A comparison of virtual and physical manipulatives in teaching visualization and spatial reasoning to middle school mathematics students.

摘要

This study investigates the effectiveness of physical and virtual manipulatives on middle school students' visualization and spatial reasoning skills. Students in two treatment groups, physical manipulatives and virtual manipulatives, were compared to students in a traditional instruction control group using a teacher-guided discussion format without the use of manipulatives. Also of interest in this investigation was the effect of manipulative use on visualization and spatial reasoning skills for students of differing mathematics abilities and attitudes. Comparisons were based on student scores on pretest and posttest measures of visualization and spatial reasoning and attitude about mathematics.;Three teachers at the same middle school taught a 4- to 5-week geometry unit to 219 sixth-grade students using physical manipulatives, virtual manipulatives, or no manipulatives during instruction. Each teacher delivered each of the three treatments to one or more classes, with students assigned to treatment groups by classes.;The research design utilized a quasi-experimental pretest-posttest non-equivalent control-group design. Pretest and posttest measures included tests of visualization and spatial reasoning skills and attitudes about mathematics. Data were collected from teacher questionnaires, classroom observations, student surveys, and archival data.;Results indicated no statistically significant differences in mathematics posttest mean scores for students in the three treatment groups, as well as for students of differing mathematics abilities and attitudes about mathematics. Students in the physical and virtual manipulative groups reported a preference for using manipulatives during instruction. Students in the virtual manipulative group had higher rates of on-task behavior than students in the physical and no manipulative groups. Posttest mathematics scores in all treatment groups were associated with the teacher, student gender, amount of homework completed during the unit, and the students' current mathematics grade.;Research is needed to further investigate the use of physical and virtual manipulatives during instruction. Suggestions for future research include longer treatment length, manipulative use during assessment, a larger sample size including students of different grade levels, and further investigation into gender differences in achievement and attitude.