Achievement differences in structured versus unstructured instructional geometry programs

This study investigated the effect of students' ability and type of instructional program, structured and unstructured, on easy and difficult posttest items. Seventh-grade students worked through 14 instructional activities in The Geometer Sketchpad, a dynamic geometry program, and accessed a Geometry tutorial developed to parallel the state math standards for geometry. Low-ability students scored higher in the less structured program, whereas high- and medium-ability learners performed better in the structured program. High- and medium-ability students outscored low-ability learners by a greater margin on the difficult items than on the easy items. Although their overall performance was poor in both programs, that low-ability learners performed relatively better in the less structured, less traditional, mathematics activities is an encouraging finding for mathematics educators and designers of open-ended learning environments that feature differentiation of instruction.