Analysis of Students’ Misconceptions and Error Patterns in Mathematics: The Case of Fractions

This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.

Seed Dispersal and Reproduction Patterns Among Everglades Plants

In this study three aspects of sexual reproduction in Everglades plants were examined to more clearly understand seed dispersal and the allocation of resources to sexual reproduction— spatial dispersal process, temporal dispersal of seeds (seedbank), and germination patterns in the dominant species, sawgrass (Cladium jamaicense). Community assembly rules for fruit dispersal were deduced by analysis of functional traits associated with this process. Seedbank ecology was investigated by monitoring emergence of germinants from sawgrass soil samples held under varying water depths to determine the fate of dispersed seeds. Fine-scale study of sawgrass fruits yielded information on contributions to variation in sexually produced propagules in this species, which primarily reproduces vegetatively. It was hypothesized that Everglades plants possess a set of functional traits that enhance diaspore dispersal. To test this, 14 traits were evaluated among 51 species by factor analysis. The factorial plot of this analysis generated groups of related traits, with four suites of traits forming dispersal syndromes. Hydrochory traits were categorized by buoyancy and appendages enhancing buoyancy. Anemochory traits were categorized by diaspore size and appendages enhancing air movement. Epizoochory traits were categorized by diaspore size, buoyancy, and appendages allowing for attachment. Endozoochory traits were categorized by diaspore size, buoyancy, and appendages aiding diaspore presentation. These patterns/trends of functional trait organization also represent dispersal community assembly rules. Seeds dispersed by hydrochory were hypothesized to be caught most often in the edge of the north side of sawgrass patches. Patterns of germination and dispersal mode of all hydrochorous macrophytes with propagules in the seedbank were elucidated by germination analysis from 90 soil samples collected from 10 sawgrass patches. Mean site seed density was 486 seeds/m2 from 13 species. Most seeds collected at the north side of patches and significantly in the outer one meter of the patch edge (p = 0.013). Sawgrass seed germination was hypothesized to vary by site, among individual plants, and within different locations of a plant’s infructescence. An analysis of sawgrass fruits with nested ANOVAs found that collection site and interaction of site x individual plant significantly affect germination ability, seed viability, and fruit size (p < 0.050). Fruit location within a plant’s infructescence did not significantly affect germination. As for allocation of resources to sexual reproduction, only 17.9% of sawgrass seeds germinated and only 4.8% of ungerminated seeds with fleshy endosperm were presumed viable, but dormant. Collectively, only 22% of all sawgrass seeds produced were viable.

Principal Component Analysis and Assessment of Language Network Activation Patterns in Pediatric Epilepsy

This dissertation establishes a novel data-driven method to identify language network activation patterns in pediatric epilepsy through the use of the Principal Component Analysis (PCA) on functional magnetic resonance imaging (fMRI). A total of 122 subjects’ data sets from five different hospitals were included in the study through a web-based repository site designed here at FIU. Research was conducted to evaluate different classification and clustering techniques in identifying hidden activation patterns and their associations with meaningful clinical variables. The results were assessed through agreement analysis with the conventional methods of lateralization index (LI) and visual rating. What is unique in this approach is the new mechanism designed for projecting language network patterns in the PCA-based decisional space. Synthetic activation maps were randomly generated from real data sets to uniquely establish nonlinear decision functions (NDF) which are then used to classify any new fMRI activation map into typical or atypical. The best nonlinear classifier was obtained on a 4D space with a complexity (nonlinearity) degree of 7. Based on the significant association of language dominance and intensities with the top eigenvectors of the PCA decisional space, a new algorithm was deployed to delineate primary cluster members without intensity normalization. In this case, three distinct activations patterns (groups) were identified (averaged kappa with rating 0.65, with LI 0.76) and were characterized by the regions of: 1) the left inferior frontal Gyrus (IFG) and left superior temporal gyrus (STG), considered typical for the language task; 2) the IFG, left mesial frontal lobe, right cerebellum regions, representing a variant left dominant pattern by higher activation; and 3) the right homologues of the first pattern in Broca's and Wernicke's language areas. Interestingly, group 2 was found to reflect a different language compensation mechanism than reorganization. Its high intensity activation suggests a possible remote effect on the right hemisphere focus on traditionally left-lateralized functions. In retrospect, this data-driven method provides new insights into mechanisms for brain compensation/reorganization and neural plasticity in pediatric epilepsy.

Investigation of spatial patterns of ground-water exchange with lakes, using a three-dimensional numerical model

Hydrogeologic variables controlling groundwater exchange with inflow and flow-through lakes were simulated using a three-dimensional numerical model (MODFLOW) to investigate and quantify spatial patterns of lake bed seepage and hydraulic head distributions in the porous medium surrounding the lakes. Also, the total annual inflow and outflow were calculated as a percentage of lake volume for flow-through lake simulations. The general exponential decline of seepage rates with distance offshore was best demonstrated at lower anisotropy ratio (i.e., Kh/Kv = 1, 10), with increasing deviation from the exponential pattern as anisotropy was increased to 100 and 1000. 2-D vertical section models constructed for comparison with 3-D models showed that groundwater heads and seepages were higher in 3-D simulations. Addition of low conductivity lake sediments decreased seepage rates nearshore and increased seepage rates offshore in inflow lakes, and increased the area of groundwater inseepage on the beds of flow-through lakes. Introduction of heterogeneity into the medium decreased the water table and seepage ratesnearshore, and increased seepage rates offshore in inflow lakes. A laterally restricted aquifer located at the downgradient side of the flow-through lake increased the area of outseepage. Recharge rate, lake depth and lake bed slope had relatively little effect on the spatial patterns of seepage rates and groundwater exchange with lakes.

Land-cover detection and landscape structure analysis in the Pachitea Basin, Peruvian Amazon

Classification procedures, including atmospheric correction satellite images as well as classification performance utilizing calibration and validation at different levels, have been investigated in the context of a coarse land-cover classification scheme for the Pachitea Basin. Two different correction methods were tested against no correction in terms of reflectance correction towards a common response for pseudo-invariant features (PIF). The accuracy of classifications derived from each of the three methods was then assessed in a discriminant analysis using crossvalidation at pixel, polygon, region, and image levels. Results indicate that only regression adjusted images using PIFs show no significant difference between images in any of the bands. A comparison of classifications at different levels suggests though that at pixel, polygon, and region levels the accuracy of the classifications do not significantly differ between corrected and uncorrected images. Spatial patterns of land-cover were analyzed in terms of colonization history, infrastructure, suitability of the land, and landownership. The actual use of the land is driven mainly by the ability to access the land and markets as is obvious in the distribution of land cover as a function of distance to rivers and roads. When considering all rivers and roads a threshold distance at which disproportional agro-pastoral land cover switches from over represented to under represented is at about 1km. Best land use suggestions seem not to affect the choice of land use. Differences in abundance of land cover between watersheds are more prevailing than differences between colonist and indigenous groups.