Visualization and Spatial Reasoning
Visualization and spatial reasoning skills are needed throughout engineering, science and mathematics. Yet, students have difficulty learning to visualize and reason spatially about the transformation of physical objects around their rotational axes. The National Science Foundation and General Electric have supported Dr. Beverly Woolf and faculty from the Department of Mechanical and Industrial Engineering and Department of Psychology to research how pervasive difficulties that students have with visualization and spatial reasoning andenabled them to design teaching aids that can overcome these difficulties.
Research focused on:
1) How students learn. Twenty psychology experiments were completed, each designed to increase understanding of the problems that students have visualizing complex spatial transformations and reasoning about these changes. Eye trackers were used to infer strategies that individuals use in tasks that require visualization and spatial reasoning and then cognitive strategies that students are using, both the successful and unsuccessful ones, were inferred. Engineers have difficulties performing simple mental rotations. The experiments identifiedfor some mental rotation tasks which parts of the task are most difficult and evaluated various strategies that students might be taught to reduce the difficulty.
2) Faculty engagement with advanced teaching technologies. Engineering and Computer Science faculty were involved in the development or modification of eleven intelligent, multimedia tutors, including six tutors in manufacturing (stamping, injection molding, forging, die casting, kinematics and finite element analysis), three in other areas of engineering, and three specifically designed to teach visualization and spatial reasoning skills (e.g., rotation, folding and drawing). Construction of these tutors required extensive knowledge not only of the topics at hand, but also of the software required to animate and capture the complex geometric transformations needed to illustrate the engineering processes.
3) Engineering tutors in the curriculum. All tutors were evaluated in the classroom. Students performed at least as well on evaluations of performance on these tutors as they did on evaluations of performance in the standard classroom format. We hope to show that student who first use the visualization and spatial reasoning tutors might show improvements in their performance on engineering problems requiring complex visualization and spatial reasoning skills.
Example Visualization Tutors.
The Engineering Drawing Tutor supports the student to draw either an orthographic or isometric view of a part .The Orthographic Projection Tutor shows the isometric view of an object along with the top and front orthographic projections of the object front projection of the presented object (Figure 1). The student is asked to draw the front projection of the presented object (left window, Figure 1). The Isometric Tutor (not shown) asks the student to draw the isometric, given three orthogonals. Both tutors provide two levels of hints: the student can place the cursor over any line or face in any of the views and see the corresponding lines or faces highlighted in all of the views including highlighting corresponding (shown in Figure 1) and the Tutor presents the correct solution (bottom left window, Figure 1) along with the number of lines which were correct, extra or missing.
|The Stamping Tutor enables students to design a part and obtain the resulting tooling for that design (Figure 2). The student creates a part by clicking on one of the features (bottom left, Figure 2), a hole, rib, emboss, or extruded hole, and dragging it onto the metal strip. Using an expert system, the Tutor generates the tooling required to manufacture this part (top window, Figure 2). In this case four distinct features have been dragged onto the strip (an arrow points to this part). Evaluations of the student’s design, the relative tooling cost for this design and a redesign suggestion, are contained in the evaluation window.|
|The Object Rotation Tutor asks the student to identify the view of the reference object that corresponds to rotations given at the top of the screen (Figure 3). As students works the tutor records the number of correct and incorrect answers, the time taken to comprehend the object (before rotating), the number of errors with respect to the number of degree and axes rotated, the number of hints received and the time to select the final view. Intelligent hint generation provides different levels of hints for the training problems, including hints, help and. answers. If the student has trouble rotating the reference object, hints are presented to provide practice rotating objects or practice recognizing a rotated view of the reference object.|
|The Kinematics Tutor provides visualization of, as well as interaction with, complex kinematic processes (Figure 4). The student can view the progressive sequence of images depicting the motion of a specific case of planetary gear trains or interact with 2 and 3 dimensional graphics of gears, by moving a single gear or arm, and seeing the resultant displacement of other gears. The effects of individual inputs on the output motion of the planet are depicted. Traditional kinematics instructional methodologies have concentrated on mathematical formulation of motion among components. However, a student of kinematics must be able to visualize the motion of components, a feature rarely emphasized in traditional kinematics curriculum.|
Tutors can be run both as PC downloads and as streaming video from the website that also provides more detail of the research activities.