Postsecondary developmental mathematics: An interactive problem-solving approach

This investigation involved the development, implementation, and evaluation of an interactive problem-solving approach to teaching developmental mathematics. The strategy, based on findings from cognitive research and recommendations from the National Council of Teachers of Mathematics, emphasized conceptual understanding and group problem-solving. A quasi-experimental study was conducted to compare students taught using this method with students in a control group taught with a conventional lecture-demonstration approach that emphasized computational skill. The experimental group performed as well as the control group on a computational test, indicating that a focus on interactive problem-solving activities does not jeopardize students' development of computational skill.;Pre/post assessments of conceptual understanding were administered in both treatment groups. While the experimental group scored slightly higher than the control group, differences were not statistically significant and both groups had low scores. Because the concept portion of examinations throughout the semester did not affect examination scores, students may not have taken the concept posttest seriously.;Students in both treatment groups completed self-assessment measures of mathematics anxiety, perceived value of mathematics, and expectancy for success in mathematics. Mathematics anxiety levels were lowered in both groups, but no significant differences between groups were detected. Perceived value of mathematics and expectancy for success in mathematics remained stable from beginning to end of semester for students in both groups. It was theorized that one semester is probably insufficient time to effect changes in attitudes developed over periods of twelve years or more.;An informal post-course attitude survey conducted in the experimental group revealed a highly favorable response to the teaching approach used. Students felt that emphasis on conceptual understanding and small-group interaction increased the effectiveness of the class.;Recommendations for further research include: (1) replication of the study incorporating a more realistic assessment of conceptual understanding, tests of problem-solving skill and confidence, and a measure of attitude toward and beliefs about mathematics; (2) qualitative studies that investigate student characteristics that might account for varying responses to developmental mathematics classes; and (3) longitudinal studies to determine the effectiveness of the experimental approach in preparing students for subsequent college-level mathematics courses.