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. ^

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.

The discrimination and association of float glass and the quantitative analysis of liquids from aerosols and microdrops using laser induced breakdown spectroscopy

Glass is a common form of trace evidence found at many scenes of crimes in the form of small fragments. These glass fragments can transfer to surrounding objects and/or persons and may provide forensic investigators valuable information to link a suspect to the scene of a crime. Since the elemental composition of different glass sources can be very similar, a highly discriminating technique is required to distinguish between fragments that have originated from different sources. ^ The research presented here demonstrates that Laser Induced Breakdown Spectroscopy (LIBS) is a viable analytical technique for the association and discrimination of glass fragments. The first part of this research describes the optimization of the LIBS experiments including the use of different laser wavelengths to investigate laser-material interaction. The use of a 266 nm excitation laser provided the best analytical figures of merit with minimal damage to the sample. The resulting analytical figures of merit are presented. The second part of this research evaluated the sensitivity of LIBS to associate or discriminate float glass samples originating from the same manufacturing plants and produced at approximately the same time period. Two different sample sets were analyzed ranging in manufacturing dates from days to years apart. Eighteen (18) atomic emission lines corresponding to the elements Sr, K, Fe, Ca, Al, Ba, Na, Mg and Ti, were chosen because of their detection above the method detection limits and for presenting differences between the samples. Ten elemental ratios producing the most discrimination were selected for each set. When all the ratios are combined in a comparison, 99% of the possible pairs were discriminated using the optimized LIBS method generating typical analytical precisions of ∼5% RSD. ^ The final study consisted of the development of a new approach for the use of LIBS as a quantitative analysis of ultra-low volume solution analysis using aerosols and microdrops. Laser induced breakdown spectroscopy demonstrated to be an effective technique for the analysis of as low as 90 pL for microdrop LIBS with 1 pg absolute LOD and 20 µL for aerosol LIBS with an absolute LOD of ∼100 fg.^

Vulnerable identities: Maya Yucatec identities in a postmodern world

In numerous anthropological works there have been preoccupations about the relationships between Indigenous and non-Indigenous peoples. Whatever social researchers have concluded, one thing is consistent: the tendency to interpret ethnographic “data” in terms of binary oppositions. This dissertation reviews the works which have been centered upon binary oppositions, as for instance, in the case of Yucatan, between the Maya and the Dzul—the Yucatec Maya term for white males—and highlights the fact that such works have failed to recognize that within and between each “pole,” or social group there are individuals that have multiple identities, and that do not recognize themselves as belonging to a homogenized “pole.” Instead, these individuals, recognize themselves as belonging to different groups and, therefore, being aware that they have not a single identity but multiple ones. ^ Analogical anthropology is highly criticized because of its emphasis on binary oppositions, its authoritarianism, and the notion of the “Other.” In contrast, dialogical anthropology places great importance on the relationship between the individuals and the anthropologist. A relation in which both, the anthropologist and the subject, are immersed in a dialogue, because of the identification between the writer and the story that is being written. ^ However, anthropologists seem to be more interested in “dialoguing” among themselves rather than with the people that they write about. Indigenous people are relegated, they are voiceless, and, therefore, we keep treating them as “objects,” and not as individuals. This is ironic, precisely because it undermines the aim of the dialogical discourse. ^ In this context, awareness of self-identity or self-identities and the various ways in which Francisco, a good friend and the main character of this dissertation, assumes them, and the way I assume them, within multicultural contexts, leads us along the road to establish and reestablish communication. The methodology is based on four considerations: positioning, fieldwork conversations, self reflexivity and vulnerability. Hence, this dissertation constitutes an attempt to break with authoritarian models of ethnography, it is a dialogue between Francisco and me, a conversation among ourselves. A dialogue that expresses the desire of hearing our voices being echoed by each other. ^

Improving novice analyst performance in modeling the sequence diagram in systems analysis: A cognitive complexity approach

The Unified Modeling Language (UML) has quickly become the industry standard for object-oriented software development. It is being widely used in organizations and institutions around the world. However, UML is often found to be too complex for novice systems analysts. Although prior research has identified difficulties novice analysts encounter in learning UML, no viable solution has been proposed to address these difficulties. Sequence-diagram modeling, in particular, has largely been overlooked. The sequence diagram models the behavioral aspects of an object-oriented software system in terms of interactions among its building blocks, i.e. objects and classes. It is one of the most commonly-used UML diagrams in practice. However, there has been little research on sequence-diagram modeling. The current literature scarcely provides effective guidelines for developing a sequence diagram. Such guidelines will be greatly beneficial to novice analysts who, unlike experienced systems analysts, do not possess relevant prior experience to easily learn how to develop a sequence diagram. There is the need for an effective sequence-diagram modeling technique for novices. This dissertation reports a research study that identified novice difficulties in modeling a sequence diagram and proposed a technique called CHOP (CHunking, Ordering, Patterning), which was designed to reduce the cognitive load by addressing the cognitive complexity of sequence-diagram modeling. The CHOP technique was evaluated in a controlled experiment against a technique recommended in a well-known textbook, which was found to be representative of approaches provided in many textbooks as well as practitioner literatures. The results indicated that novice analysts were able to perform better using the CHOP technique. This outcome seems have been enabled by pattern-based heuristics provided by the technique. Meanwhile, novice analysts rated the CHOP technique more useful although not significantly easier to use than the control technique. The study established that the CHOP technique is an effective sequence-diagram modeling technique for novice analysts.

Improving Novice Analyst Performance in Modeling the Sequence Diagram in Systems Analysis: A Cognitive Complexity Approach

The Unified Modeling Language (UML) has quickly become the industry standard for object-oriented software development. It is being widely used in organizations and institutions around the world. However, UML is often found to be too complex for novice systems analysts. Although prior research has identified difficulties novice analysts encounter in learning UML, no viable solution has been proposed to address these difficulties. Sequence-diagram modeling, in particular, has largely been overlooked. The sequence diagram models the behavioral aspects of an object-oriented software system in terms of interactions among its building blocks, i.e. objects and classes. It is one of the most commonly-used UML diagrams in practice. However, there has been little research on sequence-diagram modeling. The current literature scarcely provides effective guidelines for developing a sequence diagram. Such guidelines will be greatly beneficial to novice analysts who, unlike experienced systems analysts, do not possess relevant prior experience to easily learn how to develop a sequence diagram. There is the need for an effective sequence-diagram modeling technique for novices. This dissertation reports a research study that identified novice difficulties in modeling a sequence diagram and proposed a technique called CHOP (CHunking, Ordering, Patterning), which was designed to reduce the cognitive load by addressing the cognitive complexity of sequence-diagram modeling. The CHOP technique was evaluated in a controlled experiment against a technique recommended in a well-known textbook, which was found to be representative of approaches provided in many textbooks as well as practitioner literatures. The results indicated that novice analysts were able to perform better using the CHOP technique. This outcome seems have been enabled by pattern-based heuristics provided by the technique. Meanwhile, novice analysts rated the CHOP technique more useful although not significantly easier to use than the control technique. The study established that the CHOP technique is an effective sequence-diagram modeling technique for novice analysts.

Validation of an Analytical Method for the Identification of SmartWater CSI Forensic Marking Technology

SmartWater is a chemical taggant used as a crime deterrent. The chemical taggant is a colorless liquid that fluoresces yellow under ultra-violet (UV) light and contains distinctive, identifiable and traceable elemental composition. For instance, upon a break and entry scenario, the burglar is sprayed with a solution that has an elemental signature custom-made to a specific location. The residues of this taggant persist on skin and other objects and can be easily recovered for further analysis. The product has been effectively used in Europe as a crime deterrent and has been recently introduced in South Florida. In 2014, Fourt Lauderdale Police Department reported the use of SmartWater products with a reduction in burglaries of 14% [1]. The International Forensic Research Institute (IFRI) at FIU validated the scientific foundation of the methods of recovery and analysis of these chemical tagging systems using LA-ICP-MS. Analytical figures of merit of the method such as precision, accuracy, limits of detection, linearity and selectivity are reported in this study. Moreover, blind samples were analyzed by LA-ICP-MS to compare the chemical signatures to the company’s database and evaluate error rates and the accuracy of the method. This study demonstrated that LA-ICP-MS could be used to effectively detect these traceable taggants to assist law enforcement agencies in the United States with cases involving transfer of these forensic coding systems.