematics. Ten 5th‐grade teachers from four different schools in a large rural school district volunteered to participate in the study. Each teacher identified two students from her classroom to participate in the study, one student perceived by the teacher as successful and one perceived as unsuccessful in mathematical problem solving. Parallel interviews with teacher and students were conducted. During the interviews, a set of nine word problems was presented, and teachers predicted the likelihood that the participating students would get correct answers on each of the problems. Students were asked to solve each of the problems orally. Verbatim transcripts of the interviews were analyzed and a correlation of teachers' predictions of students' performance and the students' actual performance was considered. Four general conclusions resulted from the research. First, 5th‐grade teachers believe that problem solving in mathematics in primarily an application of computational skills. Students' beliefs about mathematical problem solving are, for the most part, consistent with the beliefs held by the teachers. Second, 5th‐grade teachers in the study basically attributed success and failure in problem solving to differences in students' ability, while students attributed success and failure to a combination of ability and effort. Third, the activities in problem solving in the 5th‐grade classrooms, if anything, enhance computational ability. The teachers' focus was primarily on right answers, and the use of calculators for problem solving was strongly discouraged. Finally, teachers tend to overestimate the students' ability to do problems involving computation and underestimate students' ability to do reasoning problems.