Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Abstract

In an earlier study of preservice elementary and middle school teachers’ beliefs about repeating decimals, Weller, Arnon, and Dubinsky (2009) reported on a comparison of the mathematical performance of 77 preservice teachers who completed an APOS-based instructional unit with 127 preservice teachers who completed traditional instruction. The purpose of the current study, based on 47 interviews conducted 4 months after the instruction, during which time there was no further instruction on this topic, is to determine the strength and stability (over time) of the students’ beliefs, to uncover thinking that did not arise in the earlier study, and to see whether the interviews yield similar comparative results. The interviews did uncover changes in student thinking. The students who received the APOS-based instruction developed stronger and more stable (over time) beliefs that a repeating decimal is a number; a repeating decimal has a fraction or integer to which it corresponds; a repeating decimal in general equals its corresponding fraction or integer; and, in particular, In addition, a number of indices and categories were developed that may prove useful in other studies consisting of the comparison of interview and questionnaire data involving a large number of interview subjects.     

A Demonstration of High-Throughput Electrophoresis

Automating electrophoresis significantly reduces the time required for loading a large number of samples, increases the speed of electrophoresis analysis, and maximizes the resolution power (clear separation of fragments) of this technique. In addition, automation increases the precision of electrophoresis analysis. Here we demonstrate an automated, high-throughput method of loading 96 samples simultaneously onto an electrophoresis gel, using the Apogent Discoveries Tango™ system and the Invitrogen™ E-Gel® 96 system.     

Quorum-sensing Cascades Governing Bacterial Multicellular Communities

Quorum sensing (QS) is an efficient mode of intercellular communication between bacteria. This mode is regulated by self-produced small chemical signals, activating dedicated receptors once accumulated. Numerous architecturally complex QS cascades are cardinal for governing bacterial behaviors, such as pathogenicity, luminescence, and bacterial competence. Importantly, QS cascades are essential for the formation of bacterial multicellular communities. Once informed via QS cascades, motile cells often organize themselves into conspicuous multicellular structures that carry out specialized tasks. This review focuses on the major QS systems, playing an active role in the rise of complex bacterial communities in different bacterial models.     

Necessary and sufficient conditions for exponential stability of a family of generalized Liénard differential equations

A class of generalized Liénard differential equations determined by prescribed bilateral bounds for the nonlinear terms is considered. Necessary and sufficient conditions for exponential stability of the system expressed in the indicated bounds are found. The results are compared with known sufficient stability conditions obtained via the Lyapunov function method.     

A bacteriophage reagent for Salmonella: molecular studies on Felix 01

Felix 01 (F01) is a bacteriophage originally isolated by Felix and Callow which lyses almost all Salmonella strains and has been widely used as a diagnostic test for this genus. Molecular information about this phage is entirely lacking. In the present study, the DNA of the phage was found to be a double-stranded linear molecule of about 80 kb. 11.5 kb has been sequenced and in this region A + T content is 60%. There are relatively few restriction endonuclease cleavage sites in the native genome and clones show this is due to their absence rather than modification. A restriction map of the genome has been constructed. The ends of the molecule cannot be ligated although they contain 5' phosphates. At least 60% of the genome must encode proteins. In the sequenced portion, many open reading frames exist and these are tightly packed together. These have been examined for homology to published proteins but only 1 to 17 shows similarity to known proteins. F01 is therefore the prototype of a new phage family. On the basis of restriction sites, codon usage and the distribution of nonsense codons in the unused reading frames, a strong case can be made for natural selection that reacts to mRNA structure and function.     

Diffusive vs. convective therapy: effects on mediators of inflammation in patient with severe systemic inflammatory response syndrome

OBJECTIVE: To compare two forms of continuous renal replacement therapy, continuous venovenous hemofiltration (CVVH) vs. continuous venovenous hemodialysis (CVVHD), in terms of the removal of inflammatory mediators from the blood of patients with systemic inflammatory response syndrome and acute renal failure. DESIGN: Randomized crossover, clinical study. SETTING: University teaching hospital. PATIENTS: Thirteen patients with systemic inflammatory response syndrome and acute renal failure receiving continuous renal replacement therapy. INTERVENTION: Patients were randomized to receive either convective clearance using CVVH or diffusive clearance using CVVHD for the first 24 hrs, followed by the other modality for 24 hrs. All treatments utilized AN69 hemofilters. CVVH was performed with an ultrafiltration rate of 2 L/hr and CVVHD with a dialysis outflow rate of 2 L/hr. MEASUREMENTS AND MAIN RESULTS: Plasma and ultrafiltrate concentrations of tumor necrosis factor (TNF)-alpha, interleukin (IL)-6, IL-10, and sL-selectin were measured at 0, 1, 3, 6, 12, and 24 hrs by radioimmunoassay. Plasma endotoxin concentrations were also measured at 0, 12, and 24 hrs by chromogenic assay. CVVH was associated with a 13% decrease in plasma TNF-alpha concentrations compared with a 23% increase while on CVVHD (p < .05). Mean plasma concentrations of IL-6, IL-10, and sL-selectin were unchanged over time and between therapies. Only minimal amounts of mediators were recovered in the effluents with either therapy except for IL-6. The clearances for IL-6 were different between therapies, 1.9+/-0.8 (SD) mL/min for CVVHD and 3.3+/-1.5 mL/min for CVVH, (p< .01). Plasma endotoxin concentrations were not different between therapies. CONCLUSION: CVVH resulted in a decrease in plasma TNF-alpha concentrations as compared with CVVHD, while the type of transport mechanism used did not influence plasma concentrations of IL-6, IL-10, soluble L-selectin, or endotoxin. Differences in clearance for IL-6 between CVVH and CVVHD did not translate into significant changes in circulating IL-6 concentrations.     

Mean-value analysis of multi-facility blocking models with state-dependent arrivals

A new mean-value type of algorithm is developed for analyzing multi-facility blocking models with state-dependent arrival rates. It can be applied to a broad class of blocking systems with simultaneous resource possession including, for example, circuit-switched networks. The underlying recursion is cast in terms of blocking probabilities and marginal state probabilities. The developments made here generalize previous results that were restricted to the case of constant arrival rates.     

Coordinated induction of plasminogen activator inhibitor-1 (PAI-1) and inhibition of plasminogen activator gene expression by hypoxia promotes pulmonary vascular fibrin deposition

PURPOSE: In a rabbit model, transposition of a muscle pedicle flap to an ischemic hind limb has been shown to result in the development of new blood vessels that connect the arterial circulation of the flap to the circulation of the limb. The hypothesis that exogenous recombinant basic fibroblast growth factor (bFGF) would enhance the development of this new blood supply was examined and the regulation of bFGF in this process was investigated. METHODS: The right common iliac artery was ligated in 12 male New Zealand white rabbits. An abdominal wall muscle flap based on the left inferior epigastric artery was transposed to the right thigh. bFGF in phosphate-buffered saline (PBS) at 3 ng/h (n = 6), or PBS alone (n = 6), was infused for 7 days via mini-osmotic pumps with an infusion catheter positioned at the flap-muscle interface. The flap-muscle interface was immunostained with anti-alpha-actin antibody to determine blood vessel density (number of vessels/mm) and with anti-bFGF antibody to evaluate bFGF distribution. RNA was isolated from these sections, and polymerase chain reaction (PCR) was used to examine endogenous bFGF messenger RNA (mRNA) expression. RESULTS: Blood vessel density was significantly increased in animals receiving exogenous bFGF (22. 0 +/- 10.6 vessels/mm vs. 10.7 +/- 8.8 vessels/mm, P =.009). In the controls, neovessels were arranged in clusters with endogenous bFGF concentrated around these clusters. In bFGF-treated animals, vessels were diffusely scattered throughout the flap-limb interface, corresponding to the distribution pattern of infused bFGF. There was no difference in bFGF mRNA expression between the control and the bFGF-treated groups. CONCLUSION: Exogenous bFGF infusion significantly augmented new blood vessel development at the flap-limb interface. Endogenous bFGF was up-regulated around the newly developed microvessels in control animals, and vessel growth correlated with the diffuse distribution of exogenous bFGF, implicating bFGF as an important factor in angiogenesis. Exogenous bFGF did not affect bFGF mRNA expression, suggesting that the regulation of bFGF is not under autocrine control.     

Differential weighting of common and distinctive components.

We investigated possible explanations of the finding that the relative weight (W) of common components in similarity judgments is higher for verbal than for pictorial stimuli. A serial presentation of stimulus components had no effect on verbal stimuli; it increased the impact of both common and distinctive components of pictorial stimuli but did not affect their relative weight. On the other hand, W was increased by manipulations that reduced the cohesiveness of composite pictures, such as separating, scrambling, and mixing their components. Furthermore, W was decreased by manipulations that enhanced the cohesiveness of composite verbal stimuli by imposing structure on their components. Verbal and pictorial representations of the same stimuli yielded no systematic differences in W. (PsycINFO Database Record (c) 2010 APA, all rights reserved)