From Concrete to Abstract: Teaching for Transfer of Learning when Using Manipulatives

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

Fluorophotometry is a sensitive method/technique to evaluate epithelial permeability in murine experimental dry eye

Purpose. Fluorophotometry is a well validated method for assessing corneal permeability in human subjects. However, with the growing importance of basic science animal research in ophthalmology, fluorophotometry’s use in animals must be further evaluated. The purpose of this study was to evaluate corneal epithelial permeability following desiccating stress using the modified Fluorotron Master™. ^ Methods. Corneal permeability was evaluated prior to and after subjecting 6-8 week old C57BL/6 mice to experimental dry eye (EDE) for 2 and 5 days (n=9/time point). Untreated mice served as controls. Ten microliters of 0.001% sodium fluorescein (NaF) were instilled topically into each mouse’s left eye to create an eye bath, and left to permeate for 3 minutes. The eye bath was followed by a generous wash with Buffered Saline Solution (BSS) and alignment with the Fluorotron Master™. Seven corneal scans using the Fluorotron Master were performed during 15 minutes (1 st post-wash scans), followed by a second wash using BSS and another set of five corneal scans (2nd post-wash scans) during the next 15 minutes. Corneal permeability was calculated using data calculated with the FM™ Mouse software. ^ Results. When comparing the difference between the Post wash #1 scans within the group and the Post wash #2 scans within the group using a repeated measurement design, there was a statistical difference in the corneal fluorescein permeability of the Post-wash #1 scans after 5 days (1160.21±108.26 vs. 1000.47±75.56 ng/mL, P<0.016 for UT-5 day comparison 8 [0.008]), but not after only 2 days of EDE compared to Untreated mice (1115.64±118.94 vs. 1000.47±75.56 ng/mL, P>0.016 for UT-2 day comparison [0.050]). There was no statistical difference between the 2 day and 5 day Post wash #1 scans (P=.299). The Post-wash #2 scans demonstrated that EDE caused a significant NaF retention at both 2 and 5 days of EDE compared to baseline, untreated controls (1017.92±116.25, 1015.40±120.68 vs. 528.22±127.85 ng/mL, P<0.05 [0.0001 for both]). There was no statistical difference between the 2 day and 5 day Post wash #2 scans (P=.503). The comparison between the Untreated post wash #1 with untreated post wash #2 scans using a Paired T-test showed a significant difference between the two sets of scans (P=0.000). There is also a significant difference between the 2 day comparison and the 5 day comparison (P values = 0.010 and 0.002, respectively). ^ Conclusion. Desiccating stress increases permeability of the corneal epithelium to NaF, and increases NaF retention in the corneal stroma. The Fluorotron Master is a useful and sensitive tool to evaluate corneal permeability in murine dry eye, and will be a useful tool to evaluate the effectiveness of dry eye treatments in animal-model drug trials.^

Improved Techniques for Acquisition and Analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging for Detecting Vascular Permeability in the Central Nervous System

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive technique for quantitative assessment of the integrity of blood-brain barrier and blood-spinal cord barrier (BSCB) in the presence of central nervous system pathologies. However, the results of DCE-MRI show substantial variability. The high variability can be caused by a number of factors including inaccurate T1 estimation, insufficient temporal resolution and poor contrast-to-noise ratio. My thesis work is to develop improved methods to reduce the variability of DCE-MRI results. To obtain fast and accurate T1 map, the Look-Locker acquisition technique was implemented with a novel and truly centric k-space segmentation scheme. In addition, an original multi-step curve fitting procedure was developed to increase the accuracy of T1 estimation. A view sharing acquisition method was implemented to increase temporal resolution, and a novel normalization method was introduced to reduce image artifacts. Finally, a new clustering algorithm was developed to reduce apparent noise in the DCE-MRI data. The performance of these proposed methods was verified by simulations and phantom studies. As part of this work, the proposed techniques were applied to an in vivo DCE-MRI study of experimental spinal cord injury (SCI). These methods have shown robust results and allow quantitative assessment of regions with very low vascular permeability. In conclusion, applications of the improved DCE-MRI acquisition and analysis methods developed in this thesis work can improve the accuracy of the DCE-MRI results.

Permeability, overburden stress and friction coefficients of ODP Hole 190-1173A and 190-1174B

Permeability measured on three samples in a triaxial cell under effective confining pressure from 0.2 to 2.5 MPa ranges from 10**-18 to 10**-19 m**2. Overall, results indicate that permeability decreases with effective confining pressure up to 1.5 MPa; however, measurements at low effective pressure are too dispersed to yield a precise general relationship between permeability and pressure. When the effective pressure is increased from 1.5 to 2.5 MPa, permeability is roughly constant (~1-4 x 10**-19 m**2). Samples deformed in the triaxial cell developed slickenlined fractures, and permeability measurements were performed before and after failure. A permeability increase is observed when the sample fails under low effective confining pressure (0.2 MPa), but not under effective pressure corresponding to the overburden stress. Under isotropic stress conditions, permeability decrease related to fracture closure occurs at a relatively high effective pressure of ~1.5 MPa. Coefficients of friction on the fractures formed in the triaxial cell are ~0.4.

Consolidation and permeability characteristics at DSDP Sites 87-582, 87-583, and 87-584

The results of nine consolidation and permeability tests are presented for sediment samples from the Japan Trench and Nankai Trough sites of Leg 87. Coring and degassing disturbance results in an underconsolidated state for most Site 582 samples; however, the compressional effects of the subduction zone and high sediment accumulation rates may also play a role in causing underconsolidation. Samples collected at Site 583 exhibit similar evidence of disturbance but are slightly overconsolidated, confirming the possibility of sediment erosion at this site. The highly diatomaceous sediments at Site 584 are all overconsolidated, but the trend of overconsolidation decreases with depth. Disturbances of the diatom clay structure may increase the sediment compressibility and create this apparent overconsolidation

Permeability measurements on sheared and unsheared samples from different IODP Holes of Leg 316 and from IODP Hole 315-C0001E and ODP Hole 190-1174B

At subduction zones, the permeability of major fault zones influences pore pressure generation, controls fluid flow pathways and rates, and affects fault slip behavior and mechanical strength by mediating effective normal stress. Therefore, there is a need for detailed and systematic permeability measurements of natural materials from fault systems, particularly measurements that allow direct comparison between the permeability of sheared and unsheared samples from the same host rock or sediment. We conducted laboratory experiments to compare the permeability of sheared and uniaxially consolidated (unsheared) marine sediments sampled during IODP Expedition 316 and ODP Leg 190 to the Nankai Trough offshore Japan. These samples were retrieved from: (1) The décollement zone and incoming trench fill offshore Shikoku Island (the Muroto transect); (2) Slope sediments sampled offshore SW Honshu (the Kumano transect) ~ 25 km landward of the trench, including material overriden by a major out-of-sequence thrust fault, termed the "megasplay"; and (3) A region of diffuse thrust faulting near the toe of the accretionary prism along the Kumano transect. Our results show that shearing reduces fault-normal permeability by up to 1 order of magnitude, and this reduction is largest for shallow (< 500 mbsf) samples. Shearing-induced permeability reduction is smaller in samples from greater depth, where pre-existing fabric from compaction and lithification may be better developed. Our results indicate that localized shearing in fault zones should result in heterogeneous permeability in the uppermost few kilometers in accretionary prisms, which favors both the trapping of fluids beneath and within major faults, and the channeling of flow parallel to fault structure. These low permeabilities promote the development of elevated pore fluid pressures during accretion and underthrusting, and will also facilitate dynamic hydrologic processes within shear zones including dilatancy hardening and thermal pressurization.

Lithologic description and vertical permeability measurements of ODP Site 180-1109

Vertical permeability testing was conducted on four samples collected from Site 1109, a borehole advanced during Ocean Drilling Program Leg 180. Closed conditions were applied during each test, and the samples were measured using a constant flow approach and permeant solutions that matched the geochemistry of nearby interstitial waters. Vertical permeabilities measured at 34.5 kPa effective stress generally decreased with depth and ranged from 10**-14 m**2 at 212.53 meters below seafloor (mbsf) to 10**-18 m**2 at 698.10 mbsf. The three deepest samples differed in permeability by less than one order of magnitude. Reconsolidation testing on the shallowest sample yielded a minimum permeability of 1.56 x 10**-16 m**2 at 276 kPa effective stress. Subsequent rebound testing yielded a hysteresis-type curve, with the final permeability measuring lower than the initial permeability by nearly 1.5 orders of magnitude. Dilution experiments indicated that use of a permeant solution matching the geochemistry of the interstitial waters may be necessary for accuracy in measurements and mitigation of clay swellage and collapse during testing, but further research is mandated.

Consolidation properties and permeability values of sediments from three ODP Leg 205 sites

Vertical permeability and sediment consolidation measurements were taken on seven whole-round drill cores from Sites 1253 (three samples), 1254 (one sample), and 1255 (three samples) drilled during Ocean Drilling Program Leg 205 in the Middle America Trench off of Costa Rica's Pacific Coast. Consolidation behavior including slopes of elastic rebound and virgin compression curves (Cc) was measured by constant rate of strain tests. Permeabilities were determined from flow-through experiments during stepped-load tests and by using coefficient of consolidation (Cv) values continuously while loading. Consolidation curves and the Casagrande method were used to determine maximum preconsolidation stress. Elastic slopes of consolidation curves ranged from 0.097 to 0.158 in pelagic sediments and 0.0075 to 0.018 in hemipelagic sediments. Cc values ranged from 1.225 to 1.427 for pelagic carbonates and 0.504 to 0.826 for hemipelagic clay-rich sediments. In samples consolidated to an axial stress of ~20 MPa, permeabilities determined by flow-through experiments ranged from a low value of 7.66 x 10**-20 m**2 in hemipelagic sediments to a maximum value of 1.03 x 10**-16 m**2 in pelagic sediments. Permeabilities calculated from Cv values in the hemipelagic sediments ranged from 4.81 x 10**-16 to 7.66 x 10**-20 m**2 for porosities 49.9%-26.1%.

Porosity, permeability, trace elements, and carbon-oxygen isotopes at DSDP Hole 77-536

Talus deposits recovered from Site 536 show evidence of aragonite dissolution, secondary porosity development, and calcite cementation. Although freshwater diagenesis could account for the petrographic features of the altered talus deposits, it does not uniquely account for isotopic or trace-element characteristics. Also, the hydrologic setting required for freshwater alteration is not easily demonstrated for the Campeche Bank. A mixing-zone model does not account for the available trace-element data, but does require somewhat less drastic assumptions about the size of the freshwater lens. Although a seawater (bottom-water) alteration model requires no hydrologic difficulties, unusual circumstances are required to account for the geochemical characteristics of the talus deposits using this model.

Porosity, gas permeability and grain density of ODP Leg 194 sites

We report analyses of porosity and permeability of core samples from Site 1193 in the Northern Marion Platform, Sites 1196 and 1199 in the Southern Marion Platform, and Sites 1194, 1195, 1197, and 1198 from the slopes of these platforms. The samples include 415 horizontal 1-in plugs, 290 vertical 1-in plugs, and 23 whole-core pieces. Porosity and permeability analyses were possible for most, but not all, samples. Grain density measurements were also obtained for the horizontal plugs. Representative photomicrographs are provided of thin sections from 139 of the horizontal plugs and the 23 whole-core pieces.