Connecting visual and analytic reasoning to improve students' spatial visualization abilities: A constructivist approach

Current reform initiatives recommend that school geometry teaching and learning include the study of three-dimensional geometric objects and provide students with opportunities to use spatial abilities in mathematical tasks. Two ways of using Geometer's Sketchpad (GSP), a dynamic and interactive computer program, in conjunction with manipulatives enable students to investigate and explore geometric concepts, especially when used in a constructivist setting. Research on spatial abilities has focused on visual reasoning to improve visualization skills. This dissertation investigated the hypothesis that connecting visual and analytic reasoning may better improve students' spatial visualization abilities as compared to instruction that makes little or no use of the connection of the two. Data were collected using the Purdue Spatial Visualization Tests (PSVT) administered as a pretest and posttest to a control and two experimental groups. Sixty-four 10th grade students in three geometry classrooms participated in the study during 6 weeks. Research questions were answered using statistical procedures. An analysis of covariance was used for a quantitative analysis, whereas a description of students' visual-analytic processing strategies was presented using qualitative methods. The quantitative results indicated that there were significant differences in gender, but not in the group factor. However, when analyzing a sub sample of 33 participants with pretest scores below the 50th percentile, males in one of the experimental groups significantly benefited from the treatment. A review of previous research also indicated that students with low visualization skills benefited more than those with higher visualization skills. The qualitative results showed that girls were more sophisticated in their visual-analytic processing strategies to solve three-dimensional tasks. It is recommended that the teaching and learning of spatial visualization start in the middle school, prior to students' more rigorous mathematics exposure in high school. A duration longer than 6 weeks for treatments in similar future research studies is also recommended.

EFFECTS OF A VISUAL HORIZON ON DROSOPHILA MELANOGASTER OBJECT-TRACKING RESPONSES

To navigate effectively in three-dimensional space, flying insects must approximate distances to nearby objects. Humans are able to use an array of cues to guide depth perception in the visual world. However, some of these cues are not available to insects that are constrained by their rigid eyes and relatively small body size. Flying fruit flies can use motion parallax to gauge the distance of nearby objects, but using this cue becomes a less effective strategy as objects become more remote. Humans are able to infer depth across far distances by comparing the angular distance of an object to the horizon. This study tested if flying fruit flies, like humans, use the relative position of the horizon as a depth cue. Fruit flies in tethered flight were stimulated with a virtual environment that displayed vertical bars of varying elevation relative to a horizon, and their tracking responses were recorded. This study showed that tracking responses of the flies were strongly increased by reducing the apparent elevation of the bar against the horizon, indicating that fruit flies may be able to assess the distance of far off objects in the natural world by comparing them against a visual horizon.