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. ^

Improving Critical Thinking and Clinical Reasoning With a Continuing Education Course

Background: Continuing education courses related to critical thinking and clinical reasoning are needed to improve the accuracy of diagnosis. Method: This study evaluated a 4-day, 16-hour continuing education course conducted in Brazil. Thirty-nine nurses completed a pretest and a posttest consisting of two written case studies designed to measure the accuracy of nurses` diagnoses. Results: There were significant differences in accuracy from pretest to posttest for case 1 (p = .008) and case 2 (p = .042) and overall (p = .001). Conclusion: Continuing education courses should be implemented to improve the accuracy of nurses` diagnoses. J Contin Educ Nurs 2009;40(3):121-127.

How human schematization and systematic errors take effect on sketch map formalizations

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Dedication and Display of Portrait Statues in Hellenistic Greece: Spatial Practices and Identity Politics

This dissertation models a new approach to the study of ancient portrait statues—one that situates them in their historical, political, and spatial contexts. By bringing into conversation bodies of evidence that have traditionally been studied in discrete categories, I investigate how statue landscapes articulated and reinforced a complex set of political and social identities, how space was utilized and manipulated on a local and a regional level, and how patrons responded to the spatial pressures and visual politics of statue dedication within a constantly changing landscape.

Instead of treating sites independently, I have found it to be more productive—and, indeed, necessary—to examine broader patterns of statue dedication. I demonstrate that a regional perspective, that is, one that takes into account the role of choice and spatial preference in setting up a statue within a regional network of available display locations, can illuminate how space shaped the ancient practice of portrait dedication. This level of analysis is a new approach to the study of portrait statues and it has proved to be a productive way of thinking about how statues and context were used together to articulate identity. Understanding how individual monuments worked within these broader landscapes of portrait dedications, how statue monuments functioned within federal systems, and how monuments set up by individuals and social groups operated along side those set up by political bodies clarifies the important place of honorific statues as an expression of power and identity within the history of the site, the region, and Hellenistic Greece.

Spatial, temporal, and human dimensions of air pollution in Brisbane

Arriving in Brisbane some six years ago, I could not help being impressed by what may be prosaically described as its atmospheric amenity resources. Perhaps this in part was due to my recent experiences in major urban centres in North America, but since that time, that sparkling quality and the blue skies seem to have progressively diminished. Unfortunately, there is also objective evidence available to suggest that this apparent deterioration is not merely the result of habituation of the senses. Air pollution data for the city show trends of increasing concentrations of those very substances that have destroyed the attractiveness of major population centres elsewhere, with climates initially as salubrious. Indeed, present figures indicate that photochemical smog in unacceptably high concentrations is rapidly becoming endemic also over Brisbane. These regrettable developments should come as no surprise. The society at large has not been inclined to respond purposefully to warnings of impending environmental problems, despite the experiences and publicity from overseas and even from other cities within Australia. Nor, up to the present, have certain politicians and government officials displayed stances beyond those necessary for the maintenance of a decorum of concern. At this stage, there still exists the possibility for meaningful government action without the embarrassment of losing political favour with the electorate. To the contrary, there is every chance that such action may be turned to advantage with increased public enlightenment. It would be more than a pity to miss perhaps the final remaining opportunity: Queensland is one of the few remaining places in the world with sufficient resources to permit both rational development and high environmental quality. The choice appears to be one of making a relatively minor investment now for a large financial and social gain the near future, or, permitting Brisbane to degenerate gradually into just another stagnated Los Angeles or Sydney. The present monograph attempts to introduce the problem by reviewing the available research on air quality in the Brisbane area. It also tries to elucidate some seemingly obvious, but so far unapplied management approaches. By necessity, such a broad treatment needs to make inroads into extensive ranges of subject areas, including political and legal practices to public perceptions, scientific measurement and statistical analysis to dynamics of air flow. Clearly, it does not pretend to be definitive in any of these fields, but it does try to emphasize those adjustable facets of the human use system of natural resources, too often neglected in favour of air pollution control technology. The crossing of disciplinary boundaries, however, needs no apology: air quality problems are ubiquitous, touching upon space, time and human interaction.

Regional-scale investigation of the spatial distribution and origin of soluble salts in central north Queensland

A method for regional assessment of the distribution of saline outbreaks is demonstrated for a large area (68 000 km(2)) in north Queensland, Australia. Soil samples were used in conjunction with a digital elevation model and a map of potentially saline discharge zones to examine the landscape distribution of soluble salts in the region. The hypothesis of atmospheric accession of salt was tested for the topographically defined catchment regions feeding into each potentially saline discharge area. Most catchments showed a salt distribution consistent with this hypothesis, i.e. %TSS was large near the discharge areas and decreased rapidly with distance uphill from the discharge areas. In some catchments, however, local saline outbreaks were apparent at significant distances uphill from discharge areas. The possibility of geological sources of this salt was examined by comparing random point distributions with the location of saline points with distance downhill from geological units (excluding points near discharge zones). The distribution of some saline outbreaks was consistent with the occurrence of Cambro-Ordovician metasediments, Devonian limestone, Upper Devonian-Lower Carboniferous volcanics, and Triassic sediments. Copyright (C) 2000 John Wiley & Sons, Ltd.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

Spatial bias and temporal lag in tactile space perception

Constructing a veridical spatial map by touch poses at least two problems for a perceptual system. First, as the hand is moved through space, the locations of features may be displaced if there is an uncorrected lag between the moment the hand encounters a feature and the time that feature is encoded on a spatial map. Second, due to the sequential nature of the process, some form of memory, which itself may be subject to spatial distortions, is required for integration of spatial samples. We investigated these issues using a task involving active haptic exploration with a stylus swept back and forth in the horizontal plane at the wrist. Remembered locations of tactile targets were shifted towards the medial axis of the forearm, suggesting a central tendency in haptic spatial memory, while evidence for a displacement of perceived locations in the direction of sweep motion was consistent with processing delays.

Spatial distribution and developmental appearance of postjunctional P2X(1) receptors on smooth muscle cells of the mouse vas deferens

P2X(1)-type purinoceptors, have been shown to mediate fast transmission between sympathetic varicosities and smooth muscle cells in the mouse vas deferens but the spatial organization of these receptors on the smooth muscle cells remains inconclusive. Voltage clamp techniques were used to estimate the amplitudes of spontaneous excitatory junction currents (SEJCs) in cells of the vas deferens longitudinal smooth muscle layer. These currents involved the activation of about 6% of the P2X-type channels present on the cell, as compared to whole cell currents produced when isolated smooth muscle cells were exposed to maximal concentrations of either ATP or alpha,beta -MeATP. Immunofluorescence staining of the vas deferens with antibodies against P2X(1) receptor showed a diffuse, grainy distribution over the entire membrane of each smooth muscle cell. Anti-P2X(1) staining was not markedly clustered beneath anti-SV2-stained sympathetic varicosities. Similar results were obtained for cells in the urinary bladder. During development, P2X(1) mRNA was detected as early as embryonic day 15 (E15). Increasing intensities of diffuse immunostaining for P2X(1) were observed in the walls of the bladder, tail artery, and aorta from E15 until 6 weeks postnatal. The vas deferens showed increasing intensities of diffuse staining of its smooth muscle layers between 2 and 6 weeks postnatal, consistent with the time-course of development of fast purinergic transmission described previously. Together, the results suggest that the response of smooth muscle of the vas deferens to ATP released from sympathetic varicosities relies on rapidly desensitizing P2X(1) receptors, distributed diffusely across the smooth muscle cell surface. Synapse 42:1-11, 2001. (C) 2001 Wiley-Liss, Inc.

Habitat complexity, spatial interference, and "minimum risk distribution": a framework for population stability

In the past century, the debate over whether or not density-dependent factors regulate populations has generally focused on changes in mean population density, ignoring the spatial variance around the mean as unimportant noise. In an attempt to provide a different framework for understanding population dynamics based on individual fitness, this paper discusses the crucial role of spatial variability itself on the stability of insect populations. The advantages of this method are the following: (1) it is founded on evolutionary principles rather than post hoc assumptions; (2) it erects hypotheses that can be tested; and (3) it links disparate ecological schools, including spatial dynamics, behavioral ecology, preference-performance, and plant apparency into an overall framework. At the core of this framework, habitat complexity governs insect spatial variance. which in turn determines population stability. First, the minimum risk distribution (MRD) is defined as the spatial distribution of individuals that results in the minimum number of premature deaths in a population given the distribution of mortality risk in the habitat (and, therefore, leading to maximized population growth). The greater the divergence of actual spatial patterns of individuals from the MRD, the greater the reduction of population growth and size from high, unstable levels. Then, based on extensive data from 29 populations of the processionary caterpillar, Ochrogaster lunifer, four steps are used to test the effect of habitat interference on population growth rates. (1) The costs (increasing the risk of scramble competition) and benefits (decreasing the risk of inverse density-dependent predation) of egg and larval aggregation are quantified. (2) These costs and benefits, along with the distribution of resources, are used to construct the MRD for each habitat. (3) The MRD is used as a benchmark against which the actual spatial pattern of individuals is compared. The degree of divergence of the actual spatial pattern from the MRD is quantified for each of the 29 habitats. (4) Finally, indices of habitat complexity are used to provide highly accurate predictions of spatial divergence from the MRD, showing that habitat interference reduces population growth rates from high, unstable levels. The reason for the divergence appears to be that high levels of background vegetation (vegetation other than host plants) interfere with female host-searching behavior. This leads to a spatial distribution of egg batches with high mortality risk, and therefore lower population growth. Knowledge of the MRD in other species should be a highly effective means of predicting trends in population dynamics. Species with high divergence between their actual spatial distribution and their MRD may display relatively stable dynamics at low population levels. In contrast, species with low divergence should experience high levels of intragenerational population growth leading to frequent habitat-wide outbreaks and unstable dynamics in the long term. Six hypotheses, erected under the framework of spatial interference, are discussed, and future tests are suggested.

Spatial structure and habitat variation in a grasshopper hybrid zone

A hybrid zone between the grasshoppers Chorthippus brunneus and C. jacobsi (Orthoptera: Acrididae) in northern Spain has been analyzed for variation in morphology and ecology. These species are readily distinguished by the number of stridulatory pegs on the hind femur. Both sexes are fully winged and inhabit disturbed habitats throughout the study area. We develop a maximum-likelihood approach to fitting a two-dimensional cline to geographical variation in quantitative traits and for estimating associations of population mean with local habitat. This method reveals a cline in peg number approximately 30 km south of the Picos de Europa Mountains that shows substantial deviations in population mean compared with the expectations of simple tension zone models. The inclusion of variation in local vegetation in the model explains a significant proportion of the residual variation in peg number, indicating that habitat-genotype associations contribute to the observed spatial pattern. However, this association is weak, and a number of populations continue to show strong deviations in mean even after habitat is included in the final model. These outliers may be the result of long-distance colonization of sites distant from the cline center or may be due to a patchy pattern of initial contact during postglacial expansion. As well as contrasting with the smooth hybrid zones described for Chorthippus parallelus, this situation also contrasts with the mosaic hybrid zones observed in Gryllus crickets and in parts of the hybrid zone between Bombina toad species, where habitat-genotype associations account for substantial amounts of among-site variation.