Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

Theoretical Foundations of a Study Examining Adolescent Literature and Rape Myth Acceptance

Adolescents are at the greatest risk for victimization and perpetration of sexual assault. This paper examines the current trends in literacy education which marginalize aesthetic reading experiences and using reader response theory, and argues that young adult literature may provide an opportunity to reduce rape myth acceptance in adolescents.

Seasonal and spatial variation in the stable isotopic composition (δ18O and δD) of precipitation in south Florida

Precipitation data collected from five sites in south Florida indicate a strong seasonal and spatial variation in δ18O and δD, despite the relatively limited geographic coverage and low-lying elevation of each of the collection sites. Based upon the weighted-mean stable isotope values, the sites were classified as coastal Atlantic, inland, and lower Florida Keys. The coastal Atlantic sites had weighted-mean values of δ18O and δD of −2.86‰ and −12.8‰, respectively, and exhibited a seasonal variation with lower δ18O and δD values in the summer wet-season precipitation (δ18O = −3.38‰, δD = −16.5‰) as compared to the winter-time precipitation (δ18O = −1.66‰, δD = −3.2‰). The inland site was characterized as having the highest d-excess value (+13.3‰), signifying a contribution of evaporated Everglades surface water to the local atmospheric moisture. In spite of its lower latitude, the lower Keys site located at Long Key had the lowest weighted-mean stable isotope values (δ18O = −3.64‰, δD = −20.2‰) as well as the lowest d-excess value of (+8.8‰). The lower δD and δ18O values observed at the Long Key site reflect the combined effects of oceanic vapor source, fractionation due to local precipitation, and slower equilibration of the larger raindrops nucleated by a maritime aerosol. Very low δ18O and δD values (δ18O < −6‰, δD < −40‰) were observed just prior to the passage of hurricanes from the Gulf of Mexico as well as during cold fronts from the north-west. These results suggest that an oceanic vapor source region to the west, may be responsible for the extremely low δD and δ18O values observed during some tropical storms and cold fronts.

Temporal and Spatial Variability of Mesozooplankton in a Shallow Sub-Tropical Bay: Influence of Top-Down Control

Quantifying the relationship between mesozooplankton and water quality parameters identifies the factors that structure the mesozooplankton community and can be used to generate hypotheses regarding the mechanisms that control the mesozooplankton population and potentially the trophic network. To investigate this relationship, mesozooplankton and water quality data were collected in Florida Bay from 1994 to 2004. Three key characteristics were found in the mesozooplankton community structure: (1) there are significant differences between the four sub-regions of Florida Bay; (2) there is a break in May of 1997 with significant differences before and after this date; and (3) there is a positive correlation between mesozooplankton abundance and salinity. The latter two characteristics are closely correlated with predator abundance, indicating the importance of top-down control. Hypersaline periods appear to provide a refuge from predators, allowing mesozooplankton to increase in abundance despite the increased physiological stress.

Borinquen, la tierra de Belen: Participatory Action Research and Transformational Theory in the Urban Chicago Puerto Rican Experience: A Critical Analysis

This paper analyzes how José Lopéz’s participatory action research and transformational learning theory addresses the oppressed Puerto Rican experience. The paper examines the historical experience of colonialism, explains these two theories, and explores Lopéz’s adult education work in the Puerto Rican community using participatory action research and transformational learning.

Effects of Family, Child, and Teacher Demographics on Prekindergarten Children's Access to and Use of Numeracy and Spatial Materials in the Early Education Setting

Florida’s Voluntary Pre-Kindergarten program (VPK) aims to ensure that all 4-year-olds are prepared to excel in K-12 mathematics. Early numeracy/spatial skills are predictive of success in K–12 mathematics. No research has examined whether VPK classrooms are equipped with the materials necessary to teach numeracy/spatial skill. The Pre-Kindergarten Numeracy and Spatial Environment Survey was created to examine the frequency of access to and use of numeracy/spatial materials in VPK classrooms. The 69-item survey was completed by the lead educator from a sample of 62 pre-kindergarten classrooms in Miami-Dade County. Regression analysis results suggest the location of the pre-kindergarten center, the sex distribution of the children in the classrooms or the number of years of experience that the educator has as a lead teacher along with the extra training courses undertaken by the teachers does not affect the access to or the use of, numeracy and spatial materials in the classrooms.

How Can Fredrickson’s Broaden-and-Build Theory Enhance Personal Resources?

Abstract: Positive psychology has garnered great attention towards understanding how individuals develop personal resources to enhance wellbeing and flow. Barbara Fredrickson’s broaden and build theory suggests when individuals imbue various personal resources with more positive affect, individuals are more likely able to develop greater resilient assets as a result.