Problem solving has been alternately viewed as the justification for the study of mathematics or as the impetus and means for studying mathematics. This study examines characteristics—attitudes toward problem solving, beliefs about problem solving, and abilities to solve problems—of elementary teachers of grades three, four, and five that relate to problem solving.
Participants completed a two-part survey to quantify their attitudes and beliefs and a problem-solving activity which quantified their problem-solving abilities. Four participants were subsequently interviewed. Analyses showed that these teachers had generally positive attitudes toward problem solving, generally positive beliefs about problem solving, and generally poor problem-solving abilities. The data showed significant (p \u3c .05) positive correlations between attitude and problem-solving ability and between attitude and beliefs (p \u3c .01). Analyses of variance showed a significant difference (p \u3c .05) in attitude for the three grades.
The interview data added to the understanding of teacher attitudes and teacher beliefs and revealed that attitude was also reflected in the way problem solving was treated in their classrooms. Teachers with very positive attitudes involved their students in mathematical problem solving in their classrooms and viewed problem solving as a means for teaching and validating mathematics and regarded computational skills as an important goal but did not view the mastery of computation skills as a necessary prerequisite to problem solving. Teachers whose attitudes were not very positive never used problem-solving activities in their mathematics instruction and believed that mastery of computational skills was a necessary prerequisite for problem solving. Three of the four interviewees limited mathematical problem solving to what is more correctly known as a word problem—a computational exercise given in verbal language.
Although certification requirements in Georgia have increased the number of mathematics courses that pre-service teachers must complete in their professional development, this study indicates that these increased requirements may not be enough. Teacher attitudes toward problem solving must also be addressed. Pre-service teacher preparation programs must address prospective teachers\u27 attitudes and focus on teaching these future teachers how to teach mathematics in addition to teaching them mathematics content. In-service elementary mathematics teachers must be involved in staff development based in dialogues about attitudes, pedagogy, and content. Interim and long-term solutions will require courage, dedication, conviction, and diligence
