Holt Geometry Practice Workbook Answer Key

[Eustacio Gadit]

MappingOur School Site (MOSS) is a program in which students practice spatial cognition skills by field mapping and analysis using Geographic Information Systems (GIS). Middle school students' spatial ability was evaluated using a Spatial Experience Survey (SES) and the revised Purdue Spatial Visualization Test: Rotations (PSVT:R). Other sources of data included interviews, group presentations, individual written conclusions, and mapping analyses. Students' problem solving identification and ability dramatically improved as they collected, evaluated, reported, and synthesized environmental data. The MOSS program combined an out of door experience with an indoor experience on the computer. This was found to be an effective approach to this type of field study.

Mapeando Nossa Escola (MOSS) um programa no qual estudantes praticam habilidades de cognio espacial com mapeamento de campo e anlises usando o Sistema de Informao Geogrfica (GIS/SIG). Habilidades espaciais de estudantes da segunda fase do Ensino Fundamental foram avaliadas usando o Levantamento de Experincias Espaciais (SES) e o teste de Visualizao Espacial de Purdue (PSVT:R). Outras fontes de dados incluram entrevistas, apresentao de grupos, concluses escritas individualmente e anlises de mapeamentos. A identificao e habilidade de resoluo de problemas aumentaram dramaticamente entre os estudantes conforme eles coletaram avaliaram, relataram e sintetizaram dados ambientais. O programa MOSS combina experincias fora da sala de aula e dentro da sala com o uso de computadores. Esta abordagem foi considerada efetiva para este tipo de estudo de campo.

Baker & Piburn (1997) define spatial reasoning as the ability to see your world in your mind, to manipulate it, and to explore it. During the last 100 years, psychologists have attempted to measure spatial ability through a battery of tests similar to ones used to evaluate intelligence. Until recently, few studies focused on finding the best way to measure an individual's spatial visualization ability. However, for the last decade, researchers have evaluated methods for measuring spatial ability and techniques for improving it (BERTOLINE; MILLER, 1990; DENO, 1995; MILLER, 1992; SORBY; BAARTMANS, 1996; WIEBE, 1993).

According to McGee (1979) and Tartre (1990) there is more than one type of spatial ability. Spatial visualization involves being able to mentally manipulate, rotate, twist or invert pictures when presented with a visual stimulus. One must be able to recognize, retain, and recall the configuration of an object that has been manipulated in three-dimensional space. Spatial orientation, on the other hand, involves the arrangement of components within a visual stimulus pattern or the ability to remain unconfused when the orientation of the stimuli changes. Spatial orientation is "the ability to determine spatial relations in which the body orientation of the observer is an essential part of the problem" (Mc-GEE, 1979, p.3-4). This study used the revised PSVT:R developed by Branoff (BRANOFF, 2000) to measure the spatial visualization of middle school students. Using labeled coordinate axes eliminates gender differences previously found using this test. In addition, to eliminate age differences, participants taking the test were given unlimited time to complete the test, though most participants completed the 30 item test in one class period or 55 minutes.

Prior experience can affect an individual's spatial ability. A spatial experience survey (SES) developed by Deno (1995) and Parolini (1994) determines the importance of prior experiences on spatial abilities. Deno's SES was developed by compiling a list of previously validated spatial activities from research done at Purdue University (GUAY, 1977; GUAY; McDANIEL, 1979), Pennsylvania State University (NEWCOMBE, 1982; NEWCOMBE; HUTTENLOCHER, 2000) and the University of Maryland (OLSON, 1985). Similar to Deno's study, Parolini's SES also includes spatial experiences in school such as courses in drafting, art, design, and shop as well as geometry mathematics courses. An important addition to Parolini's SES is the inclusion of computer and video games. Tartre (1990), in a study of 58 Harvard students, found that after playing video games for only 5 hours, spatial visualization scores of female subjects increased dramatically. In 1993, 1,012 engineering freshman took Parolini's SES, which consisted of a 14 item questionnaire. Results were correlated to scores on the PSVT: R for spatial visualization. Experiences in courses such as mechanical drawing, drafting, CAD drawing, and art were shown to be predictors of success on the PSVT:R. In addition, experience with toys such as blocks, LEGO bricks, and other building toys, as well as time spent playing video/computer games were found to be important predictors of success. Gender was significant but this could have been due to the unrevised, gender-biased PSVT:R test used rather than the SES (BRANOFF, 1998).

In this study, a Spatial Reasoning Survey (SES) was developed from the results of these two studies and administered to students along with the 30 item revised PSVT:R. Items on the SES were broken down into the following three categories, background experiences such as academic courses (geometry, drafting classes), non-academic activities (toys, computer games), and sports activities. Gender, age and handedness were included.

Hagevik (2003) developed the Mapping Our School Site (MOSS) program, a field-based unit of study that explores and enhances students' learning of earth and environmental concepts such as regional geology; components of the ecosystem such as animals, trees and vegetation cover and aspects of the microclimate such as soil, air and water chemistry.

MOSS begins with an ill structured and messy problem, how do the living and non-living components of the environment relate to each other. The MOSS program relates a three dimensional outdoor environment to a two dimensional virtual environment. In the MOSS program, students choose a 10 meter x 10 meter study site that has a variety of vegetation and possibly a water source. They then measure, survey, and stake out the site. Students use a data collection grid and a compass to spatially orient themselves. All points on the grid, data table, and associated attribute table are located by x, y coordinates shown by Figure 1.

The grid is not georeferenced to real world coordinates. However, it is possible to subsequently georeference the grid to an aerial photograph. As a first step, students collect data following established procedures such as vegetation/ ground cover, animals, pitfall traps, trees, and abiotic (STUBBS; HAGEVIK; HESSLER, 2003). These characteristics and procedures, see Table 1, can be viewed in detail on the MOSS website (HAGEVIK, 1999).

Students use the ArcGIS (ENVIRONMENTAL SYSTEMS RESEARCH INSTITUTE, 2004) brand of desktop Geographic Information Software (GIS) to analyze spatial patterns and formulate problem questions. Then, the students develop additional protocols based on existing scientific models for example the GLOBE Program (UCAR/CSU, 2004) to collect additional data in order to answer their problem questions. After performing additional spatial analysis, students present their conclusions in a report and presentation to their peers.

GIS, a visual-spatial technology, allows users to instantaneously visualize multiple layers of map representations and descriptions leading to an infinite number of connections and analyses (MacEACHREN, 1994). Students use GIS to visualize and analyze their spatial data, revealing spatial patterns and trends. This type form of computer-aided instruction compels students to collect data precisely and accurately, teaches them to design spatial data tables, and to thoroughly test hypotheses. Students receive immediate feedback because GIS allows instantaneous multiple map representations.

The student subjects for the study were recruited through three teachers trained in a MOSS workshop. All three teachers were experienced, certified teachers who had been at their schools for over ten years. Data was collected from 164 seventh and eighth grade students (ages 12-15), ninety-six from one public urban middle school and sixty-eight from another public urban middle school in a different county. All students in the study completed the online Spatial Experience Survey (SES) and the revised Purdue Spatial Visualization Test: Rotations (PSVT:R), before beginning the mapping technology units. These scores were used to measure spatial ability. Other data sources included interviews, group presentations, individual written conclusions, and mapping analyses. Interviews, mapping analyses, and student interviews as well as the teachers interviews were videotaped, transcribed and analyzed using ATLAS. tiTM qualitative software (National Research Council, 1996; Scientific Software Developments, 2003). Statistical measures were used to compare the spatial ability scores to the SES.

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