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.

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. ^

A youth vision of the city: The socio-spatial lives and exclusion of street girls in Bogota, Colombia

This dissertation documents the everyday lives and spaces of a population of youth typically constructed as out of place, and the broader urban context in which they are rendered as such. Thirty-three female and transgender street youth participated in the development of this youth-based participatory action research (YPAR) project utilizing geo-ethnographic methods, auto-photography, and archival research throughout a six-phase, eighteen-month research process in Bogotá, Colombia. ^ This dissertation details the participatory writing process that enabled the YPAR research team to destabilize dominant representations of both street girls and urban space and the participatory mapping process that enabled the development of a youth vision of the city through cartographic images. The maps display individual and aggregate spatial data indicating trends within and making comparisons between three subgroups of the research population according to nine spatial variables. These spatial data, coupled with photographic and ethnographic data, substantiate that street girls’ mobilities and activity spaces intersect with and are altered by state-sponsored urban renewal projects and paramilitary-led social cleansing killings, both efforts to clean up Bogotá by purging the city center of deviant populations and places. ^ Advancing an ethical approach to conducting research with excluded populations, this dissertation argues for the enactment of critical field praxis and care ethics within a YPAR framework to incorporate young people as principal research actors rather than merely voices represented in adultist academic discourse. Interjection of considerations of space, gender, and participation into the study of street youth produce new ways of envisioning the city and the role of young people in research. Instead of seeing the city from a panoptic view, Bogotá is revealed through the eyes of street youth who participated in the construction and feminist visualization of a new cartography and counter-map of the city grounded in embodied, situated praxis. This dissertation presents a socially responsible approach to conducting action-research with high-risk youth by documenting how street girls reclaim their right to the city on paper and in practice; through maps of their everyday exclusion in Bogotá followed by activism to fight against it.^

Scaling geospatial searches in large spatial databases

Modern geographical databases, which are at the core of geographic information systems (GIS), store a rich set of aspatial attributes in addition to geographic data. Typically, aspatial information comes in textual and numeric format. Retrieving information constrained on spatial and aspatial data from geodatabases provides GIS users the ability to perform more interesting spatial analyses, and for applications to support composite location-aware searches; for example, in a real estate database: “Find the nearest homes for sale to my current location that have backyard and whose prices are between $50,000 and $80,000”. Efficient processing of such queries require combined indexing strategies of multiple types of data. Existing spatial query engines commonly apply a two-filter approach (spatial filter followed by nonspatial filter, or viceversa), which can incur large performance overheads. On the other hand, more recently, the amount of geolocation data has grown rapidly in databases due in part to advances in geolocation technologies (e.g., GPS-enabled smartphones) that allow users to associate location data to objects or events. The latter poses potential data ingestion challenges of large data volumes for practical GIS databases. In this dissertation, we first show how indexing spatial data with R-trees (a typical data pre-processing task) can be scaled in MapReduce—a widely-adopted parallel programming model for data intensive problems. The evaluation of our algorithms in a Hadoop cluster showed close to linear scalability in building R-tree indexes. Subsequently, we develop efficient algorithms for processing spatial queries with aspatial conditions. Novel techniques for simultaneously indexing spatial with textual and numeric data are developed to that end. Experimental evaluations with real-world, large spatial datasets measured query response times within the sub-second range for most cases, and up to a few seconds for a small number of cases, which is reasonable for interactive applications. Overall, the previous results show that the MapReduce parallel model is suitable for indexing tasks in spatial databases, and the adequate combination of spatial and aspatial attribute indexes can attain acceptable response times for interactive spatial queries with constraints on aspatial data.

Mixed spatial and nonspatial problems in location based services

With hundreds of millions of users reporting locations and embracing mobile technologies, Location Based Services (LBSs) are raising new challenges. In this dissertation, we address three emerging problems in location services, where geolocation data plays a central role. First, to handle the unprecedented growth of generated geolocation data, existing location services rely on geospatial database systems. However, their inability to leverage combined geographical and textual information in analytical queries (e.g. spatial similarity joins) remains an open problem. To address this, we introduce SpsJoin, a framework for computing spatial set-similarity joins. SpsJoin handles combined similarity queries that involve textual and spatial constraints simultaneously. LBSs use this system to tackle different types of problems, such as deduplication, geolocation enhancement and record linkage. We define the spatial set-similarity join problem in a general case and propose an algorithm for its efficient computation. Our solution utilizes parallel computing with MapReduce to handle scalability issues in large geospatial databases. Second, applications that use geolocation data are seldom concerned with ensuring the privacy of participating users. To motivate participation and address privacy concerns, we propose iSafe, a privacy preserving algorithm for computing safety snapshots of co-located mobile devices as well as geosocial network users. iSafe combines geolocation data extracted from crime datasets and geosocial networks such as Yelp. In order to enhance iSafe's ability to compute safety recommendations, even when crime information is incomplete or sparse, we need to identify relationships between Yelp venues and crime indices at their locations. To achieve this, we use SpsJoin on two datasets (Yelp venues and geolocated businesses) to find venues that have not been reviewed and to further compute the crime indices of their locations. Our results show a statistically significant dependence between location crime indices and Yelp features. Third, review centered LBSs (e.g., Yelp) are increasingly becoming targets of malicious campaigns that aim to bias the public image of represented businesses. Although Yelp actively attempts to detect and filter fraudulent reviews, our experiments showed that Yelp is still vulnerable. Fraudulent LBS information also impacts the ability of iSafe to provide correct safety values. We take steps toward addressing this problem by proposing SpiDeR, an algorithm that takes advantage of the richness of information available in Yelp to detect abnormal review patterns. We propose a fake venue detection solution that applies SpsJoin on Yelp and U.S. housing datasets. We validate the proposed solutions using ground truth data extracted by our experiments and reviews filtered by Yelp.

Preschooler’s Comprehension of Spatial Terms

This study aims to understand individual differences in preschooler’s early comprehension of spatial language. Spatial language is defined as terms describing location, direction, shape, dimension, features, orientation, and quantity (e.g location, shape). Spatial language is considered to be one of the important factors in the development of spatial reasoning in the preschool years (Pruden, Levine, & Huttenlocher, 2011). In recent years, research has shown spatial reasoning is an important predictor of successes in STEM (Science, Technology, Engineering, and Mathematics) fields (e.g. Shea, Lubinski & Benbow, 2001; Wai, Lubinksi &Benbow, 2009). The current study focuses on when children begin to comprehend spatial terms, while previous work has mainly focused on production of spatial language. Identifying when children begin to comprehend spatial terms could lead to a better understanding of how spatial reasoning develops. We use the Intermodal Preferential Looking paradigm (IPLP) to examine three-year-old children’s ability to map spatial terms to visual representations. Fourteen spatial terms were used to test these abilities (e.g. bottom, diamond, longer). For each test trial children were presented with two different stimuli simultaneously on the left and right sides of a television screen. A female voice prompted the child to find the target spatial relation (e.g. “can you find the boy pointing to the bottom of the window”; Figure 1). A Tobii X60 eye-tracker was used to record the child’s eye gaze for each trial. For each child the proportion of looking to the target image divided by their total looking during the trial was calculated; this served as the dependent variable. Proportions above .50 indicated that the child had correctly mapped the spatial term to the target image. Preliminary data shows that the number of words comprehended in the IPLP task is correlated to parental report of the child’s comprehension of spatial terms (r[14]=.500, p<.05).

Preschooler’s Comprehension of Spatial Terms

This study aims to understand individual differences in preschooler’s early comprehension of spatial language. Spatial language is defined as terms describing location, direction, shape, dimension, features, orientation, and quantity (e.g location, shape). Spatial language is considered to be one of the important factors in the development of spatial reasoning in the preschool years (Pruden, Levine, & Huttenlocher, 2011). In recent years, research has shown spatial reasoning is an important predictor of successes in STEM (Science, Technology, Engineering, and Mathematics) fields (e.g. Shea, Lubinski & Benbow, 2001; Wai, Lubinksi &Benbow, 2009). The current study focuses on when children begin to comprehend spatial terms, while previous work has mainly focused on production of spatial language. Identifying when children begin to comprehend spatial terms could lead to a better understanding of how spatial reasoning develops. We use the Intermodal Preferential Looking paradigm (IPLP) to examine three-year-old children’s ability to map spatial terms to visual representations. Fourteen spatial terms were used to test these abilities (e.g. bottom, diamond, longer). For each test trial children were presented with two different stimuli simultaneously on the left and right sides of a television screen. A female voice prompted the child to find the target spatial relation (e.g. “can you find the boy pointing to the bottom of the window”; Figure 1). A Tobii X60 eye-tracker was used to record the child’s eye gaze for each trial. For each child the proportion of looking to the target image divided by their total looking during the trial was calculated; this served as the dependent variable. Proportions above .50 indicated that the child had correctly mapped the spatial term to the target image. Preliminary data shows that the number of words comprehended in the IPLP task is correlated to parental report of the child’s comprehension of spatial terms (r[14]=.500, p<.05).

Mixed Spatial and Nonspatial Problems in Location Based Services

With hundreds of millions of users reporting locations and embracing mobile technologies, Location Based Services (LBSs) are raising new challenges. In this dissertation, we address three emerging problems in location services, where geolocation data plays a central role. First, to handle the unprecedented growth of generated geolocation data, existing location services rely on geospatial database systems. However, their inability to leverage combined geographical and textual information in analytical queries (e.g. spatial similarity joins) remains an open problem. To address this, we introduce SpsJoin, a framework for computing spatial set-similarity joins. SpsJoin handles combined similarity queries that involve textual and spatial constraints simultaneously. LBSs use this system to tackle different types of problems, such as deduplication, geolocation enhancement and record linkage. We define the spatial set-similarity join problem in a general case and propose an algorithm for its efficient computation. Our solution utilizes parallel computing with MapReduce to handle scalability issues in large geospatial databases. Second, applications that use geolocation data are seldom concerned with ensuring the privacy of participating users. To motivate participation and address privacy concerns, we propose iSafe, a privacy preserving algorithm for computing safety snapshots of co-located mobile devices as well as geosocial network users. iSafe combines geolocation data extracted from crime datasets and geosocial networks such as Yelp. In order to enhance iSafe's ability to compute safety recommendations, even when crime information is incomplete or sparse, we need to identify relationships between Yelp venues and crime indices at their locations. To achieve this, we use SpsJoin on two datasets (Yelp venues and geolocated businesses) to find venues that have not been reviewed and to further compute the crime indices of their locations. Our results show a statistically significant dependence between location crime indices and Yelp features. Third, review centered LBSs (e.g., Yelp) are increasingly becoming targets of malicious campaigns that aim to bias the public image of represented businesses. Although Yelp actively attempts to detect and filter fraudulent reviews, our experiments showed that Yelp is still vulnerable. Fraudulent LBS information also impacts the ability of iSafe to provide correct safety values. We take steps toward addressing this problem by proposing SpiDeR, an algorithm that takes advantage of the richness of information available in Yelp to detect abnormal review patterns. We propose a fake venue detection solution that applies SpsJoin on Yelp and U.S. housing datasets. We validate the proposed solutions using ground truth data extracted by our experiments and reviews filtered by Yelp.

Geospatial Data Indexing Analysis and Visualization via Web Services with Autonomic Resource Management

With the exponential growth of the usage of web-based map services, the web GIS application has become more and more popular. Spatial data index, search, analysis, visualization and the resource management of such services are becoming increasingly important to deliver user-desired Quality of Service. First, spatial indexing is typically time-consuming and is not available to end-users. To address this, we introduce TerraFly sksOpen, an open-sourced an Online Indexing and Querying System for Big Geospatial Data. Integrated with the TerraFly Geospatial database [1-9], sksOpen is an efficient indexing and query engine for processing Top-k Spatial Boolean Queries. Further, we provide ergonomic visualization of query results on interactive maps to facilitate the user’s data analysis. Second, due to the highly complex and dynamic nature of GIS systems, it is quite challenging for the end users to quickly understand and analyze the spatial data, and to efficiently share their own data and analysis results with others. Built on the TerraFly Geo spatial database, TerraFly GeoCloud is an extra layer running upon the TerraFly map and can efficiently support many different visualization functions and spatial data analysis models. Furthermore, users can create unique URLs to visualize and share the analysis results. TerraFly GeoCloud also enables the MapQL technology to customize map visualization using SQL-like statements [10]. Third, map systems often serve dynamic web workloads and involve multiple CPU and I/O intensive tiers, which make it challenging to meet the response time targets of map requests while using the resources efficiently. Virtualization facilitates the deployment of web map services and improves their resource utilization through encapsulation and consolidation. Autonomic resource management allows resources to be automatically provisioned to a map service and its internal tiers on demand. v-TerraFly are techniques to predict the demand of map workloads online and optimize resource allocations, considering both response time and data freshness as the QoS target. The proposed v-TerraFly system is prototyped on TerraFly, a production web map service, and evaluated using real TerraFly workloads. The results show that v-TerraFly can accurately predict the workload demands: 18.91% more accurate; and efficiently allocate resources to meet the QoS target: improves the QoS by 26.19% and saves resource usages by 20.83% compared to traditional peak load-based resource allocation.